[
  {
    "path": ".gitignore",
    "content": ".DS_Store\ntest.py\n*.pyc\noutput/"
  },
  {
    "path": ".python-version",
    "content": "3.13\n"
  },
  {
    "path": "0_getting_started/readme.md",
    "content": "# Getting Started with Solid Simulation\n\nFree fall, spring, and mass-spring solid simulation with symplectic Euler time integration.\n\n## Dependencies\n```\npip install numpy scipy pygame\n```\n\n## Run\nFree falling particle:\n```\npython simulator0.py\n```\nHanging particle:\n```\npython simulator1.py\n```\nHanging square:\n```\npython simulator2.py\n```"
  },
  {
    "path": "0_getting_started/simulator0.py",
    "content": "# Free Fall Simulation\n\nimport math\nimport numpy as np  # for vector data structure and computations\nimport pygame       # for visualization\n\n# simulation setup\nx = np.array([0.0, 0.0])    # position of particle\nv = np.array([0.0, 0.0])    # velocity of particle\ng = np.array([0.0, -10.0])  # gravitational acceleration\nh = 0.01                    # time step size in seconds\n\n# visualization/rendering setup\npygame.init()\nrender_FPS = 100                    # number of frames to render per second\nresolution = np.array([900, 900])   # visualization window size in pixels\noffset = resolution / 2             # offset between window coordinates and simulated coordinates\nscale = 200                         # scale between window coordinates and simulated coordinates\ndef screen_projection(x):           # convert simulated coordinates to window coordinates\n    return [offset[0] + scale * x[0], resolution[1] - (offset[1] + scale * x[1])]\nscreen = pygame.display.set_mode(resolution)    # initialize visualizer\n\ntime_step = 0   # the number of the current time step\nrunning = True  # flag indicating whether the simulation is still running\nwhile running:\n    # run until the user asks to quit\n    for event in pygame.event.get():\n        if event.type == pygame.QUIT:\n            running = False\n    \n    # update the frame to display according to render_FPS\n    if time_step % int(math.ceil((1.0 / render_FPS) / h)) == 0:\n        # fill the background with white color, display simulation time at the top,\n        # render a floor at y=-1, and render the particle as a circle:\n        screen.fill((255, 255, 255))    \n        pygame.display.set_caption('Current time: ' + f'{time_step * h: .2f}s')\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection([-2, -1]), screen_projection([2, -1]))\n        pygame.draw.circle(screen, (0, 0, 255), screen_projection(x), 0.1 * scale)\n        pygame.display.flip()   # flip the display\n        pygame.time.wait(int(1000.0 / render_FPS))  # wait to render the next frame\n\n    # pause the simulation when the particle touches on the ground \n    if x[1] <= -1:\n        input()\n        break\n\n    # step forward the simulation by updating particle velocity and position\n    v += h * g\n    x += h * v\n\n    time_step += 1  # update time step counter"
  },
  {
    "path": "0_getting_started/simulator1.py",
    "content": "# Spring Simulation\n\nimport math\nimport numpy as np  # for vector data structure and computations\nimport pygame       # for visualization\n\n# simulation setup\nm = 1000                    # mass of particle\nx = np.array([0.4, 0.0])    # position of particle\nv = np.array([0.0, 0.0])    # velocity of particle\ng = np.array([0.0, -10.0])  # gravitational acceleration\nspring_rest_len = 0.3       # rest length of the spring ###\nspring_stiffness = 1e5      # stiffness of the spring ###\nh = 0.01                    # time step size in seconds\n\n# visualization/rendering setup\npygame.init()\nrender_FPS = 100                    # number of frames to render per second\nresolution = np.array([900, 900])   # visualization window size in pixels\noffset = resolution / 2             # offset between window coordinates and simulated coordinates\nscale = 200                         # scale between window coordinates and simulated coordinates\ndef screen_projection(x):           # convert simulated coordinates to window coordinates\n    return [offset[0] + scale * x[0], resolution[1] - (offset[1] + scale * x[1])]\nscreen = pygame.display.set_mode(resolution)    # initialize visualizer\n\ntime_step = 0   # the number of the current time step\nrunning = True  # flag indicating whether the simulation is still running\nwhile running:\n    # run until the user asks to quit\n    for event in pygame.event.get():\n        if event.type == pygame.QUIT:\n            running = False\n    \n    # update the frame to display according to render_FPS\n    if time_step % int(math.ceil((1.0 / render_FPS) / h)) == 0:\n        # fill the background with white color, display simulation time at the top,\n        # draw the spring segment, and render the particle as a circle:\n        screen.fill((255, 255, 255))    \n        pygame.display.set_caption('Current time: ' + f'{time_step * h: .2f}s')\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection([0, 0]), screen_projection(x)) ###\n        pygame.draw.circle(screen, (0, 0, 255), screen_projection(x), 0.1 * scale)\n        pygame.display.flip()   # flip the display\n        pygame.time.wait(int(1000.0 / render_FPS))  # wait to render the next frame\n\n    # step forward the simulation by updating particle velocity and position\n    spring_cur_len = math.sqrt(x[0] * x[0] + x[1] * x[1]) ###\n    spring_displacement = spring_cur_len - spring_rest_len ###\n    spring_force = -spring_stiffness * spring_displacement * (x / spring_cur_len) ###\n    v += h * (g + spring_force / m)\n    x += h * v\n\n    time_step += 1  # update time step counter"
  },
  {
    "path": "0_getting_started/simulator2.py",
    "content": "# Mass-Spring Solid Simulation\n\nimport math\nimport numpy as np  # for vector data structure and computations\nimport pygame       # for visualization\nimport square_mesh  # for generating a square mesh\n\n# simulation setup\nside_length = 1             # side length of the square\nn_seg = 4                   # number of springs per side of the square\nm = 1000                    # mass of each particle\n[x, e] = square_mesh.generate(side_length, n_seg)   # array of particle positions and springs   ###\nv = np.array([[0.0, 0.0]] * len(x))     # velocity array of particles ###\ng = np.array([0.0, -10.0])  # gravitational acceleration\nspring_rest_len = []        # rest length array of the springs ###\nfor i in range(0, len(e)):  # calculate the rest length of each spring\n    spring_vec = x[e[i][0]] - x[e[i][1]]    # the vector connecting two ends of spring i\n    spring_rest_len.append(math.sqrt(spring_vec[0] * spring_vec[0] + spring_vec[1] * spring_vec[1]))\nspring_stiffness = 1e6      # stiffness of the spring\nh = 0.01                    # time step size in seconds\n\n# visualization/rendering setup\npygame.init()\nrender_FPS = 100                    # number of frames to render per second\nresolution = np.array([900, 900])   # visualization window size in pixels\noffset = resolution / 2             # offset between window coordinates and simulated coordinates\nscale = 200                         # scale between window coordinates and simulated coordinates\ndef screen_projection(x):           # convert simulated coordinates to window coordinates\n    return [offset[0] + scale * x[0], resolution[1] - (offset[1] + scale * x[1])]\nscreen = pygame.display.set_mode(resolution)    # initialize visualizer\n\ntime_step = 0   # the number of the current time step\nrunning = True  # flag indicating whether the simulation is still running\nwhile running:\n    # run until the user asks to quit\n    for event in pygame.event.get():\n        if event.type == pygame.QUIT:\n            running = False\n    \n    # update the frame to display according to render_FPS\n    if time_step % int(math.ceil((1.0 / render_FPS) / h)) == 0:\n        # fill the background with white color, display simulation time at the top,\n        # draw each spring segment, and render each particle as a circle:\n        screen.fill((255, 255, 255))    \n        pygame.display.set_caption('Current time: ' + f'{time_step * h: .2f}s')\n        for i in range(0, len(e)):  ###\n            pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[e[i][0]]), screen_projection(x[e[i][1]]))\n        for i in range(0, len(x)):  ###\n            pygame.draw.circle(screen, (0, 0, 255), screen_projection(x[i]), 0.02 * scale)\n        pygame.display.flip()   # flip the display\n        pygame.time.wait(int(1000.0 / render_FPS))  # wait to render the next frame\n\n    # step forward the simulation by updating particle velocity and position ###\n    for i in range(0, len(e)):\n        # calculate elasticity force of spring i:\n        spring_vec = x[e[i][0]] - x[e[i][1]]\n        spring_cur_len = math.sqrt(spring_vec[0] * spring_vec[0] + spring_vec[1] * spring_vec[1])\n        spring_displacement = spring_cur_len - spring_rest_len[i]\n        spring_force = -spring_stiffness * spring_displacement * (spring_vec / spring_cur_len)\n        # update the velocity of the two ends of spring i\n        v[e[i][0]] += h * (g + spring_force / m)\n        v[e[i][1]] += h * (g - spring_force / m)\n    # fix the top left and top right corner by setting velocity to 0:\n    v[n_seg] = v[(n_seg + 1) * (n_seg + 1) - 1] = np.array([0, 0])\n    # update the position of each particle:\n    for i in range(0, len(x)):\n        x[i] += h * v[i]\n\n    time_step += 1  # update time step counter"
  },
  {
    "path": "0_getting_started/square_mesh.py",
    "content": "import numpy as np\n\ndef generate(side_length, n_seg):\n    # sample nodes uniformly on a square\n    x = np.array([[0.0, 0.0]] * ((n_seg + 1) ** 2))\n    step = side_length / n_seg\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg + 1):\n            x[i * (n_seg + 1) + j] = [-side_length / 2 + i * step, -side_length / 2 + j * step]\n    \n    # connect the nodes with edges\n    e = []\n    # horizontal edges\n    for i in range(0, n_seg):\n        for j in range(0, n_seg + 1):\n            e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j])\n    # vertical edges\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg):\n            e.append([i * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n    # diagonals\n    for i in range(0, n_seg):\n        for j in range(0, n_seg):\n            e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1])\n            e.append([(i + 1) * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n\n    return [x, e]"
  },
  {
    "path": "10_mpm_elasticity/readme.md",
    "content": "# Two Colliding Elastic Blocks in 2D\n\nTwo elastic blocks with opposite initial velocities collide head-on using the simplest PIC transfer scheme, illustrating a minimal yet complete implementation of the Material Point Method (MPM).\n\n![results](results.gif)\n\n## Dependencies\n```\npip install numpy taichi\n```\n\n## Run\n```\npython simulator.py\n```"
  },
  {
    "path": "10_mpm_elasticity/simulator.py",
    "content": "# Material Point Method Simulation\nimport numpy as np  # numpy for linear algebra\nimport taichi as ti # taichi for fast and parallelized computation \n\nti.init(arch=ti.cpu)\n\n# ANCHOR: property_def\n# simulation setup\ngrid_size = 128 # background Eulerian grid's resolution, in 2D is [128, 128]\ndx = 1.0 / grid_size # the domain size is [1m, 1m] in 2D, so dx for each cell is (1/128)m\ndt = 2e-4 # time step size in second\nppc = 8 # average particles per cell\n\ndensity = 1000 # mass density, unit: kg / m^3\nE, nu = 1e4, 0.3 # block's Young's modulus and Poisson's ratio\nmu, lam = E / (2 * (1 + nu)), E * nu / ((1 + nu) * (1 - 2 * nu)) # Lame parameters\n# ANCHOR_END: property_def\n\n# ANCHOR: setting\n# uniformly sampling material particles\ndef uniform_grid(x0, y0, x1, y1, dx):\n    xx, yy = np.meshgrid(np.arange(x0, x1 + dx, dx), np.arange(y0, y1 + dx, dx))\n    return np.column_stack((xx.ravel(), yy.ravel()))\n\nbox1_samples = uniform_grid(0.2, 0.4, 0.4, 0.6, dx / np.sqrt(ppc))\nbox1_velocities = np.tile(np.array([10.0, 0]), (len(box1_samples), 1))\nbox2_samples = uniform_grid(0.6, 0.4, 0.8, 0.6, dx / np.sqrt(ppc))\nbox2_velocities = np.tile(np.array([-10.0, 0]), (len(box1_samples), 1))\nall_samples = np.concatenate([box1_samples, box2_samples], axis=0)\nall_velocities = np.concatenate([box1_velocities, box2_velocities], axis=0)\n# ANCHOR_END: setting\n\n# ANCHOR: data_def\n# material particles data\nN_particles = len(all_samples)\nx = ti.Vector.field(2, float, N_particles) # the position of particles\nx.from_numpy(all_samples)\nv = ti.Vector.field(2, float, N_particles) # the velocity of particles\nv.from_numpy(all_velocities)\nvol = ti.field(float, N_particles)         # the volume of particle\nvol.fill(0.2 * 0.4 / N_particles) # get the volume of each particle as V_rest / N_particles\nm = ti.field(float, N_particles)           # the mass of particle\nm.fill(vol[0] * density)\nF = ti.Matrix.field(2, 2, float, N_particles)  # the deformation gradient of particles\nF.from_numpy(np.tile(np.eye(2), (N_particles, 1, 1)))\n\n# grid data\ngrid_m = ti.field(float, (grid_size, grid_size))\ngrid_v = ti.Vector.field(2, float, (grid_size, grid_size))\n# ANCHOR_END: data_def\n\n# ANCHOR: reset_grid\ndef reset_grid():\n    # after each transfer, the grid is reset\n    grid_m.fill(0)\n    grid_v.fill(0)\n# ANCHOR_END: reset_grid\n\n################################\n# Stvk Hencky Elasticity\n################################\n# ANCHOR: stvk\n@ti.func\ndef StVK_Hencky_PK1_2D(F):\n    U, sig, V = ti.svd(F)\n    inv_sig = sig.inverse()\n    e = ti.Matrix([[ti.log(sig[0, 0]), 0], [0, ti.log(sig[1, 1])]])\n    return U @ (2 * mu * inv_sig @ e + lam * e.trace() * inv_sig) @ V.transpose()\n# ANCHOR_END: stvk\n\n# Particle-to-Grid (P2G) Transfers\n# ANCHOR: p2g\n@ti.kernel\ndef particle_to_grid_transfer():\n    for p in range(N_particles):\n        base = (x[p] / dx - 0.5).cast(int)\n        fx = x[p] / dx - base.cast(float)\n        # quadratic B-spline interpolating functions (Section 26.2)\n        w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2]\n        # gradient of the interpolating function (Section 26.2)\n        dw_dx = [fx - 1.5, 2 * (1.0 - fx), fx - 0.5]\n\n        P = StVK_Hencky_PK1_2D(F[p])\n        for i in ti.static(range(3)):\n            for j in ti.static(range(3)):\n                offset = ti.Vector([i, j])\n                weight = w[i][0] * w[j][1]\n                grad_weight = ti.Vector([(1. / dx) * dw_dx[i][0] * w[j][1], \n                                          w[i][0] * (1. / dx) * dw_dx[j][1]])\n\n                grid_m[base + offset] += weight * m[p] # mass transfer\n                grid_v[base + offset] += weight * m[p] * v[p] # momentum Transfer, PIC formulation\n                # internal force (stress) transfer\n                fi = -vol[p] * P @ F[p].transpose() @ grad_weight\n                grid_v[base + offset] += dt * fi\n# ANCHOR_END: p2g\n\n# Grid Update\n# ANCHOR: grid_update\n@ti.kernel\ndef update_grid():\n    for i, j in grid_m:\n        if grid_m[i, j] > 0:\n            grid_v[i, j] = grid_v[i, j] / grid_m[i, j] # extract updated nodal velocity from transferred nodal momentum\n\n            # Dirichlet BC near the bounding box\n            if i <= 3 or i > grid_size - 3 or j <= 2 or j > grid_size - 3:\n                grid_v[i, j] = 0\n# ANCHOR_END: grid_update\n\n\n# Grid-to-Particle (G2P) Transfers\n# ANCHOR: g2p\n@ti.kernel\ndef grid_to_particle_transfer():\n    for p in range(N_particles):\n        base = (x[p] / dx - 0.5).cast(int)\n        fx = x[p] / dx - base.cast(float)\n        # quadratic B-spline interpolating functions (Section 26.2)\n        w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2]\n        # gradient of the interpolating function (Section 26.2)\n        dw_dx = [fx - 1.5, 2 * (1.0 - fx), fx - 0.5]\n\n        new_v = ti.Vector.zero(float, 2)\n        v_grad_wT = ti.Matrix.zero(float, 2, 2)\n        for i in ti.static(range(3)):\n            for j in ti.static(range(3)):\n                offset = ti.Vector([i, j])\n                weight = w[i][0] * w[j][1]\n                grad_weight = ti.Vector([(1. / dx) * dw_dx[i][0] * w[j][1], \n                                          w[i][0] * (1. / dx) * dw_dx[j][1]])\n\n                new_v += weight * grid_v[base + offset]\n                v_grad_wT += grid_v[base + offset].outer_product(grad_weight)\n\n        v[p] = new_v\n        F[p] = (ti.Matrix.identity(float, 2) + dt * v_grad_wT) @ F[p]\n# ANCHOR_END: g2p\n\n# Deformation Gradient and Particle State Update\n# ANCHOR: particle_update\n@ti.kernel\ndef update_particle_state():\n    for p in range(N_particles):\n        x[p] += dt * v[p] # advection\n# ANCHOR_END: particle_update\n\n# ANCHOR: time_step\ndef step():\n    # a single time step of the Material Point Method (MPM) simulation\n    reset_grid()\n    particle_to_grid_transfer()\n    update_grid()\n    grid_to_particle_transfer()\n    update_particle_state()\n# ANCHOR_END: time_step\n\n################################\n# Main \n################################\ngui = ti.GUI(\"2D MPM Elasticity\", res = 512, background_color = 0xFFFFFF)\nwhile True:\n    for s in range(50): step()\n\n    gui.circles(x.to_numpy()[:len(box1_samples)], radius=3, color=0xFF0000)\n    gui.circles(x.to_numpy()[len(box1_samples):], radius=3, color=0x0000FF)\n    gui.show()"
  },
  {
    "path": "11_mpm_plastic/readme.md",
    "content": "# 2D Sand with a Sphere Collider\n\nA 2D sand block falling onto a static red sphere collider simulated by Material Point Method (MPM). The sand undergoes irreversible deformation and splashing upon impact, demonstrating granular flow and frictional boundary response.\n\n![results](results.gif)\n\n## Dependencies\n```\npip install numpy taichi\n```\n\n## Run\n```\npython simulator.py\n```"
  },
  {
    "path": "11_mpm_plastic/simulator.py",
    "content": "# Material Point Method Simulation\nimport numpy as np  # numpy for linear algebra\nimport taichi as ti # taichi for fast and parallelized computation \n\nti.init(arch=ti.cpu)\n\n# sampling material particles with poisson-disk sampling\n################################\n# Poisson Disk Sampling Tool\n################################\ndef poisson_disk_sampling(radius, domain_size, k=30):\n    \"\"\"Bridson's algorithm for Poisson-disk sampling in 2D\"\"\"\n    cell_size = radius / np.sqrt(2)\n    grid_shape = (int(domain_size[0] / cell_size) + 1, int(domain_size[1] / cell_size) + 1)\n    grid = -np.ones(grid_shape, dtype=int)\n    samples = []\n    active_list = []\n\n    def in_domain(p):\n        return 0 <= p[0] < domain_size[0] and 0 <= p[1] < domain_size[1]\n\n    def get_cell_coords(p):\n        return int(p[0] / cell_size), int(p[1] / cell_size)\n\n    def get_nearby_samples(p):\n        i, j = get_cell_coords(p)\n        neighbors = []\n        for di in [-2, -1, 0, 1, 2]:\n            for dj in [-2, -1, 0, 1, 2]:\n                ni, nj = i + di, j + dj\n                if 0 <= ni < grid.shape[0] and 0 <= nj < grid.shape[1]:\n                    idx = grid[ni, nj]\n                    if idx != -1:\n                        neighbors.append(samples[idx])\n        return neighbors\n\n    # Start with a random point\n    first_point = np.array([np.random.uniform(0, domain_size[0]), np.random.uniform(0, domain_size[1])])\n    samples.append(first_point)\n    active_list.append(0)\n    grid[get_cell_coords(first_point)] = 0\n\n    while active_list:\n        idx = np.random.choice(active_list)\n        base_point = samples[idx]\n        found = False\n        for _ in range(k):\n            angle = np.random.uniform(0, 2 * np.pi)\n            r = np.random.uniform(radius, 2 * radius)\n            new_point = base_point + r * np.array([np.cos(angle), np.sin(angle)])\n            if in_domain(new_point):\n                neighbors = get_nearby_samples(new_point)\n                if all(np.linalg.norm(new_point - n) >= radius for n in neighbors):\n                    samples.append(new_point)\n                    active_list.append(len(samples) - 1)\n                    grid[get_cell_coords(new_point)] = len(samples) - 1\n                    found = True\n        if not found:\n            active_list.remove(idx)\n    return np.array(samples)\n\n# ANCHOR: data_def\n# simulation setup\ngrid_size = 128 # background Eulerian grid's resolution, in 2D is [128, 128]\ndx = 1.0 / grid_size # the domain size is [1m, 1m] in 2D, so dx for each cell is (1/128)m\ndt = 2e-4 # time step size in second\nppc = 8 # average particle-per-cell\n\ndensity = 400 # kg / m^3\nE, nu = 3.537e5, 0.3 # sand's Young's modulus and Poisson's ratio\nmu, lam = E / (2 * (1 + nu)), E * nu / ((1 + nu) * (1 - 2 * nu)) # sand's Lame parameters\nsdf_friction = 0.5 # frictional coefficient of SDF boundary condition\nfriction_angle_in_degrees = 25.0 # Drucker Prager friction angle\n# ANCHOR: D_def\nD = (1./4.) * dx * dx # constant D for Quadratic B-spline used for APIC\n# ANCHOR_END: D_def\n\n# sampling material particles with poisson-disk sampling\npoisson_samples = poisson_disk_sampling(dx / np.sqrt(ppc), [0.2, 0.4]) # simulating a [30cm, 50cm] sand block\n\n# material particles data\nN_particles = len(poisson_samples)\nx = ti.Vector.field(2, float, N_particles) # the position of particles\nx.from_numpy(np.array(poisson_samples) + [0.4, 0.55])\nv = ti.Vector.field(2, float, N_particles) # the velocity of particles\nvol = ti.field(float, N_particles)         # the volume of particle\nvol.fill(0.2 * 0.4 / N_particles) # get the volume of each particle as V_rest / N_particles\nm = ti.field(float, N_particles)           # the mass of particle\nm.fill(vol[0] * density)\nF = ti.Matrix.field(2, 2, float, N_particles)  # the deformation gradient of particles\nF.from_numpy(np.tile(np.eye(2), (N_particles, 1, 1)))\nC = ti.Matrix.field(2, 2, float, N_particles)  # the affine-matrix of particles\n\ndiff_log_J = ti.field(float, N_particles) # tracks changes in the log of the volume gained during extension\n\n# grid data\ngrid_m = ti.field(float, (grid_size, grid_size))\ngrid_v = ti.Vector.field(2, float, (grid_size, grid_size))\n# ANCHOR_END: data_def\n\n# ANCHOR: reset_grid\ndef reset_grid():\n    # after each transfer, the grid is reset\n    grid_m.fill(0)\n    grid_v.fill(0)\n# ANCHOR_END: reset_grid\n\n################################\n# Stvk Hencky Elasticity\n################################\n# ANCHOR: stvk\n@ti.func\ndef StVK_Hencky_PK1_2D(F):\n    U, sig, V = ti.svd(F)\n    inv_sig = sig.inverse()\n    e = ti.Matrix([[ti.log(sig[0, 0]), 0], [0, ti.log(sig[1, 1])]])\n    return U @ (2 * mu * inv_sig @ e + lam * e.trace() * inv_sig) @ V.transpose()\n# ANCHOR_END: stvk\n\n################################\n# Drucker Prager plasticity\n################################\n# ANCHOR: drucker_prager\n@ti.func\ndef Drucker_Prager_return_mapping(F, diff_log_J):\n    dim = ti.static(F.n)\n    sin_phi = ti.sin(friction_angle_in_degrees/ 180.0 * ti.math.pi)\n    friction_alpha = ti.sqrt(2.0 / 3.0) * 2.0 * sin_phi / (3.0 - sin_phi)\n    U, sig_diag, V = ti.svd(F)\n    sig = ti.Vector([ti.max(sig_diag[i,i], 0.05) for i in ti.static(range(dim))])\n    epsilon = ti.log(sig)\n    epsilon += diff_log_J / dim # volume correction treatment\n    trace_epsilon = epsilon.sum()\n    shifted_trace = trace_epsilon\n    if shifted_trace >= 0:\n        for d in ti.static(range(dim)):\n            epsilon[d] = 0.\n    else:\n        epsilon_hat = epsilon - (trace_epsilon / dim)\n        epsilon_hat_norm = ti.sqrt(epsilon_hat.dot(epsilon_hat)+1e-8)\n        delta_gamma = epsilon_hat_norm + (dim * lam + 2. * mu) / (2. * mu) * (shifted_trace) * friction_alpha\n        epsilon -= (ti.max(delta_gamma, 0) / epsilon_hat_norm) * epsilon_hat\n    sig_out = ti.exp(epsilon)\n    for d in ti.static(range(dim)):\n        sig_diag[d,d] = sig_out[d]\n    return U @ sig_diag @ V.transpose()\n# ANCHOR_END: drucker_prager\n\n# Particle-to-Grid (P2G) Transfers\n# ANCHOR: p2g\n@ti.kernel\ndef particle_to_grid_transfer():\n    for p in range(N_particles):\n        base = (x[p] / dx - 0.5).cast(int)\n        fx = x[p] / dx - base.cast(float)\n        # quadratic B-spline interpolating functions\n        w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2]\n        # gradient of the interpolating function\n        dw_dx = [fx - 1.5, 2 * (1.0 - fx), fx - 0.5]\n\n        P = StVK_Hencky_PK1_2D(F[p])\n        for i in ti.static(range(3)):\n            for j in ti.static(range(3)):\n                offset = ti.Vector([i, j])\n                dpos = (offset.cast(float) - fx) * dx\n                weight = w[i][0] * w[j][1]\n                grad_weight = ti.Vector([(1. / dx) * dw_dx[i][0] * w[j][1], \n                                          w[i][0] * (1. / dx) * dw_dx[j][1]])\n\n                grid_m[base + offset] += weight * m[p] # mass transfer\n                # ANCHOR: apic_p2g\n                grid_v[base + offset] += weight * m[p] * (v[p] + C[p] @ dpos) # momentum Transfer, APIC formulation\n                # ANCHOR_END: apic_p2g\n                # internal force (stress) transfer\n                fi = -vol[p] * P @ F[p].transpose() @ grad_weight\n                grid_v[base + offset] += dt * fi\n# ANCHOR_END: p2g\n\n# Grid Update\n@ti.kernel\ndef update_grid():\n    for i, j in grid_m:\n        if grid_m[i, j] > 0:\n            grid_v[i, j] = grid_v[i, j] / grid_m[i, j] # extract updated nodal velocity from transferred nodal momentum\n            grid_v[i, j] += ti.Vector([0, -9.81]) * dt # gravity\n\n            # Dirichlet BC near the bounding box\n            if i <= 3 or i > grid_size - 3 or j <= 2 or j > grid_size - 3:\n                grid_v[i, j] = 0\n            \n            x_i = (ti.Vector([i, j])) * dx # position of the grid-node\n            \n            # ANCHOR: sphere_sdf\n            # a sphere SDF as boundary condition\n            sphere_center = ti.Vector([0.5, 0.5])\n            sphere_radius = 0.05 + dx # add a dx-gap to avoid penetration\n            if (x_i - sphere_center).norm() < sphere_radius:\n                normal = (x_i - sphere_center).normalized()\n                diff_vel = -grid_v[i, j]\n                dotnv = normal.dot(diff_vel)\n                dotnv_frac = dotnv * (1.0 - sdf_friction)\n                grid_v[i, j] += diff_vel * sdf_friction + normal * dotnv_frac\n            # ANCHOR_END: sphere_sdf\n\n\n# Grid-to-Particle (G2P) Transfers\n# ANCHOR: g2p\n@ti.kernel\ndef grid_to_particle_transfer():\n    for p in range(N_particles):\n        base = (x[p] / dx - 0.5).cast(int)\n        fx = x[p] / dx - base.cast(float)\n        # quadratic B-spline interpolating functions \n        w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2]\n        # gradient of the interpolating function\n        dw_dx = [fx - 1.5, 2 * (1.0 - fx), fx - 0.5]\n\n        new_v = ti.Vector.zero(float, 2)\n        new_C = ti.Matrix.zero(float, 2, 2)\n        v_grad_wT = ti.Matrix.zero(float, 2, 2)\n        for i in ti.static(range(3)):\n            for j in ti.static(range(3)):\n                offset = ti.Vector([i, j])\n                dpos = (offset.cast(float) - fx) * dx\n                weight = w[i][0] * w[j][1]\n                grad_weight = ti.Vector([(1. / dx) * dw_dx[i][0] * w[j][1], \n                                          w[i][0] * (1. / dx) * dw_dx[j][1]])\n\n                new_v += weight * grid_v[base + offset]\n                # ANCHOR: apic_g2p\n                new_C += weight * grid_v[base + offset].outer_product(dpos) / D\n                # ANCHOR_END: apic_g2p\n                v_grad_wT += grid_v[base + offset].outer_product(grad_weight)\n\n        v[p] = new_v\n        C[p] = new_C\n        # note the updated F here is the trial elastic deformation gradient\n        F[p] = (ti.Matrix.identity(float, 2) + dt * v_grad_wT) @ F[p]\n# ANCHOR_END: g2p\n\n# Deformation Gradient and Particle State Update\n# ANCHOR: particle_update\n@ti.kernel\ndef update_particle_state():\n    for p in range(N_particles):\n        # trial elastic deformation gradient\n        F_tr = F[p]\n        # apply return mapping to correct the trial elastic state, projecting the stress induced by F_tr\n        # back onto the yield surface, following the direction specified by the plastic flow rule.\n        new_F = Drucker_Prager_return_mapping(F_tr, diff_log_J[p])\n        # track the volume change incurred by return mapping to correct volume, following https://dl.acm.org/doi/10.1145/3072959.3073651 sec 4.3.4\n        diff_log_J[p] += -ti.log(new_F.determinant()) + ti.log(F_tr.determinant()) \n        F[p] = new_F\n        # advection\n        x[p] += dt * v[p]\n# ANCHOR_END: particle_update\n\n# ANCHOR: time_step\ndef step():\n    # a single time step of the Material Point Method (MPM) simulation\n    reset_grid()\n    particle_to_grid_transfer()\n    update_grid()\n    grid_to_particle_transfer()\n    update_particle_state()\n# ANCHOR_END: time_step\n\n################################\n# Main \n################################\ngui = ti.GUI(\"2D MPM Sand\", res = 512, background_color = 0xFFFFFF)\nframe = 0\nwhile True:\n    for s in range(50):\n        step()\n\n    gui.circles(np.array([[0.5, 0.5]]), radius = 0.05 * gui.res[0], color = 0xFF0000)\n    gui.circles(x.to_numpy(), radius = 1.5, color = 0xD6B588)\n    gui.show()"
  },
  {
    "path": "11_mpm_plastic/simulator_viscoplastic.py",
    "content": "import taichi as ti\nimport os\nimport shutil\n\nti.init(arch=ti.cuda)\n\nquality = 6\nn_particles, n_grid = 9000 * quality**2, 256 * quality\ndx, inv_dx = 1 / n_grid, float(n_grid)\ndt = 1e-4 / quality\np_vol, p_rho = (dx * 0.5) ** 2, 1\np_mass = p_vol * p_rho\n\nnu = 0.2\nE_toothpaste = 350.0\nmu_toothpaste = E_toothpaste / (2 * (1 + nu))\nlam_toothpaste = E_toothpaste * nu / ((1 + nu) * (1 - 2 * nu))\n\nyield_stress_bar1 = 1.2\nplastic_viscosity_bar1 = 0.7\nyield_stress_bar2 = 1.0\nplastic_viscosity_bar2 = 0.3\n\nground_friction = 0.3\n\nx = ti.Vector.field(2, dtype=float, shape=n_particles)\nv = ti.Vector.field(2, dtype=float, shape=n_particles)\nC = ti.Matrix.field(2, 2, dtype=float, shape=n_particles)\nF = ti.Matrix.field(2, 2, dtype=float, shape=n_particles)\ncolor_stripe = ti.field(dtype=int, shape=n_particles)\nyield_stress = ti.field(dtype=float, shape=n_particles)\nplastic_viscosity = ti.field(dtype=float, shape=n_particles)\ngrid_v = ti.Vector.field(2, dtype=float, shape=(n_grid, n_grid))\ngrid_m = ti.field(dtype=float, shape=(n_grid, n_grid))\ngravity = ti.Vector.field(2, dtype=float, shape=())\n\n\n@ti.func\ndef viscoplastic_return_mapping_stvk_2d(F_trial, mu_p, lam_p, yield_stress_p, plastic_viscosity_p, dt_val):\n    \"\"\"Viscoplastic return mapping for toothpaste-like material (2D version)\"\"\"\n    U, sig, V = ti.svd(F_trial)\n    \n    # Clamp singular values to prevent numerical issues\n    sig0 = ti.max(sig[0, 0], 0.01)\n    sig1 = ti.max(sig[1, 1], 0.01)\n    \n    # Compute logarithmic strain (2D)\n    epsilon = ti.Vector([ti.log(sig0), ti.log(sig1)])\n    trace_epsilon = epsilon[0] + epsilon[1]\n    \n    # Deviatoric strain\n    epsilon_hat = epsilon - ti.Vector([trace_epsilon / 2.0, trace_epsilon / 2.0])\n    \n    # Deviatoric stress in logarithmic strain space\n    s_trial = 2.0 * mu_p * epsilon_hat\n    s_trial_norm = s_trial.norm()\n    \n    # Yield condition - using similar factor to 3D version (sqrt(2/3) ≈ 0.816)\n    # For 2D, we use sqrt(2/3) to match the 3D implementation's scaling\n    y = s_trial_norm - ti.sqrt(2.0 / 3.0) * yield_stress_p\n    \n    F_elastic_res = F_trial\n    if y > 0:\n        # Compute b_trial for mu_hat (2D adaptation)\n        b_trial = sig0 * sig0 + sig1 * sig1\n        mu_hat = mu_p * b_trial / 2.0\n        \n        # Rate-dependent plastic flow\n        denom = 1.0 + plastic_viscosity_p / (2.0 * mu_hat * dt_val)\n        s_new_norm = s_trial_norm - y / denom\n        s_scale = s_new_norm / s_trial_norm if s_trial_norm > 1e-10 else 1.0\n        s_new = s_scale * s_trial\n        \n        # Reconstruct strain\n        epsilon_new = 1.0 / (2.0 * mu_p) * s_new + ti.Vector([trace_epsilon / 2.0, trace_epsilon / 2.0])\n        \n        # Reconstruct deformation gradient\n        sig_elastic = ti.Matrix([[ti.exp(epsilon_new[0]), 0.0], [0.0, ti.exp(epsilon_new[1])]])\n        F_elastic_res = U @ sig_elastic @ V.transpose()\n    \n    return F_elastic_res\n\n\n@ti.func\ndef stvk_stress_2d(F_elastic, U, V, sig, mu_p, lam_p):\n    \"\"\"Saint Venant-Kirchhoff stress model (2D version)\"\"\"\n    sig0 = ti.max(sig[0, 0], 0.01)\n    sig1 = ti.max(sig[1, 1], 0.01)\n    \n    epsilon = ti.Vector([ti.log(sig0), ti.log(sig1)])\n    log_sig_sum = ti.log(sig0) + ti.log(sig1)\n    \n    ONE = ti.Vector([1.0, 1.0])\n    tau = 2.0 * mu_p * epsilon + lam_p * log_sig_sum * ONE\n    \n    tau_mat = ti.Matrix([[tau[0], 0.0], [0.0, tau[1]]])\n    return U @ tau_mat @ V.transpose() @ F_elastic.transpose()\n\n\n@ti.kernel\ndef p2g2p():\n    for i, j in grid_m:\n        grid_v[i, j] = [0, 0]\n        grid_m[i, j] = 0\n    for p in x:\n        if x[p][0] < 0.0 or x[p][1] < 0.0 or x[p][0] > 1.0 or x[p][1] > 1.0:\n            continue\n        \n        base = (x[p] * inv_dx - 0.5).cast(int)\n        fx = x[p] * inv_dx - base.cast(float)\n        w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2]\n        F_trial = (ti.Matrix.identity(float, 2) + dt * C[p]) @ F[p]\n        \n        F[p] = viscoplastic_return_mapping_stvk_2d(\n            F_trial, mu_toothpaste, lam_toothpaste, yield_stress[p], plastic_viscosity[p], dt\n        )\n        \n        U, sig, V = ti.svd(F[p])\n        stress = stvk_stress_2d(F[p], U, V, sig, mu_toothpaste, lam_toothpaste)\n        \n        stress = (-dt * p_vol * 4 * inv_dx * inv_dx) * stress\n        affine = stress + p_mass * C[p]\n        for i, j in ti.static(ti.ndrange(3, 3)):\n            offset = ti.Vector([i, j])\n            dpos = (offset.cast(float) - fx) * dx\n            weight = w[i][0] * w[j][1]\n            grid_v[base + offset] += weight * (p_mass * v[p] + affine @ dpos)\n            grid_m[base + offset] += weight * p_mass\n    for i, j in grid_m:\n        if grid_m[i, j] > 0:\n            grid_v[i, j] = (1 / grid_m[i, j]) * grid_v[i, j]\n            grid_v[i, j] += dt * gravity[None] * 30\n            \n            if i < 3 and grid_v[i, j][0] < 0:\n                grid_v[i, j][0] = 0\n            if i > n_grid - 3 and grid_v[i, j][0] > 0:\n                grid_v[i, j][0] = 0\n            \n            if j < 3 and grid_v[i, j][1] < 0:\n                v_y = grid_v[i, j][1]\n                v_x = grid_v[i, j][0]\n                normal_component = ti.abs(v_y)\n                tangential_velocity = v_x\n                \n                if ti.abs(tangential_velocity) > 1e-20:\n                    friction_reduction = ground_friction * normal_component\n                    v_x_new = tangential_velocity\n                    if v_x_new > 0:\n                        v_x_new = ti.max(0.0, v_x_new - friction_reduction)\n                    else:\n                        v_x_new = ti.min(0.0, v_x_new + friction_reduction)\n                    grid_v[i, j] = ti.Vector([v_x_new, 0.0])\n                else:\n                    grid_v[i, j] = ti.Vector([0.0, 0.0])\n            \n            if j > n_grid - 3 and grid_v[i, j][1] > 0:\n                grid_v[i, j][1] = 0\n    for p in x:\n        if x[p][0] < 0.0 or x[p][1] < 0.0 or x[p][0] > 1.0 or x[p][1] > 1.0:\n            continue\n        \n        base = (x[p] * inv_dx - 0.5).cast(int)\n        fx = x[p] * inv_dx - base.cast(float)\n        w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1.0) ** 2, 0.5 * (fx - 0.5) ** 2]\n        new_v = ti.Vector.zero(float, 2)\n        new_C = ti.Matrix.zero(float, 2, 2)\n        for i, j in ti.static(ti.ndrange(3, 3)):\n            dpos = ti.Vector([i, j]).cast(float) - fx\n            g_v = grid_v[base + ti.Vector([i, j])]\n            weight = w[i][0] * w[j][1]\n            new_v += weight * g_v\n            new_C += 4 * inv_dx * weight * g_v.outer_product(dpos)\n        v[p], C[p] = new_v, new_C\n        x[p] += dt * v[p]\n\n\n@ti.kernel\ndef reset():\n    bar_width = 0.015\n    bar_height = 0.85\n    bar_bottom_y = 0.1\n    bar_spacing = 0.2\n    bar1_center_x = 0.5 - bar_spacing / 2.0\n    bar2_center_x = 0.5 + bar_spacing / 2.0\n    \n    particles_per_bar = n_particles // 2\n    \n    for i in range(n_particles):\n        bar_center_x = 0.5\n        bar_yield_stress = 1.2\n        bar_plastic_viscosity = 0.7\n        \n        if i < particles_per_bar:\n            bar_center_x = bar1_center_x\n            bar_yield_stress = 1.2\n            bar_plastic_viscosity = 0.7\n        else:\n            bar_center_x = bar2_center_x\n            bar_yield_stress = 1.0\n            bar_plastic_viscosity = 0.3\n        \n        x_pos = ti.random() * bar_width + (bar_center_x - bar_width / 2.0)\n        y_pos = ti.random() * bar_height + bar_bottom_y\n        \n        x[i] = [x_pos, y_pos]\n        \n        stripe_width = bar_width / 3.0\n        relative_x = x_pos - (bar_center_x - bar_width / 2.0)\n        if relative_x < stripe_width:\n            color_stripe[i] = 0\n        elif relative_x < 2.0 * stripe_width:\n            color_stripe[i] = 1\n        else:\n            color_stripe[i] = 2\n        \n        v[i] = [0, 0]\n        F[i] = ti.Matrix([[1, 0], [0, 1]])\n        C[i] = ti.Matrix.zero(float, 2, 2)\n        yield_stress[i] = bar_yield_stress\n        plastic_viscosity[i] = bar_plastic_viscosity\n\n\ngui = ti.GUI(\"Taichi MLS-MPM-128\", res=1024, background_color=0xEEEEF0, show_gui=False)\nreset()\ngravity[None] = [0, -1]\n\nsave_duration = 10.0\noutput_fps = 30\nframe_time = 3e-2\ntotal_frames_to_run = int(save_duration / frame_time)\nframes_per_save = int(1.0 / (output_fps * frame_time))\ntotal_saves = int(save_duration * output_fps)\nsave_counter = 0\n\noutput_dir = os.path.join(os.path.dirname(__file__), \"frames\")\nos.makedirs(output_dir, exist_ok=True)\nvideo_output = os.path.join(os.path.dirname(__file__), \"viscoplastic_animation.mp4\")\n\n\nfor frame in range(total_frames_to_run):\n    substeps_per_frame = int(2e-3 // dt)\n    \n    for s in range(substeps_per_frame):\n        p2g2p()\n    \n    if frame % frames_per_save == 0 and save_counter < total_saves:\n        gui.circles(\n            x.to_numpy(),\n            radius=1.5,\n            palette=[0x3366FF, 0xFFFF00, 0xFF3333],\n            palette_indices=color_stripe,\n        )\n        filename = os.path.join(output_dir, f'{save_counter:06d}.png')\n        gui.show(filename)\n        save_counter += 1\n        if save_counter % 30 == 0:\n            print(f\"Saved {save_counter}/{total_saves} frames...\")\n\nprint(f\"Frame saving complete! Saved {save_counter} frames.\")\n\nffmpeg_path = shutil.which(\"ffmpeg\")\nif ffmpeg_path is not None and save_counter > 0:\n    pattern = os.path.join(output_dir, \"%06d.png\")\n    cmd = (\n        f'\"{ffmpeg_path}\" -y -framerate {output_fps} -i \"{pattern}\" '\n        f'-c:v libx264 -pix_fmt yuv420p -crf 18 \"{video_output}\"'\n    )\n    print(\"Running:\", cmd)\n    os.system(cmd)\n    print(f\"Video written to: {video_output}\")\nelse:\n    print(\"ffmpeg not found or no frames saved. To build video manually, run:\")\n    print(\n        f\"ffmpeg -y -framerate {output_fps} -i '{os.path.join(output_dir, '%06d.png')}' \"\n        f\"-c:v libx264 -pix_fmt yuv420p -crf 18 '{video_output}'\"\n    )"
  },
  {
    "path": "11_mpm_sand/readme.md",
    "content": "# 2D Sand with a Sphere Collider\n\nA 2D sand block falling onto a static red sphere collider simulated by Material Point Method (MPM). The sand undergoes irreversible deformation and splashing upon impact, demonstrating granular flow and frictional boundary response.\n\n![results](results.gif)\n\n## Dependencies\n```\npip install numpy taichi\n```\n\n## Run\n```\npython simulator.py\n```"
  },
  {
    "path": "11_mpm_sand/simulator.py",
    "content": "# Material Point Method Simulation\nimport numpy as np  # numpy for linear algebra\nimport taichi as ti # taichi for fast and parallelized computation \n\nti.init(arch=ti.cpu)\n\n# sampling material particles with poisson-disk sampling\n################################\n# Poisson Disk Sampling Tool\n################################\ndef poisson_disk_sampling(radius, domain_size, k=30):\n    \"\"\"Bridson's algorithm for Poisson-disk sampling in 2D\"\"\"\n    cell_size = radius / np.sqrt(2)\n    grid_shape = (int(domain_size[0] / cell_size) + 1, int(domain_size[1] / cell_size) + 1)\n    grid = -np.ones(grid_shape, dtype=int)\n    samples = []\n    active_list = []\n\n    def in_domain(p):\n        return 0 <= p[0] < domain_size[0] and 0 <= p[1] < domain_size[1]\n\n    def get_cell_coords(p):\n        return int(p[0] / cell_size), int(p[1] / cell_size)\n\n    def get_nearby_samples(p):\n        i, j = get_cell_coords(p)\n        neighbors = []\n        for di in [-2, -1, 0, 1, 2]:\n            for dj in [-2, -1, 0, 1, 2]:\n                ni, nj = i + di, j + dj\n                if 0 <= ni < grid.shape[0] and 0 <= nj < grid.shape[1]:\n                    idx = grid[ni, nj]\n                    if idx != -1:\n                        neighbors.append(samples[idx])\n        return neighbors\n\n    # Start with a random point\n    first_point = np.array([np.random.uniform(0, domain_size[0]), np.random.uniform(0, domain_size[1])])\n    samples.append(first_point)\n    active_list.append(0)\n    grid[get_cell_coords(first_point)] = 0\n\n    while active_list:\n        idx = np.random.choice(active_list)\n        base_point = samples[idx]\n        found = False\n        for _ in range(k):\n            angle = np.random.uniform(0, 2 * np.pi)\n            r = np.random.uniform(radius, 2 * radius)\n            new_point = base_point + r * np.array([np.cos(angle), np.sin(angle)])\n            if in_domain(new_point):\n                neighbors = get_nearby_samples(new_point)\n                if all(np.linalg.norm(new_point - n) >= radius for n in neighbors):\n                    samples.append(new_point)\n                    active_list.append(len(samples) - 1)\n                    grid[get_cell_coords(new_point)] = len(samples) - 1\n                    found = True\n        if not found:\n            active_list.remove(idx)\n    return np.array(samples)\n\n# ANCHOR: data_def\n# simulation setup\ngrid_size = 128 # background Eulerian grid's resolution, in 2D is [128, 128]\ndx = 1.0 / grid_size # the domain size is [1m, 1m] in 2D, so dx for each cell is (1/128)m\ndt = 2e-4 # time step size in second\nppc = 8 # average particle-per-cell\n\ndensity = 400 # kg / m^3\nE, nu = 3.537e5, 0.3 # sand's Young's modulus and Poisson's ratio\nmu, lam = E / (2 * (1 + nu)), E * nu / ((1 + nu) * (1 - 2 * nu)) # sand's Lame parameters\nsdf_friction = 0.5 # frictional coefficient of SDF boundary condition\nfriction_angle_in_degrees = 25.0 # Drucker Prager friction angle\n# ANCHOR: D_def\nD = (1./4.) * dx * dx # constant D for Quadratic B-spline used for APIC\n# ANCHOR_END: D_def\n\n# sampling material particles with poisson-disk sampling\npoisson_samples = poisson_disk_sampling(dx / np.sqrt(ppc), [0.2, 0.4]) # simulating a [30cm, 50cm] sand block\n\n# material particles data\nN_particles = len(poisson_samples)\nx = ti.Vector.field(2, float, N_particles) # the position of particles\nx.from_numpy(np.array(poisson_samples) + [0.4, 0.55])\nv = ti.Vector.field(2, float, N_particles) # the velocity of particles\nvol = ti.field(float, N_particles)         # the volume of particle\nvol.fill(0.2 * 0.4 / N_particles) # get the volume of each particle as V_rest / N_particles\nm = ti.field(float, N_particles)           # the mass of particle\nm.fill(vol[0] * density)\nF = ti.Matrix.field(2, 2, float, N_particles)  # the deformation gradient of particles\nF.from_numpy(np.tile(np.eye(2), (N_particles, 1, 1)))\nC = ti.Matrix.field(2, 2, float, N_particles)  # the affine-matrix of particles\n\ndiff_log_J = ti.field(float, N_particles) # tracks changes in the log of the volume gained during extension\n\n# grid data\ngrid_m = ti.field(float, (grid_size, grid_size))\ngrid_v = ti.Vector.field(2, float, (grid_size, grid_size))\n# ANCHOR_END: data_def\n\n# ANCHOR: reset_grid\ndef reset_grid():\n    # after each transfer, the grid is reset\n    grid_m.fill(0)\n    grid_v.fill(0)\n# ANCHOR_END: reset_grid\n\n################################\n# Stvk Hencky Elasticity\n################################\n# ANCHOR: stvk\n@ti.func\ndef StVK_Hencky_PK1_2D(F):\n    U, sig, V = ti.svd(F)\n    inv_sig = sig.inverse()\n    e = ti.Matrix([[ti.log(sig[0, 0]), 0], [0, ti.log(sig[1, 1])]])\n    return U @ (2 * mu * inv_sig @ e + lam * e.trace() * inv_sig) @ V.transpose()\n# ANCHOR_END: stvk\n\n################################\n# Drucker Prager plasticity\n################################\n# ANCHOR: drucker_prager\n@ti.func\ndef Drucker_Prager_return_mapping(F, diff_log_J):\n    dim = ti.static(F.n)\n    sin_phi = ti.sin(friction_angle_in_degrees/ 180.0 * ti.math.pi)\n    friction_alpha = ti.sqrt(2.0 / 3.0) * 2.0 * sin_phi / (3.0 - sin_phi)\n    U, sig_diag, V = ti.svd(F)\n    sig = ti.Vector([ti.max(sig_diag[i,i], 0.05) for i in ti.static(range(dim))])\n    epsilon = ti.log(sig)\n    epsilon += diff_log_J / dim # volume correction treatment\n    trace_epsilon = epsilon.sum()\n    shifted_trace = trace_epsilon\n    if shifted_trace >= 0:\n        for d in ti.static(range(dim)):\n            epsilon[d] = 0.\n    else:\n        epsilon_hat = epsilon - (trace_epsilon / dim)\n        epsilon_hat_norm = ti.sqrt(epsilon_hat.dot(epsilon_hat)+1e-8)\n        delta_gamma = epsilon_hat_norm + (dim * lam + 2. * mu) / (2. * mu) * (shifted_trace) * friction_alpha\n        epsilon -= (ti.max(delta_gamma, 0) / epsilon_hat_norm) * epsilon_hat\n    sig_out = ti.exp(epsilon)\n    for d in ti.static(range(dim)):\n        sig_diag[d,d] = sig_out[d]\n    return U @ sig_diag @ V.transpose()\n# ANCHOR_END: drucker_prager\n\n# Particle-to-Grid (P2G) Transfers\n# ANCHOR: p2g\n@ti.kernel\ndef particle_to_grid_transfer():\n    for p in range(N_particles):\n        base = (x[p] / dx - 0.5).cast(int)\n        fx = x[p] / dx - base.cast(float)\n        # quadratic B-spline interpolating functions\n        w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2]\n        # gradient of the interpolating function\n        dw_dx = [fx - 1.5, 2 * (1.0 - fx), fx - 0.5]\n\n        P = StVK_Hencky_PK1_2D(F[p])\n        for i in ti.static(range(3)):\n            for j in ti.static(range(3)):\n                offset = ti.Vector([i, j])\n                dpos = (offset.cast(float) - fx) * dx\n                weight = w[i][0] * w[j][1]\n                grad_weight = ti.Vector([(1. / dx) * dw_dx[i][0] * w[j][1], \n                                          w[i][0] * (1. / dx) * dw_dx[j][1]])\n\n                grid_m[base + offset] += weight * m[p] # mass transfer\n                # ANCHOR: apic_p2g\n                grid_v[base + offset] += weight * m[p] * (v[p] + C[p] @ dpos) # momentum Transfer, APIC formulation\n                # ANCHOR_END: apic_p2g\n                # internal force (stress) transfer\n                fi = -vol[p] * P @ F[p].transpose() @ grad_weight\n                grid_v[base + offset] += dt * fi\n# ANCHOR_END: p2g\n\n# Grid Update\n@ti.kernel\ndef update_grid():\n    for i, j in grid_m:\n        if grid_m[i, j] > 0:\n            grid_v[i, j] = grid_v[i, j] / grid_m[i, j] # extract updated nodal velocity from transferred nodal momentum\n            grid_v[i, j] += ti.Vector([0, -9.81]) * dt # gravity\n\n            # Dirichlet BC near the bounding box\n            if i <= 3 or i > grid_size - 3 or j <= 2 or j > grid_size - 3:\n                grid_v[i, j] = 0\n            \n            x_i = (ti.Vector([i, j])) * dx # position of the grid-node\n            \n            # ANCHOR: sphere_sdf\n            # a sphere SDF as boundary condition\n            sphere_center = ti.Vector([0.5, 0.5])\n            sphere_radius = 0.05 + dx # add a dx-gap to avoid penetration\n            if (x_i - sphere_center).norm() < sphere_radius:\n                normal = (x_i - sphere_center).normalized()\n                diff_vel = -grid_v[i, j]\n                dotnv = normal.dot(diff_vel)\n                dotnv_frac = dotnv * (1.0 - sdf_friction)\n                grid_v[i, j] += diff_vel * sdf_friction + normal * dotnv_frac\n            # ANCHOR_END: sphere_sdf\n\n\n# Grid-to-Particle (G2P) Transfers\n# ANCHOR: g2p\n@ti.kernel\ndef grid_to_particle_transfer():\n    for p in range(N_particles):\n        base = (x[p] / dx - 0.5).cast(int)\n        fx = x[p] / dx - base.cast(float)\n        # quadratic B-spline interpolating functions \n        w = [0.5 * (1.5 - fx) ** 2, 0.75 - (fx - 1) ** 2, 0.5 * (fx - 0.5) ** 2]\n        # gradient of the interpolating function\n        dw_dx = [fx - 1.5, 2 * (1.0 - fx), fx - 0.5]\n\n        new_v = ti.Vector.zero(float, 2)\n        new_C = ti.Matrix.zero(float, 2, 2)\n        v_grad_wT = ti.Matrix.zero(float, 2, 2)\n        for i in ti.static(range(3)):\n            for j in ti.static(range(3)):\n                offset = ti.Vector([i, j])\n                dpos = (offset.cast(float) - fx) * dx\n                weight = w[i][0] * w[j][1]\n                grad_weight = ti.Vector([(1. / dx) * dw_dx[i][0] * w[j][1], \n                                          w[i][0] * (1. / dx) * dw_dx[j][1]])\n\n                new_v += weight * grid_v[base + offset]\n                # ANCHOR: apic_g2p\n                new_C += weight * grid_v[base + offset].outer_product(dpos) / D\n                # ANCHOR_END: apic_g2p\n                v_grad_wT += grid_v[base + offset].outer_product(grad_weight)\n\n        v[p] = new_v\n        C[p] = new_C\n        # note the updated F here is the trial elastic deformation gradient\n        F[p] = (ti.Matrix.identity(float, 2) + dt * v_grad_wT) @ F[p]\n# ANCHOR_END: g2p\n\n# Deformation Gradient and Particle State Update\n# ANCHOR: particle_update\n@ti.kernel\ndef update_particle_state():\n    for p in range(N_particles):\n        # trial elastic deformation gradient\n        F_tr = F[p]\n        # apply return mapping to correct the trial elastic state, projecting the stress induced by F_tr\n        # back onto the yield surface, following the direction specified by the plastic flow rule.\n        new_F = Drucker_Prager_return_mapping(F_tr, diff_log_J[p])\n        # track the volume change incurred by return mapping to correct volume, following https://dl.acm.org/doi/10.1145/3072959.3073651 sec 4.3.4\n        diff_log_J[p] += -ti.log(new_F.determinant()) + ti.log(F_tr.determinant()) \n        F[p] = new_F\n        # advection\n        x[p] += dt * v[p]\n# ANCHOR_END: particle_update\n\n# ANCHOR: time_step\ndef step():\n    # a single time step of the Material Point Method (MPM) simulation\n    reset_grid()\n    particle_to_grid_transfer()\n    update_grid()\n    grid_to_particle_transfer()\n    update_particle_state()\n# ANCHOR_END: time_step\n\n################################\n# Main \n################################\ngui = ti.GUI(\"2D MPM Sand\", res = 512, background_color = 0xFFFFFF)\nframe = 0\nwhile True:\n    for s in range(50):\n        step()\n\n    gui.circles(np.array([[0.5, 0.5]]), radius = 0.05 * gui.res[0], color = 0xFF0000)\n    gui.circles(x.to_numpy(), radius = 1.5, color = 0xD6B588)\n    gui.show()"
  },
  {
    "path": "12_pbd_cloth/cloth_data.json",
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0.120000, 0.475859, -0.000000,  0.090000, 0.425859, -0.000000,  0.120000, 0.435859, -0.000000,  \n\t\t\t\t\t\t0.090000, 0.385859, -0.000000,  0.120000, 0.395859, -0.000000,  0.090000, 0.345859, -0.000000,  0.120000, 0.355859, -0.000000,  0.150000, 1.145859, -0.000000,  \n\t\t\t\t\t\t0.130000, 1.105859, -0.000000,  0.160000, 1.115859, -0.000000,  0.130000, 1.065859, -0.000000,  0.160000, 1.075859, -0.000000,  0.130000, 1.025859, -0.000000,  \n\t\t\t\t\t\t0.160000, 1.035859, -0.000000,  0.130000, 0.985859, -0.000000,  0.160000, 0.995859, -0.000000,  0.130000, 0.945859, -0.000000,  0.160000, 0.955859, -0.000000,  \n\t\t\t\t\t\t0.130000, 0.905859, -0.000000,  0.160000, 0.915859, -0.000000,  0.130000, 0.865859, -0.000000,  0.160000, 0.875859, -0.000000,  0.130000, 0.825859, -0.000000,  \n\t\t\t\t\t\t0.160000, 0.835859, -0.000000,  0.130000, 0.785859, -0.000000,  0.160000, 0.795859, -0.000000,  0.130000, 0.745859, -0.000000,  0.160000, 0.755859, -0.000000,  \n\t\t\t\t\t\t0.130000, 0.705859, 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-0.090000, 0.675859, -0.000000,  \n\t\t\t\t\t\t-0.090000, 0.715859, -0.000000,  -0.090000, 0.755859, -0.000000,  -0.090000, 0.795859, -0.000000,  -0.090000, 0.835859, -0.000000,  -0.090000, 0.875859, -0.000000,  \n\t\t\t\t\t\t-0.090000, 0.915859, -0.000000,  -0.090000, 0.955859, -0.000000,  -0.090000, 0.995859, -0.000000,  -0.090000, 1.035859, -0.000000,  -0.090000, 1.075859, -0.000000,  \n\t\t\t\t\t\t-0.090000, 1.115859, -0.000000,  -0.130000, 0.355859, -0.000000,  -0.130000, 0.395859, -0.000000,  -0.130000, 0.435859, -0.000000,  -0.130000, 0.475859, -0.000000,  \n\t\t\t\t\t\t-0.130000, 0.515859, -0.000000,  -0.130000, 0.555859, -0.000000,  -0.130000, 0.595859, -0.000000,  -0.130000, 0.635859, -0.000000,  -0.130000, 0.675859, -0.000000,  \n\t\t\t\t\t\t-0.130000, 0.715859, -0.000000,  -0.130000, 0.755859, -0.000000,  -0.130000, 0.795859, -0.000000,  -0.130000, 0.835859, -0.000000,  -0.130000, 0.875859, -0.000000,  \n\t\t\t\t\t\t-0.130000, 0.915859, -0.000000,  -0.130000, 0.955859, -0.000000,  -0.130000, 0.995859, -0.000000,  -0.130000, 1.035859, -0.000000,  -0.130000, 1.075859, -0.000000,  \n\t\t\t\t\t\t-0.130000, 1.115859, -0.000000,  -0.170000, 0.355859, -0.000000,  -0.170000, 0.395859, -0.000000,  -0.170000, 0.435859, -0.000000,  -0.170000, 0.475859, -0.000000,  \n\t\t\t\t\t\t-0.170000, 0.515859, -0.000000,  -0.170000, 0.555859, -0.000000,  -0.170000, 0.595859, -0.000000,  -0.170000, 0.635859, -0.000000,  -0.170000, 0.675859, -0.000000,  \n\t\t\t\t\t\t-0.170000, 0.715859, -0.000000,  -0.170000, 0.755859, -0.000000,  -0.170000, 0.795859, -0.000000,  -0.170000, 0.835859, -0.000000,  -0.170000, 0.875859, -0.000000,  \n\t\t\t\t\t\t-0.170000, 0.915859, -0.000000,  -0.170000, 0.955859, -0.000000,  -0.170000, 0.995859, -0.000000,  -0.170000, 1.035859, -0.000000,  -0.170000, 1.075859, -0.000000,  \n\t\t\t\t\t\t-0.170000, 1.115859, -0.000000\n\t\t\t\t\t],\n\t\t\t\t\t\"faceTriIds\" : [\n\t\t\t\t\t\t863, 1294, 3320,  866, 1297, 3319,  869, 1300, 3318,  872, 1303, 3317,  875, 1306, 3316,  \n\t\t\t\t\t\t878, 1309, 3315,  3314, 28, 1312,  3313, 29, 1315,  887, 1318, 3312,  3311, 31, 1321,  \n\t\t\t\t\t\t893, 1324, 3310,  896, 1327, 3309,  3308, 34, 1330,  902, 1333, 3307,  905, 1336, 3306,  \n\t\t\t\t\t\t908, 1339, 3305,  911, 1342, 3304,  914, 1345, 3303,  917, 1348, 3302,  920, 1351, 3301,  \n\t\t\t\t\t\t923, 1354, 3300,  925, 1356, 3299,  927, 1358, 3298,  929, 1360, 3297,  931, 1362, 3296,  \n\t\t\t\t\t\t933, 1364, 3295,  935, 1366, 3294,  937, 1368, 3293,  939, 1370, 3292,  941, 1372, 3291,  \n\t\t\t\t\t\t943, 1374, 3290,  945, 1376, 3289,  947, 1378, 3288,  949, 1380, 3287,  951, 1382, 3286,  \n\t\t\t\t\t\t953, 1384, 3285,  955, 1386, 3284,  957, 1388, 3283,  959, 1390, 3282,  961, 1392, 3281,  \n\t\t\t\t\t\t964, 1395, 3280,  966, 1397, 3279,  968, 1399, 3278,  970, 1401, 3277,  972, 1403, 3276,  \n\t\t\t\t\t\t3275, 69, 1405,  976, 1407, 3274,  978, 1409, 3273,  980, 1411, 3272,  982, 1413, 3271,  \n\t\t\t\t\t\t984, 1415, 3270,  3269, 75, 1417,  988, 1419, 3268,  3267, 77, 1421,  992, 1423, 3266,  \n\t\t\t\t\t\t994, 1425, 3265,  996, 1427, 3264,  998, 1429, 3263,  1000, 1431, 3262,  1002, 1433, 3261,  \n\t\t\t\t\t\t1005, 1436, 3260,  1007, 1438, 3259,  3258, 87, 1440,  1011, 1442, 3257,  3256, 89, 1444,  \n\t\t\t\t\t\t3255, 90, 1446,  1017, 1448, 3254,  3253, 92, 1450,  1021, 1452, 3252,  1023, 1454, 3251,  \n\t\t\t\t\t\t3250, 95, 1456,  1027, 1458, 3249,  1029, 1460, 3248,  1031, 1462, 3247,  1033, 1464, 3246,  \n\t\t\t\t\t\t3245, 100, 1466,  1037, 1468, 3244,  1039, 1470, 3243,  1041, 1472, 3242,  3241, 104, 1474,  \n\t\t\t\t\t\t3240, 106, 1477,  1048, 1479, 3239,  1050, 1481, 3238,  3237, 109, 1483,  1054, 1485, 3236,  \n\t\t\t\t\t\t3235, 111, 1487,  1058, 1489, 3234,  1060, 1491, 3233,  1062, 1493, 3232,  1064, 1495, 3231,  \n\t\t\t\t\t\t1066, 1497, 3230,  3229, 117, 1499,  1070, 1501, 3228,  3227, 119, 1503,  1074, 1505, 3226,  \n\t\t\t\t\t\t1076, 1507, 3225,  3224, 122, 1509,  3223, 123, 1511,  3222, 124, 1513,  3221, 125, 1515,  \n\t\t\t\t\t\t1087, 1518, 3220,  1089, 1520, 3219,  3218, 129, 1522,  1093, 1524, 3217,  1095, 1526, 3216,  \n\t\t\t\t\t\t1097, 1528, 3215,  1099, 1530, 3214,  1101, 1532, 3213,  3212, 135, 1534,  1105, 1536, 3211,  \n\t\t\t\t\t\t3210, 137, 1538,  1109, 1540, 3209,  1111, 1542, 3208,  1113, 1544, 3207,  1115, 1546, 3206,  \n\t\t\t\t\t\t1117, 1548, 3205,  3204, 143, 1550,  1121, 1552, 3203,  1123, 1554, 3202,  1125, 1556, 3201,  \n\t\t\t\t\t\t1128, 1559, 3200,  1130, 1561, 3199,  1132, 1563, 3198,  3197, 151, 1565,  1136, 1567, 3196,  \n\t\t\t\t\t\t1138, 1569, 3195,  1140, 1571, 3194,  3193, 155, 1573,  1144, 1575, 3192,  1146, 1577, 3191,  \n\t\t\t\t\t\t1148, 1579, 3190,  3189, 159, 1581,  1152, 1583, 3188,  1154, 1585, 3187,  3186, 162, 1587,  \n\t\t\t\t\t\t1158, 1589, 3185,  1160, 1591, 3184,  1162, 1593, 3183,  3182, 166, 1595,  1166, 1597, 3181,  \n\t\t\t\t\t\t1169, 1600, 3180,  1171, 1602, 3179,  1173, 1604, 3178,  1175, 1606, 3177,  1177, 1608, 3176,  \n\t\t\t\t\t\t1179, 1610, 3175,  1181, 1612, 3174,  1183, 1614, 3173,  1185, 1616, 3172,  1187, 1618, 3171,  \n\t\t\t\t\t\t1189, 1620, 3170,  1191, 1622, 3169,  1193, 1624, 3168,  3167, 182, 1626,  1197, 1628, 3166,  \n\t\t\t\t\t\t1199, 1630, 3165,  1201, 1632, 3164,  1203, 1634, 3163,  1205, 1636, 3162,  1207, 1638, 3161,  \n\t\t\t\t\t\t1210, 1641, 3160,  1212, 1643, 3159,  1214, 1645, 3158,  1216, 1647, 3157,  1218, 1649, 3156,  \n\t\t\t\t\t\t1220, 1651, 3155,  1222, 1653, 3154,  1224, 1655, 3153,  1226, 1657, 3152,  1228, 1659, 3151,  \n\t\t\t\t\t\t1230, 1661, 3150,  1232, 1663, 3149,  1234, 1665, 3148,  3147, 203, 1667,  1238, 1669, 3146,  \n\t\t\t\t\t\t1240, 1671, 3145,  1242, 1673, 3144,  1244, 1675, 3143,  1246, 1677, 3142,  1248, 1679, 3141,  \n\t\t\t\t\t\t1251, 1682, 3140,  1253, 1684, 3139,  1255, 1686, 3138,  3137, 214, 1688,  1259, 1690, 3136,  \n\t\t\t\t\t\t1261, 1692, 3135,  3134, 217, 1694,  1265, 1696, 3133,  1267, 1698, 3132,  3131, 220, 1700,  \n\t\t\t\t\t\t1271, 1702, 3130,  1273, 1704, 3129,  1275, 1706, 3128,  3127, 224, 1708,  1279, 1710, 3126,  \n\t\t\t\t\t\t1281, 1712, 3125,  1283, 1714, 3124,  1285, 1716, 3123,  1287, 1718, 3122,  1289, 1720, 3121,  \n\t\t\t\t\t\t1721, 1290, 3120,  3119, 661, 1723,  1719, 1724, 3118,  1725, 1288, 3117,  1726, 1727, 3116,  \n\t\t\t\t\t\t1717, 1728, 3115,  1729, 1286, 3114,  1730, 1731, 3113,  1715, 1732, 3112,  1733, 1284, 3111,  \n\t\t\t\t\t\t3110, 664, 1735,  1713, 1736, 3109,  1737, 1282, 3108,  1738, 1739, 3107,  1711, 1740, 3106,  \n\t\t\t\t\t\t1741, 1280, 3105,  1742, 1743, 3104,  1709, 1744, 3103,  1745, 1278, 3102,  1746, 1747, 3101,  \n\t\t\t\t\t\t1707, 1748, 3100,  1749, 1276, 3099,  1750, 1751, 3098,  1705, 1752, 3097,  1753, 1274, 3096,  \n\t\t\t\t\t\t1754, 1755, 3095,  1703, 1756, 3094,  3093, 642, 1272,  3092, 670, 1759,  1701, 1760, 3091,  \n\t\t\t\t\t\t1761, 1270, 3090,  1762, 1763, 3089,  1699, 1764, 3088,  1765, 1268, 3087,  1766, 1767, 3086,  \n\t\t\t\t\t\t1697, 1768, 3085,  1769, 1266, 3084,  1770, 1771, 3083,  1695, 1772, 3082,  1773, 1264, 3081,  \n\t\t\t\t\t\t1774, 1775, 3080,  3079, 633, 1776,  1777, 1262, 3078,  1778, 1779, 3077,  1691, 1780, 3076,  \n\t\t\t\t\t\t1781, 1260, 3075,  1782, 1783, 3074,  1689, 1784, 3073,  3072, 628, 1258,  3071, 677, 1787,  \n\t\t\t\t\t\t3070, 627, 1788,  1789, 1256, 3069,  1790, 1791, 3068,  1685, 1792, 3067,  1793, 1254, 3066,  \n\t\t\t\t\t\t1794, 1795, 3065,  1683, 1796, 3064,  1797, 1252, 3063,  1798, 1799, 3062,  1681, 1800, 3061,  \n\t\t\t\t\t\t1801, 1249, 3060,  1802, 1803, 3059,  1678, 1804, 3058,  1805, 1247, 3057,  1806, 1807, 3056,  \n\t\t\t\t\t\t1676, 1808, 3055,  1809, 1245, 3054,  1810, 1811, 3053,  1674, 1812, 3052,  1813, 1243, 3051,  \n\t\t\t\t\t\t1814, 1815, 3050,  1672, 1816, 3049,  1817, 1241, 3048,  1818, 1819, 3047,  1670, 1820, 3046,  \n\t\t\t\t\t\t1821, 1239, 3045,  1822, 1823, 3044,  1668, 1824, 3043,  1825, 1237, 3042,  1826, 1827, 3041,  \n\t\t\t\t\t\t1666, 1828, 3040,  1829, 1235, 3039,  1830, 1831, 3038,  1664, 1832, 3037,  1833, 1233, 3036,  \n\t\t\t\t\t\t1834, 1835, 3035,  1662, 1836, 3034,  1837, 1231, 3033,  1838, 1839, 3032,  1660, 1840, 3031,  \n\t\t\t\t\t\t1841, 1229, 3030,  1842, 1843, 3029,  3028, 598, 1844,  1845, 1227, 3027,  1846, 1847, 3026,  \n\t\t\t\t\t\t1656, 1848, 3025,  1849, 1225, 3024,  1850, 1851, 3023,  1654, 1852, 3022,  1853, 1223, 3021,  \n\t\t\t\t\t\t1854, 1855, 3020,  1652, 1856, 3019,  1857, 1221, 3018,  1858, 1859, 3017,  1650, 1860, 3016,  \n\t\t\t\t\t\t1861, 1219, 3015,  1862, 1863, 3014,  1648, 1864, 3013,  3012, 587, 1217,  3011, 697, 1867,  \n\t\t\t\t\t\t1646, 1868, 3010,  1869, 1215, 3009,  1870, 1871, 3008,  1644, 1872, 3007,  1873, 1213, 3006,  \n\t\t\t\t\t\t1874, 1875, 3005,  1642, 1876, 3004,  1877, 1211, 3003,  1878, 1879, 3002,  1640, 1880, 3001,  \n\t\t\t\t\t\t1881, 1208, 3000,  1882, 1883, 2999,  1637, 1884, 2998,  1885, 1206, 2997,  2996, 702, 1887,  \n\t\t\t\t\t\t2995, 575, 1888,  1889, 1204, 2994,  1890, 1891, 2993,  1633, 1892, 2992,  1893, 1202, 2991,  \n\t\t\t\t\t\t1894, 1895, 2990,  1631, 1896, 2989,  1897, 1200, 2988,  1898, 1899, 2987,  1629, 1900, 2986,  \n\t\t\t\t\t\t1901, 1198, 2985,  1902, 1903, 2984,  1627, 1904, 2983,  1905, 1196, 2982,  1906, 1907, 2981,  \n\t\t\t\t\t\t2980, 565, 1908,  1909, 1194, 2979,  1910, 1911, 2978,  1623, 1912, 2977,  1913, 1192, 2976,  \n\t\t\t\t\t\t1914, 1915, 2975,  1621, 1916, 2974,  1917, 1190, 2973,  1918, 1919, 2972,  1619, 1920, 2971,  \n\t\t\t\t\t\t1921, 1188, 2970,  1922, 1923, 2969,  1617, 1924, 2968,  1925, 1186, 2967,  1926, 1927, 2966,  \n\t\t\t\t\t\t1615, 1928, 2965,  1929, 1184, 2964,  1930, 1931, 2963,  2962, 553, 1932,  1933, 1182, 2961,  \n\t\t\t\t\t\t1934, 1935, 2960,  1611, 1936, 2959,  1937, 1180, 2958,  1938, 1939, 2957,  1609, 1940, 2956,  \n\t\t\t\t\t\t1941, 1178, 2955,  1942, 1943, 2954,  1607, 1944, 2953,  2952, 546, 1176,  2951, 717, 1947,  \n\t\t\t\t\t\t1605, 1948, 2950,  1949, 1174, 2949,  1950, 1951, 2948,  1603, 1952, 2947,  1953, 1172, 2946,  \n\t\t\t\t\t\t1954, 1955, 2945,  1601, 1956, 2944,  1957, 1170, 2943,  1958, 1959, 2942,  1599, 1960, 2941,  \n\t\t\t\t\t\t1961, 1167, 2940,  1962, 1963, 2939,  1596, 1964, 2938,  2937, 535, 1165,  2936, 722, 1967,  \n\t\t\t\t\t\t1594, 1968, 2935,  1969, 1163, 2934,  1970, 1971, 2933,  1592, 1972, 2932,  1973, 1161, 2931,  \n\t\t\t\t\t\t2930, 724, 1975,  1590, 1976, 2929,  1977, 1159, 2928,  1978, 1979, 2927,  1588, 1980, 2926,  \n\t\t\t\t\t\t2925, 527, 1157,  2924, 726, 1983,  2923, 526, 1984,  1985, 1155, 2922,  1986, 1987, 2921,  \n\t\t\t\t\t\t1584, 1988, 2920,  2919, 523, 1153,  1990, 1991, 2918,  1582, 1992, 2917,  1993, 1151, 2916,  \n\t\t\t\t\t\t1994, 1995, 2915,  2914, 520, 1996,  1997, 1149, 2913,  1998, 1999, 2912,  1578, 2000, 2911,  \n\t\t\t\t\t\t2001, 1147, 2910,  2002, 2003, 2909,  1576, 2004, 2908,  2005, 1145, 2907,  2006, 2007, 2906,  \n\t\t\t\t\t\t1574, 2008, 2905,  2009, 1143, 2904,  2010, 2011, 2903,  2902, 512, 2012,  2013, 1141, 2901,  \n\t\t\t\t\t\t2014, 2015, 2900,  1570, 2016, 2899,  2017, 1139, 2898,  2018, 2019, 2897,  1568, 2020, 2896,  \n\t\t\t\t\t\t2021, 1137, 2895,  2022, 2023, 2894,  1566, 2024, 2893,  2892, 505, 1135,  2026, 2027, 2891,  \n\t\t\t\t\t\t1564, 2028, 2890,  2889, 503, 1133,  2888, 738, 2031,  1562, 2032, 2887,  2033, 1131, 2886,  \n\t\t\t\t\t\t2034, 2035, 2885,  1560, 2036, 2884,  2037, 1129, 2883,  2038, 2039, 2882,  1558, 2040, 2881,  \n\t\t\t\t\t\t2041, 1126, 2880,  2042, 2043, 2879,  1555, 2044, 2878,  2045, 1124, 2877,  2046, 2047, 2876,  \n\t\t\t\t\t\t1553, 2048, 2875,  2874, 492, 1122,  2873, 743, 2051,  2872, 491, 2052,  2871, 490, 1120,  \n\t\t\t\t\t\t2054, 2055, 2870,  1549, 2056, 2869,  2057, 1118, 2868,  2058, 2059, 2867,  1547, 2060, 2866,  \n\t\t\t\t\t\t2061, 1116, 2865,  2062, 2063, 2864,  1545, 2064, 2863,  2862, 484, 1114,  2861, 747, 2067,  \n\t\t\t\t\t\t2860, 483, 2068,  2069, 1112, 2859,  2070, 2071, 2858,  1541, 2072, 2857,  2073, 1110, 2856,  \n\t\t\t\t\t\t2855, 749, 2075,  2854, 479, 2076,  2077, 1108, 2853,  2078, 2079, 2852,  1537, 2080, 2851,  \n\t\t\t\t\t\t2081, 1106, 2850,  2082, 2083, 2849,  1535, 2084, 2848,  2085, 1104, 2847,  2846, 752, 2087,  \n\t\t\t\t\t\t2845, 473, 2088,  2844, 472, 1102,  2090, 2091, 2843,  1531, 2092, 2842,  2093, 1100, 2841,  \n\t\t\t\t\t\t2840, 754, 2095,  1529, 2096, 2839,  2097, 1098, 2838,  2098, 2099, 2837,  1527, 2100, 2836,  \n\t\t\t\t\t\t2835, 466, 1096,  2102, 2103, 2834,  1525, 2104, 2833,  2105, 1094, 2832,  2106, 2107, 2831,  \n\t\t\t\t\t\t2830, 463, 2108,  2829, 462, 1092,  2110, 2111, 2828,  2827, 461, 2112,  2113, 1090, 2826,  \n\t\t\t\t\t\t2114, 2115, 2825,  1519, 2116, 2824,  2117, 1088, 2823,  2118, 2119, 2822,  1517, 2120, 2821,  \n\t\t\t\t\t\t2820, 455, 1085,  2819, 761, 2123,  2818, 454, 2124,  2817, 453, 1083,  2126, 2127, 2816,  \n\t\t\t\t\t\t1512, 2128, 2815,  2814, 451, 1081,  2813, 763, 2131,  2812, 450, 2132,  2133, 1079, 2811,  \n\t\t\t\t\t\t2134, 2135, 2810,  1508, 2136, 2809,  2137, 1077, 2808,  2807, 765, 2139,  1506, 2140, 2806,  \n\t\t\t\t\t\t2141, 1075, 2805,  2142, 2143, 2804,  1504, 2144, 2803,  2802, 443, 1073,  2801, 767, 2147,  \n\t\t\t\t\t\t1502, 2148, 2800,  2149, 1071, 2799,  2150, 2151, 2798,  1500, 2152, 2797,  2796, 439, 1069,  \n\t\t\t\t\t\t2795, 769, 2155,  1498, 2156, 2794,  2157, 1067, 2793,  2158, 2159, 2792,  2791, 436, 2160,  \n\t\t\t\t\t\t2790, 435, 1065,  2162, 2163, 2789,  1494, 2164, 2788,  2787, 433, 1063,  2166, 2167, 2786,  \n\t\t\t\t\t\t1492, 2168, 2785,  2169, 1061, 2784,  2170, 2171, 2783,  2782, 430, 2172,  2781, 429, 1059,  \n\t\t\t\t\t\t2780, 774, 2175,  1488, 2176, 2779,  2177, 1057, 2778,  2777, 775, 2179,  2776, 426, 2180,  \n\t\t\t\t\t\t2181, 1055, 2775,  2182, 2183, 2774,  1484, 2184, 2773,  2772, 423, 1053,  2771, 777, 2187,  \n\t\t\t\t\t\t2770, 422, 2188,  2189, 1051, 2769,  2190, 2191, 2768,  1480, 2192, 2767,  2193, 1049, 2766,  \n\t\t\t\t\t\t2194, 2195, 2765,  1478, 2196, 2764,  2197, 1047, 2763,  2198, 2199, 2762,  2761, 416, 2200,  \n\t\t\t\t\t\t2201, 1044, 2760,  2759, 781, 2203,  1473, 2204, 2758,  2205, 1042, 2757,  2206, 2207, 2756,  \n\t\t\t\t\t\t1471, 2208, 2755,  2209, 1040, 2754,  2210, 2211, 2753,  1469, 2212, 2752,  2213, 1038, 2751,  \n\t\t\t\t\t\t2214, 2215, 2750,  1467, 2216, 2749,  2748, 406, 1036,  2218, 2219, 2747,  1465, 2220, 2746,  \n\t\t\t\t\t\t2221, 1034, 2745,  2222, 2223, 2744,  1463, 2224, 2743,  2225, 1032, 2742,  2226, 2227, 2741,  \n\t\t\t\t\t\t1461, 2228, 2740,  2229, 1030, 2739,  2230, 2231, 2738,  1459, 2232, 2737,  2233, 1028, 2736,  \n\t\t\t\t\t\t2234, 2235, 2735,  2734, 397, 2236,  2237, 1026, 2733,  2238, 2239, 2732,  1455, 2240, 2731,  \n\t\t\t\t\t\t2241, 1024, 2730,  2242, 2243, 2729,  1453, 2244, 2728,  2245, 1022, 2727,  2726, 792, 2247,  \n\t\t\t\t\t\t1451, 2248, 2725,  2249, 1020, 2724,  2250, 2251, 2723,  1449, 2252, 2722,  2253, 1018, 2721,  \n\t\t\t\t\t\t2254, 2255, 2720,  1447, 2256, 2719,  2718, 386, 1016,  2258, 2259, 2717,  2716, 385, 2260,  \n\t\t\t\t\t\t2261, 1014, 2715,  2262, 2263, 2714,  1443, 2264, 2713,  2265, 1012, 2712,  2266, 2267, 2711,  \n\t\t\t\t\t\t1441, 2268, 2710,  2269, 1010, 2709,  2708, 798, 2271,  2707, 379, 2272,  2273, 1008, 2706,  \n\t\t\t\t\t\t2274, 2275, 2705,  1437, 2276, 2704,  2277, 1006, 2703,  2278, 2279, 2702,  1435, 2280, 2701,  \n\t\t\t\t\t\t2281, 1003, 2700,  2282, 2283, 2699,  1432, 2284, 2698,  2285, 1001, 2697,  2286, 2287, 2696,  \n\t\t\t\t\t\t1430, 2288, 2695,  2289, 999, 2694,  2290, 2291, 2693,  1428, 2292, 2692,  2293, 997, 2691,  \n\t\t\t\t\t\t2294, 2295, 2690,  1426, 2296, 2689,  2297, 995, 2688,  2298, 2299, 2687,  1424, 2300, 2686,  \n\t\t\t\t\t\t2301, 993, 2685,  2302, 2303, 2684,  1422, 2304, 2683,  2305, 991, 2682,  2306, 2307, 2681,  \n\t\t\t\t\t\t2680, 360, 2308,  2309, 989, 2679,  2310, 2311, 2678,  1418, 2312, 2677,  2313, 987, 2676,  \n\t\t\t\t\t\t2314, 2315, 2675,  1416, 2316, 2674,  2317, 985, 2673,  2318, 2319, 2672,  1414, 2320, 2671,  \n\t\t\t\t\t\t2321, 983, 2670,  2322, 2323, 2669,  1412, 2324, 2668,  2325, 981, 2667,  2326, 2327, 2666,  \n\t\t\t\t\t\t1410, 2328, 2665,  2329, 979, 2664,  2330, 2331, 2663,  1408, 2332, 2662,  2661, 347, 977,  \n\t\t\t\t\t\t2660, 814, 2335,  1406, 2336, 2659,  2337, 975, 2658,  2338, 2339, 2657,  1404, 2340, 2656,  \n\t\t\t\t\t\t2341, 973, 2655,  2342, 2343, 2654,  1402, 2344, 2653,  2345, 971, 2652,  2346, 2347, 2651,  \n\t\t\t\t\t\t1400, 2348, 2650,  2649, 339, 969,  2648, 818, 2351,  1398, 2352, 2647,  2353, 967, 2646,  \n\t\t\t\t\t\t2354, 2355, 2645,  1396, 2356, 2644,  2357, 965, 2643,  2358, 2359, 2642,  1394, 2360, 2641,  \n\t\t\t\t\t\t2361, 962, 2640,  2362, 2363, 2639,  1391, 2364, 2638,  2365, 960, 2637,  2366, 2367, 2636,  \n\t\t\t\t\t\t1389, 2368, 2635,  2369, 958, 2634,  2370, 2371, 2633,  1387, 2372, 2632,  2373, 956, 2631,  \n\t\t\t\t\t\t2374, 2375, 2630,  1385, 2376, 2629,  2377, 954, 2628,  2378, 2379, 2627,  1383, 2380, 2626,  \n\t\t\t\t\t\t2381, 952, 2625,  2382, 2383, 2624,  1381, 2384, 2623,  2385, 950, 2622,  2386, 2387, 2621,  \n\t\t\t\t\t\t1379, 2388, 2620,  2389, 948, 2619,  2390, 2391, 2618,  1377, 2392, 2617,  2393, 946, 2616,  \n\t\t\t\t\t\t2394, 2395, 2615,  1375, 2396, 2614,  2397, 944, 2613,  2398, 2399, 2612,  1373, 2400, 2611,  \n\t\t\t\t\t\t2401, 942, 2610,  2402, 2403, 2609,  1371, 2404, 2608,  2405, 940, 2607,  2406, 2407, 2606,  \n\t\t\t\t\t\t1369, 2408, 2605,  2409, 938, 2604,  2410, 2411, 2603,  1367, 2412, 2602,  2413, 936, 2601,  \n\t\t\t\t\t\t2600, 834, 2415,  1365, 2416, 2599,  2417, 934, 2598,  2418, 2419, 2597,  1363, 2420, 2596,  \n\t\t\t\t\t\t2421, 932, 2595,  2422, 2423, 2594,  1361, 2424, 2593,  2425, 930, 2592,  2426, 2427, 2591,  \n\t\t\t\t\t\t1359, 2428, 2590,  2429, 928, 2589,  2430, 2431, 2588,  1357, 2432, 2587,  2433, 926, 2586,  \n\t\t\t\t\t\t2434, 2435, 2585,  1355, 2436, 2584,  2437, 924, 2583,  2438, 2439, 2582,  1353, 2440, 2581,  \n\t\t\t\t\t\t2441, 921, 2580,  2442, 2443, 2579,  1350, 2444, 2578,  2445, 918, 2577,  2446, 2447, 2576,  \n\t\t\t\t\t\t1347, 2448, 2575,  2449, 915, 2574,  2450, 2451, 2573,  1344, 2452, 2572,  2453, 912, 2571,  \n\t\t\t\t\t\t2570, 844, 2455,  2569, 281, 2456,  2457, 909, 2568,  2458, 2459, 2567,  1338, 2460, 2566,  \n\t\t\t\t\t\t2461, 906, 2565,  2462, 2463, 2564,  1335, 2464, 2563,  2465, 903, 2562,  2466, 2467, 2561,  \n\t\t\t\t\t\t1332, 2468, 2560,  2469, 900, 2559,  2470, 2471, 2558,  1329, 2472, 2557,  2473, 897, 2556,  \n\t\t\t\t\t\t2474, 2475, 2555,  1326, 2476, 2554,  2553, 264, 894,  2552, 850, 2479,  1323, 2480, 2551,  \n\t\t\t\t\t\t2550, 261, 891,  2482, 2483, 2549,  1320, 2484, 2548,  2547, 258, 888,  2486, 2487, 2546,  \n\t\t\t\t\t\t1317, 2488, 2545,  2544, 255, 885,  2490, 2491, 2543,  2542, 254, 2492,  2493, 882, 2541,  \n\t\t\t\t\t\t2494, 2495, 2540,  1311, 2496, 2539,  2497, 879, 2538,  2498, 2499, 2537,  1308, 2500, 2536,  \n\t\t\t\t\t\t2535, 246, 876,  2502, 2503, 2534,  1305, 2504, 2533,  2505, 873, 2532,  2506, 2507, 2531,  \n\t\t\t\t\t\t2530, 242, 2508,  2509, 870, 2529,  2510, 2511, 2528,  1299, 2512, 2527,  2526, 237, 867,  \n\t\t\t\t\t\t2514, 2515, 2525,  1296, 2516, 2524,  2523, 234, 864,  2518, 2519, 2522,  2521, 233, 2520,  \n\t\t\t\t\t\t2521, 860, 2518,  232, 2521, 2518,  862, 1293, 2521,  2522, 231, 861,  1292, 861, 0,  \n\t\t\t\t\t\t232, 2522, 1292,  2523, 21, 1291,  231, 2523, 1291,  2519, 2517, 2523,  2524, 859, 2514,  \n\t\t\t\t\t\t865, 2514, 235,  2, 2524, 865,  1293, 2515, 233,  1295, 1293, 1,  235, 2525, 1295,  \n\t\t\t\t\t\t863, 867, 22,  233, 2526, 863,  2515, 2513, 2526,  2527, 858, 2510,  868, 2510, 238,  \n\t\t\t\t\t\t3, 2527, 868,  2528, 236, 1296,  1298, 1296, 2,  238, 2528, 1298,  2529, 23, 866,  \n\t\t\t\t\t\t2511, 866, 236,  858, 2529, 2511,  2506, 2508, 857,  241, 2530, 2506,  871, 1302, 2530,  \n\t\t\t\t\t\t2531, 239, 1299,  1301, 1299, 3,  1301, 2506, 2531,  2532, 24, 869,  2507, 869, 239,  \n\t\t\t\t\t\t857, 2532, 2507,  2533, 856, 2502,  874, 2502, 244,  5, 2533, 874,  1302, 2503, 242,  \n\t\t\t\t\t\t1304, 1302, 4,  244, 2534, 1304,  872, 876, 25,  242, 2535, 872,  2503, 2501, 2535,  \n\t\t\t\t\t\t2536, 855, 2498,  877, 2498, 247,  6, 2536, 877,  2537, 245, 1305,  1307, 1305, 5,  \n\t\t\t\t\t\t247, 2537, 1307,  2538, 26, 875,  2499, 875, 245,  855, 2538, 2499,  2539, 854, 2494,  \n\t\t\t\t\t\t880, 2494, 250,  7, 2539, 880,  1308, 2495, 248,  6, 2540, 1308,  250, 2540, 1310,  \n\t\t\t\t\t\t2541, 27, 878,  2495, 878, 248,  854, 2541, 2495,  2542, 853, 2490,  883, 2490, 253,  \n\t\t\t\t\t\t8, 2542, 883,  2543, 251, 1311,  1313, 1311, 7,  253, 2543, 1313,  881, 885, 28,  \n\t\t\t\t\t\t251, 2544, 881,  2491, 2489, 2544,  2545, 852, 2486,  886, 2486, 256,  9, 2545, 886,  \n\t\t\t\t\t\t1314, 2487, 254,  1316, 1314, 8,  256, 2546, 1316,  884, 888, 29,  254, 2547, 884,  \n\t\t\t\t\t\t2487, 2485, 2547,  2482, 2484, 851,  889, 2482, 259,  889, 1320, 2548,  2549, 257, 1317,  \n\t\t\t\t\t\t1319, 1317, 9,  259, 2549, 1319,  887, 891, 30,  2483, 887, 257,  851, 2550, 2483,  \n\t\t\t\t\t\t2551, 850, 2478,  892, 2478, 262,  892, 1323, 2551,  1320, 2479, 260,  10, 2552, 1320,  \n\t\t\t\t\t\t1322, 2478, 2552,  2553, 31, 890,  2479, 890, 260,  2479, 2477, 2553,  2554, 849, 2474,  \n\t\t\t\t\t\t895, 2474, 265,  12, 2554, 895,  2555, 263, 1323,  1325, 1323, 11,  265, 2555, 1325,  \n\t\t\t\t\t\t2556, 32, 893,  2475, 893, 263,  849, 2556, 2475,  2557, 848, 2470,  898, 2470, 268,  \n\t\t\t\t\t\t13, 2557, 898,  2558, 266, 1326,  1328, 1326, 12,  268, 2558, 1328,  2559, 33, 896,  \n\t\t\t\t\t\t2471, 896, 266,  848, 2559, 2471,  2560, 847, 2466,  901, 2466, 271,  14, 2560, 901,  \n\t\t\t\t\t\t2561, 269, 1329,  1331, 1329, 13,  271, 2561, 1331,  2562, 34, 899,  2467, 899, 269,  \n\t\t\t\t\t\t847, 2562, 2467,  2563, 846, 2462,  904, 2462, 274,  15, 2563, 904,  2564, 272, 1332,  \n\t\t\t\t\t\t1334, 1332, 14,  274, 2564, 1334,  2565, 35, 902,  2463, 902, 272,  846, 2565, 2463,  \n\t\t\t\t\t\t2566, 845, 2458,  907, 2458, 277,  16, 2566, 907,  2567, 275, 1335,  1337, 1335, 15,  \n\t\t\t\t\t\t277, 2567, 1337,  905, 909, 36,  2459, 905, 275,  845, 2568, 2459,  2454, 2456, 844,  \n\t\t\t\t\t\t910, 2454, 280,  910, 1341, 2569,  2570, 278, 1338,  16, 2570, 1338,  1340, 2454, 2570,  \n\t\t\t\t\t\t2571, 37, 908,  2455, 908, 278,  2455, 2453, 2571,  2572, 843, 2450,  913, 2450, 283,  \n\t\t\t\t\t\t18, 2572, 913,  2573, 281, 1341,  1343, 1341, 17,  283, 2573, 1343,  2574, 38, 911,  \n\t\t\t\t\t\t2451, 911, 281,  843, 2574, 2451,  2575, 842, 2446,  916, 2446, 286,  19, 2575, 916,  \n\t\t\t\t\t\t2576, 284, 1344,  1346, 1344, 18,  286, 2576, 1346,  2577, 39, 914,  2447, 914, 284,  \n\t\t\t\t\t\t842, 2577, 2447,  2578, 841, 2442,  919, 2442, 289,  919, 1350, 2578,  2579, 287, 1347,  \n\t\t\t\t\t\t1349, 1347, 19,  289, 2579, 1349,  2580, 40, 917,  2443, 917, 287,  841, 2580, 2443,  \n\t\t\t\t\t\t2581, 840, 2438,  1294, 2438, 234,  22, 2581, 1294,  2582, 292, 922,  864, 922, 21,  \n\t\t\t\t\t\t234, 2582, 864,  2583, 42, 1352,  2439, 1352, 292,  840, 2583, 2439,  2584, 839, 2434,  \n\t\t\t\t\t\t1297, 2434, 237,  23, 2584, 1297,  2585, 293, 1353,  867, 1353, 22,  237, 2585, 867,  \n\t\t\t\t\t\t2586, 43, 923,  2435, 923, 293,  839, 2586, 2435,  2587, 838, 2430,  1300, 2430, 240,  \n\t\t\t\t\t\t24, 2587, 1300,  2588, 295, 1355,  870, 1355, 23,  240, 2588, 870,  2589, 44, 925,  \n\t\t\t\t\t\t2431, 925, 295,  838, 2589, 2431,  2590, 837, 2426,  1303, 2426, 243,  25, 2590, 1303,  \n\t\t\t\t\t\t2591, 297, 1357,  873, 1357, 24,  243, 2591, 873,  2592, 45, 927,  2427, 927, 297,  \n\t\t\t\t\t\t837, 2592, 2427,  2593, 836, 2422,  1306, 2422, 246,  26, 2593, 1306,  2594, 299, 1359,  \n\t\t\t\t\t\t876, 1359, 25,  246, 2594, 876,  2595, 46, 929,  2423, 929, 299,  836, 2595, 2423,  \n\t\t\t\t\t\t2596, 835, 2418,  1309, 2418, 249,  27, 2596, 1309,  2597, 301, 1361,  879, 1361, 26,  \n\t\t\t\t\t\t249, 2597, 879,  2598, 47, 931,  2419, 931, 301,  835, 2598, 2419,  2414, 2416, 834,  \n\t\t\t\t\t\t1312, 2414, 252,  28, 2599, 1312,  2600, 303, 1363,  882, 1363, 27,  252, 2600, 882,  \n\t\t\t\t\t\t933, 936, 48,  2415, 933, 303,  2415, 2413, 2601,  2602, 833, 2410,  1315, 2410, 255,  \n\t\t\t\t\t\t29, 2602, 1315,  2603, 305, 1365,  885, 1365, 28,  255, 2603, 885,  2604, 49, 935,  \n\t\t\t\t\t\t2411, 935, 305,  833, 2604, 2411,  2605, 832, 2406,  1318, 2406, 258,  30, 2605, 1318,  \n\t\t\t\t\t\t2606, 307, 1367,  888, 1367, 29,  258, 2606, 888,  2607, 50, 937,  2407, 937, 307,  \n\t\t\t\t\t\t832, 2607, 2407,  2608, 831, 2402,  1321, 2402, 261,  31, 2608, 1321,  2609, 309, 1369,  \n\t\t\t\t\t\t891, 1369, 30,  261, 2609, 891,  2610, 51, 939,  2403, 939, 309,  831, 2610, 2403,  \n\t\t\t\t\t\t2611, 830, 2398,  1324, 2398, 264,  32, 2611, 1324,  2612, 311, 1371,  894, 1371, 31,  \n\t\t\t\t\t\t264, 2612, 894,  2613, 52, 941,  2399, 941, 311,  830, 2613, 2399,  2614, 829, 2394,  \n\t\t\t\t\t\t1327, 2394, 267,  33, 2614, 1327,  2615, 313, 1373,  897, 1373, 32,  267, 2615, 897,  \n\t\t\t\t\t\t2616, 53, 943,  2395, 943, 313,  829, 2616, 2395,  2617, 828, 2390,  1330, 2390, 270,  \n\t\t\t\t\t\t1330, 1377, 2617,  2618, 315, 1375,  900, 1375, 33,  270, 2618, 900,  2619, 54, 945,  \n\t\t\t\t\t\t2391, 945, 315,  828, 2619, 2391,  2620, 827, 2386,  1333, 2386, 273,  35, 2620, 1333,  \n\t\t\t\t\t\t1377, 2387, 317,  903, 1377, 34,  273, 2621, 903,  2622, 55, 947,  317, 2622, 947,  \n\t\t\t\t\t\t827, 2622, 2387,  2623, 826, 2382,  1336, 2382, 276,  36, 2623, 1336,  2624, 319, 1379,  \n\t\t\t\t\t\t906, 1379, 35,  276, 2624, 906,  2625, 56, 949,  2383, 949, 319,  826, 2625, 2383,  \n\t\t\t\t\t\t2626, 825, 2378,  1339, 2378, 279,  37, 2626, 1339,  1381, 2379, 321,  36, 2627, 1381,  \n\t\t\t\t\t\t279, 2627, 909,  2628, 57, 951,  2379, 951, 321,  825, 2628, 2379,  2629, 824, 2374,  \n\t\t\t\t\t\t1342, 2374, 282,  38, 2629, 1342,  2630, 323, 1383,  912, 1383, 37,  282, 2630, 912,  \n\t\t\t\t\t\t2631, 58, 953,  2375, 953, 323,  824, 2631, 2375,  2632, 823, 2370,  1345, 2370, 285,  \n\t\t\t\t\t\t39, 2632, 1345,  2633, 325, 1385,  915, 1385, 38,  285, 2633, 915,  2634, 59, 955,  \n\t\t\t\t\t\t2371, 955, 325,  823, 2634, 2371,  2635, 822, 2366,  1348, 2366, 288,  40, 2635, 1348,  \n\t\t\t\t\t\t2636, 327, 1387,  918, 1387, 39,  288, 2636, 918,  2637, 60, 957,  2367, 957, 327,  \n\t\t\t\t\t\t822, 2637, 2367,  2638, 821, 2362,  1351, 2362, 291,  41, 2638, 1351,  2639, 329, 1389,  \n\t\t\t\t\t\t921, 1389, 40,  291, 2639, 921,  2640, 61, 959,  2363, 959, 329,  821, 2640, 2363,  \n\t\t\t\t\t\t2641, 820, 2358,  1354, 2358, 294,  43, 2641, 1354,  2642, 333, 963,  924, 963, 42,  \n\t\t\t\t\t\t294, 2642, 924,  2643, 63, 1393,  2359, 1393, 333,  820, 2643, 2359,  2644, 819, 2354,  \n\t\t\t\t\t\t1356, 2354, 296,  1356, 1396, 2644,  2645, 334, 1394,  926, 1394, 43,  296, 2645, 926,  \n\t\t\t\t\t\t2646, 64, 964,  2355, 964, 334,  819, 2646, 2355,  2647, 818, 2350,  1358, 2350, 298,  \n\t\t\t\t\t\t45, 2647, 1358,  1396, 2351, 336,  44, 2648, 1396,  298, 2648, 928,  966, 969, 65,  \n\t\t\t\t\t\t336, 2649, 966,  2351, 2349, 2649,  2650, 817, 2346,  1360, 2346, 300,  46, 2650, 1360,  \n\t\t\t\t\t\t2651, 338, 1398,  930, 1398, 45,  300, 2651, 930,  2652, 66, 968,  2347, 968, 338,  \n\t\t\t\t\t\t817, 2652, 2347,  2653, 816, 2342,  1362, 2342, 302,  47, 2653, 1362,  2654, 340, 1400,  \n\t\t\t\t\t\t932, 1400, 46,  302, 2654, 932,  2655, 67, 970,  2343, 970, 340,  816, 2655, 2343,  \n\t\t\t\t\t\t2656, 815, 2338,  1364, 2338, 304,  48, 2656, 1364,  2657, 342, 1402,  934, 1402, 47,  \n\t\t\t\t\t\t304, 2657, 934,  2658, 68, 972,  2339, 972, 342,  815, 2658, 2339,  2659, 814, 2334,  \n\t\t\t\t\t\t1366, 2334, 306,  49, 2659, 1366,  1404, 2335, 344,  48, 2660, 1404,  306, 2660, 936,  \n\t\t\t\t\t\t974, 977, 69,  344, 2661, 974,  2335, 2333, 2661,  2662, 813, 2330,  1368, 2330, 308,  \n\t\t\t\t\t\t50, 2662, 1368,  2663, 346, 1406,  938, 1406, 49,  308, 2663, 938,  2664, 70, 976,  \n\t\t\t\t\t\t2331, 976, 346,  813, 2664, 2331,  2665, 812, 2326,  1370, 2326, 310,  51, 2665, 1370,  \n\t\t\t\t\t\t2666, 348, 1408,  940, 1408, 50,  310, 2666, 940,  978, 981, 71,  2327, 978, 348,  \n\t\t\t\t\t\t812, 2667, 2327,  2668, 811, 2322,  1372, 2322, 312,  52, 2668, 1372,  2669, 350, 1410,  \n\t\t\t\t\t\t942, 1410, 51,  312, 2669, 942,  2670, 72, 980,  2323, 980, 350,  811, 2670, 2323,  \n\t\t\t\t\t\t2671, 810, 2318,  1374, 2318, 314,  53, 2671, 1374,  2672, 352, 1412,  944, 1412, 52,  \n\t\t\t\t\t\t314, 2672, 944,  2673, 73, 982,  2319, 982, 352,  810, 2673, 2319,  2674, 809, 2314,  \n\t\t\t\t\t\t1376, 2314, 316,  54, 2674, 1376,  2675, 354, 1414,  946, 1414, 53,  316, 2675, 946,  \n\t\t\t\t\t\t2676, 74, 984,  2315, 984, 354,  809, 2676, 2315,  2677, 808, 2310,  1378, 2310, 318,  \n\t\t\t\t\t\t55, 2677, 1378,  2678, 356, 1416,  948, 1416, 54,  318, 2678, 948,  986, 989, 75,  \n\t\t\t\t\t\t356, 2679, 986,  808, 2679, 2311,  2680, 807, 2306,  1380, 2306, 320,  1380, 1420, 2680,  \n\t\t\t\t\t\t1418, 2307, 358,  55, 2681, 1418,  320, 2681, 950,  2682, 76, 988,  2307, 988, 358,  \n\t\t\t\t\t\t807, 2682, 2307,  2683, 806, 2302,  1382, 2302, 322,  57, 2683, 1382,  2684, 360, 1420,  \n\t\t\t\t\t\t952, 1420, 56,  322, 2684, 952,  2685, 77, 990,  2303, 990, 360,  806, 2685, 2303,  \n\t\t\t\t\t\t2686, 805, 2298,  1384, 2298, 324,  58, 2686, 1384,  2687, 362, 1422,  954, 1422, 57,  \n\t\t\t\t\t\t324, 2687, 954,  2688, 78, 992,  2299, 992, 362,  805, 2688, 2299,  2689, 804, 2294,  \n\t\t\t\t\t\t1386, 2294, 326,  59, 2689, 1386,  2690, 364, 1424,  956, 1424, 58,  326, 2690, 956,  \n\t\t\t\t\t\t2691, 79, 994,  2295, 994, 364,  804, 2691, 2295,  2692, 803, 2290,  1388, 2290, 328,  \n\t\t\t\t\t\t60, 2692, 1388,  2693, 366, 1426,  958, 1426, 59,  328, 2693, 958,  2694, 80, 996,  \n\t\t\t\t\t\t2291, 996, 366,  803, 2694, 2291,  2695, 802, 2286,  1390, 2286, 330,  61, 2695, 1390,  \n\t\t\t\t\t\t2696, 368, 1428,  960, 1428, 60,  330, 2696, 960,  2697, 81, 998,  2287, 998, 368,  \n\t\t\t\t\t\t802, 2697, 2287,  2698, 801, 2282,  1392, 2282, 332,  62, 2698, 1392,  2699, 370, 1430,  \n\t\t\t\t\t\t962, 1430, 61,  332, 2699, 962,  2700, 82, 1000,  2283, 1000, 370,  801, 2700, 2283,  \n\t\t\t\t\t\t2701, 800, 2278,  1395, 2278, 335,  64, 2701, 1395,  2702, 374, 1004,  965, 1004, 63,  \n\t\t\t\t\t\t335, 2702, 965,  2703, 84, 1434,  2279, 1434, 374,  800, 2703, 2279,  2704, 799, 2274,  \n\t\t\t\t\t\t1397, 2274, 337,  65, 2704, 1397,  2705, 375, 1435,  967, 1435, 64,  337, 2705, 967,  \n\t\t\t\t\t\t2706, 85, 1005,  2275, 1005, 375,  799, 2706, 2275,  2707, 798, 2270,  339, 2707, 2270,  \n\t\t\t\t\t\t66, 2707, 1399,  2708, 377, 1437,  969, 1437, 65,  969, 2270, 2708,  2709, 86, 1007,  \n\t\t\t\t\t\t2271, 1007, 377,  798, 2709, 2271,  2710, 797, 2266,  1401, 2266, 341,  67, 2710, 1401,  \n\t\t\t\t\t\t2711, 379, 1439,  971, 1439, 66,  341, 2711, 971,  2712, 87, 1009,  2267, 1009, 379,  \n\t\t\t\t\t\t797, 2712, 2267,  2713, 796, 2262,  1403, 2262, 343,  68, 2713, 1403,  2714, 381, 1441,  \n\t\t\t\t\t\t973, 1441, 67,  343, 2714, 973,  2715, 88, 1011,  2263, 1011, 381,  796, 2715, 2263,  \n\t\t\t\t\t\t2716, 795, 2258,  1405, 2258, 345,  1405, 1445, 2716,  1443, 2259, 383,  68, 2717, 1443,  \n\t\t\t\t\t\t345, 2717, 975,  1013, 1016, 89,  383, 2718, 1013,  2259, 2257, 2718,  2719, 794, 2254,  \n\t\t\t\t\t\t1407, 2254, 347,  70, 2719, 1407,  2720, 385, 1445,  977, 1445, 69,  347, 2720, 977,  \n\t\t\t\t\t\t1015, 1018, 90,  2255, 1015, 385,  794, 2721, 2255,  2722, 793, 2250,  1409, 2250, 349,  \n\t\t\t\t\t\t71, 2722, 1409,  2723, 387, 1447,  979, 1447, 70,  349, 2723, 979,  2724, 91, 1017,  \n\t\t\t\t\t\t2251, 1017, 387,  793, 2724, 2251,  2725, 792, 2246,  1411, 2246, 351,  72, 2725, 1411,  \n\t\t\t\t\t\t2726, 389, 1449,  71, 2726, 1449,  351, 2726, 981,  2727, 92, 1019,  2247, 1019, 389,  \n\t\t\t\t\t\t792, 2727, 2247,  2728, 791, 2242,  1413, 2242, 353,  73, 2728, 1413,  2729, 391, 1451,  \n\t\t\t\t\t\t983, 1451, 72,  353, 2729, 983,  1021, 1024, 93,  391, 2730, 1021,  791, 2730, 2243,  \n\t\t\t\t\t\t2731, 790, 2238,  1415, 2238, 355,  74, 2731, 1415,  2732, 393, 1453,  985, 1453, 73,  \n\t\t\t\t\t\t355, 2732, 985,  2733, 94, 1023,  2239, 1023, 393,  790, 2733, 2239,  2734, 789, 2234,  \n\t\t\t\t\t\t1417, 2234, 357,  1417, 1457, 2734,  1455, 2235, 395,  74, 2735, 1455,  357, 2735, 987,  \n\t\t\t\t\t\t2736, 95, 1025,  395, 2736, 1025,  789, 2736, 2235,  2737, 788, 2230,  1419, 2230, 359,  \n\t\t\t\t\t\t76, 2737, 1419,  2738, 397, 1457,  75, 2738, 1457,  359, 2738, 989,  2739, 96, 1027,  \n\t\t\t\t\t\t2231, 1027, 397,  788, 2739, 2231,  2740, 787, 2226,  1421, 2226, 361,  77, 2740, 1421,  \n\t\t\t\t\t\t2741, 399, 1459,  991, 1459, 76,  361, 2741, 991,  2742, 97, 1029,  2227, 1029, 399,  \n\t\t\t\t\t\t787, 2742, 2227,  2743, 786, 2222,  1423, 2222, 363,  78, 2743, 1423,  2744, 401, 1461,  \n\t\t\t\t\t\t993, 1461, 77,  363, 2744, 993,  2745, 98, 1031,  2223, 1031, 401,  786, 2745, 2223,  \n\t\t\t\t\t\t2746, 785, 2218,  1425, 2218, 365,  79, 2746, 1425,  2747, 403, 1463,  995, 1463, 78,  \n\t\t\t\t\t\t365, 2747, 995,  2748, 99, 1033,  2219, 1033, 403,  785, 2748, 2219,  2749, 784, 2214,  \n\t\t\t\t\t\t1427, 2214, 367,  80, 2749, 1427,  2750, 405, 1465,  997, 1465, 79,  367, 2750, 997,  \n\t\t\t\t\t\t2751, 100, 1035,  2215, 1035, 405,  784, 2751, 2215,  2752, 783, 2210,  1429, 2210, 369,  \n\t\t\t\t\t\t81, 2752, 1429,  2753, 407, 1467,  999, 1467, 80,  369, 2753, 999,  2754, 101, 1037,  \n\t\t\t\t\t\t2211, 1037, 407,  783, 2754, 2211,  2755, 782, 2206,  1431, 2206, 371,  82, 2755, 1431,  \n\t\t\t\t\t\t2756, 409, 1469,  1001, 1469, 81,  371, 2756, 1001,  2757, 102, 1039,  2207, 1039, 409,  \n\t\t\t\t\t\t782, 2757, 2207,  2758, 781, 2202,  1433, 2202, 373,  83, 2758, 1433,  2759, 411, 1471,  \n\t\t\t\t\t\t1003, 1471, 82,  1003, 2202, 2759,  1041, 1044, 103,  411, 2760, 1041,  2203, 2201, 2760,  \n\t\t\t\t\t\t2198, 2200, 780,  376, 2761, 2198,  85, 2761, 1436,  2762, 415, 1045,  1006, 1045, 84,  \n\t\t\t\t\t\t1006, 2198, 2762,  1475, 1047, 105,  2199, 1475, 415,  780, 2763, 2199,  2764, 779, 2194,  \n\t\t\t\t\t\t1438, 2194, 378,  86, 2764, 1438,  2765, 416, 1476,  1008, 1476, 85,  378, 2765, 1008,  \n\t\t\t\t\t\t1046, 1049, 106,  2195, 1046, 416,  779, 2766, 2195,  2767, 778, 2190,  1440, 2190, 380,  \n\t\t\t\t\t\t87, 2767, 1440,  2768, 418, 1478,  1010, 1478, 86,  380, 2768, 1010,  2769, 107, 1048,  \n\t\t\t\t\t\t2191, 1048, 418,  778, 2769, 2191,  2186, 2188, 777,  382, 2770, 2186,  88, 2770, 1442,  \n\t\t\t\t\t\t2771, 420, 1480,  1012, 1480, 87,  1012, 2186, 2771,  1050, 1053, 108,  420, 2772, 1050,  \n\t\t\t\t\t\t2187, 2185, 2772,  2773, 776, 2182,  1444, 2182, 384,  89, 2773, 1444,  2774, 422, 1482,  \n\t\t\t\t\t\t1014, 1482, 88,  384, 2774, 1014,  1052, 1055, 109,  2183, 1052, 422,  776, 2775, 2183,  \n\t\t\t\t\t\t2178, 2180, 775,  386, 2776, 2178,  1446, 1486, 2776,  1484, 2179, 424,  89, 2777, 1484,  \n\t\t\t\t\t\t1016, 2178, 2777,  1054, 1057, 110,  424, 2778, 1054,  2179, 2177, 2778,  2779, 774, 2174,  \n\t\t\t\t\t\t1448, 2174, 388,  91, 2779, 1448,  2780, 426, 1486,  1018, 1486, 90,  388, 2780, 1018,  \n\t\t\t\t\t\t1056, 1059, 111,  2175, 1056, 426,  2175, 2173, 2781,  2782, 773, 2170,  1450, 2170, 390,  \n\t\t\t\t\t\t1450, 1490, 2782,  2783, 428, 1488,  1020, 1488, 91,  390, 2783, 1020,  2784, 112, 1058,  \n\t\t\t\t\t\t2171, 1058, 428,  773, 2784, 2171,  2785, 772, 2166,  1452, 2166, 392,  93, 2785, 1452,  \n\t\t\t\t\t\t1490, 2167, 430,  1022, 1490, 92,  392, 2786, 1022,  1060, 1063, 113,  430, 2787, 1060,  \n\t\t\t\t\t\t772, 2787, 2167,  2788, 771, 2162,  1454, 2162, 394,  94, 2788, 1454,  2789, 432, 1492,  \n\t\t\t\t\t\t93, 2789, 1492,  394, 2789, 1024,  2790, 114, 1062,  2163, 1062, 432,  2163, 2161, 2790,  \n\t\t\t\t\t\t2791, 770, 2158,  1456, 2158, 396,  1456, 1496, 2791,  2792, 434, 1494,  1026, 1494, 94,  \n\t\t\t\t\t\t396, 2792, 1026,  2793, 115, 1064,  2159, 1064, 434,  770, 2793, 2159,  2154, 2156, 769,  \n\t\t\t\t\t\t1458, 2154, 398,  96, 2794, 1458,  1496, 2155, 436,  95, 2795, 1496,  1028, 2154, 2795,  \n\t\t\t\t\t\t2796, 116, 1066,  436, 2796, 1066,  2155, 2153, 2796,  2797, 768, 2150,  1460, 2150, 400,  \n\t\t\t\t\t\t97, 2797, 1460,  2798, 438, 1498,  1030, 1498, 96,  400, 2798, 1030,  2799, 117, 1068,  \n\t\t\t\t\t\t2151, 1068, 438,  768, 2799, 2151,  2800, 767, 2146,  1462, 2146, 402,  98, 2800, 1462,  \n\t\t\t\t\t\t2801, 440, 1500,  1032, 1500, 97,  1032, 2146, 2801,  1070, 1073, 118,  2147, 1070, 440,  \n\t\t\t\t\t\t2147, 2145, 2802,  2803, 766, 2142,  1464, 2142, 404,  99, 2803, 1464,  2804, 442, 1502,  \n\t\t\t\t\t\t1034, 1502, 98,  404, 2804, 1034,  2805, 119, 1072,  2143, 1072, 442,  766, 2805, 2143,  \n\t\t\t\t\t\t2806, 765, 2138,  406, 2806, 2138,  1466, 1506, 2806,  2807, 444, 1504,  99, 2807, 1504,  \n\t\t\t\t\t\t1036, 2138, 2807,  2808, 120, 1074,  2139, 1074, 444,  765, 2808, 2139,  2809, 764, 2134,  \n\t\t\t\t\t\t1468, 2134, 408,  101, 2809, 1468,  2810, 446, 1506,  1038, 1506, 100,  408, 2810, 1038,  \n\t\t\t\t\t\t2811, 121, 1076,  2135, 1076, 446,  764, 2811, 2135,  2130, 2132, 763,  410, 2812, 2130,  \n\t\t\t\t\t\t102, 2812, 1470,  2813, 448, 1508,  1040, 1508, 101,  1040, 2130, 2813,  1078, 1081, 122,  \n\t\t\t\t\t\t448, 2814, 1078,  2131, 2129, 2814,  2815, 762, 2126,  1472, 2126, 412,  103, 2815, 1472,  \n\t\t\t\t\t\t2816, 450, 1510,  1042, 1510, 102,  412, 2816, 1042,  1080, 1083, 123,  2127, 1080, 450,  \n\t\t\t\t\t\t762, 2817, 2127,  2122, 2124, 761,  414, 2818, 2122,  1474, 1514, 2818,  1512, 2123, 452,  \n\t\t\t\t\t\t103, 2819, 1512,  1044, 2122, 2819,  1082, 1085, 124,  452, 2820, 1082,  2123, 2121, 2820,  \n\t\t\t\t\t\t2821, 760, 2118,  1477, 2118, 417,  106, 2821, 1477,  2822, 456, 1086,  1047, 1086, 105,  \n\t\t\t\t\t\t417, 2822, 1047,  2823, 126, 1516,  2119, 1516, 456,  760, 2823, 2119,  2824, 759, 2114,  \n\t\t\t\t\t\t1479, 2114, 419,  107, 2824, 1479,  2825, 457, 1517,  1049, 1517, 106,  419, 2825, 1049,  \n\t\t\t\t\t\t2826, 127, 1087,  2115, 1087, 457,  759, 2826, 2115,  2110, 2112, 758,  1481, 2110, 421,  \n\t\t\t\t\t\t108, 2827, 1481,  1519, 2111, 459,  107, 2828, 1519,  421, 2828, 1051,  1089, 1092, 128,  \n\t\t\t\t\t\t459, 2829, 1089,  2111, 2109, 2829,  2106, 2108, 757,  423, 2830, 2106,  1483, 1523, 2830,  \n\t\t\t\t\t\t1521, 2107, 461,  108, 2831, 1521,  1053, 2106, 2831,  2832, 129, 1091,  2107, 1091, 461,  \n\t\t\t\t\t\t757, 2832, 2107,  2833, 756, 2102,  1485, 2102, 425,  110, 2833, 1485,  2834, 463, 1523,  \n\t\t\t\t\t\t1055, 1523, 109,  425, 2834, 1055,  1093, 1096, 130,  2103, 1093, 463,  2103, 2101, 2835,  \n\t\t\t\t\t\t2836, 755, 2098,  1487, 2098, 427,  111, 2836, 1487,  2837, 465, 1525,  1057, 1525, 110,  \n\t\t\t\t\t\t427, 2837, 1057,  2838, 131, 1095,  2099, 1095, 465,  755, 2838, 2099,  2094, 2096, 754,  \n\t\t\t\t\t\t429, 2839, 2094,  112, 2839, 1489,  1527, 2095, 467,  111, 2840, 1527,  1059, 2094, 2840,  \n\t\t\t\t\t\t2841, 132, 1097,  467, 2841, 1097,  2095, 2093, 2841,  2842, 753, 2090,  1491, 2090, 431,  \n\t\t\t\t\t\t113, 2842, 1491,  2843, 469, 1529,  1061, 1529, 112,  431, 2843, 1061,  2844, 133, 1099,  \n\t\t\t\t\t\t2091, 1099, 469,  753, 2844, 2091,  2845, 752, 2086,  433, 2845, 2086,  114, 2845, 1493,  \n\t\t\t\t\t\t2846, 471, 1531,  113, 2846, 1531,  1063, 2086, 2846,  2847, 134, 1101,  2087, 1101, 471,  \n\t\t\t\t\t\t2087, 2085, 2847,  2848, 751, 2082,  1495, 2082, 435,  1495, 1535, 2848,  2849, 473, 1533,  \n\t\t\t\t\t\t1065, 1533, 114,  435, 2849, 1065,  1103, 1106, 135,  473, 2850, 1103,  751, 2850, 2083,  \n\t\t\t\t\t\t2851, 750, 2078,  1497, 2078, 437,  116, 2851, 1497,  2852, 475, 1535,  1067, 1535, 115,  \n\t\t\t\t\t\t437, 2852, 1067,  2853, 136, 1105,  475, 2853, 1105,  750, 2853, 2079,  2854, 749, 2074,  \n\t\t\t\t\t\t1499, 2074, 439,  117, 2854, 1499,  2855, 477, 1537,  1069, 1537, 116,  439, 2855, 1069,  \n\t\t\t\t\t\t2856, 137, 1107,  2075, 1107, 477,  749, 2856, 2075,  2857, 748, 2070,  1501, 2070, 441,  \n\t\t\t\t\t\t118, 2857, 1501,  2858, 479, 1539,  1071, 1539, 117,  441, 2858, 1071,  1109, 1112, 138,  \n\t\t\t\t\t\t479, 2859, 1109,  748, 2859, 2071,  2066, 2068, 747,  443, 2860, 2066,  1503, 1543, 2860,  \n\t\t\t\t\t\t1541, 2067, 481,  118, 2861, 1541,  1073, 2066, 2861,  2862, 139, 1111,  2067, 1111, 481,  \n\t\t\t\t\t\t2067, 2065, 2862,  2863, 746, 2062,  1505, 2062, 445,  120, 2863, 1505,  2864, 483, 1543,  \n\t\t\t\t\t\t1075, 1543, 119,  445, 2864, 1075,  2865, 140, 1113,  2063, 1113, 483,  746, 2865, 2063,  \n\t\t\t\t\t\t2866, 745, 2058,  1507, 2058, 447,  121, 2866, 1507,  2867, 485, 1545,  1077, 1545, 120,  \n\t\t\t\t\t\t447, 2867, 1077,  2868, 141, 1115,  2059, 1115, 485,  745, 2868, 2059,  2054, 2056, 744,  \n\t\t\t\t\t\t1509, 2054, 449,  122, 2869, 1509,  2870, 487, 1547,  1079, 1547, 121,  449, 2870, 1079,  \n\t\t\t\t\t\t1117, 1120, 142,  487, 2871, 1117,  2055, 2053, 2871,  2050, 2052, 743,  451, 2872, 2050,  \n\t\t\t\t\t\t1511, 1551, 2872,  1549, 2051, 489,  122, 2873, 1549,  1081, 2050, 2873,  2874, 143, 1119,  \n\t\t\t\t\t\t489, 2874, 1119,  2051, 2049, 2874,  2875, 742, 2046,  1513, 2046, 453,  124, 2875, 1513,  \n\t\t\t\t\t\t2876, 491, 1551,  1083, 1551, 123,  453, 2876, 1083,  2877, 144, 1121,  2047, 1121, 491,  \n\t\t\t\t\t\t742, 2877, 2047,  2878, 741, 2042,  1515, 2042, 455,  1515, 1555, 2878,  2879, 493, 1553,  \n\t\t\t\t\t\t1085, 1553, 124,  455, 2879, 1085,  2880, 145, 1123,  2043, 1123, 493,  741, 2880, 2043,  \n\t\t\t\t\t\t2881, 740, 2038,  1518, 2038, 458,  127, 2881, 1518,  2882, 497, 1127,  1088, 1127, 126,  \n\t\t\t\t\t\t458, 2882, 1088,  2883, 147, 1557,  2039, 1557, 497,  740, 2883, 2039,  2884, 739, 2034,  \n\t\t\t\t\t\t1520, 2034, 460,  128, 2884, 1520,  2885, 498, 1558,  1090, 1558, 127,  460, 2885, 1090,  \n\t\t\t\t\t\t2886, 148, 1128,  2035, 1128, 498,  739, 2886, 2035,  2030, 2032, 738,  462, 2887, 2030,  \n\t\t\t\t\t\t1522, 1562, 2887,  1560, 2031, 500,  128, 2888, 1560,  1092, 2030, 2888,  2889, 149, 1130,  \n\t\t\t\t\t\t2031, 1130, 500,  2031, 2029, 2889,  2890, 737, 2026,  1524, 2026, 464,  130, 2890, 1524,  \n\t\t\t\t\t\t2891, 502, 1562,  1094, 1562, 129,  464, 2891, 1094,  1132, 1135, 150,  2027, 1132, 502,  \n\t\t\t\t\t\t2027, 2025, 2892,  2022, 2024, 736,  466, 2893, 2022,  1526, 1566, 2893,  2894, 504, 1564,  \n\t\t\t\t\t\t1096, 1564, 130,  466, 2894, 1096,  2895, 151, 1134,  2023, 1134, 504,  736, 2895, 2023,  \n\t\t\t\t\t\t2896, 735, 2018,  1528, 2018, 468,  132, 2896, 1528,  2897, 506, 1566,  1098, 1566, 131,  \n\t\t\t\t\t\t468, 2897, 1098,  2898, 152, 1136,  2019, 1136, 506,  735, 2898, 2019,  2899, 734, 2014,  \n\t\t\t\t\t\t1530, 2014, 470,  133, 2899, 1530,  2900, 508, 1568,  1100, 1568, 132,  470, 2900, 1100,  \n\t\t\t\t\t\t2901, 153, 1138,  2015, 1138, 508,  734, 2901, 2015,  2010, 2012, 733,  472, 2902, 2010,  \n\t\t\t\t\t\t134, 2902, 1532,  2903, 510, 1570,  1102, 1570, 133,  1102, 2010, 2903,  2904, 154, 1140,  \n\t\t\t\t\t\t2011, 1140, 510,  733, 2904, 2011,  2905, 732, 2006,  1534, 2006, 474,  1534, 1574, 2905,  \n\t\t\t\t\t\t1572, 2007, 512,  1104, 1572, 134,  474, 2906, 1104,  1142, 1145, 155,  512, 2907, 1142,  \n\t\t\t\t\t\t732, 2907, 2007,  2908, 731, 2002,  1536, 2002, 476,  136, 2908, 1536,  2909, 514, 1574,  \n\t\t\t\t\t\t1106, 1574, 135,  476, 2909, 1106,  2910, 156, 1144,  2003, 1144, 514,  731, 2910, 2003,  \n\t\t\t\t\t\t2911, 730, 1998,  1538, 1998, 478,  1538, 1578, 2911,  2912, 516, 1576,  1108, 1576, 136,  \n\t\t\t\t\t\t478, 2912, 1108,  2913, 157, 1146,  1999, 1146, 516,  730, 2913, 1999,  2914, 729, 1994,  \n\t\t\t\t\t\t1540, 1994, 480,  138, 2914, 1540,  2915, 518, 1578,  1110, 1578, 137,  480, 2915, 1110,  \n\t\t\t\t\t\t2916, 158, 1148,  1995, 1148, 518,  729, 2916, 1995,  2917, 728, 1990,  1542, 1990, 482,  \n\t\t\t\t\t\t1542, 1582, 2917,  2918, 520, 1580,  138, 2918, 1580,  482, 2918, 1112,  1150, 1153, 159,  \n\t\t\t\t\t\t1991, 1150, 520,  728, 2919, 1991,  1986, 1988, 727,  484, 2920, 1986,  1544, 1584, 2920,  \n\t\t\t\t\t\t2921, 522, 1582,  139, 2921, 1582,  1114, 1986, 2921,  2922, 160, 1152,  1987, 1152, 522,  \n\t\t\t\t\t\t727, 2922, 1987,  1982, 1984, 726,  486, 2923, 1982,  1546, 1586, 2923,  2924, 524, 1584,  \n\t\t\t\t\t\t140, 2924, 1584,  486, 2924, 1116,  1154, 1157, 161,  524, 2925, 1154,  1983, 1981, 2925,  \n\t\t\t\t\t\t2926, 725, 1978,  1548, 1978, 488,  142, 2926, 1548,  1586, 1979, 526,  1118, 1586, 141,  \n\t\t\t\t\t\t488, 2927, 1118,  2928, 162, 1156,  526, 2928, 1156,  725, 2928, 1979,  2929, 724, 1974,  \n\t\t\t\t\t\t490, 2929, 1974,  1550, 1590, 2929,  2930, 528, 1588,  142, 2930, 1588,  1120, 1974, 2930,  \n\t\t\t\t\t\t2931, 163, 1158,  1975, 1158, 528,  724, 2931, 1975,  2932, 723, 1970,  1552, 1970, 492,  \n\t\t\t\t\t\t144, 2932, 1552,  2933, 530, 1590,  1122, 1590, 143,  492, 2933, 1122,  2934, 164, 1160,  \n\t\t\t\t\t\t1971, 1160, 530,  723, 2934, 1971,  1966, 1968, 722,  494, 2935, 1966,  145, 2935, 1554,  \n\t\t\t\t\t\t2936, 532, 1592,  1124, 1592, 144,  494, 2936, 1124,  1162, 1165, 165,  1967, 1162, 532,  \n\t\t\t\t\t\t1967, 1965, 2937,  2938, 721, 1962,  1556, 1962, 496,  146, 2938, 1556,  2939, 534, 1594,  \n\t\t\t\t\t\t1126, 1594, 145,  496, 2939, 1126,  2940, 166, 1164,  1963, 1164, 534,  721, 2940, 1963,  \n\t\t\t\t\t\t2941, 720, 1958,  1559, 1958, 499,  148, 2941, 1559,  2942, 538, 1168,  1129, 1168, 147,  \n\t\t\t\t\t\t499, 2942, 1129,  2943, 168, 1598,  1959, 1598, 538,  720, 2943, 1959,  2944, 719, 1954,  \n\t\t\t\t\t\t1561, 1954, 501,  149, 2944, 1561,  2945, 539, 1599,  1131, 1599, 148,  501, 2945, 1131,  \n\t\t\t\t\t\t2946, 169, 1169,  1955, 1169, 539,  719, 2946, 1955,  2947, 718, 1950,  1563, 1950, 503,  \n\t\t\t\t\t\t150, 2947, 1563,  2948, 541, 1601,  1133, 1601, 149,  503, 2948, 1133,  2949, 170, 1171,  \n\t\t\t\t\t\t1951, 1171, 541,  718, 2949, 1951,  1946, 1948, 717,  505, 2950, 1946,  1565, 1605, 2950,  \n\t\t\t\t\t\t2951, 543, 1603,  150, 2951, 1603,  1135, 1946, 2951,  2952, 171, 1173,  1947, 1173, 543,  \n\t\t\t\t\t\t1947, 1945, 2952,  2953, 716, 1942,  1567, 1942, 507,  152, 2953, 1567,  2954, 545, 1605,  \n\t\t\t\t\t\t1137, 1605, 151,  507, 2954, 1137,  2955, 172, 1175,  1943, 1175, 545,  716, 2955, 1943,  \n\t\t\t\t\t\t2956, 715, 1938,  1569, 1938, 509,  153, 2956, 1569,  2957, 547, 1607,  1139, 1607, 152,  \n\t\t\t\t\t\t509, 2957, 1139,  2958, 173, 1177,  1939, 1177, 547,  715, 2958, 1939,  2959, 714, 1934,  \n\t\t\t\t\t\t1571, 1934, 511,  154, 2959, 1571,  2960, 549, 1609,  1141, 1609, 153,  511, 2960, 1141,  \n\t\t\t\t\t\t2961, 174, 1179,  1935, 1179, 549,  714, 2961, 1935,  2962, 713, 1930,  1573, 1930, 513,  \n\t\t\t\t\t\t1573, 1613, 2962,  1611, 1931, 551,  154, 2963, 1611,  513, 2963, 1143,  1181, 1184, 175,  \n\t\t\t\t\t\t551, 2964, 1181,  713, 2964, 1931,  2965, 712, 1926,  1575, 1926, 515,  156, 2965, 1575,  \n\t\t\t\t\t\t2966, 553, 1613,  155, 2966, 1613,  515, 2966, 1145,  2967, 176, 1183,  1927, 1183, 553,  \n\t\t\t\t\t\t712, 2967, 1927,  2968, 711, 1922,  1577, 1922, 517,  157, 2968, 1577,  2969, 555, 1615,  \n\t\t\t\t\t\t1147, 1615, 156,  517, 2969, 1147,  2970, 177, 1185,  1923, 1185, 555,  711, 2970, 1923,  \n\t\t\t\t\t\t2971, 710, 1918,  1579, 1918, 519,  158, 2971, 1579,  2972, 557, 1617,  1149, 1617, 157,  \n\t\t\t\t\t\t519, 2972, 1149,  2973, 178, 1187,  1919, 1187, 557,  710, 2973, 1919,  2974, 709, 1914,  \n\t\t\t\t\t\t1581, 1914, 521,  1581, 1621, 2974,  2975, 559, 1619,  1151, 1619, 158,  521, 2975, 1151,  \n\t\t\t\t\t\t2976, 179, 1189,  1915, 1189, 559,  709, 2976, 1915,  2977, 708, 1910,  1583, 1910, 523,  \n\t\t\t\t\t\t160, 2977, 1583,  2978, 561, 1621,  1153, 1621, 159,  523, 2978, 1153,  2979, 180, 1191,  \n\t\t\t\t\t\t1911, 1191, 561,  708, 2979, 1911,  1906, 1908, 707,  525, 2980, 1906,  1585, 1625, 2980,  \n\t\t\t\t\t\t2981, 563, 1623,  1155, 1623, 160,  525, 2981, 1155,  2982, 181, 1193,  1907, 1193, 563,  \n\t\t\t\t\t\t707, 2982, 1907,  2983, 706, 1902,  1587, 1902, 527,  162, 2983, 1587,  2984, 565, 1625,  \n\t\t\t\t\t\t161, 2984, 1625,  527, 2984, 1157,  2985, 182, 1195,  1903, 1195, 565,  706, 2985, 1903,  \n\t\t\t\t\t\t2986, 705, 1898,  1589, 1898, 529,  163, 2986, 1589,  2987, 567, 1627,  1159, 1627, 162,  \n\t\t\t\t\t\t529, 2987, 1159,  2988, 183, 1197,  1899, 1197, 567,  705, 2988, 1899,  2989, 704, 1894,  \n\t\t\t\t\t\t1591, 1894, 531,  164, 2989, 1591,  2990, 569, 1629,  1161, 1629, 163,  531, 2990, 1161,  \n\t\t\t\t\t\t2991, 184, 1199,  1895, 1199, 569,  704, 2991, 1895,  2992, 703, 1890,  1593, 1890, 533,  \n\t\t\t\t\t\t165, 2992, 1593,  2993, 571, 1631,  1163, 1631, 164,  533, 2993, 1163,  2994, 185, 1201,  \n\t\t\t\t\t\t1891, 1201, 571,  703, 2994, 1891,  1886, 1888, 702,  535, 2995, 1886,  1595, 1635, 2995,  \n\t\t\t\t\t\t2996, 573, 1633,  165, 2996, 1633,  1165, 1886, 2996,  2997, 186, 1203,  1887, 1203, 573,  \n\t\t\t\t\t\t1887, 1885, 2997,  2998, 701, 1882,  1597, 1882, 537,  167, 2998, 1597,  2999, 575, 1635,  \n\t\t\t\t\t\t1167, 1635, 166,  537, 2999, 1167,  3000, 187, 1205,  1883, 1205, 575,  701, 3000, 1883,  \n\t\t\t\t\t\t3001, 700, 1878,  1600, 1878, 540,  169, 3001, 1600,  3002, 579, 1209,  1170, 1209, 168,  \n\t\t\t\t\t\t540, 3002, 1170,  3003, 189, 1639,  1879, 1639, 579,  700, 3003, 1879,  3004, 699, 1874,  \n\t\t\t\t\t\t1602, 1874, 542,  170, 3004, 1602,  3005, 580, 1640,  1172, 1640, 169,  542, 3005, 1172,  \n\t\t\t\t\t\t3006, 190, 1210,  1875, 1210, 580,  699, 3006, 1875,  3007, 698, 1870,  1604, 1870, 544,  \n\t\t\t\t\t\t171, 3007, 1604,  3008, 582, 1642,  1174, 1642, 170,  544, 3008, 1174,  3009, 191, 1212,  \n\t\t\t\t\t\t1871, 1212, 582,  698, 3009, 1871,  1866, 1868, 697,  546, 3010, 1866,  172, 3010, 1606,  \n\t\t\t\t\t\t3011, 584, 1644,  1176, 1644, 171,  1176, 1866, 3011,  3012, 192, 1214,  1867, 1214, 584,  \n\t\t\t\t\t\t1867, 1865, 3012,  3013, 696, 1862,  1608, 1862, 548,  173, 3013, 1608,  3014, 586, 1646,  \n\t\t\t\t\t\t1178, 1646, 172,  548, 3014, 1178,  3015, 193, 1216,  1863, 1216, 586,  696, 3015, 1863,  \n\t\t\t\t\t\t3016, 695, 1858,  1610, 1858, 550,  174, 3016, 1610,  3017, 588, 1648,  1180, 1648, 173,  \n\t\t\t\t\t\t550, 3017, 1180,  3018, 194, 1218,  1859, 1218, 588,  695, 3018, 1859,  3019, 694, 1854,  \n\t\t\t\t\t\t1612, 1854, 552,  175, 3019, 1612,  3020, 590, 1650,  1182, 1650, 174,  552, 3020, 1182,  \n\t\t\t\t\t\t3021, 195, 1220,  1855, 1220, 590,  694, 3021, 1855,  3022, 693, 1850,  1614, 1850, 554,  \n\t\t\t\t\t\t176, 3022, 1614,  1652, 1851, 592,  175, 3023, 1652,  554, 3023, 1184,  1222, 1225, 196,  \n\t\t\t\t\t\t592, 3024, 1222,  693, 3024, 1851,  3025, 692, 1846,  1616, 1846, 556,  177, 3025, 1616,  \n\t\t\t\t\t\t3026, 594, 1654,  1186, 1654, 176,  556, 3026, 1186,  3027, 197, 1224,  1847, 1224, 594,  \n\t\t\t\t\t\t692, 3027, 1847,  3028, 691, 1842,  1618, 1842, 558,  178, 3028, 1618,  3029, 596, 1656,  \n\t\t\t\t\t\t1188, 1656, 177,  558, 3029, 1188,  3030, 198, 1226,  1843, 1226, 596,  691, 3030, 1843,  \n\t\t\t\t\t\t3031, 690, 1838,  1620, 1838, 560,  179, 3031, 1620,  3032, 598, 1658,  1190, 1658, 178,  \n\t\t\t\t\t\t560, 3032, 1190,  3033, 199, 1228,  1839, 1228, 598,  690, 3033, 1839,  3034, 689, 1834,  \n\t\t\t\t\t\t1622, 1834, 562,  180, 3034, 1622,  3035, 600, 1660,  1192, 1660, 179,  562, 3035, 1192,  \n\t\t\t\t\t\t3036, 200, 1230,  1835, 1230, 600,  689, 3036, 1835,  3037, 688, 1830,  1624, 1830, 564,  \n\t\t\t\t\t\t181, 3037, 1624,  3038, 602, 1662,  1194, 1662, 180,  564, 3038, 1194,  3039, 201, 1232,  \n\t\t\t\t\t\t1831, 1232, 602,  688, 3039, 1831,  3040, 687, 1826,  1626, 1826, 566,  1626, 1666, 3040,  \n\t\t\t\t\t\t3041, 604, 1664,  1196, 1664, 181,  566, 3041, 1196,  3042, 202, 1234,  1827, 1234, 604,  \n\t\t\t\t\t\t687, 3042, 1827,  3043, 686, 1822,  1628, 1822, 568,  183, 3043, 1628,  3044, 606, 1666,  \n\t\t\t\t\t\t1198, 1666, 182,  568, 3044, 1198,  3045, 203, 1236,  1823, 1236, 606,  686, 3045, 1823,  \n\t\t\t\t\t\t3046, 685, 1818,  1630, 1818, 570,  184, 3046, 1630,  3047, 608, 1668,  1200, 1668, 183,  \n\t\t\t\t\t\t570, 3047, 1200,  3048, 204, 1238,  1819, 1238, 608,  685, 3048, 1819,  3049, 684, 1814,  \n\t\t\t\t\t\t1632, 1814, 572,  185, 3049, 1632,  3050, 610, 1670,  1202, 1670, 184,  572, 3050, 1202,  \n\t\t\t\t\t\t3051, 205, 1240,  1815, 1240, 610,  684, 3051, 1815,  3052, 683, 1810,  1634, 1810, 574,  \n\t\t\t\t\t\t186, 3052, 1634,  3053, 612, 1672,  1204, 1672, 185,  574, 3053, 1204,  3054, 206, 1242,  \n\t\t\t\t\t\t1811, 1242, 612,  683, 3054, 1811,  3055, 682, 1806,  1636, 1806, 576,  187, 3055, 1636,  \n\t\t\t\t\t\t3056, 614, 1674,  1206, 1674, 186,  576, 3056, 1206,  3057, 207, 1244,  1807, 1244, 614,  \n\t\t\t\t\t\t682, 3057, 1807,  3058, 681, 1802,  1638, 1802, 578,  188, 3058, 1638,  3059, 616, 1676,  \n\t\t\t\t\t\t1208, 1676, 187,  578, 3059, 1208,  3060, 208, 1246,  1803, 1246, 616,  681, 3060, 1803,  \n\t\t\t\t\t\t3061, 680, 1798,  1641, 1798, 581,  190, 3061, 1641,  3062, 620, 1250,  1211, 1250, 189,  \n\t\t\t\t\t\t581, 3062, 1211,  3063, 210, 1680,  1799, 1680, 620,  680, 3063, 1799,  3064, 679, 1794,  \n\t\t\t\t\t\t1643, 1794, 583,  191, 3064, 1643,  3065, 621, 1681,  1213, 1681, 190,  583, 3065, 1213,  \n\t\t\t\t\t\t1251, 1254, 211,  621, 3066, 1251,  679, 3066, 1795,  3067, 678, 1790,  1645, 1790, 585,  \n\t\t\t\t\t\t192, 3067, 1645,  3068, 623, 1683,  1215, 1683, 191,  585, 3068, 1215,  3069, 212, 1253,  \n\t\t\t\t\t\t1791, 1253, 623,  678, 3069, 1791,  1786, 1788, 677,  587, 3070, 1786,  193, 3070, 1647,  \n\t\t\t\t\t\t1685, 1787, 625,  192, 3071, 1685,  1217, 1786, 3071,  1255, 1258, 213,  625, 3072, 1255,  \n\t\t\t\t\t\t1787, 1785, 3072,  3073, 676, 1782,  1649, 1782, 589,  194, 3073, 1649,  3074, 627, 1687,  \n\t\t\t\t\t\t1219, 1687, 193,  589, 3074, 1219,  3075, 214, 1257,  1783, 1257, 627,  676, 3075, 1783,  \n\t\t\t\t\t\t3076, 675, 1778,  1651, 1778, 591,  195, 3076, 1651,  3077, 629, 1689,  1221, 1689, 194,  \n\t\t\t\t\t\t591, 3077, 1221,  3078, 215, 1259,  1779, 1259, 629,  675, 3078, 1779,  3079, 674, 1774,  \n\t\t\t\t\t\t1653, 1774, 593,  1653, 1693, 3079,  3080, 631, 1691,  1223, 1691, 195,  593, 3080, 1223,  \n\t\t\t\t\t\t3081, 216, 1261,  1775, 1261, 631,  674, 3081, 1775,  3082, 673, 1770,  1655, 1770, 595,  \n\t\t\t\t\t\t197, 3082, 1655,  1693, 1771, 633,  196, 3083, 1693,  595, 3083, 1225,  3084, 217, 1263,  \n\t\t\t\t\t\t1771, 1263, 633,  673, 3084, 1771,  3085, 672, 1766,  1657, 1766, 597,  198, 3085, 1657,  \n\t\t\t\t\t\t3086, 635, 1695,  1227, 1695, 197,  597, 3086, 1227,  3087, 218, 1265,  1767, 1265, 635,  \n\t\t\t\t\t\t672, 3087, 1767,  1762, 1764, 671,  1659, 1762, 599,  199, 3088, 1659,  3089, 637, 1697,  \n\t\t\t\t\t\t1229, 1697, 198,  1229, 1762, 3089,  3090, 219, 1267,  1763, 1267, 637,  671, 3090, 1763,  \n\t\t\t\t\t\t3091, 670, 1758,  601, 3091, 1758,  200, 3091, 1661,  1699, 1759, 639,  1231, 1699, 199,  \n\t\t\t\t\t\t601, 3092, 1231,  1269, 1272, 220,  639, 3093, 1269,  1759, 1757, 3093,  3094, 669, 1754,  \n\t\t\t\t\t\t1663, 1754, 603,  201, 3094, 1663,  3095, 641, 1701,  1233, 1701, 200,  603, 3095, 1233,  \n\t\t\t\t\t\t3096, 221, 1271,  1755, 1271, 641,  669, 3096, 1755,  3097, 668, 1750,  1665, 1750, 605,  \n\t\t\t\t\t\t202, 3097, 1665,  3098, 643, 1703,  1235, 1703, 201,  605, 3098, 1235,  3099, 222, 1273,  \n\t\t\t\t\t\t1751, 1273, 643,  668, 3099, 1751,  1746, 1748, 667,  1667, 1746, 607,  1667, 1707, 3100,  \n\t\t\t\t\t\t3101, 645, 1705,  1237, 1705, 202,  607, 3101, 1237,  3102, 223, 1275,  1747, 1275, 645,  \n\t\t\t\t\t\t667, 3102, 1747,  3103, 666, 1742,  1669, 1742, 609,  204, 3103, 1669,  3104, 647, 1707,  \n\t\t\t\t\t\t1239, 1707, 203,  609, 3104, 1239,  3105, 224, 1277,  1743, 1277, 647,  666, 3105, 1743,  \n\t\t\t\t\t\t3106, 665, 1738,  1671, 1738, 611,  1671, 1711, 3106,  3107, 649, 1709,  1241, 1709, 204,  \n\t\t\t\t\t\t611, 3107, 1241,  3108, 225, 1279,  1739, 1279, 649,  665, 3108, 1739,  3109, 664, 1734,  \n\t\t\t\t\t\t1673, 1734, 613,  206, 3109, 1673,  1711, 1735, 651,  205, 3110, 1711,  613, 3110, 1243,  \n\t\t\t\t\t\t3111, 226, 1281,  1735, 1281, 651,  664, 3111, 1735,  3112, 663, 1730,  1675, 1730, 615,  \n\t\t\t\t\t\t1675, 1715, 3112,  3113, 653, 1713,  1245, 1713, 206,  615, 3113, 1245,  3114, 227, 1283,  \n\t\t\t\t\t\t1731, 1283, 653,  663, 3114, 1731,  3115, 662, 1726,  617, 3115, 1726,  1677, 1717, 3115,  \n\t\t\t\t\t\t3116, 655, 1715,  207, 3116, 1715,  1247, 1726, 3116,  3117, 228, 1285,  1727, 1285, 655,  \n\t\t\t\t\t\t662, 3117, 1727,  3118, 661, 1722,  1679, 1722, 619,  209, 3118, 1679,  1717, 1723, 657,  \n\t\t\t\t\t\t208, 3119, 1717,  619, 3119, 1249,  3120, 229, 1287,  1723, 1287, 657,  661, 3120, 1723,  \n\t\t\t\t\t\t3121, 660, 1721,  1724, 1721, 661,  659, 3121, 1724,  3122, 658, 1725,  1728, 1725, 662,  \n\t\t\t\t\t\t657, 3122, 1728,  3123, 656, 1729,  1732, 1729, 663,  655, 3123, 1732,  3124, 654, 1733,  \n\t\t\t\t\t\t1736, 1733, 664,  653, 3124, 1736,  3125, 652, 1737,  1740, 1737, 665,  651, 3125, 1740,  \n\t\t\t\t\t\t3126, 650, 1741,  1744, 1741, 666,  649, 3126, 1744,  1745, 1708, 648,  667, 3127, 1745,  \n\t\t\t\t\t\t1748, 1277, 3127,  3128, 646, 1749,  1752, 1749, 668,  645, 3128, 1752,  3129, 644, 1753,  \n\t\t\t\t\t\t1756, 1753, 669,  643, 3129, 1756,  1757, 1702, 642,  670, 3130, 1757,  641, 3130, 1760,  \n\t\t\t\t\t\t1761, 1700, 640,  671, 3131, 1761,  639, 3131, 1764,  3132, 638, 1765,  1768, 1765, 672,  \n\t\t\t\t\t\t637, 3132, 1768,  3133, 636, 1769,  1772, 1769, 673,  635, 3133, 1772,  3134, 634, 1773,  \n\t\t\t\t\t\t1776, 1773, 674,  1776, 1263, 3134,  3135, 632, 1777,  1780, 1777, 675,  631, 3135, 1780,  \n\t\t\t\t\t\t3136, 630, 1781,  1784, 1781, 676,  629, 3136, 1784,  1785, 1688, 628,  677, 3137, 1785,  \n\t\t\t\t\t\t1788, 1257, 3137,  3138, 626, 1789,  1792, 1789, 678,  625, 3138, 1792,  3139, 624, 1793,  \n\t\t\t\t\t\t1796, 1793, 679,  623, 3139, 1796,  3140, 622, 1797,  1800, 1797, 680,  621, 3140, 1800,  \n\t\t\t\t\t\t3141, 619, 1801,  1804, 1801, 681,  618, 3141, 1804,  3142, 617, 1805,  1808, 1805, 682,  \n\t\t\t\t\t\t616, 3142, 1808,  3143, 615, 1809,  1812, 1809, 683,  614, 3143, 1812,  3144, 613, 1813,  \n\t\t\t\t\t\t1816, 1813, 684,  612, 3144, 1816,  3145, 611, 1817,  1820, 1817, 685,  610, 3145, 1820,  \n\t\t\t\t\t\t3146, 609, 1821,  1824, 1821, 686,  608, 3146, 1824,  3147, 607, 1825,  1828, 1825, 687,  \n\t\t\t\t\t\t606, 3147, 1828,  3148, 605, 1829,  1832, 1829, 688,  604, 3148, 1832,  3149, 603, 1833,  \n\t\t\t\t\t\t1836, 1833, 689,  602, 3149, 1836,  3150, 601, 1837,  1840, 1837, 690,  600, 3150, 1840,  \n\t\t\t\t\t\t3151, 599, 1841,  1844, 1841, 691,  598, 3151, 1844,  3152, 597, 1845,  1848, 1845, 692,  \n\t\t\t\t\t\t596, 3152, 1848,  3153, 595, 1849,  1852, 1849, 693,  594, 3153, 1852,  3154, 593, 1853,  \n\t\t\t\t\t\t1856, 1853, 694,  592, 3154, 1856,  3155, 591, 1857,  1860, 1857, 695,  590, 3155, 1860,  \n\t\t\t\t\t\t3156, 589, 1861,  1864, 1861, 696,  588, 3156, 1864,  1865, 1647, 587,  697, 3157, 1865,  \n\t\t\t\t\t\t586, 3157, 1868,  3158, 585, 1869,  1872, 1869, 698,  584, 3158, 1872,  3159, 583, 1873,  \n\t\t\t\t\t\t1876, 1873, 699,  582, 3159, 1876,  3160, 581, 1877,  1880, 1877, 700,  580, 3160, 1880,  \n\t\t\t\t\t\t3161, 578, 1881,  1884, 1881, 701,  577, 3161, 1884,  1885, 1636, 576,  702, 3162, 1885,  \n\t\t\t\t\t\t575, 3162, 1888,  3163, 574, 1889,  1892, 1889, 703,  573, 3163, 1892,  3164, 572, 1893,  \n\t\t\t\t\t\t1896, 1893, 704,  571, 3164, 1896,  3165, 570, 1897,  1900, 1897, 705,  569, 3165, 1900,  \n\t\t\t\t\t\t3166, 568, 1901,  1904, 1901, 706,  567, 3166, 1904,  3167, 566, 1905,  707, 3167, 1905,  \n\t\t\t\t\t\t1908, 1195, 3167,  3168, 564, 1909,  1912, 1909, 708,  563, 3168, 1912,  3169, 562, 1913,  \n\t\t\t\t\t\t1916, 1913, 709,  561, 3169, 1916,  3170, 560, 1917,  1920, 1917, 710,  559, 3170, 1920,  \n\t\t\t\t\t\t3171, 558, 1921,  1924, 1921, 711,  557, 3171, 1924,  3172, 556, 1925,  1928, 1925, 712,  \n\t\t\t\t\t\t555, 3172, 1928,  3173, 554, 1929,  1932, 1929, 713,  553, 3173, 1932,  3174, 552, 1933,  \n\t\t\t\t\t\t1936, 1933, 714,  551, 3174, 1936,  3175, 550, 1937,  1940, 1937, 715,  549, 3175, 1940,  \n\t\t\t\t\t\t3176, 548, 1941,  1944, 1941, 716,  547, 3176, 1944,  1945, 1606, 546,  717, 3177, 1945,  \n\t\t\t\t\t\t545, 3177, 1948,  3178, 544, 1949,  1952, 1949, 718,  543, 3178, 1952,  3179, 542, 1953,  \n\t\t\t\t\t\t1956, 1953, 719,  541, 3179, 1956,  3180, 540, 1957,  1960, 1957, 720,  539, 3180, 1960,  \n\t\t\t\t\t\t3181, 537, 1961,  1964, 1961, 721,  536, 3181, 1964,  1965, 1595, 535,  722, 3182, 1965,  \n\t\t\t\t\t\t1968, 1164, 3182,  3183, 533, 1969,  1972, 1969, 723,  532, 3183, 1972,  3184, 531, 1973,  \n\t\t\t\t\t\t1976, 1973, 724,  530, 3184, 1976,  3185, 529, 1977,  1980, 1977, 725,  528, 3185, 1980,  \n\t\t\t\t\t\t1981, 1587, 527,  726, 3186, 1981,  1984, 1156, 3186,  3187, 525, 1985,  727, 3187, 1985,  \n\t\t\t\t\t\t524, 3187, 1988,  1989, 1583, 523,  1992, 1989, 728,  522, 3188, 1992,  3189, 521, 1993,  \n\t\t\t\t\t\t1996, 1993, 729,  1996, 1150, 3189,  3190, 519, 1997,  2000, 1997, 730,  518, 3190, 2000,  \n\t\t\t\t\t\t3191, 517, 2001,  2004, 2001, 731,  516, 3191, 2004,  3192, 515, 2005,  2008, 2005, 732,  \n\t\t\t\t\t\t514, 3192, 2008,  3193, 513, 2009,  2012, 2009, 733,  2012, 1142, 3193,  3194, 511, 2013,  \n\t\t\t\t\t\t2016, 2013, 734,  510, 3194, 2016,  3195, 509, 2017,  2020, 2017, 735,  508, 3195, 2020,  \n\t\t\t\t\t\t3196, 507, 2021,  2024, 2021, 736,  506, 3196, 2024,  2025, 1565, 505,  737, 3197, 2025,  \n\t\t\t\t\t\t504, 3197, 2028,  3198, 503, 2029,  738, 3198, 2029,  502, 3198, 2032,  3199, 501, 2033,  \n\t\t\t\t\t\t2036, 2033, 739,  500, 3199, 2036,  3200, 499, 2037,  2040, 2037, 740,  498, 3200, 2040,  \n\t\t\t\t\t\t3201, 496, 2041,  2044, 2041, 741,  495, 3201, 2044,  3202, 494, 2045,  2048, 2045, 742,  \n\t\t\t\t\t\t493, 3202, 2048,  3203, 492, 2049,  743, 3203, 2049,  2052, 1121, 3203,  2053, 1550, 490,  \n\t\t\t\t\t\t744, 3204, 2053,  489, 3204, 2056,  3205, 488, 2057,  2060, 2057, 745,  487, 3205, 2060,  \n\t\t\t\t\t\t3206, 486, 2061,  2064, 2061, 746,  485, 3206, 2064,  2065, 1544, 484,  747, 3207, 2065,  \n\t\t\t\t\t\t483, 3207, 2068,  3208, 482, 2069,  2072, 2069, 748,  481, 3208, 2072,  3209, 480, 2073,  \n\t\t\t\t\t\t2076, 2073, 749,  2076, 1109, 3209,  3210, 478, 2077,  2080, 2077, 750,  2080, 1107, 3210,  \n\t\t\t\t\t\t3211, 476, 2081,  2084, 2081, 751,  475, 3211, 2084,  3212, 474, 2085,  2088, 2085, 752,  \n\t\t\t\t\t\t473, 3212, 2088,  3213, 472, 2089,  2092, 2089, 753,  471, 3213, 2092,  2093, 1530, 470,  \n\t\t\t\t\t\t754, 3214, 2093,  469, 3214, 2096,  3215, 468, 2097,  2100, 2097, 755,  467, 3215, 2100,  \n\t\t\t\t\t\t2101, 1526, 466,  756, 3216, 2101,  465, 3216, 2104,  3217, 464, 2105,  2108, 2105, 757,  \n\t\t\t\t\t\t463, 3217, 2108,  2109, 1522, 462,  758, 3218, 2109,  2112, 1091, 3218,  3219, 460, 2113,  \n\t\t\t\t\t\t2116, 2113, 759,  459, 3219, 2116,  3220, 458, 2117,  2120, 2117, 760,  457, 3220, 2120,  \n\t\t\t\t\t\t3221, 455, 2121,  761, 3221, 2121,  2124, 1084, 3221,  2125, 1513, 453,  2128, 2125, 762,  \n\t\t\t\t\t\t452, 3222, 2128,  2129, 1511, 451,  763, 3223, 2129,  2132, 1080, 3223,  3224, 449, 2133,  \n\t\t\t\t\t\t764, 3224, 2133,  2136, 1078, 3224,  3225, 447, 2137,  2140, 2137, 765,  446, 3225, 2140,  \n\t\t\t\t\t\t3226, 445, 2141,  2144, 2141, 766,  444, 3226, 2144,  2145, 1503, 443,  767, 3227, 2145,  \n\t\t\t\t\t\t442, 3227, 2148,  3228, 441, 2149,  2152, 2149, 768,  440, 3228, 2152,  2153, 1499, 439,  \n\t\t\t\t\t\t769, 3229, 2153,  2156, 1068, 3229,  3230, 437, 2157,  2160, 2157, 770,  2160, 1066, 3230,  \n\t\t\t\t\t\t2161, 1495, 435,  771, 3231, 2161,  434, 3231, 2164,  2165, 1493, 433,  2168, 2165, 772,  \n\t\t\t\t\t\t432, 3232, 2168,  3233, 431, 2169,  2172, 2169, 773,  430, 3233, 2172,  3234, 429, 2173,  \n\t\t\t\t\t\t774, 3234, 2173,  428, 3234, 2176,  3235, 427, 2177,  2180, 2177, 775,  2180, 1056, 3235,  \n\t\t\t\t\t\t3236, 425, 2181,  2184, 2181, 776,  424, 3236, 2184,  2185, 1483, 423,  777, 3237, 2185,  \n\t\t\t\t\t\t2188, 1052, 3237,  3238, 421, 2189,  2192, 2189, 778,  420, 3238, 2192,  3239, 419, 2193,  \n\t\t\t\t\t\t2196, 2193, 779,  418, 3239, 2196,  3240, 417, 2197,  780, 3240, 2197,  2200, 1046, 3240,  \n\t\t\t\t\t\t3241, 414, 2201,  2204, 2201, 781,  413, 3241, 2204,  3242, 412, 2205,  2208, 2205, 782,  \n\t\t\t\t\t\t411, 3242, 2208,  3243, 410, 2209,  2212, 2209, 783,  409, 3243, 2212,  3244, 408, 2213,  \n\t\t\t\t\t\t2216, 2213, 784,  407, 3244, 2216,  2217, 1466, 406,  785, 3245, 2217,  405, 3245, 2220,  \n\t\t\t\t\t\t3246, 404, 2221,  2224, 2221, 786,  403, 3246, 2224,  3247, 402, 2225,  2228, 2225, 787,  \n\t\t\t\t\t\t401, 3247, 2228,  3248, 400, 2229,  2232, 2229, 788,  399, 3248, 2232,  3249, 398, 2233,  \n\t\t\t\t\t\t2236, 2233, 789,  397, 3249, 2236,  3250, 396, 2237,  2240, 2237, 790,  2240, 1025, 3250,  \n\t\t\t\t\t\t3251, 394, 2241,  2244, 2241, 791,  393, 3251, 2244,  3252, 392, 2245,  2248, 2245, 792,  \n\t\t\t\t\t\t391, 3252, 2248,  3253, 390, 2249,  2252, 2249, 793,  389, 3253, 2252,  3254, 388, 2253,  \n\t\t\t\t\t\t2256, 2253, 794,  387, 3254, 2256,  2257, 1446, 386,  795, 3255, 2257,  2260, 1015, 3255,  \n\t\t\t\t\t\t3256, 384, 2261,  2264, 2261, 796,  383, 3256, 2264,  3257, 382, 2265,  2268, 2265, 797,  \n\t\t\t\t\t\t381, 3257, 2268,  3258, 380, 2269,  2272, 2269, 798,  2272, 1009, 3258,  3259, 378, 2273,  \n\t\t\t\t\t\t2276, 2273, 799,  377, 3259, 2276,  3260, 376, 2277,  2280, 2277, 800,  375, 3260, 2280,  \n\t\t\t\t\t\t3261, 373, 2281,  2284, 2281, 801,  372, 3261, 2284,  3262, 371, 2285,  2288, 2285, 802,  \n\t\t\t\t\t\t370, 3262, 2288,  3263, 369, 2289,  2292, 2289, 803,  368, 3263, 2292,  3264, 367, 2293,  \n\t\t\t\t\t\t2296, 2293, 804,  366, 3264, 2296,  3265, 365, 2297,  2300, 2297, 805,  364, 3265, 2300,  \n\t\t\t\t\t\t3266, 363, 2301,  2304, 2301, 806,  362, 3266, 2304,  3267, 361, 2305,  2308, 2305, 807,  \n\t\t\t\t\t\t2308, 990, 3267,  3268, 359, 2309,  2312, 2309, 808,  358, 3268, 2312,  3269, 357, 2313,  \n\t\t\t\t\t\t2316, 2313, 809,  356, 3269, 2316,  3270, 355, 2317,  2320, 2317, 810,  354, 3270, 2320,  \n\t\t\t\t\t\t3271, 353, 2321,  2324, 2321, 811,  352, 3271, 2324,  3272, 351, 2325,  2328, 2325, 812,  \n\t\t\t\t\t\t350, 3272, 2328,  3273, 349, 2329,  2332, 2329, 813,  348, 3273, 2332,  3274, 347, 2333,  \n\t\t\t\t\t\t2336, 2333, 814,  346, 3274, 2336,  3275, 345, 2337,  2340, 2337, 815,  344, 3275, 2340,  \n\t\t\t\t\t\t3276, 343, 2341,  2344, 2341, 816,  342, 3276, 2344,  3277, 341, 2345,  2348, 2345, 817,  \n\t\t\t\t\t\t340, 3277, 2348,  2349, 1399, 339,  2352, 2349, 818,  338, 3278, 2352,  3279, 337, 2353,  \n\t\t\t\t\t\t2356, 2353, 819,  336, 3279, 2356,  3280, 335, 2357,  2360, 2357, 820,  334, 3280, 2360,  \n\t\t\t\t\t\t3281, 332, 2361,  2364, 2361, 821,  331, 3281, 2364,  3282, 330, 2365,  2368, 2365, 822,  \n\t\t\t\t\t\t329, 3282, 2368,  3283, 328, 2369,  2372, 2369, 823,  327, 3283, 2372,  3284, 326, 2373,  \n\t\t\t\t\t\t2376, 2373, 824,  325, 3284, 2376,  3285, 324, 2377,  2380, 2377, 825,  323, 3285, 2380,  \n\t\t\t\t\t\t3286, 322, 2381,  2384, 2381, 826,  321, 3286, 2384,  3287, 320, 2385,  2388, 2385, 827,  \n\t\t\t\t\t\t2388, 949, 3287,  3288, 318, 2389,  2392, 2389, 828,  317, 3288, 2392,  3289, 316, 2393,  \n\t\t\t\t\t\t2396, 2393, 829,  315, 3289, 2396,  3290, 314, 2397,  2400, 2397, 830,  313, 3290, 2400,  \n\t\t\t\t\t\t3291, 312, 2401,  2404, 2401, 831,  311, 3291, 2404,  3292, 310, 2405,  2408, 2405, 832,  \n\t\t\t\t\t\t309, 3292, 2408,  3293, 308, 2409,  2412, 2409, 833,  307, 3293, 2412,  2413, 1366, 306,  \n\t\t\t\t\t\t834, 3294, 2413,  305, 3294, 2416,  3295, 304, 2417,  2420, 2417, 835,  303, 3295, 2420,  \n\t\t\t\t\t\t3296, 302, 2421,  2424, 2421, 836,  301, 3296, 2424,  3297, 300, 2425,  2428, 2425, 837,  \n\t\t\t\t\t\t299, 3297, 2428,  3298, 298, 2429,  2432, 2429, 838,  297, 3298, 2432,  3299, 296, 2433,  \n\t\t\t\t\t\t2436, 2433, 839,  295, 3299, 2436,  3300, 294, 2437,  2440, 2437, 840,  293, 3300, 2440,  \n\t\t\t\t\t\t3301, 291, 2441,  2444, 2441, 841,  290, 3301, 2444,  3302, 288, 2445,  2448, 2445, 842,  \n\t\t\t\t\t\t287, 3302, 2448,  3303, 285, 2449,  2452, 2449, 843,  284, 3303, 2452,  2453, 1342, 282,  \n\t\t\t\t\t\t844, 3304, 2453,  281, 3304, 2456,  3305, 279, 2457,  2460, 2457, 845,  278, 3305, 2460,  \n\t\t\t\t\t\t3306, 276, 2461,  2464, 2461, 846,  275, 3306, 2464,  3307, 273, 2465,  2468, 2465, 847,  \n\t\t\t\t\t\t272, 3307, 2468,  3308, 270, 2469,  2472, 2469, 848,  2472, 899, 3308,  3309, 267, 2473,  \n\t\t\t\t\t\t2476, 2473, 849,  266, 3309, 2476,  2477, 1324, 264,  850, 3310, 2477,  263, 3310, 2480,  \n\t\t\t\t\t\t2481, 1321, 261,  851, 3311, 2481,  2484, 890, 3311,  2485, 1318, 258,  2488, 2485, 852,  \n\t\t\t\t\t\t257, 3312, 2488,  2489, 1315, 255,  853, 3313, 2489,  2492, 884, 3313,  2493, 1312, 252,  \n\t\t\t\t\t\t2496, 2493, 854,  2496, 881, 3314,  3315, 249, 2497,  2500, 2497, 855,  248, 3315, 2500,  \n\t\t\t\t\t\t2501, 1306, 246,  2504, 2501, 856,  245, 3316, 2504,  3317, 243, 2505,  2508, 2505, 857,  \n\t\t\t\t\t\t2508, 872, 3317,  3318, 240, 2509,  2512, 2509, 858,  239, 3318, 2512,  2513, 1297, 237,  \n\t\t\t\t\t\t2516, 2513, 859,  236, 3319, 2516,  2517, 1294, 234,  2520, 2517, 860,  2520, 863, 3320,  \n\t\t\t\t\t\t863, 22, 1294,  866, 23, 1297,  869, 24, 1300,  872, 25, 1303,  875, 26, 1306,  \n\t\t\t\t\t\t878, 27, 1309,  3314, 881, 28,  3313, 884, 29,  887, 30, 1318,  3311, 890, 31,  \n\t\t\t\t\t\t893, 32, 1324,  896, 33, 1327,  3308, 899, 34,  902, 35, 1333,  905, 36, 1336,  \n\t\t\t\t\t\t908, 37, 1339,  911, 38, 1342,  914, 39, 1345,  917, 40, 1348,  920, 41, 1351,  \n\t\t\t\t\t\t923, 43, 1354,  925, 44, 1356,  927, 45, 1358,  929, 46, 1360,  931, 47, 1362,  \n\t\t\t\t\t\t933, 48, 1364,  935, 49, 1366,  937, 50, 1368,  939, 51, 1370,  941, 52, 1372,  \n\t\t\t\t\t\t943, 53, 1374,  945, 54, 1376,  947, 55, 1378,  949, 56, 1380,  951, 57, 1382,  \n\t\t\t\t\t\t953, 58, 1384,  955, 59, 1386,  957, 60, 1388,  959, 61, 1390,  961, 62, 1392,  \n\t\t\t\t\t\t964, 64, 1395,  966, 65, 1397,  968, 66, 1399,  970, 67, 1401,  972, 68, 1403,  \n\t\t\t\t\t\t3275, 974, 69,  976, 70, 1407,  978, 71, 1409,  980, 72, 1411,  982, 73, 1413,  \n\t\t\t\t\t\t984, 74, 1415,  3269, 986, 75,  988, 76, 1419,  3267, 990, 77,  992, 78, 1423,  \n\t\t\t\t\t\t994, 79, 1425,  996, 80, 1427,  998, 81, 1429,  1000, 82, 1431,  1002, 83, 1433,  \n\t\t\t\t\t\t1005, 85, 1436,  1007, 86, 1438,  3258, 1009, 87,  1011, 88, 1442,  3256, 1013, 89,  \n\t\t\t\t\t\t3255, 1015, 90,  1017, 91, 1448,  3253, 1019, 92,  1021, 93, 1452,  1023, 94, 1454,  \n\t\t\t\t\t\t3250, 1025, 95,  1027, 96, 1458,  1029, 97, 1460,  1031, 98, 1462,  1033, 99, 1464,  \n\t\t\t\t\t\t3245, 1035, 100,  1037, 101, 1468,  1039, 102, 1470,  1041, 103, 1472,  3241, 1043, 104,  \n\t\t\t\t\t\t3240, 1046, 106,  1048, 107, 1479,  1050, 108, 1481,  3237, 1052, 109,  1054, 110, 1485,  \n\t\t\t\t\t\t3235, 1056, 111,  1058, 112, 1489,  1060, 113, 1491,  1062, 114, 1493,  1064, 115, 1495,  \n\t\t\t\t\t\t1066, 116, 1497,  3229, 1068, 117,  1070, 118, 1501,  3227, 1072, 119,  1074, 120, 1505,  \n\t\t\t\t\t\t1076, 121, 1507,  3224, 1078, 122,  3223, 1080, 123,  3222, 1082, 124,  3221, 1084, 125,  \n\t\t\t\t\t\t1087, 127, 1518,  1089, 128, 1520,  3218, 1091, 129,  1093, 130, 1524,  1095, 131, 1526,  \n\t\t\t\t\t\t1097, 132, 1528,  1099, 133, 1530,  1101, 134, 1532,  3212, 1103, 135,  1105, 136, 1536,  \n\t\t\t\t\t\t3210, 1107, 137,  1109, 138, 1540,  1111, 139, 1542,  1113, 140, 1544,  1115, 141, 1546,  \n\t\t\t\t\t\t1117, 142, 1548,  3204, 1119, 143,  1121, 144, 1552,  1123, 145, 1554,  1125, 146, 1556,  \n\t\t\t\t\t\t1128, 148, 1559,  1130, 149, 1561,  1132, 150, 1563,  3197, 1134, 151,  1136, 152, 1567,  \n\t\t\t\t\t\t1138, 153, 1569,  1140, 154, 1571,  3193, 1142, 155,  1144, 156, 1575,  1146, 157, 1577,  \n\t\t\t\t\t\t1148, 158, 1579,  3189, 1150, 159,  1152, 160, 1583,  1154, 161, 1585,  3186, 1156, 162,  \n\t\t\t\t\t\t1158, 163, 1589,  1160, 164, 1591,  1162, 165, 1593,  3182, 1164, 166,  1166, 167, 1597,  \n\t\t\t\t\t\t1169, 169, 1600,  1171, 170, 1602,  1173, 171, 1604,  1175, 172, 1606,  1177, 173, 1608,  \n\t\t\t\t\t\t1179, 174, 1610,  1181, 175, 1612,  1183, 176, 1614,  1185, 177, 1616,  1187, 178, 1618,  \n\t\t\t\t\t\t1189, 179, 1620,  1191, 180, 1622,  1193, 181, 1624,  3167, 1195, 182,  1197, 183, 1628,  \n\t\t\t\t\t\t1199, 184, 1630,  1201, 185, 1632,  1203, 186, 1634,  1205, 187, 1636,  1207, 188, 1638,  \n\t\t\t\t\t\t1210, 190, 1641,  1212, 191, 1643,  1214, 192, 1645,  1216, 193, 1647,  1218, 194, 1649,  \n\t\t\t\t\t\t1220, 195, 1651,  1222, 196, 1653,  1224, 197, 1655,  1226, 198, 1657,  1228, 199, 1659,  \n\t\t\t\t\t\t1230, 200, 1661,  1232, 201, 1663,  1234, 202, 1665,  3147, 1236, 203,  1238, 204, 1669,  \n\t\t\t\t\t\t1240, 205, 1671,  1242, 206, 1673,  1244, 207, 1675,  1246, 208, 1677,  1248, 209, 1679,  \n\t\t\t\t\t\t1251, 211, 1682,  1253, 212, 1684,  1255, 213, 1686,  3137, 1257, 214,  1259, 215, 1690,  \n\t\t\t\t\t\t1261, 216, 1692,  3134, 1263, 217,  1265, 218, 1696,  1267, 219, 1698,  3131, 1269, 220,  \n\t\t\t\t\t\t1271, 221, 1702,  1273, 222, 1704,  1275, 223, 1706,  3127, 1277, 224,  1279, 225, 1710,  \n\t\t\t\t\t\t1281, 226, 1712,  1283, 227, 1714,  1285, 228, 1716,  1287, 229, 1718,  1289, 230, 1720,  \n\t\t\t\t\t\t1721, 660, 1290,  3119, 1722, 661,  1719, 659, 1724,  1725, 658, 1288,  1726, 662, 1727,  \n\t\t\t\t\t\t1717, 657, 1728,  1729, 656, 1286,  1730, 663, 1731,  1715, 655, 1732,  1733, 654, 1284,  \n\t\t\t\t\t\t3110, 1734, 664,  1713, 653, 1736,  1737, 652, 1282,  1738, 665, 1739,  1711, 651, 1740,  \n\t\t\t\t\t\t1741, 650, 1280,  1742, 666, 1743,  1709, 649, 1744,  1745, 648, 1278,  1746, 667, 1747,  \n\t\t\t\t\t\t1707, 647, 1748,  1749, 646, 1276,  1750, 668, 1751,  1705, 645, 1752,  1753, 644, 1274,  \n\t\t\t\t\t\t1754, 669, 1755,  1703, 643, 1756,  3093, 1757, 642,  3092, 1758, 670,  1701, 641, 1760,  \n\t\t\t\t\t\t1761, 640, 1270,  1762, 671, 1763,  1699, 639, 1764,  1765, 638, 1268,  1766, 672, 1767,  \n\t\t\t\t\t\t1697, 637, 1768,  1769, 636, 1266,  1770, 673, 1771,  1695, 635, 1772,  1773, 634, 1264,  \n\t\t\t\t\t\t1774, 674, 1775,  3079, 1693, 633,  1777, 632, 1262,  1778, 675, 1779,  1691, 631, 1780,  \n\t\t\t\t\t\t1781, 630, 1260,  1782, 676, 1783,  1689, 629, 1784,  3072, 1785, 628,  3071, 1786, 677,  \n\t\t\t\t\t\t3070, 1687, 627,  1789, 626, 1256,  1790, 678, 1791,  1685, 625, 1792,  1793, 624, 1254,  \n\t\t\t\t\t\t1794, 679, 1795,  1683, 623, 1796,  1797, 622, 1252,  1798, 680, 1799,  1681, 621, 1800,  \n\t\t\t\t\t\t1801, 619, 1249,  1802, 681, 1803,  1678, 618, 1804,  1805, 617, 1247,  1806, 682, 1807,  \n\t\t\t\t\t\t1676, 616, 1808,  1809, 615, 1245,  1810, 683, 1811,  1674, 614, 1812,  1813, 613, 1243,  \n\t\t\t\t\t\t1814, 684, 1815,  1672, 612, 1816,  1817, 611, 1241,  1818, 685, 1819,  1670, 610, 1820,  \n\t\t\t\t\t\t1821, 609, 1239,  1822, 686, 1823,  1668, 608, 1824,  1825, 607, 1237,  1826, 687, 1827,  \n\t\t\t\t\t\t1666, 606, 1828,  1829, 605, 1235,  1830, 688, 1831,  1664, 604, 1832,  1833, 603, 1233,  \n\t\t\t\t\t\t1834, 689, 1835,  1662, 602, 1836,  1837, 601, 1231,  1838, 690, 1839,  1660, 600, 1840,  \n\t\t\t\t\t\t1841, 599, 1229,  1842, 691, 1843,  3028, 1658, 598,  1845, 597, 1227,  1846, 692, 1847,  \n\t\t\t\t\t\t1656, 596, 1848,  1849, 595, 1225,  1850, 693, 1851,  1654, 594, 1852,  1853, 593, 1223,  \n\t\t\t\t\t\t1854, 694, 1855,  1652, 592, 1856,  1857, 591, 1221,  1858, 695, 1859,  1650, 590, 1860,  \n\t\t\t\t\t\t1861, 589, 1219,  1862, 696, 1863,  1648, 588, 1864,  3012, 1865, 587,  3011, 1866, 697,  \n\t\t\t\t\t\t1646, 586, 1868,  1869, 585, 1215,  1870, 698, 1871,  1644, 584, 1872,  1873, 583, 1213,  \n\t\t\t\t\t\t1874, 699, 1875,  1642, 582, 1876,  1877, 581, 1211,  1878, 700, 1879,  1640, 580, 1880,  \n\t\t\t\t\t\t1881, 578, 1208,  1882, 701, 1883,  1637, 577, 1884,  1885, 576, 1206,  2996, 1886, 702,  \n\t\t\t\t\t\t2995, 1635, 575,  1889, 574, 1204,  1890, 703, 1891,  1633, 573, 1892,  1893, 572, 1202,  \n\t\t\t\t\t\t1894, 704, 1895,  1631, 571, 1896,  1897, 570, 1200,  1898, 705, 1899,  1629, 569, 1900,  \n\t\t\t\t\t\t1901, 568, 1198,  1902, 706, 1903,  1627, 567, 1904,  1905, 566, 1196,  1906, 707, 1907,  \n\t\t\t\t\t\t2980, 1625, 565,  1909, 564, 1194,  1910, 708, 1911,  1623, 563, 1912,  1913, 562, 1192,  \n\t\t\t\t\t\t1914, 709, 1915,  1621, 561, 1916,  1917, 560, 1190,  1918, 710, 1919,  1619, 559, 1920,  \n\t\t\t\t\t\t1921, 558, 1188,  1922, 711, 1923,  1617, 557, 1924,  1925, 556, 1186,  1926, 712, 1927,  \n\t\t\t\t\t\t1615, 555, 1928,  1929, 554, 1184,  1930, 713, 1931,  2962, 1613, 553,  1933, 552, 1182,  \n\t\t\t\t\t\t1934, 714, 1935,  1611, 551, 1936,  1937, 550, 1180,  1938, 715, 1939,  1609, 549, 1940,  \n\t\t\t\t\t\t1941, 548, 1178,  1942, 716, 1943,  1607, 547, 1944,  2952, 1945, 546,  2951, 1946, 717,  \n\t\t\t\t\t\t1605, 545, 1948,  1949, 544, 1174,  1950, 718, 1951,  1603, 543, 1952,  1953, 542, 1172,  \n\t\t\t\t\t\t1954, 719, 1955,  1601, 541, 1956,  1957, 540, 1170,  1958, 720, 1959,  1599, 539, 1960,  \n\t\t\t\t\t\t1961, 537, 1167,  1962, 721, 1963,  1596, 536, 1964,  2937, 1965, 535,  2936, 1966, 722,  \n\t\t\t\t\t\t1594, 534, 1968,  1969, 533, 1163,  1970, 723, 1971,  1592, 532, 1972,  1973, 531, 1161,  \n\t\t\t\t\t\t2930, 1974, 724,  1590, 530, 1976,  1977, 529, 1159,  1978, 725, 1979,  1588, 528, 1980,  \n\t\t\t\t\t\t2925, 1981, 527,  2924, 1982, 726,  2923, 1586, 526,  1985, 525, 1155,  1986, 727, 1987,  \n\t\t\t\t\t\t1584, 524, 1988,  2919, 1989, 523,  1990, 728, 1991,  1582, 522, 1992,  1993, 521, 1151,  \n\t\t\t\t\t\t1994, 729, 1995,  2914, 1580, 520,  1997, 519, 1149,  1998, 730, 1999,  1578, 518, 2000,  \n\t\t\t\t\t\t2001, 517, 1147,  2002, 731, 2003,  1576, 516, 2004,  2005, 515, 1145,  2006, 732, 2007,  \n\t\t\t\t\t\t1574, 514, 2008,  2009, 513, 1143,  2010, 733, 2011,  2902, 1572, 512,  2013, 511, 1141,  \n\t\t\t\t\t\t2014, 734, 2015,  1570, 510, 2016,  2017, 509, 1139,  2018, 735, 2019,  1568, 508, 2020,  \n\t\t\t\t\t\t2021, 507, 1137,  2022, 736, 2023,  1566, 506, 2024,  2892, 2025, 505,  2026, 737, 2027,  \n\t\t\t\t\t\t1564, 504, 2028,  2889, 2029, 503,  2888, 2030, 738,  1562, 502, 2032,  2033, 501, 1131,  \n\t\t\t\t\t\t2034, 739, 2035,  1560, 500, 2036,  2037, 499, 1129,  2038, 740, 2039,  1558, 498, 2040,  \n\t\t\t\t\t\t2041, 496, 1126,  2042, 741, 2043,  1555, 495, 2044,  2045, 494, 1124,  2046, 742, 2047,  \n\t\t\t\t\t\t1553, 493, 2048,  2874, 2049, 492,  2873, 2050, 743,  2872, 1551, 491,  2871, 2053, 490,  \n\t\t\t\t\t\t2054, 744, 2055,  1549, 489, 2056,  2057, 488, 1118,  2058, 745, 2059,  1547, 487, 2060,  \n\t\t\t\t\t\t2061, 486, 1116,  2062, 746, 2063,  1545, 485, 2064,  2862, 2065, 484,  2861, 2066, 747,  \n\t\t\t\t\t\t2860, 1543, 483,  2069, 482, 1112,  2070, 748, 2071,  1541, 481, 2072,  2073, 480, 1110,  \n\t\t\t\t\t\t2855, 2074, 749,  2854, 1539, 479,  2077, 478, 1108,  2078, 750, 2079,  1537, 477, 2080,  \n\t\t\t\t\t\t2081, 476, 1106,  2082, 751, 2083,  1535, 475, 2084,  2085, 474, 1104,  2846, 2086, 752,  \n\t\t\t\t\t\t2845, 1533, 473,  2844, 2089, 472,  2090, 753, 2091,  1531, 471, 2092,  2093, 470, 1100,  \n\t\t\t\t\t\t2840, 2094, 754,  1529, 469, 2096,  2097, 468, 1098,  2098, 755, 2099,  1527, 467, 2100,  \n\t\t\t\t\t\t2835, 2101, 466,  2102, 756, 2103,  1525, 465, 2104,  2105, 464, 1094,  2106, 757, 2107,  \n\t\t\t\t\t\t2830, 1523, 463,  2829, 2109, 462,  2110, 758, 2111,  2827, 1521, 461,  2113, 460, 1090,  \n\t\t\t\t\t\t2114, 759, 2115,  1519, 459, 2116,  2117, 458, 1088,  2118, 760, 2119,  1517, 457, 2120,  \n\t\t\t\t\t\t2820, 2121, 455,  2819, 2122, 761,  2818, 1514, 454,  2817, 2125, 453,  2126, 762, 2127,  \n\t\t\t\t\t\t1512, 452, 2128,  2814, 2129, 451,  2813, 2130, 763,  2812, 1510, 450,  2133, 449, 1079,  \n\t\t\t\t\t\t2134, 764, 2135,  1508, 448, 2136,  2137, 447, 1077,  2807, 2138, 765,  1506, 446, 2140,  \n\t\t\t\t\t\t2141, 445, 1075,  2142, 766, 2143,  1504, 444, 2144,  2802, 2145, 443,  2801, 2146, 767,  \n\t\t\t\t\t\t1502, 442, 2148,  2149, 441, 1071,  2150, 768, 2151,  1500, 440, 2152,  2796, 2153, 439,  \n\t\t\t\t\t\t2795, 2154, 769,  1498, 438, 2156,  2157, 437, 1067,  2158, 770, 2159,  2791, 1496, 436,  \n\t\t\t\t\t\t2790, 2161, 435,  2162, 771, 2163,  1494, 434, 2164,  2787, 2165, 433,  2166, 772, 2167,  \n\t\t\t\t\t\t1492, 432, 2168,  2169, 431, 1061,  2170, 773, 2171,  2782, 1490, 430,  2781, 2173, 429,  \n\t\t\t\t\t\t2780, 2174, 774,  1488, 428, 2176,  2177, 427, 1057,  2777, 2178, 775,  2776, 1486, 426,  \n\t\t\t\t\t\t2181, 425, 1055,  2182, 776, 2183,  1484, 424, 2184,  2772, 2185, 423,  2771, 2186, 777,  \n\t\t\t\t\t\t2770, 1482, 422,  2189, 421, 1051,  2190, 778, 2191,  1480, 420, 2192,  2193, 419, 1049,  \n\t\t\t\t\t\t2194, 779, 2195,  1478, 418, 2196,  2197, 417, 1047,  2198, 780, 2199,  2761, 1476, 416,  \n\t\t\t\t\t\t2201, 414, 1044,  2759, 2202, 781,  1473, 413, 2204,  2205, 412, 1042,  2206, 782, 2207,  \n\t\t\t\t\t\t1471, 411, 2208,  2209, 410, 1040,  2210, 783, 2211,  1469, 409, 2212,  2213, 408, 1038,  \n\t\t\t\t\t\t2214, 784, 2215,  1467, 407, 2216,  2748, 2217, 406,  2218, 785, 2219,  1465, 405, 2220,  \n\t\t\t\t\t\t2221, 404, 1034,  2222, 786, 2223,  1463, 403, 2224,  2225, 402, 1032,  2226, 787, 2227,  \n\t\t\t\t\t\t1461, 401, 2228,  2229, 400, 1030,  2230, 788, 2231,  1459, 399, 2232,  2233, 398, 1028,  \n\t\t\t\t\t\t2234, 789, 2235,  2734, 1457, 397,  2237, 396, 1026,  2238, 790, 2239,  1455, 395, 2240,  \n\t\t\t\t\t\t2241, 394, 1024,  2242, 791, 2243,  1453, 393, 2244,  2245, 392, 1022,  2726, 2246, 792,  \n\t\t\t\t\t\t1451, 391, 2248,  2249, 390, 1020,  2250, 793, 2251,  1449, 389, 2252,  2253, 388, 1018,  \n\t\t\t\t\t\t2254, 794, 2255,  1447, 387, 2256,  2718, 2257, 386,  2258, 795, 2259,  2716, 1445, 385,  \n\t\t\t\t\t\t2261, 384, 1014,  2262, 796, 2263,  1443, 383, 2264,  2265, 382, 1012,  2266, 797, 2267,  \n\t\t\t\t\t\t1441, 381, 2268,  2269, 380, 1010,  2708, 2270, 798,  2707, 1439, 379,  2273, 378, 1008,  \n\t\t\t\t\t\t2274, 799, 2275,  1437, 377, 2276,  2277, 376, 1006,  2278, 800, 2279,  1435, 375, 2280,  \n\t\t\t\t\t\t2281, 373, 1003,  2282, 801, 2283,  1432, 372, 2284,  2285, 371, 1001,  2286, 802, 2287,  \n\t\t\t\t\t\t1430, 370, 2288,  2289, 369, 999,  2290, 803, 2291,  1428, 368, 2292,  2293, 367, 997,  \n\t\t\t\t\t\t2294, 804, 2295,  1426, 366, 2296,  2297, 365, 995,  2298, 805, 2299,  1424, 364, 2300,  \n\t\t\t\t\t\t2301, 363, 993,  2302, 806, 2303,  1422, 362, 2304,  2305, 361, 991,  2306, 807, 2307,  \n\t\t\t\t\t\t2680, 1420, 360,  2309, 359, 989,  2310, 808, 2311,  1418, 358, 2312,  2313, 357, 987,  \n\t\t\t\t\t\t2314, 809, 2315,  1416, 356, 2316,  2317, 355, 985,  2318, 810, 2319,  1414, 354, 2320,  \n\t\t\t\t\t\t2321, 353, 983,  2322, 811, 2323,  1412, 352, 2324,  2325, 351, 981,  2326, 812, 2327,  \n\t\t\t\t\t\t1410, 350, 2328,  2329, 349, 979,  2330, 813, 2331,  1408, 348, 2332,  2661, 2333, 347,  \n\t\t\t\t\t\t2660, 2334, 814,  1406, 346, 2336,  2337, 345, 975,  2338, 815, 2339,  1404, 344, 2340,  \n\t\t\t\t\t\t2341, 343, 973,  2342, 816, 2343,  1402, 342, 2344,  2345, 341, 971,  2346, 817, 2347,  \n\t\t\t\t\t\t1400, 340, 2348,  2649, 2349, 339,  2648, 2350, 818,  1398, 338, 2352,  2353, 337, 967,  \n\t\t\t\t\t\t2354, 819, 2355,  1396, 336, 2356,  2357, 335, 965,  2358, 820, 2359,  1394, 334, 2360,  \n\t\t\t\t\t\t2361, 332, 962,  2362, 821, 2363,  1391, 331, 2364,  2365, 330, 960,  2366, 822, 2367,  \n\t\t\t\t\t\t1389, 329, 2368,  2369, 328, 958,  2370, 823, 2371,  1387, 327, 2372,  2373, 326, 956,  \n\t\t\t\t\t\t2374, 824, 2375,  1385, 325, 2376,  2377, 324, 954,  2378, 825, 2379,  1383, 323, 2380,  \n\t\t\t\t\t\t2381, 322, 952,  2382, 826, 2383,  1381, 321, 2384,  2385, 320, 950,  2386, 827, 2387,  \n\t\t\t\t\t\t1379, 319, 2388,  2389, 318, 948,  2390, 828, 2391,  1377, 317, 2392,  2393, 316, 946,  \n\t\t\t\t\t\t2394, 829, 2395,  1375, 315, 2396,  2397, 314, 944,  2398, 830, 2399,  1373, 313, 2400,  \n\t\t\t\t\t\t2401, 312, 942,  2402, 831, 2403,  1371, 311, 2404,  2405, 310, 940,  2406, 832, 2407,  \n\t\t\t\t\t\t1369, 309, 2408,  2409, 308, 938,  2410, 833, 2411,  1367, 307, 2412,  2413, 306, 936,  \n\t\t\t\t\t\t2600, 2414, 834,  1365, 305, 2416,  2417, 304, 934,  2418, 835, 2419,  1363, 303, 2420,  \n\t\t\t\t\t\t2421, 302, 932,  2422, 836, 2423,  1361, 301, 2424,  2425, 300, 930,  2426, 837, 2427,  \n\t\t\t\t\t\t1359, 299, 2428,  2429, 298, 928,  2430, 838, 2431,  1357, 297, 2432,  2433, 296, 926,  \n\t\t\t\t\t\t2434, 839, 2435,  1355, 295, 2436,  2437, 294, 924,  2438, 840, 2439,  1353, 293, 2440,  \n\t\t\t\t\t\t2441, 291, 921,  2442, 841, 2443,  1350, 290, 2444,  2445, 288, 918,  2446, 842, 2447,  \n\t\t\t\t\t\t1347, 287, 2448,  2449, 285, 915,  2450, 843, 2451,  1344, 284, 2452,  2453, 282, 912,  \n\t\t\t\t\t\t2570, 2454, 844,  2569, 1341, 281,  2457, 279, 909,  2458, 845, 2459,  1338, 278, 2460,  \n\t\t\t\t\t\t2461, 276, 906,  2462, 846, 2463,  1335, 275, 2464,  2465, 273, 903,  2466, 847, 2467,  \n\t\t\t\t\t\t1332, 272, 2468,  2469, 270, 900,  2470, 848, 2471,  1329, 269, 2472,  2473, 267, 897,  \n\t\t\t\t\t\t2474, 849, 2475,  1326, 266, 2476,  2553, 2477, 264,  2552, 2478, 850,  1323, 263, 2480,  \n\t\t\t\t\t\t2550, 2481, 261,  2482, 851, 2483,  1320, 260, 2484,  2547, 2485, 258,  2486, 852, 2487,  \n\t\t\t\t\t\t1317, 257, 2488,  2544, 2489, 255,  2490, 853, 2491,  2542, 1314, 254,  2493, 252, 882,  \n\t\t\t\t\t\t2494, 854, 2495,  1311, 251, 2496,  2497, 249, 879,  2498, 855, 2499,  1308, 248, 2500,  \n\t\t\t\t\t\t2535, 2501, 246,  2502, 856, 2503,  1305, 245, 2504,  2505, 243, 873,  2506, 857, 2507,  \n\t\t\t\t\t\t2530, 1302, 242,  2509, 240, 870,  2510, 858, 2511,  1299, 239, 2512,  2526, 2513, 237,  \n\t\t\t\t\t\t2514, 859, 2515,  1296, 236, 2516,  2523, 2517, 234,  2518, 860, 2519,  2521, 1293, 233,  \n\t\t\t\t\t\t2521, 2520, 860,  232, 862, 2521,  862, 1, 1293,  2522, 2519, 231,  1292, 2522, 861,  \n\t\t\t\t\t\t232, 2518, 2522,  2523, 864, 21,  231, 2519, 2523,  2519, 860, 2517,  2524, 2516, 859,  \n\t\t\t\t\t\t865, 2524, 2514,  2, 1296, 2524,  1293, 2525, 2515,  1295, 2525, 1293,  235, 2514, 2525,  \n\t\t\t\t\t\t863, 2526, 867,  233, 2515, 2526,  2515, 859, 2513,  2527, 2512, 858,  868, 2527, 2510,  \n\t\t\t\t\t\t3, 1299, 2527,  2528, 2511, 236,  1298, 2528, 1296,  238, 2510, 2528,  2529, 870, 23,  \n\t\t\t\t\t\t2511, 2529, 866,  858, 2509, 2529,  2506, 2530, 2508,  241, 871, 2530,  871, 4, 1302,  \n\t\t\t\t\t\t2531, 2507, 239,  1301, 2531, 1299,  1301, 241, 2506,  2532, 873, 24,  2507, 2532, 869,  \n\t\t\t\t\t\t857, 2505, 2532,  2533, 2504, 856,  874, 2533, 2502,  5, 1305, 2533,  1302, 2534, 2503,  \n\t\t\t\t\t\t1304, 2534, 1302,  244, 2502, 2534,  872, 2535, 876,  242, 2503, 2535,  2503, 856, 2501,  \n\t\t\t\t\t\t2536, 2500, 855,  877, 2536, 2498,  6, 1308, 2536,  2537, 2499, 245,  1307, 2537, 1305,  \n\t\t\t\t\t\t247, 2498, 2537,  2538, 879, 26,  2499, 2538, 875,  855, 2497, 2538,  2539, 2496, 854,  \n\t\t\t\t\t\t880, 2539, 2494,  7, 1311, 2539,  1308, 2540, 2495,  6, 1310, 2540,  250, 2494, 2540,  \n\t\t\t\t\t\t2541, 882, 27,  2495, 2541, 878,  854, 2493, 2541,  2542, 2492, 853,  883, 2542, 2490,  \n\t\t\t\t\t\t8, 1314, 2542,  2543, 2491, 251,  1313, 2543, 1311,  253, 2490, 2543,  881, 2544, 885,  \n\t\t\t\t\t\t251, 2491, 2544,  2491, 853, 2489,  2545, 2488, 852,  886, 2545, 2486,  9, 1317, 2545,  \n\t\t\t\t\t\t1314, 2546, 2487,  1316, 2546, 1314,  256, 2486, 2546,  884, 2547, 888,  254, 2487, 2547,  \n\t\t\t\t\t\t2487, 852, 2485,  2482, 2548, 2484,  889, 2548, 2482,  889, 10, 1320,  2549, 2483, 257,  \n\t\t\t\t\t\t1319, 2549, 1317,  259, 2482, 2549,  887, 2550, 891,  2483, 2550, 887,  851, 2481, 2550,  \n\t\t\t\t\t\t2551, 2480, 850,  892, 2551, 2478,  892, 11, 1323,  1320, 2552, 2479,  10, 1322, 2552,  \n\t\t\t\t\t\t1322, 262, 2478,  2553, 894, 31,  2479, 2553, 890,  2479, 850, 2477,  2554, 2476, 849,  \n\t\t\t\t\t\t895, 2554, 2474,  12, 1326, 2554,  2555, 2475, 263,  1325, 2555, 1323,  265, 2474, 2555,  \n\t\t\t\t\t\t2556, 897, 32,  2475, 2556, 893,  849, 2473, 2556,  2557, 2472, 848,  898, 2557, 2470,  \n\t\t\t\t\t\t13, 1329, 2557,  2558, 2471, 266,  1328, 2558, 1326,  268, 2470, 2558,  2559, 900, 33,  \n\t\t\t\t\t\t2471, 2559, 896,  848, 2469, 2559,  2560, 2468, 847,  901, 2560, 2466,  14, 1332, 2560,  \n\t\t\t\t\t\t2561, 2467, 269,  1331, 2561, 1329,  271, 2466, 2561,  2562, 903, 34,  2467, 2562, 899,  \n\t\t\t\t\t\t847, 2465, 2562,  2563, 2464, 846,  904, 2563, 2462,  15, 1335, 2563,  2564, 2463, 272,  \n\t\t\t\t\t\t1334, 2564, 1332,  274, 2462, 2564,  2565, 906, 35,  2463, 2565, 902,  846, 2461, 2565,  \n\t\t\t\t\t\t2566, 2460, 845,  907, 2566, 2458,  16, 1338, 2566,  2567, 2459, 275,  1337, 2567, 1335,  \n\t\t\t\t\t\t277, 2458, 2567,  905, 2568, 909,  2459, 2568, 905,  845, 2457, 2568,  2454, 2569, 2456,  \n\t\t\t\t\t\t910, 2569, 2454,  910, 17, 1341,  2570, 2455, 278,  16, 1340, 2570,  1340, 280, 2454,  \n\t\t\t\t\t\t2571, 912, 37,  2455, 2571, 908,  2455, 844, 2453,  2572, 2452, 843,  913, 2572, 2450,  \n\t\t\t\t\t\t18, 1344, 2572,  2573, 2451, 281,  1343, 2573, 1341,  283, 2450, 2573,  2574, 915, 38,  \n\t\t\t\t\t\t2451, 2574, 911,  843, 2449, 2574,  2575, 2448, 842,  916, 2575, 2446,  19, 1347, 2575,  \n\t\t\t\t\t\t2576, 2447, 284,  1346, 2576, 1344,  286, 2446, 2576,  2577, 918, 39,  2447, 2577, 914,  \n\t\t\t\t\t\t842, 2445, 2577,  2578, 2444, 841,  919, 2578, 2442,  919, 20, 1350,  2579, 2443, 287,  \n\t\t\t\t\t\t1349, 2579, 1347,  289, 2442, 2579,  2580, 921, 40,  2443, 2580, 917,  841, 2441, 2580,  \n\t\t\t\t\t\t2581, 2440, 840,  1294, 2581, 2438,  22, 1353, 2581,  2582, 2439, 292,  864, 2582, 922,  \n\t\t\t\t\t\t234, 2438, 2582,  2583, 924, 42,  2439, 2583, 1352,  840, 2437, 2583,  2584, 2436, 839,  \n\t\t\t\t\t\t1297, 2584, 2434,  23, 1355, 2584,  2585, 2435, 293,  867, 2585, 1353,  237, 2434, 2585,  \n\t\t\t\t\t\t2586, 926, 43,  2435, 2586, 923,  839, 2433, 2586,  2587, 2432, 838,  1300, 2587, 2430,  \n\t\t\t\t\t\t24, 1357, 2587,  2588, 2431, 295,  870, 2588, 1355,  240, 2430, 2588,  2589, 928, 44,  \n\t\t\t\t\t\t2431, 2589, 925,  838, 2429, 2589,  2590, 2428, 837,  1303, 2590, 2426,  25, 1359, 2590,  \n\t\t\t\t\t\t2591, 2427, 297,  873, 2591, 1357,  243, 2426, 2591,  2592, 930, 45,  2427, 2592, 927,  \n\t\t\t\t\t\t837, 2425, 2592,  2593, 2424, 836,  1306, 2593, 2422,  26, 1361, 2593,  2594, 2423, 299,  \n\t\t\t\t\t\t876, 2594, 1359,  246, 2422, 2594,  2595, 932, 46,  2423, 2595, 929,  836, 2421, 2595,  \n\t\t\t\t\t\t2596, 2420, 835,  1309, 2596, 2418,  27, 1363, 2596,  2597, 2419, 301,  879, 2597, 1361,  \n\t\t\t\t\t\t249, 2418, 2597,  2598, 934, 47,  2419, 2598, 931,  835, 2417, 2598,  2414, 2599, 2416,  \n\t\t\t\t\t\t1312, 2599, 2414,  28, 1365, 2599,  2600, 2415, 303,  882, 2600, 1363,  252, 2414, 2600,  \n\t\t\t\t\t\t933, 2601, 936,  2415, 2601, 933,  2415, 834, 2413,  2602, 2412, 833,  1315, 2602, 2410,  \n\t\t\t\t\t\t29, 1367, 2602,  2603, 2411, 305,  885, 2603, 1365,  255, 2410, 2603,  2604, 938, 49,  \n\t\t\t\t\t\t2411, 2604, 935,  833, 2409, 2604,  2605, 2408, 832,  1318, 2605, 2406,  30, 1369, 2605,  \n\t\t\t\t\t\t2606, 2407, 307,  888, 2606, 1367,  258, 2406, 2606,  2607, 940, 50,  2407, 2607, 937,  \n\t\t\t\t\t\t832, 2405, 2607,  2608, 2404, 831,  1321, 2608, 2402,  31, 1371, 2608,  2609, 2403, 309,  \n\t\t\t\t\t\t891, 2609, 1369,  261, 2402, 2609,  2610, 942, 51,  2403, 2610, 939,  831, 2401, 2610,  \n\t\t\t\t\t\t2611, 2400, 830,  1324, 2611, 2398,  32, 1373, 2611,  2612, 2399, 311,  894, 2612, 1371,  \n\t\t\t\t\t\t264, 2398, 2612,  2613, 944, 52,  2399, 2613, 941,  830, 2397, 2613,  2614, 2396, 829,  \n\t\t\t\t\t\t1327, 2614, 2394,  33, 1375, 2614,  2615, 2395, 313,  897, 2615, 1373,  267, 2394, 2615,  \n\t\t\t\t\t\t2616, 946, 53,  2395, 2616, 943,  829, 2393, 2616,  2617, 2392, 828,  1330, 2617, 2390,  \n\t\t\t\t\t\t1330, 34, 1377,  2618, 2391, 315,  900, 2618, 1375,  270, 2390, 2618,  2619, 948, 54,  \n\t\t\t\t\t\t2391, 2619, 945,  828, 2389, 2619,  2620, 2388, 827,  1333, 2620, 2386,  35, 1379, 2620,  \n\t\t\t\t\t\t1377, 2621, 2387,  903, 2621, 1377,  273, 2386, 2621,  2622, 950, 55,  317, 2387, 2622,  \n\t\t\t\t\t\t827, 2385, 2622,  2623, 2384, 826,  1336, 2623, 2382,  36, 1381, 2623,  2624, 2383, 319,  \n\t\t\t\t\t\t906, 2624, 1379,  276, 2382, 2624,  2625, 952, 56,  2383, 2625, 949,  826, 2381, 2625,  \n\t\t\t\t\t\t2626, 2380, 825,  1339, 2626, 2378,  37, 1383, 2626,  1381, 2627, 2379,  36, 909, 2627,  \n\t\t\t\t\t\t279, 2378, 2627,  2628, 954, 57,  2379, 2628, 951,  825, 2377, 2628,  2629, 2376, 824,  \n\t\t\t\t\t\t1342, 2629, 2374,  38, 1385, 2629,  2630, 2375, 323,  912, 2630, 1383,  282, 2374, 2630,  \n\t\t\t\t\t\t2631, 956, 58,  2375, 2631, 953,  824, 2373, 2631,  2632, 2372, 823,  1345, 2632, 2370,  \n\t\t\t\t\t\t39, 1387, 2632,  2633, 2371, 325,  915, 2633, 1385,  285, 2370, 2633,  2634, 958, 59,  \n\t\t\t\t\t\t2371, 2634, 955,  823, 2369, 2634,  2635, 2368, 822,  1348, 2635, 2366,  40, 1389, 2635,  \n\t\t\t\t\t\t2636, 2367, 327,  918, 2636, 1387,  288, 2366, 2636,  2637, 960, 60,  2367, 2637, 957,  \n\t\t\t\t\t\t822, 2365, 2637,  2638, 2364, 821,  1351, 2638, 2362,  41, 1391, 2638,  2639, 2363, 329,  \n\t\t\t\t\t\t921, 2639, 1389,  291, 2362, 2639,  2640, 962, 61,  2363, 2640, 959,  821, 2361, 2640,  \n\t\t\t\t\t\t2641, 2360, 820,  1354, 2641, 2358,  43, 1394, 2641,  2642, 2359, 333,  924, 2642, 963,  \n\t\t\t\t\t\t294, 2358, 2642,  2643, 965, 63,  2359, 2643, 1393,  820, 2357, 2643,  2644, 2356, 819,  \n\t\t\t\t\t\t1356, 2644, 2354,  1356, 44, 1396,  2645, 2355, 334,  926, 2645, 1394,  296, 2354, 2645,  \n\t\t\t\t\t\t2646, 967, 64,  2355, 2646, 964,  819, 2353, 2646,  2647, 2352, 818,  1358, 2647, 2350,  \n\t\t\t\t\t\t45, 1398, 2647,  1396, 2648, 2351,  44, 928, 2648,  298, 2350, 2648,  966, 2649, 969,  \n\t\t\t\t\t\t336, 2351, 2649,  2351, 818, 2349,  2650, 2348, 817,  1360, 2650, 2346,  46, 1400, 2650,  \n\t\t\t\t\t\t2651, 2347, 338,  930, 2651, 1398,  300, 2346, 2651,  2652, 971, 66,  2347, 2652, 968,  \n\t\t\t\t\t\t817, 2345, 2652,  2653, 2344, 816,  1362, 2653, 2342,  47, 1402, 2653,  2654, 2343, 340,  \n\t\t\t\t\t\t932, 2654, 1400,  302, 2342, 2654,  2655, 973, 67,  2343, 2655, 970,  816, 2341, 2655,  \n\t\t\t\t\t\t2656, 2340, 815,  1364, 2656, 2338,  48, 1404, 2656,  2657, 2339, 342,  934, 2657, 1402,  \n\t\t\t\t\t\t304, 2338, 2657,  2658, 975, 68,  2339, 2658, 972,  815, 2337, 2658,  2659, 2336, 814,  \n\t\t\t\t\t\t1366, 2659, 2334,  49, 1406, 2659,  1404, 2660, 2335,  48, 936, 2660,  306, 2334, 2660,  \n\t\t\t\t\t\t974, 2661, 977,  344, 2335, 2661,  2335, 814, 2333,  2662, 2332, 813,  1368, 2662, 2330,  \n\t\t\t\t\t\t50, 1408, 2662,  2663, 2331, 346,  938, 2663, 1406,  308, 2330, 2663,  2664, 979, 70,  \n\t\t\t\t\t\t2331, 2664, 976,  813, 2329, 2664,  2665, 2328, 812,  1370, 2665, 2326,  51, 1410, 2665,  \n\t\t\t\t\t\t2666, 2327, 348,  940, 2666, 1408,  310, 2326, 2666,  978, 2667, 981,  2327, 2667, 978,  \n\t\t\t\t\t\t812, 2325, 2667,  2668, 2324, 811,  1372, 2668, 2322,  52, 1412, 2668,  2669, 2323, 350,  \n\t\t\t\t\t\t942, 2669, 1410,  312, 2322, 2669,  2670, 983, 72,  2323, 2670, 980,  811, 2321, 2670,  \n\t\t\t\t\t\t2671, 2320, 810,  1374, 2671, 2318,  53, 1414, 2671,  2672, 2319, 352,  944, 2672, 1412,  \n\t\t\t\t\t\t314, 2318, 2672,  2673, 985, 73,  2319, 2673, 982,  810, 2317, 2673,  2674, 2316, 809,  \n\t\t\t\t\t\t1376, 2674, 2314,  54, 1416, 2674,  2675, 2315, 354,  946, 2675, 1414,  316, 2314, 2675,  \n\t\t\t\t\t\t2676, 987, 74,  2315, 2676, 984,  809, 2313, 2676,  2677, 2312, 808,  1378, 2677, 2310,  \n\t\t\t\t\t\t55, 1418, 2677,  2678, 2311, 356,  948, 2678, 1416,  318, 2310, 2678,  986, 2679, 989,  \n\t\t\t\t\t\t356, 2311, 2679,  808, 2309, 2679,  2680, 2308, 807,  1380, 2680, 2306,  1380, 56, 1420,  \n\t\t\t\t\t\t1418, 2681, 2307,  55, 950, 2681,  320, 2306, 2681,  2682, 991, 76,  2307, 2682, 988,  \n\t\t\t\t\t\t807, 2305, 2682,  2683, 2304, 806,  1382, 2683, 2302,  57, 1422, 2683,  2684, 2303, 360,  \n\t\t\t\t\t\t952, 2684, 1420,  322, 2302, 2684,  2685, 993, 77,  2303, 2685, 990,  806, 2301, 2685,  \n\t\t\t\t\t\t2686, 2300, 805,  1384, 2686, 2298,  58, 1424, 2686,  2687, 2299, 362,  954, 2687, 1422,  \n\t\t\t\t\t\t324, 2298, 2687,  2688, 995, 78,  2299, 2688, 992,  805, 2297, 2688,  2689, 2296, 804,  \n\t\t\t\t\t\t1386, 2689, 2294,  59, 1426, 2689,  2690, 2295, 364,  956, 2690, 1424,  326, 2294, 2690,  \n\t\t\t\t\t\t2691, 997, 79,  2295, 2691, 994,  804, 2293, 2691,  2692, 2292, 803,  1388, 2692, 2290,  \n\t\t\t\t\t\t60, 1428, 2692,  2693, 2291, 366,  958, 2693, 1426,  328, 2290, 2693,  2694, 999, 80,  \n\t\t\t\t\t\t2291, 2694, 996,  803, 2289, 2694,  2695, 2288, 802,  1390, 2695, 2286,  61, 1430, 2695,  \n\t\t\t\t\t\t2696, 2287, 368,  960, 2696, 1428,  330, 2286, 2696,  2697, 1001, 81,  2287, 2697, 998,  \n\t\t\t\t\t\t802, 2285, 2697,  2698, 2284, 801,  1392, 2698, 2282,  62, 1432, 2698,  2699, 2283, 370,  \n\t\t\t\t\t\t962, 2699, 1430,  332, 2282, 2699,  2700, 1003, 82,  2283, 2700, 1000,  801, 2281, 2700,  \n\t\t\t\t\t\t2701, 2280, 800,  1395, 2701, 2278,  64, 1435, 2701,  2702, 2279, 374,  965, 2702, 1004,  \n\t\t\t\t\t\t335, 2278, 2702,  2703, 1006, 84,  2279, 2703, 1434,  800, 2277, 2703,  2704, 2276, 799,  \n\t\t\t\t\t\t1397, 2704, 2274,  65, 1437, 2704,  2705, 2275, 375,  967, 2705, 1435,  337, 2274, 2705,  \n\t\t\t\t\t\t2706, 1008, 85,  2275, 2706, 1005,  799, 2273, 2706,  2707, 2272, 798,  339, 1399, 2707,  \n\t\t\t\t\t\t66, 1439, 2707,  2708, 2271, 377,  969, 2708, 1437,  969, 339, 2270,  2709, 1010, 86,  \n\t\t\t\t\t\t2271, 2709, 1007,  798, 2269, 2709,  2710, 2268, 797,  1401, 2710, 2266,  67, 1441, 2710,  \n\t\t\t\t\t\t2711, 2267, 379,  971, 2711, 1439,  341, 2266, 2711,  2712, 1012, 87,  2267, 2712, 1009,  \n\t\t\t\t\t\t797, 2265, 2712,  2713, 2264, 796,  1403, 2713, 2262,  68, 1443, 2713,  2714, 2263, 381,  \n\t\t\t\t\t\t973, 2714, 1441,  343, 2262, 2714,  2715, 1014, 88,  2263, 2715, 1011,  796, 2261, 2715,  \n\t\t\t\t\t\t2716, 2260, 795,  1405, 2716, 2258,  1405, 69, 1445,  1443, 2717, 2259,  68, 975, 2717,  \n\t\t\t\t\t\t345, 2258, 2717,  1013, 2718, 1016,  383, 2259, 2718,  2259, 795, 2257,  2719, 2256, 794,  \n\t\t\t\t\t\t1407, 2719, 2254,  70, 1447, 2719,  2720, 2255, 385,  977, 2720, 1445,  347, 2254, 2720,  \n\t\t\t\t\t\t1015, 2721, 1018,  2255, 2721, 1015,  794, 2253, 2721,  2722, 2252, 793,  1409, 2722, 2250,  \n\t\t\t\t\t\t71, 1449, 2722,  2723, 2251, 387,  979, 2723, 1447,  349, 2250, 2723,  2724, 1020, 91,  \n\t\t\t\t\t\t2251, 2724, 1017,  793, 2249, 2724,  2725, 2248, 792,  1411, 2725, 2246,  72, 1451, 2725,  \n\t\t\t\t\t\t2726, 2247, 389,  71, 981, 2726,  351, 2246, 2726,  2727, 1022, 92,  2247, 2727, 1019,  \n\t\t\t\t\t\t792, 2245, 2727,  2728, 2244, 791,  1413, 2728, 2242,  73, 1453, 2728,  2729, 2243, 391,  \n\t\t\t\t\t\t983, 2729, 1451,  353, 2242, 2729,  1021, 2730, 1024,  391, 2243, 2730,  791, 2241, 2730,  \n\t\t\t\t\t\t2731, 2240, 790,  1415, 2731, 2238,  74, 1455, 2731,  2732, 2239, 393,  985, 2732, 1453,  \n\t\t\t\t\t\t355, 2238, 2732,  2733, 1026, 94,  2239, 2733, 1023,  790, 2237, 2733,  2734, 2236, 789,  \n\t\t\t\t\t\t1417, 2734, 2234,  1417, 75, 1457,  1455, 2735, 2235,  74, 987, 2735,  357, 2234, 2735,  \n\t\t\t\t\t\t2736, 1028, 95,  395, 2235, 2736,  789, 2233, 2736,  2737, 2232, 788,  1419, 2737, 2230,  \n\t\t\t\t\t\t76, 1459, 2737,  2738, 2231, 397,  75, 989, 2738,  359, 2230, 2738,  2739, 1030, 96,  \n\t\t\t\t\t\t2231, 2739, 1027,  788, 2229, 2739,  2740, 2228, 787,  1421, 2740, 2226,  77, 1461, 2740,  \n\t\t\t\t\t\t2741, 2227, 399,  991, 2741, 1459,  361, 2226, 2741,  2742, 1032, 97,  2227, 2742, 1029,  \n\t\t\t\t\t\t787, 2225, 2742,  2743, 2224, 786,  1423, 2743, 2222,  78, 1463, 2743,  2744, 2223, 401,  \n\t\t\t\t\t\t993, 2744, 1461,  363, 2222, 2744,  2745, 1034, 98,  2223, 2745, 1031,  786, 2221, 2745,  \n\t\t\t\t\t\t2746, 2220, 785,  1425, 2746, 2218,  79, 1465, 2746,  2747, 2219, 403,  995, 2747, 1463,  \n\t\t\t\t\t\t365, 2218, 2747,  2748, 1036, 99,  2219, 2748, 1033,  785, 2217, 2748,  2749, 2216, 784,  \n\t\t\t\t\t\t1427, 2749, 2214,  80, 1467, 2749,  2750, 2215, 405,  997, 2750, 1465,  367, 2214, 2750,  \n\t\t\t\t\t\t2751, 1038, 100,  2215, 2751, 1035,  784, 2213, 2751,  2752, 2212, 783,  1429, 2752, 2210,  \n\t\t\t\t\t\t81, 1469, 2752,  2753, 2211, 407,  999, 2753, 1467,  369, 2210, 2753,  2754, 1040, 101,  \n\t\t\t\t\t\t2211, 2754, 1037,  783, 2209, 2754,  2755, 2208, 782,  1431, 2755, 2206,  82, 1471, 2755,  \n\t\t\t\t\t\t2756, 2207, 409,  1001, 2756, 1469,  371, 2206, 2756,  2757, 1042, 102,  2207, 2757, 1039,  \n\t\t\t\t\t\t782, 2205, 2757,  2758, 2204, 781,  1433, 2758, 2202,  83, 1473, 2758,  2759, 2203, 411,  \n\t\t\t\t\t\t1003, 2759, 1471,  1003, 373, 2202,  1041, 2760, 1044,  411, 2203, 2760,  2203, 781, 2201,  \n\t\t\t\t\t\t2198, 2761, 2200,  376, 1436, 2761,  85, 1476, 2761,  2762, 2199, 415,  1006, 2762, 1045,  \n\t\t\t\t\t\t1006, 376, 2198,  1475, 2763, 1047,  2199, 2763, 1475,  780, 2197, 2763,  2764, 2196, 779,  \n\t\t\t\t\t\t1438, 2764, 2194,  86, 1478, 2764,  2765, 2195, 416,  1008, 2765, 1476,  378, 2194, 2765,  \n\t\t\t\t\t\t1046, 2766, 1049,  2195, 2766, 1046,  779, 2193, 2766,  2767, 2192, 778,  1440, 2767, 2190,  \n\t\t\t\t\t\t87, 1480, 2767,  2768, 2191, 418,  1010, 2768, 1478,  380, 2190, 2768,  2769, 1051, 107,  \n\t\t\t\t\t\t2191, 2769, 1048,  778, 2189, 2769,  2186, 2770, 2188,  382, 1442, 2770,  88, 1482, 2770,  \n\t\t\t\t\t\t2771, 2187, 420,  1012, 2771, 1480,  1012, 382, 2186,  1050, 2772, 1053,  420, 2187, 2772,  \n\t\t\t\t\t\t2187, 777, 2185,  2773, 2184, 776,  1444, 2773, 2182,  89, 1484, 2773,  2774, 2183, 422,  \n\t\t\t\t\t\t1014, 2774, 1482,  384, 2182, 2774,  1052, 2775, 1055,  2183, 2775, 1052,  776, 2181, 2775,  \n\t\t\t\t\t\t2178, 2776, 2180,  386, 1446, 2776,  1446, 90, 1486,  1484, 2777, 2179,  89, 1016, 2777,  \n\t\t\t\t\t\t1016, 386, 2178,  1054, 2778, 1057,  424, 2179, 2778,  2179, 775, 2177,  2779, 2176, 774,  \n\t\t\t\t\t\t1448, 2779, 2174,  91, 1488, 2779,  2780, 2175, 426,  1018, 2780, 1486,  388, 2174, 2780,  \n\t\t\t\t\t\t1056, 2781, 1059,  2175, 2781, 1056,  2175, 774, 2173,  2782, 2172, 773,  1450, 2782, 2170,  \n\t\t\t\t\t\t1450, 92, 1490,  2783, 2171, 428,  1020, 2783, 1488,  390, 2170, 2783,  2784, 1061, 112,  \n\t\t\t\t\t\t2171, 2784, 1058,  773, 2169, 2784,  2785, 2168, 772,  1452, 2785, 2166,  93, 1492, 2785,  \n\t\t\t\t\t\t1490, 2786, 2167,  1022, 2786, 1490,  392, 2166, 2786,  1060, 2787, 1063,  430, 2167, 2787,  \n\t\t\t\t\t\t772, 2165, 2787,  2788, 2164, 771,  1454, 2788, 2162,  94, 1494, 2788,  2789, 2163, 432,  \n\t\t\t\t\t\t93, 1024, 2789,  394, 2162, 2789,  2790, 1065, 114,  2163, 2790, 1062,  2163, 771, 2161,  \n\t\t\t\t\t\t2791, 2160, 770,  1456, 2791, 2158,  1456, 95, 1496,  2792, 2159, 434,  1026, 2792, 1494,  \n\t\t\t\t\t\t396, 2158, 2792,  2793, 1067, 115,  2159, 2793, 1064,  770, 2157, 2793,  2154, 2794, 2156,  \n\t\t\t\t\t\t1458, 2794, 2154,  96, 1498, 2794,  1496, 2795, 2155,  95, 1028, 2795,  1028, 398, 2154,  \n\t\t\t\t\t\t2796, 1069, 116,  436, 2155, 2796,  2155, 769, 2153,  2797, 2152, 768,  1460, 2797, 2150,  \n\t\t\t\t\t\t97, 1500, 2797,  2798, 2151, 438,  1030, 2798, 1498,  400, 2150, 2798,  2799, 1071, 117,  \n\t\t\t\t\t\t2151, 2799, 1068,  768, 2149, 2799,  2800, 2148, 767,  1462, 2800, 2146,  98, 1502, 2800,  \n\t\t\t\t\t\t2801, 2147, 440,  1032, 2801, 1500,  1032, 402, 2146,  1070, 2802, 1073,  2147, 2802, 1070,  \n\t\t\t\t\t\t2147, 767, 2145,  2803, 2144, 766,  1464, 2803, 2142,  99, 1504, 2803,  2804, 2143, 442,  \n\t\t\t\t\t\t1034, 2804, 1502,  404, 2142, 2804,  2805, 1075, 119,  2143, 2805, 1072,  766, 2141, 2805,  \n\t\t\t\t\t\t2806, 2140, 765,  406, 1466, 2806,  1466, 100, 1506,  2807, 2139, 444,  99, 1036, 2807,  \n\t\t\t\t\t\t1036, 406, 2138,  2808, 1077, 120,  2139, 2808, 1074,  765, 2137, 2808,  2809, 2136, 764,  \n\t\t\t\t\t\t1468, 2809, 2134,  101, 1508, 2809,  2810, 2135, 446,  1038, 2810, 1506,  408, 2134, 2810,  \n\t\t\t\t\t\t2811, 1079, 121,  2135, 2811, 1076,  764, 2133, 2811,  2130, 2812, 2132,  410, 1470, 2812,  \n\t\t\t\t\t\t102, 1510, 2812,  2813, 2131, 448,  1040, 2813, 1508,  1040, 410, 2130,  1078, 2814, 1081,  \n\t\t\t\t\t\t448, 2131, 2814,  2131, 763, 2129,  2815, 2128, 762,  1472, 2815, 2126,  103, 1512, 2815,  \n\t\t\t\t\t\t2816, 2127, 450,  1042, 2816, 1510,  412, 2126, 2816,  1080, 2817, 1083,  2127, 2817, 1080,  \n\t\t\t\t\t\t762, 2125, 2817,  2122, 2818, 2124,  414, 1474, 2818,  1474, 104, 1514,  1512, 2819, 2123,  \n\t\t\t\t\t\t103, 1044, 2819,  1044, 414, 2122,  1082, 2820, 1085,  452, 2123, 2820,  2123, 761, 2121,  \n\t\t\t\t\t\t2821, 2120, 760,  1477, 2821, 2118,  106, 1517, 2821,  2822, 2119, 456,  1047, 2822, 1086,  \n\t\t\t\t\t\t417, 2118, 2822,  2823, 1088, 126,  2119, 2823, 1516,  760, 2117, 2823,  2824, 2116, 759,  \n\t\t\t\t\t\t1479, 2824, 2114,  107, 1519, 2824,  2825, 2115, 457,  1049, 2825, 1517,  419, 2114, 2825,  \n\t\t\t\t\t\t2826, 1090, 127,  2115, 2826, 1087,  759, 2113, 2826,  2110, 2827, 2112,  1481, 2827, 2110,  \n\t\t\t\t\t\t108, 1521, 2827,  1519, 2828, 2111,  107, 1051, 2828,  421, 2110, 2828,  1089, 2829, 1092,  \n\t\t\t\t\t\t459, 2111, 2829,  2111, 758, 2109,  2106, 2830, 2108,  423, 1483, 2830,  1483, 109, 1523,  \n\t\t\t\t\t\t1521, 2831, 2107,  108, 1053, 2831,  1053, 423, 2106,  2832, 1094, 129,  2107, 2832, 1091,  \n\t\t\t\t\t\t757, 2105, 2832,  2833, 2104, 756,  1485, 2833, 2102,  110, 1525, 2833,  2834, 2103, 463,  \n\t\t\t\t\t\t1055, 2834, 1523,  425, 2102, 2834,  1093, 2835, 1096,  2103, 2835, 1093,  2103, 756, 2101,  \n\t\t\t\t\t\t2836, 2100, 755,  1487, 2836, 2098,  111, 1527, 2836,  2837, 2099, 465,  1057, 2837, 1525,  \n\t\t\t\t\t\t427, 2098, 2837,  2838, 1098, 131,  2099, 2838, 1095,  755, 2097, 2838,  2094, 2839, 2096,  \n\t\t\t\t\t\t429, 1489, 2839,  112, 1529, 2839,  1527, 2840, 2095,  111, 1059, 2840,  1059, 429, 2094,  \n\t\t\t\t\t\t2841, 1100, 132,  467, 2095, 2841,  2095, 754, 2093,  2842, 2092, 753,  1491, 2842, 2090,  \n\t\t\t\t\t\t113, 1531, 2842,  2843, 2091, 469,  1061, 2843, 1529,  431, 2090, 2843,  2844, 1102, 133,  \n\t\t\t\t\t\t2091, 2844, 1099,  753, 2089, 2844,  2845, 2088, 752,  433, 1493, 2845,  114, 1533, 2845,  \n\t\t\t\t\t\t2846, 2087, 471,  113, 1063, 2846,  1063, 433, 2086,  2847, 1104, 134,  2087, 2847, 1101,  \n\t\t\t\t\t\t2087, 752, 2085,  2848, 2084, 751,  1495, 2848, 2082,  1495, 115, 1535,  2849, 2083, 473,  \n\t\t\t\t\t\t1065, 2849, 1533,  435, 2082, 2849,  1103, 2850, 1106,  473, 2083, 2850,  751, 2081, 2850,  \n\t\t\t\t\t\t2851, 2080, 750,  1497, 2851, 2078,  116, 1537, 2851,  2852, 2079, 475,  1067, 2852, 1535,  \n\t\t\t\t\t\t437, 2078, 2852,  2853, 1108, 136,  475, 2079, 2853,  750, 2077, 2853,  2854, 2076, 749,  \n\t\t\t\t\t\t1499, 2854, 2074,  117, 1539, 2854,  2855, 2075, 477,  1069, 2855, 1537,  439, 2074, 2855,  \n\t\t\t\t\t\t2856, 1110, 137,  2075, 2856, 1107,  749, 2073, 2856,  2857, 2072, 748,  1501, 2857, 2070,  \n\t\t\t\t\t\t118, 1541, 2857,  2858, 2071, 479,  1071, 2858, 1539,  441, 2070, 2858,  1109, 2859, 1112,  \n\t\t\t\t\t\t479, 2071, 2859,  748, 2069, 2859,  2066, 2860, 2068,  443, 1503, 2860,  1503, 119, 1543,  \n\t\t\t\t\t\t1541, 2861, 2067,  118, 1073, 2861,  1073, 443, 2066,  2862, 1114, 139,  2067, 2862, 1111,  \n\t\t\t\t\t\t2067, 747, 2065,  2863, 2064, 746,  1505, 2863, 2062,  120, 1545, 2863,  2864, 2063, 483,  \n\t\t\t\t\t\t1075, 2864, 1543,  445, 2062, 2864,  2865, 1116, 140,  2063, 2865, 1113,  746, 2061, 2865,  \n\t\t\t\t\t\t2866, 2060, 745,  1507, 2866, 2058,  121, 1547, 2866,  2867, 2059, 485,  1077, 2867, 1545,  \n\t\t\t\t\t\t447, 2058, 2867,  2868, 1118, 141,  2059, 2868, 1115,  745, 2057, 2868,  2054, 2869, 2056,  \n\t\t\t\t\t\t1509, 2869, 2054,  122, 1549, 2869,  2870, 2055, 487,  1079, 2870, 1547,  449, 2054, 2870,  \n\t\t\t\t\t\t1117, 2871, 1120,  487, 2055, 2871,  2055, 744, 2053,  2050, 2872, 2052,  451, 1511, 2872,  \n\t\t\t\t\t\t1511, 123, 1551,  1549, 2873, 2051,  122, 1081, 2873,  1081, 451, 2050,  2874, 1122, 143,  \n\t\t\t\t\t\t489, 2051, 2874,  2051, 743, 2049,  2875, 2048, 742,  1513, 2875, 2046,  124, 1553, 2875,  \n\t\t\t\t\t\t2876, 2047, 491,  1083, 2876, 1551,  453, 2046, 2876,  2877, 1124, 144,  2047, 2877, 1121,  \n\t\t\t\t\t\t742, 2045, 2877,  2878, 2044, 741,  1515, 2878, 2042,  1515, 125, 1555,  2879, 2043, 493,  \n\t\t\t\t\t\t1085, 2879, 1553,  455, 2042, 2879,  2880, 1126, 145,  2043, 2880, 1123,  741, 2041, 2880,  \n\t\t\t\t\t\t2881, 2040, 740,  1518, 2881, 2038,  127, 1558, 2881,  2882, 2039, 497,  1088, 2882, 1127,  \n\t\t\t\t\t\t458, 2038, 2882,  2883, 1129, 147,  2039, 2883, 1557,  740, 2037, 2883,  2884, 2036, 739,  \n\t\t\t\t\t\t1520, 2884, 2034,  128, 1560, 2884,  2885, 2035, 498,  1090, 2885, 1558,  460, 2034, 2885,  \n\t\t\t\t\t\t2886, 1131, 148,  2035, 2886, 1128,  739, 2033, 2886,  2030, 2887, 2032,  462, 1522, 2887,  \n\t\t\t\t\t\t1522, 129, 1562,  1560, 2888, 2031,  128, 1092, 2888,  1092, 462, 2030,  2889, 1133, 149,  \n\t\t\t\t\t\t2031, 2889, 1130,  2031, 738, 2029,  2890, 2028, 737,  1524, 2890, 2026,  130, 1564, 2890,  \n\t\t\t\t\t\t2891, 2027, 502,  1094, 2891, 1562,  464, 2026, 2891,  1132, 2892, 1135,  2027, 2892, 1132,  \n\t\t\t\t\t\t2027, 737, 2025,  2022, 2893, 2024,  466, 1526, 2893,  1526, 131, 1566,  2894, 2023, 504,  \n\t\t\t\t\t\t1096, 2894, 1564,  466, 2022, 2894,  2895, 1137, 151,  2023, 2895, 1134,  736, 2021, 2895,  \n\t\t\t\t\t\t2896, 2020, 735,  1528, 2896, 2018,  132, 1568, 2896,  2897, 2019, 506,  1098, 2897, 1566,  \n\t\t\t\t\t\t468, 2018, 2897,  2898, 1139, 152,  2019, 2898, 1136,  735, 2017, 2898,  2899, 2016, 734,  \n\t\t\t\t\t\t1530, 2899, 2014,  133, 1570, 2899,  2900, 2015, 508,  1100, 2900, 1568,  470, 2014, 2900,  \n\t\t\t\t\t\t2901, 1141, 153,  2015, 2901, 1138,  734, 2013, 2901,  2010, 2902, 2012,  472, 1532, 2902,  \n\t\t\t\t\t\t134, 1572, 2902,  2903, 2011, 510,  1102, 2903, 1570,  1102, 472, 2010,  2904, 1143, 154,  \n\t\t\t\t\t\t2011, 2904, 1140,  733, 2009, 2904,  2905, 2008, 732,  1534, 2905, 2006,  1534, 135, 1574,  \n\t\t\t\t\t\t1572, 2906, 2007,  1104, 2906, 1572,  474, 2006, 2906,  1142, 2907, 1145,  512, 2007, 2907,  \n\t\t\t\t\t\t732, 2005, 2907,  2908, 2004, 731,  1536, 2908, 2002,  136, 1576, 2908,  2909, 2003, 514,  \n\t\t\t\t\t\t1106, 2909, 1574,  476, 2002, 2909,  2910, 1147, 156,  2003, 2910, 1144,  731, 2001, 2910,  \n\t\t\t\t\t\t2911, 2000, 730,  1538, 2911, 1998,  1538, 137, 1578,  2912, 1999, 516,  1108, 2912, 1576,  \n\t\t\t\t\t\t478, 1998, 2912,  2913, 1149, 157,  1999, 2913, 1146,  730, 1997, 2913,  2914, 1996, 729,  \n\t\t\t\t\t\t1540, 2914, 1994,  138, 1580, 2914,  2915, 1995, 518,  1110, 2915, 1578,  480, 1994, 2915,  \n\t\t\t\t\t\t2916, 1151, 158,  1995, 2916, 1148,  729, 1993, 2916,  2917, 1992, 728,  1542, 2917, 1990,  \n\t\t\t\t\t\t1542, 139, 1582,  2918, 1991, 520,  138, 1112, 2918,  482, 1990, 2918,  1150, 2919, 1153,  \n\t\t\t\t\t\t1991, 2919, 1150,  728, 1989, 2919,  1986, 2920, 1988,  484, 1544, 2920,  1544, 140, 1584,  \n\t\t\t\t\t\t2921, 1987, 522,  139, 1114, 2921,  1114, 484, 1986,  2922, 1155, 160,  1987, 2922, 1152,  \n\t\t\t\t\t\t727, 1985, 2922,  1982, 2923, 1984,  486, 1546, 2923,  1546, 141, 1586,  2924, 1983, 524,  \n\t\t\t\t\t\t140, 1116, 2924,  486, 1982, 2924,  1154, 2925, 1157,  524, 1983, 2925,  1983, 726, 1981,  \n\t\t\t\t\t\t2926, 1980, 725,  1548, 2926, 1978,  142, 1588, 2926,  1586, 2927, 1979,  1118, 2927, 1586,  \n\t\t\t\t\t\t488, 1978, 2927,  2928, 1159, 162,  526, 1979, 2928,  725, 1977, 2928,  2929, 1976, 724,  \n\t\t\t\t\t\t490, 1550, 2929,  1550, 143, 1590,  2930, 1975, 528,  142, 1120, 2930,  1120, 490, 1974,  \n\t\t\t\t\t\t2931, 1161, 163,  1975, 2931, 1158,  724, 1973, 2931,  2932, 1972, 723,  1552, 2932, 1970,  \n\t\t\t\t\t\t144, 1592, 2932,  2933, 1971, 530,  1122, 2933, 1590,  492, 1970, 2933,  2934, 1163, 164,  \n\t\t\t\t\t\t1971, 2934, 1160,  723, 1969, 2934,  1966, 2935, 1968,  494, 1554, 2935,  145, 1594, 2935,  \n\t\t\t\t\t\t2936, 1967, 532,  1124, 2936, 1592,  494, 1966, 2936,  1162, 2937, 1165,  1967, 2937, 1162,  \n\t\t\t\t\t\t1967, 722, 1965,  2938, 1964, 721,  1556, 2938, 1962,  146, 1596, 2938,  2939, 1963, 534,  \n\t\t\t\t\t\t1126, 2939, 1594,  496, 1962, 2939,  2940, 1167, 166,  1963, 2940, 1164,  721, 1961, 2940,  \n\t\t\t\t\t\t2941, 1960, 720,  1559, 2941, 1958,  148, 1599, 2941,  2942, 1959, 538,  1129, 2942, 1168,  \n\t\t\t\t\t\t499, 1958, 2942,  2943, 1170, 168,  1959, 2943, 1598,  720, 1957, 2943,  2944, 1956, 719,  \n\t\t\t\t\t\t1561, 2944, 1954,  149, 1601, 2944,  2945, 1955, 539,  1131, 2945, 1599,  501, 1954, 2945,  \n\t\t\t\t\t\t2946, 1172, 169,  1955, 2946, 1169,  719, 1953, 2946,  2947, 1952, 718,  1563, 2947, 1950,  \n\t\t\t\t\t\t150, 1603, 2947,  2948, 1951, 541,  1133, 2948, 1601,  503, 1950, 2948,  2949, 1174, 170,  \n\t\t\t\t\t\t1951, 2949, 1171,  718, 1949, 2949,  1946, 2950, 1948,  505, 1565, 2950,  1565, 151, 1605,  \n\t\t\t\t\t\t2951, 1947, 543,  150, 1135, 2951,  1135, 505, 1946,  2952, 1176, 171,  1947, 2952, 1173,  \n\t\t\t\t\t\t1947, 717, 1945,  2953, 1944, 716,  1567, 2953, 1942,  152, 1607, 2953,  2954, 1943, 545,  \n\t\t\t\t\t\t1137, 2954, 1605,  507, 1942, 2954,  2955, 1178, 172,  1943, 2955, 1175,  716, 1941, 2955,  \n\t\t\t\t\t\t2956, 1940, 715,  1569, 2956, 1938,  153, 1609, 2956,  2957, 1939, 547,  1139, 2957, 1607,  \n\t\t\t\t\t\t509, 1938, 2957,  2958, 1180, 173,  1939, 2958, 1177,  715, 1937, 2958,  2959, 1936, 714,  \n\t\t\t\t\t\t1571, 2959, 1934,  154, 1611, 2959,  2960, 1935, 549,  1141, 2960, 1609,  511, 1934, 2960,  \n\t\t\t\t\t\t2961, 1182, 174,  1935, 2961, 1179,  714, 1933, 2961,  2962, 1932, 713,  1573, 2962, 1930,  \n\t\t\t\t\t\t1573, 155, 1613,  1611, 2963, 1931,  154, 1143, 2963,  513, 1930, 2963,  1181, 2964, 1184,  \n\t\t\t\t\t\t551, 1931, 2964,  713, 1929, 2964,  2965, 1928, 712,  1575, 2965, 1926,  156, 1615, 2965,  \n\t\t\t\t\t\t2966, 1927, 553,  155, 1145, 2966,  515, 1926, 2966,  2967, 1186, 176,  1927, 2967, 1183,  \n\t\t\t\t\t\t712, 1925, 2967,  2968, 1924, 711,  1577, 2968, 1922,  157, 1617, 2968,  2969, 1923, 555,  \n\t\t\t\t\t\t1147, 2969, 1615,  517, 1922, 2969,  2970, 1188, 177,  1923, 2970, 1185,  711, 1921, 2970,  \n\t\t\t\t\t\t2971, 1920, 710,  1579, 2971, 1918,  158, 1619, 2971,  2972, 1919, 557,  1149, 2972, 1617,  \n\t\t\t\t\t\t519, 1918, 2972,  2973, 1190, 178,  1919, 2973, 1187,  710, 1917, 2973,  2974, 1916, 709,  \n\t\t\t\t\t\t1581, 2974, 1914,  1581, 159, 1621,  2975, 1915, 559,  1151, 2975, 1619,  521, 1914, 2975,  \n\t\t\t\t\t\t2976, 1192, 179,  1915, 2976, 1189,  709, 1913, 2976,  2977, 1912, 708,  1583, 2977, 1910,  \n\t\t\t\t\t\t160, 1623, 2977,  2978, 1911, 561,  1153, 2978, 1621,  523, 1910, 2978,  2979, 1194, 180,  \n\t\t\t\t\t\t1911, 2979, 1191,  708, 1909, 2979,  1906, 2980, 1908,  525, 1585, 2980,  1585, 161, 1625,  \n\t\t\t\t\t\t2981, 1907, 563,  1155, 2981, 1623,  525, 1906, 2981,  2982, 1196, 181,  1907, 2982, 1193,  \n\t\t\t\t\t\t707, 1905, 2982,  2983, 1904, 706,  1587, 2983, 1902,  162, 1627, 2983,  2984, 1903, 565,  \n\t\t\t\t\t\t161, 1157, 2984,  527, 1902, 2984,  2985, 1198, 182,  1903, 2985, 1195,  706, 1901, 2985,  \n\t\t\t\t\t\t2986, 1900, 705,  1589, 2986, 1898,  163, 1629, 2986,  2987, 1899, 567,  1159, 2987, 1627,  \n\t\t\t\t\t\t529, 1898, 2987,  2988, 1200, 183,  1899, 2988, 1197,  705, 1897, 2988,  2989, 1896, 704,  \n\t\t\t\t\t\t1591, 2989, 1894,  164, 1631, 2989,  2990, 1895, 569,  1161, 2990, 1629,  531, 1894, 2990,  \n\t\t\t\t\t\t2991, 1202, 184,  1895, 2991, 1199,  704, 1893, 2991,  2992, 1892, 703,  1593, 2992, 1890,  \n\t\t\t\t\t\t165, 1633, 2992,  2993, 1891, 571,  1163, 2993, 1631,  533, 1890, 2993,  2994, 1204, 185,  \n\t\t\t\t\t\t1891, 2994, 1201,  703, 1889, 2994,  1886, 2995, 1888,  535, 1595, 2995,  1595, 166, 1635,  \n\t\t\t\t\t\t2996, 1887, 573,  165, 1165, 2996,  1165, 535, 1886,  2997, 1206, 186,  1887, 2997, 1203,  \n\t\t\t\t\t\t1887, 702, 1885,  2998, 1884, 701,  1597, 2998, 1882,  167, 1637, 2998,  2999, 1883, 575,  \n\t\t\t\t\t\t1167, 2999, 1635,  537, 1882, 2999,  3000, 1208, 187,  1883, 3000, 1205,  701, 1881, 3000,  \n\t\t\t\t\t\t3001, 1880, 700,  1600, 3001, 1878,  169, 1640, 3001,  3002, 1879, 579,  1170, 3002, 1209,  \n\t\t\t\t\t\t540, 1878, 3002,  3003, 1211, 189,  1879, 3003, 1639,  700, 1877, 3003,  3004, 1876, 699,  \n\t\t\t\t\t\t1602, 3004, 1874,  170, 1642, 3004,  3005, 1875, 580,  1172, 3005, 1640,  542, 1874, 3005,  \n\t\t\t\t\t\t3006, 1213, 190,  1875, 3006, 1210,  699, 1873, 3006,  3007, 1872, 698,  1604, 3007, 1870,  \n\t\t\t\t\t\t171, 1644, 3007,  3008, 1871, 582,  1174, 3008, 1642,  544, 1870, 3008,  3009, 1215, 191,  \n\t\t\t\t\t\t1871, 3009, 1212,  698, 1869, 3009,  1866, 3010, 1868,  546, 1606, 3010,  172, 1646, 3010,  \n\t\t\t\t\t\t3011, 1867, 584,  1176, 3011, 1644,  1176, 546, 1866,  3012, 1217, 192,  1867, 3012, 1214,  \n\t\t\t\t\t\t1867, 697, 1865,  3013, 1864, 696,  1608, 3013, 1862,  173, 1648, 3013,  3014, 1863, 586,  \n\t\t\t\t\t\t1178, 3014, 1646,  548, 1862, 3014,  3015, 1219, 193,  1863, 3015, 1216,  696, 1861, 3015,  \n\t\t\t\t\t\t3016, 1860, 695,  1610, 3016, 1858,  174, 1650, 3016,  3017, 1859, 588,  1180, 3017, 1648,  \n\t\t\t\t\t\t550, 1858, 3017,  3018, 1221, 194,  1859, 3018, 1218,  695, 1857, 3018,  3019, 1856, 694,  \n\t\t\t\t\t\t1612, 3019, 1854,  175, 1652, 3019,  3020, 1855, 590,  1182, 3020, 1650,  552, 1854, 3020,  \n\t\t\t\t\t\t3021, 1223, 195,  1855, 3021, 1220,  694, 1853, 3021,  3022, 1852, 693,  1614, 3022, 1850,  \n\t\t\t\t\t\t176, 1654, 3022,  1652, 3023, 1851,  175, 1184, 3023,  554, 1850, 3023,  1222, 3024, 1225,  \n\t\t\t\t\t\t592, 1851, 3024,  693, 1849, 3024,  3025, 1848, 692,  1616, 3025, 1846,  177, 1656, 3025,  \n\t\t\t\t\t\t3026, 1847, 594,  1186, 3026, 1654,  556, 1846, 3026,  3027, 1227, 197,  1847, 3027, 1224,  \n\t\t\t\t\t\t692, 1845, 3027,  3028, 1844, 691,  1618, 3028, 1842,  178, 1658, 3028,  3029, 1843, 596,  \n\t\t\t\t\t\t1188, 3029, 1656,  558, 1842, 3029,  3030, 1229, 198,  1843, 3030, 1226,  691, 1841, 3030,  \n\t\t\t\t\t\t3031, 1840, 690,  1620, 3031, 1838,  179, 1660, 3031,  3032, 1839, 598,  1190, 3032, 1658,  \n\t\t\t\t\t\t560, 1838, 3032,  3033, 1231, 199,  1839, 3033, 1228,  690, 1837, 3033,  3034, 1836, 689,  \n\t\t\t\t\t\t1622, 3034, 1834,  180, 1662, 3034,  3035, 1835, 600,  1192, 3035, 1660,  562, 1834, 3035,  \n\t\t\t\t\t\t3036, 1233, 200,  1835, 3036, 1230,  689, 1833, 3036,  3037, 1832, 688,  1624, 3037, 1830,  \n\t\t\t\t\t\t181, 1664, 3037,  3038, 1831, 602,  1194, 3038, 1662,  564, 1830, 3038,  3039, 1235, 201,  \n\t\t\t\t\t\t1831, 3039, 1232,  688, 1829, 3039,  3040, 1828, 687,  1626, 3040, 1826,  1626, 182, 1666,  \n\t\t\t\t\t\t3041, 1827, 604,  1196, 3041, 1664,  566, 1826, 3041,  3042, 1237, 202,  1827, 3042, 1234,  \n\t\t\t\t\t\t687, 1825, 3042,  3043, 1824, 686,  1628, 3043, 1822,  183, 1668, 3043,  3044, 1823, 606,  \n\t\t\t\t\t\t1198, 3044, 1666,  568, 1822, 3044,  3045, 1239, 203,  1823, 3045, 1236,  686, 1821, 3045,  \n\t\t\t\t\t\t3046, 1820, 685,  1630, 3046, 1818,  184, 1670, 3046,  3047, 1819, 608,  1200, 3047, 1668,  \n\t\t\t\t\t\t570, 1818, 3047,  3048, 1241, 204,  1819, 3048, 1238,  685, 1817, 3048,  3049, 1816, 684,  \n\t\t\t\t\t\t1632, 3049, 1814,  185, 1672, 3049,  3050, 1815, 610,  1202, 3050, 1670,  572, 1814, 3050,  \n\t\t\t\t\t\t3051, 1243, 205,  1815, 3051, 1240,  684, 1813, 3051,  3052, 1812, 683,  1634, 3052, 1810,  \n\t\t\t\t\t\t186, 1674, 3052,  3053, 1811, 612,  1204, 3053, 1672,  574, 1810, 3053,  3054, 1245, 206,  \n\t\t\t\t\t\t1811, 3054, 1242,  683, 1809, 3054,  3055, 1808, 682,  1636, 3055, 1806,  187, 1676, 3055,  \n\t\t\t\t\t\t3056, 1807, 614,  1206, 3056, 1674,  576, 1806, 3056,  3057, 1247, 207,  1807, 3057, 1244,  \n\t\t\t\t\t\t682, 1805, 3057,  3058, 1804, 681,  1638, 3058, 1802,  188, 1678, 3058,  3059, 1803, 616,  \n\t\t\t\t\t\t1208, 3059, 1676,  578, 1802, 3059,  3060, 1249, 208,  1803, 3060, 1246,  681, 1801, 3060,  \n\t\t\t\t\t\t3061, 1800, 680,  1641, 3061, 1798,  190, 1681, 3061,  3062, 1799, 620,  1211, 3062, 1250,  \n\t\t\t\t\t\t581, 1798, 3062,  3063, 1252, 210,  1799, 3063, 1680,  680, 1797, 3063,  3064, 1796, 679,  \n\t\t\t\t\t\t1643, 3064, 1794,  191, 1683, 3064,  3065, 1795, 621,  1213, 3065, 1681,  583, 1794, 3065,  \n\t\t\t\t\t\t1251, 3066, 1254,  621, 1795, 3066,  679, 1793, 3066,  3067, 1792, 678,  1645, 3067, 1790,  \n\t\t\t\t\t\t192, 1685, 3067,  3068, 1791, 623,  1215, 3068, 1683,  585, 1790, 3068,  3069, 1256, 212,  \n\t\t\t\t\t\t1791, 3069, 1253,  678, 1789, 3069,  1786, 3070, 1788,  587, 1647, 3070,  193, 1687, 3070,  \n\t\t\t\t\t\t1685, 3071, 1787,  192, 1217, 3071,  1217, 587, 1786,  1255, 3072, 1258,  625, 1787, 3072,  \n\t\t\t\t\t\t1787, 677, 1785,  3073, 1784, 676,  1649, 3073, 1782,  194, 1689, 3073,  3074, 1783, 627,  \n\t\t\t\t\t\t1219, 3074, 1687,  589, 1782, 3074,  3075, 1260, 214,  1783, 3075, 1257,  676, 1781, 3075,  \n\t\t\t\t\t\t3076, 1780, 675,  1651, 3076, 1778,  195, 1691, 3076,  3077, 1779, 629,  1221, 3077, 1689,  \n\t\t\t\t\t\t591, 1778, 3077,  3078, 1262, 215,  1779, 3078, 1259,  675, 1777, 3078,  3079, 1776, 674,  \n\t\t\t\t\t\t1653, 3079, 1774,  1653, 196, 1693,  3080, 1775, 631,  1223, 3080, 1691,  593, 1774, 3080,  \n\t\t\t\t\t\t3081, 1264, 216,  1775, 3081, 1261,  674, 1773, 3081,  3082, 1772, 673,  1655, 3082, 1770,  \n\t\t\t\t\t\t197, 1695, 3082,  1693, 3083, 1771,  196, 1225, 3083,  595, 1770, 3083,  3084, 1266, 217,  \n\t\t\t\t\t\t1771, 3084, 1263,  673, 1769, 3084,  3085, 1768, 672,  1657, 3085, 1766,  198, 1697, 3085,  \n\t\t\t\t\t\t3086, 1767, 635,  1227, 3086, 1695,  597, 1766, 3086,  3087, 1268, 218,  1767, 3087, 1265,  \n\t\t\t\t\t\t672, 1765, 3087,  1762, 3088, 1764,  1659, 3088, 1762,  199, 1699, 3088,  3089, 1763, 637,  \n\t\t\t\t\t\t1229, 3089, 1697,  1229, 599, 1762,  3090, 1270, 219,  1763, 3090, 1267,  671, 1761, 3090,  \n\t\t\t\t\t\t3091, 1760, 670,  601, 1661, 3091,  200, 1701, 3091,  1699, 3092, 1759,  1231, 3092, 1699,  \n\t\t\t\t\t\t601, 1758, 3092,  1269, 3093, 1272,  639, 1759, 3093,  1759, 670, 1757,  3094, 1756, 669,  \n\t\t\t\t\t\t1663, 3094, 1754,  201, 1703, 3094,  3095, 1755, 641,  1233, 3095, 1701,  603, 1754, 3095,  \n\t\t\t\t\t\t3096, 1274, 221,  1755, 3096, 1271,  669, 1753, 3096,  3097, 1752, 668,  1665, 3097, 1750,  \n\t\t\t\t\t\t202, 1705, 3097,  3098, 1751, 643,  1235, 3098, 1703,  605, 1750, 3098,  3099, 1276, 222,  \n\t\t\t\t\t\t1751, 3099, 1273,  668, 1749, 3099,  1746, 3100, 1748,  1667, 3100, 1746,  1667, 203, 1707,  \n\t\t\t\t\t\t3101, 1747, 645,  1237, 3101, 1705,  607, 1746, 3101,  3102, 1278, 223,  1747, 3102, 1275,  \n\t\t\t\t\t\t667, 1745, 3102,  3103, 1744, 666,  1669, 3103, 1742,  204, 1709, 3103,  3104, 1743, 647,  \n\t\t\t\t\t\t1239, 3104, 1707,  609, 1742, 3104,  3105, 1280, 224,  1743, 3105, 1277,  666, 1741, 3105,  \n\t\t\t\t\t\t3106, 1740, 665,  1671, 3106, 1738,  1671, 205, 1711,  3107, 1739, 649,  1241, 3107, 1709,  \n\t\t\t\t\t\t611, 1738, 3107,  3108, 1282, 225,  1739, 3108, 1279,  665, 1737, 3108,  3109, 1736, 664,  \n\t\t\t\t\t\t1673, 3109, 1734,  206, 1713, 3109,  1711, 3110, 1735,  205, 1243, 3110,  613, 1734, 3110,  \n\t\t\t\t\t\t3111, 1284, 226,  1735, 3111, 1281,  664, 1733, 3111,  3112, 1732, 663,  1675, 3112, 1730,  \n\t\t\t\t\t\t1675, 207, 1715,  3113, 1731, 653,  1245, 3113, 1713,  615, 1730, 3113,  3114, 1286, 227,  \n\t\t\t\t\t\t1731, 3114, 1283,  663, 1729, 3114,  3115, 1728, 662,  617, 1677, 3115,  1677, 208, 1717,  \n\t\t\t\t\t\t3116, 1727, 655,  207, 1247, 3116,  1247, 617, 1726,  3117, 1288, 228,  1727, 3117, 1285,  \n\t\t\t\t\t\t662, 1725, 3117,  3118, 1724, 661,  1679, 3118, 1722,  209, 1719, 3118,  1717, 3119, 1723,  \n\t\t\t\t\t\t208, 1249, 3119,  619, 1722, 3119,  3120, 1290, 229,  1723, 3120, 1287,  661, 1721, 3120,  \n\t\t\t\t\t\t3121, 1720, 660,  1724, 3121, 1721,  659, 1289, 3121,  3122, 1718, 658,  1728, 3122, 1725,  \n\t\t\t\t\t\t657, 1287, 3122,  3123, 1716, 656,  1732, 3123, 1729,  655, 1285, 3123,  3124, 1714, 654,  \n\t\t\t\t\t\t1736, 3124, 1733,  653, 1283, 3124,  3125, 1712, 652,  1740, 3125, 1737,  651, 1281, 3125,  \n\t\t\t\t\t\t3126, 1710, 650,  1744, 3126, 1741,  649, 1279, 3126,  1745, 3127, 1708,  667, 1748, 3127,  \n\t\t\t\t\t\t1748, 647, 1277,  3128, 1706, 646,  1752, 3128, 1749,  645, 1275, 3128,  3129, 1704, 644,  \n\t\t\t\t\t\t1756, 3129, 1753,  643, 1273, 3129,  1757, 3130, 1702,  670, 1760, 3130,  641, 1271, 3130,  \n\t\t\t\t\t\t1761, 3131, 1700,  671, 1764, 3131,  639, 1269, 3131,  3132, 1698, 638,  1768, 3132, 1765,  \n\t\t\t\t\t\t637, 1267, 3132,  3133, 1696, 636,  1772, 3133, 1769,  635, 1265, 3133,  3134, 1694, 634,  \n\t\t\t\t\t\t1776, 3134, 1773,  1776, 633, 1263,  3135, 1692, 632,  1780, 3135, 1777,  631, 1261, 3135,  \n\t\t\t\t\t\t3136, 1690, 630,  1784, 3136, 1781,  629, 1259, 3136,  1785, 3137, 1688,  677, 1788, 3137,  \n\t\t\t\t\t\t1788, 627, 1257,  3138, 1686, 626,  1792, 3138, 1789,  625, 1255, 3138,  3139, 1684, 624,  \n\t\t\t\t\t\t1796, 3139, 1793,  623, 1253, 3139,  3140, 1682, 622,  1800, 3140, 1797,  621, 1251, 3140,  \n\t\t\t\t\t\t3141, 1679, 619,  1804, 3141, 1801,  618, 1248, 3141,  3142, 1677, 617,  1808, 3142, 1805,  \n\t\t\t\t\t\t616, 1246, 3142,  3143, 1675, 615,  1812, 3143, 1809,  614, 1244, 3143,  3144, 1673, 613,  \n\t\t\t\t\t\t1816, 3144, 1813,  612, 1242, 3144,  3145, 1671, 611,  1820, 3145, 1817,  610, 1240, 3145,  \n\t\t\t\t\t\t3146, 1669, 609,  1824, 3146, 1821,  608, 1238, 3146,  3147, 1667, 607,  1828, 3147, 1825,  \n\t\t\t\t\t\t606, 1236, 3147,  3148, 1665, 605,  1832, 3148, 1829,  604, 1234, 3148,  3149, 1663, 603,  \n\t\t\t\t\t\t1836, 3149, 1833,  602, 1232, 3149,  3150, 1661, 601,  1840, 3150, 1837,  600, 1230, 3150,  \n\t\t\t\t\t\t3151, 1659, 599,  1844, 3151, 1841,  598, 1228, 3151,  3152, 1657, 597,  1848, 3152, 1845,  \n\t\t\t\t\t\t596, 1226, 3152,  3153, 1655, 595,  1852, 3153, 1849,  594, 1224, 3153,  3154, 1653, 593,  \n\t\t\t\t\t\t1856, 3154, 1853,  592, 1222, 3154,  3155, 1651, 591,  1860, 3155, 1857,  590, 1220, 3155,  \n\t\t\t\t\t\t3156, 1649, 589,  1864, 3156, 1861,  588, 1218, 3156,  1865, 3157, 1647,  697, 1868, 3157,  \n\t\t\t\t\t\t586, 1216, 3157,  3158, 1645, 585,  1872, 3158, 1869,  584, 1214, 3158,  3159, 1643, 583,  \n\t\t\t\t\t\t1876, 3159, 1873,  582, 1212, 3159,  3160, 1641, 581,  1880, 3160, 1877,  580, 1210, 3160,  \n\t\t\t\t\t\t3161, 1638, 578,  1884, 3161, 1881,  577, 1207, 3161,  1885, 3162, 1636,  702, 1888, 3162,  \n\t\t\t\t\t\t575, 1205, 3162,  3163, 1634, 574,  1892, 3163, 1889,  573, 1203, 3163,  3164, 1632, 572,  \n\t\t\t\t\t\t1896, 3164, 1893,  571, 1201, 3164,  3165, 1630, 570,  1900, 3165, 1897,  569, 1199, 3165,  \n\t\t\t\t\t\t3166, 1628, 568,  1904, 3166, 1901,  567, 1197, 3166,  3167, 1626, 566,  707, 1908, 3167,  \n\t\t\t\t\t\t1908, 565, 1195,  3168, 1624, 564,  1912, 3168, 1909,  563, 1193, 3168,  3169, 1622, 562,  \n\t\t\t\t\t\t1916, 3169, 1913,  561, 1191, 3169,  3170, 1620, 560,  1920, 3170, 1917,  559, 1189, 3170,  \n\t\t\t\t\t\t3171, 1618, 558,  1924, 3171, 1921,  557, 1187, 3171,  3172, 1616, 556,  1928, 3172, 1925,  \n\t\t\t\t\t\t555, 1185, 3172,  3173, 1614, 554,  1932, 3173, 1929,  553, 1183, 3173,  3174, 1612, 552,  \n\t\t\t\t\t\t1936, 3174, 1933,  551, 1181, 3174,  3175, 1610, 550,  1940, 3175, 1937,  549, 1179, 3175,  \n\t\t\t\t\t\t3176, 1608, 548,  1944, 3176, 1941,  547, 1177, 3176,  1945, 3177, 1606,  717, 1948, 3177,  \n\t\t\t\t\t\t545, 1175, 3177,  3178, 1604, 544,  1952, 3178, 1949,  543, 1173, 3178,  3179, 1602, 542,  \n\t\t\t\t\t\t1956, 3179, 1953,  541, 1171, 3179,  3180, 1600, 540,  1960, 3180, 1957,  539, 1169, 3180,  \n\t\t\t\t\t\t3181, 1597, 537,  1964, 3181, 1961,  536, 1166, 3181,  1965, 3182, 1595,  722, 1968, 3182,  \n\t\t\t\t\t\t1968, 534, 1164,  3183, 1593, 533,  1972, 3183, 1969,  532, 1162, 3183,  3184, 1591, 531,  \n\t\t\t\t\t\t1976, 3184, 1973,  530, 1160, 3184,  3185, 1589, 529,  1980, 3185, 1977,  528, 1158, 3185,  \n\t\t\t\t\t\t1981, 3186, 1587,  726, 1984, 3186,  1984, 526, 1156,  3187, 1585, 525,  727, 1988, 3187,  \n\t\t\t\t\t\t524, 1154, 3187,  1989, 3188, 1583,  1992, 3188, 1989,  522, 1152, 3188,  3189, 1581, 521,  \n\t\t\t\t\t\t1996, 3189, 1993,  1996, 520, 1150,  3190, 1579, 519,  2000, 3190, 1997,  518, 1148, 3190,  \n\t\t\t\t\t\t3191, 1577, 517,  2004, 3191, 2001,  516, 1146, 3191,  3192, 1575, 515,  2008, 3192, 2005,  \n\t\t\t\t\t\t514, 1144, 3192,  3193, 1573, 513,  2012, 3193, 2009,  2012, 512, 1142,  3194, 1571, 511,  \n\t\t\t\t\t\t2016, 3194, 2013,  510, 1140, 3194,  3195, 1569, 509,  2020, 3195, 2017,  508, 1138, 3195,  \n\t\t\t\t\t\t3196, 1567, 507,  2024, 3196, 2021,  506, 1136, 3196,  2025, 3197, 1565,  737, 2028, 3197,  \n\t\t\t\t\t\t504, 1134, 3197,  3198, 1563, 503,  738, 2032, 3198,  502, 1132, 3198,  3199, 1561, 501,  \n\t\t\t\t\t\t2036, 3199, 2033,  500, 1130, 3199,  3200, 1559, 499,  2040, 3200, 2037,  498, 1128, 3200,  \n\t\t\t\t\t\t3201, 1556, 496,  2044, 3201, 2041,  495, 1125, 3201,  3202, 1554, 494,  2048, 3202, 2045,  \n\t\t\t\t\t\t493, 1123, 3202,  3203, 1552, 492,  743, 2052, 3203,  2052, 491, 1121,  2053, 3204, 1550,  \n\t\t\t\t\t\t744, 2056, 3204,  489, 1119, 3204,  3205, 1548, 488,  2060, 3205, 2057,  487, 1117, 3205,  \n\t\t\t\t\t\t3206, 1546, 486,  2064, 3206, 2061,  485, 1115, 3206,  2065, 3207, 1544,  747, 2068, 3207,  \n\t\t\t\t\t\t483, 1113, 3207,  3208, 1542, 482,  2072, 3208, 2069,  481, 1111, 3208,  3209, 1540, 480,  \n\t\t\t\t\t\t2076, 3209, 2073,  2076, 479, 1109,  3210, 1538, 478,  2080, 3210, 2077,  2080, 477, 1107,  \n\t\t\t\t\t\t3211, 1536, 476,  2084, 3211, 2081,  475, 1105, 3211,  3212, 1534, 474,  2088, 3212, 2085,  \n\t\t\t\t\t\t473, 1103, 3212,  3213, 1532, 472,  2092, 3213, 2089,  471, 1101, 3213,  2093, 3214, 1530,  \n\t\t\t\t\t\t754, 2096, 3214,  469, 1099, 3214,  3215, 1528, 468,  2100, 3215, 2097,  467, 1097, 3215,  \n\t\t\t\t\t\t2101, 3216, 1526,  756, 2104, 3216,  465, 1095, 3216,  3217, 1524, 464,  2108, 3217, 2105,  \n\t\t\t\t\t\t463, 1093, 3217,  2109, 3218, 1522,  758, 2112, 3218,  2112, 461, 1091,  3219, 1520, 460,  \n\t\t\t\t\t\t2116, 3219, 2113,  459, 1089, 3219,  3220, 1518, 458,  2120, 3220, 2117,  457, 1087, 3220,  \n\t\t\t\t\t\t3221, 1515, 455,  761, 2124, 3221,  2124, 454, 1084,  2125, 3222, 1513,  2128, 3222, 2125,  \n\t\t\t\t\t\t452, 1082, 3222,  2129, 3223, 1511,  763, 2132, 3223,  2132, 450, 1080,  3224, 1509, 449,  \n\t\t\t\t\t\t764, 2136, 3224,  2136, 448, 1078,  3225, 1507, 447,  2140, 3225, 2137,  446, 1076, 3225,  \n\t\t\t\t\t\t3226, 1505, 445,  2144, 3226, 2141,  444, 1074, 3226,  2145, 3227, 1503,  767, 2148, 3227,  \n\t\t\t\t\t\t442, 1072, 3227,  3228, 1501, 441,  2152, 3228, 2149,  440, 1070, 3228,  2153, 3229, 1499,  \n\t\t\t\t\t\t769, 2156, 3229,  2156, 438, 1068,  3230, 1497, 437,  2160, 3230, 2157,  2160, 436, 1066,  \n\t\t\t\t\t\t2161, 3231, 1495,  771, 2164, 3231,  434, 1064, 3231,  2165, 3232, 1493,  2168, 3232, 2165,  \n\t\t\t\t\t\t432, 1062, 3232,  3233, 1491, 431,  2172, 3233, 2169,  430, 1060, 3233,  3234, 1489, 429,  \n\t\t\t\t\t\t774, 2176, 3234,  428, 1058, 3234,  3235, 1487, 427,  2180, 3235, 2177,  2180, 426, 1056,  \n\t\t\t\t\t\t3236, 1485, 425,  2184, 3236, 2181,  424, 1054, 3236,  2185, 3237, 1483,  777, 2188, 3237,  \n\t\t\t\t\t\t2188, 422, 1052,  3238, 1481, 421,  2192, 3238, 2189,  420, 1050, 3238,  3239, 1479, 419,  \n\t\t\t\t\t\t2196, 3239, 2193,  418, 1048, 3239,  3240, 1477, 417,  780, 2200, 3240,  2200, 416, 1046,  \n\t\t\t\t\t\t3241, 1474, 414,  2204, 3241, 2201,  413, 1043, 3241,  3242, 1472, 412,  2208, 3242, 2205,  \n\t\t\t\t\t\t411, 1041, 3242,  3243, 1470, 410,  2212, 3243, 2209,  409, 1039, 3243,  3244, 1468, 408,  \n\t\t\t\t\t\t2216, 3244, 2213,  407, 1037, 3244,  2217, 3245, 1466,  785, 2220, 3245,  405, 1035, 3245,  \n\t\t\t\t\t\t3246, 1464, 404,  2224, 3246, 2221,  403, 1033, 3246,  3247, 1462, 402,  2228, 3247, 2225,  \n\t\t\t\t\t\t401, 1031, 3247,  3248, 1460, 400,  2232, 3248, 2229,  399, 1029, 3248,  3249, 1458, 398,  \n\t\t\t\t\t\t2236, 3249, 2233,  397, 1027, 3249,  3250, 1456, 396,  2240, 3250, 2237,  2240, 395, 1025,  \n\t\t\t\t\t\t3251, 1454, 394,  2244, 3251, 2241,  393, 1023, 3251,  3252, 1452, 392,  2248, 3252, 2245,  \n\t\t\t\t\t\t391, 1021, 3252,  3253, 1450, 390,  2252, 3253, 2249,  389, 1019, 3253,  3254, 1448, 388,  \n\t\t\t\t\t\t2256, 3254, 2253,  387, 1017, 3254,  2257, 3255, 1446,  795, 2260, 3255,  2260, 385, 1015,  \n\t\t\t\t\t\t3256, 1444, 384,  2264, 3256, 2261,  383, 1013, 3256,  3257, 1442, 382,  2268, 3257, 2265,  \n\t\t\t\t\t\t381, 1011, 3257,  3258, 1440, 380,  2272, 3258, 2269,  2272, 379, 1009,  3259, 1438, 378,  \n\t\t\t\t\t\t2276, 3259, 2273,  377, 1007, 3259,  3260, 1436, 376,  2280, 3260, 2277,  375, 1005, 3260,  \n\t\t\t\t\t\t3261, 1433, 373,  2284, 3261, 2281,  372, 1002, 3261,  3262, 1431, 371,  2288, 3262, 2285,  \n\t\t\t\t\t\t370, 1000, 3262,  3263, 1429, 369,  2292, 3263, 2289,  368, 998, 3263,  3264, 1427, 367,  \n\t\t\t\t\t\t2296, 3264, 2293,  366, 996, 3264,  3265, 1425, 365,  2300, 3265, 2297,  364, 994, 3265,  \n\t\t\t\t\t\t3266, 1423, 363,  2304, 3266, 2301,  362, 992, 3266,  3267, 1421, 361,  2308, 3267, 2305,  \n\t\t\t\t\t\t2308, 360, 990,  3268, 1419, 359,  2312, 3268, 2309,  358, 988, 3268,  3269, 1417, 357,  \n\t\t\t\t\t\t2316, 3269, 2313,  356, 986, 3269,  3270, 1415, 355,  2320, 3270, 2317,  354, 984, 3270,  \n\t\t\t\t\t\t3271, 1413, 353,  2324, 3271, 2321,  352, 982, 3271,  3272, 1411, 351,  2328, 3272, 2325,  \n\t\t\t\t\t\t350, 980, 3272,  3273, 1409, 349,  2332, 3273, 2329,  348, 978, 3273,  3274, 1407, 347,  \n\t\t\t\t\t\t2336, 3274, 2333,  346, 976, 3274,  3275, 1405, 345,  2340, 3275, 2337,  344, 974, 3275,  \n\t\t\t\t\t\t3276, 1403, 343,  2344, 3276, 2341,  342, 972, 3276,  3277, 1401, 341,  2348, 3277, 2345,  \n\t\t\t\t\t\t340, 970, 3277,  2349, 3278, 1399,  2352, 3278, 2349,  338, 968, 3278,  3279, 1397, 337,  \n\t\t\t\t\t\t2356, 3279, 2353,  336, 966, 3279,  3280, 1395, 335,  2360, 3280, 2357,  334, 964, 3280,  \n\t\t\t\t\t\t3281, 1392, 332,  2364, 3281, 2361,  331, 961, 3281,  3282, 1390, 330,  2368, 3282, 2365,  \n\t\t\t\t\t\t329, 959, 3282,  3283, 1388, 328,  2372, 3283, 2369,  327, 957, 3283,  3284, 1386, 326,  \n\t\t\t\t\t\t2376, 3284, 2373,  325, 955, 3284,  3285, 1384, 324,  2380, 3285, 2377,  323, 953, 3285,  \n\t\t\t\t\t\t3286, 1382, 322,  2384, 3286, 2381,  321, 951, 3286,  3287, 1380, 320,  2388, 3287, 2385,  \n\t\t\t\t\t\t2388, 319, 949,  3288, 1378, 318,  2392, 3288, 2389,  317, 947, 3288,  3289, 1376, 316,  \n\t\t\t\t\t\t2396, 3289, 2393,  315, 945, 3289,  3290, 1374, 314,  2400, 3290, 2397,  313, 943, 3290,  \n\t\t\t\t\t\t3291, 1372, 312,  2404, 3291, 2401,  311, 941, 3291,  3292, 1370, 310,  2408, 3292, 2405,  \n\t\t\t\t\t\t309, 939, 3292,  3293, 1368, 308,  2412, 3293, 2409,  307, 937, 3293,  2413, 3294, 1366,  \n\t\t\t\t\t\t834, 2416, 3294,  305, 935, 3294,  3295, 1364, 304,  2420, 3295, 2417,  303, 933, 3295,  \n\t\t\t\t\t\t3296, 1362, 302,  2424, 3296, 2421,  301, 931, 3296,  3297, 1360, 300,  2428, 3297, 2425,  \n\t\t\t\t\t\t299, 929, 3297,  3298, 1358, 298,  2432, 3298, 2429,  297, 927, 3298,  3299, 1356, 296,  \n\t\t\t\t\t\t2436, 3299, 2433,  295, 925, 3299,  3300, 1354, 294,  2440, 3300, 2437,  293, 923, 3300,  \n\t\t\t\t\t\t3301, 1351, 291,  2444, 3301, 2441,  290, 920, 3301,  3302, 1348, 288,  2448, 3302, 2445,  \n\t\t\t\t\t\t287, 917, 3302,  3303, 1345, 285,  2452, 3303, 2449,  284, 914, 3303,  2453, 3304, 1342,  \n\t\t\t\t\t\t844, 2456, 3304,  281, 911, 3304,  3305, 1339, 279,  2460, 3305, 2457,  278, 908, 3305,  \n\t\t\t\t\t\t3306, 1336, 276,  2464, 3306, 2461,  275, 905, 3306,  3307, 1333, 273,  2468, 3307, 2465,  \n\t\t\t\t\t\t272, 902, 3307,  3308, 1330, 270,  2472, 3308, 2469,  2472, 269, 899,  3309, 1327, 267,  \n\t\t\t\t\t\t2476, 3309, 2473,  266, 896, 3309,  2477, 3310, 1324,  850, 2480, 3310,  263, 893, 3310,  \n\t\t\t\t\t\t2481, 3311, 1321,  851, 2484, 3311,  2484, 260, 890,  2485, 3312, 1318,  2488, 3312, 2485,  \n\t\t\t\t\t\t257, 887, 3312,  2489, 3313, 1315,  853, 2492, 3313,  2492, 254, 884,  2493, 3314, 1312,  \n\t\t\t\t\t\t2496, 3314, 2493,  2496, 251, 881,  3315, 1309, 249,  2500, 3315, 2497,  248, 878, 3315,  \n\t\t\t\t\t\t2501, 3316, 1306,  2504, 3316, 2501,  245, 875, 3316,  3317, 1303, 243,  2508, 3317, 2505,  \n\t\t\t\t\t\t2508, 242, 872,  3318, 1300, 240,  2512, 3318, 2509,  239, 869, 3318,  2513, 3319, 1297,  \n\t\t\t\t\t\t2516, 3319, 2513,  236, 866, 3319,  2517, 3320, 1294,  2520, 3320, 2517,  2520, 233, 863\n\t\t\t\t\t]\n\t\t\t\t}"
  },
  {
    "path": "12_pbd_cloth/constraints/__init__.py",
    "content": "from .stretching import solve_stretching_constraints\nfrom .bending import solve_bending_constraints\n\n__all__ = [\n    'solve_stretching_constraints',\n    'solve_bending_constraints',\n]\n"
  },
  {
    "path": "12_pbd_cloth/constraints/bending.py",
    "content": "import taichi as ti\n\n\n@ti.kernel\ndef solve_bending_constraints(\n    compliance: ti.f64, dt: ti.f64, num_bending_constraints: ti.i32,\n    pos: ti.template(), bending_ids: ti.template(), bending_lengths: ti.template(),\n    inv_mass: ti.template(), lambdas: ti.template()\n):\n    alpha = compliance / (dt * dt)\n    for i in range(num_bending_constraints):\n        id0, id1 = bending_ids[i, 0], bending_ids[i, 1]\n        w0, w1 = inv_mass[id0], inv_mass[id1]\n        w_sum = w0 + w1\n        if w_sum == 0.0: continue\n        p0, p1 = pos[id0], pos[id1]\n        delta = p0 - p1\n        dist = delta.norm()\n        if dist == 0.0: continue\n        grad = delta / dist\n        C = dist - bending_lengths[i]\n        dlambda = -(C + alpha * lambdas[i]) / (w_sum + alpha)\n        lambdas[i] += dlambda\n        pos[id0] += dlambda * w0 * grad\n        pos[id1] -= dlambda * w1 * grad\n"
  },
  {
    "path": "12_pbd_cloth/constraints/stretching.py",
    "content": "import taichi as ti\n\n\n@ti.kernel\ndef solve_stretching_constraints(\n    compliance: ti.f64, dt: ti.f64, num_stretching_constraints: ti.i32,\n    pos: ti.template(), stretching_ids: ti.template(), stretching_lengths: ti.template(),\n    inv_mass: ti.template(), lambdas: ti.template()\n):\n    alpha = compliance / (dt * dt)\n    for i in range(num_stretching_constraints):\n        id0, id1 = stretching_ids[i, 0], stretching_ids[i, 1]\n        w0, w1 = inv_mass[id0], inv_mass[id1]\n        w_sum = w0 + w1\n        if w_sum == 0.0: continue\n        p0, p1 = pos[id0], pos[id1]\n        delta = p0 - p1\n        dist = delta.norm()\n        if dist == 0.0: continue\n        grad = delta / dist\n        C = dist - stretching_lengths[i]\n        dlambda = -(C + alpha * lambdas[i]) / (w_sum + alpha)\n        lambdas[i] += dlambda\n        pos[id0] += dlambda * w0 * grad\n        pos[id1] -= dlambda * w1 * grad\n"
  },
  {
    "path": "12_pbd_cloth/imgui.ini",
    "content": "[Window][Debug##Default]\nPos=60,60\nSize=400,400\nCollapsed=0\n\n[Window][Controls]\nPos=51,51\nSize=307,409\nCollapsed=0\n\n"
  },
  {
    "path": "12_pbd_cloth/main.py",
    "content": "import taichi as ti\nimport numpy as np\nimport time\nimport warp as wp\nimport warp.render\n\n# Import all modules\nfrom xpbd_base import init_physics, pre_solve, post_solve\nfrom constraints import solve_stretching_constraints, solve_bending_constraints\nfrom utils import (\n    load_cloth_data_from_json, find_constraint_indices, find_bottom_corner, calculate_quadratic_path_pos,\n    pin_top_vertices, apply_grab, initialize_colors\n)\n\nti.init(arch=ti.cpu, default_fp=ti.f64)\n\n\nclass USDExporter:\n    \"\"\"USD animation exporter for Blender compatibility.\"\"\"\n    \n    def __init__(self, output_path=\"cloth_animation.usd\", fps=60, scale=10.0):\n        self.output_path = output_path\n        self.fps = fps\n        self.scale = scale\n        self.frame_dt = 1.0 / fps\n        self.sim_time = 0.0\n        self.frame_count = 0\n        \n        self.renderer = wp.render.UsdRenderer(output_path, scaling=scale)\n        self.renderer.render_ground()\n        \n        print(f\"USD exporter initialized: {output_path}\")\n        print(f\"FPS: {fps}\")\n        print(f\"Scale: {scale}x\")\n    \n    def export_frame(self, positions, indices):\n        \"\"\"Export a single frame to the USD file.\"\"\"\n        self.renderer.begin_frame(self.sim_time)\n        self.renderer.render_mesh(\n            name=\"cloth_mesh\",\n            points=positions,\n            indices=indices\n        )\n        self.renderer.end_frame()\n        \n        self.frame_count += 1\n        self.sim_time += self.frame_dt\n        \n        if self.frame_count % 60 == 0:\n            print(f\"Exported frame {self.frame_count} at time {self.sim_time:.3f}s\")\n        \n    def save(self):\n        \"\"\"Finalize and save the USD file.\"\"\"\n        self.renderer.save()\n        print(f\"\\nUSD animation saved: {self.output_path}\")\n        print(f\"Total frames: {self.frame_count}\")\n        print(f\"Duration: {self.sim_time:.3f} seconds\")\n        print(f\"\\nTo import into Blender:\")\n        print(f\"1. File > Import > Universal Scene Description (.usd)\")\n        print(f\"2. Select '{self.output_path}'\")\n        print(f\"3. The animation will be imported as a single animated sequence!\")\n\n\n# ============================================================================\n# Load Mesh Data\n# ============================================================================\n\nverts_np, face_tri_ids_np = load_cloth_data_from_json()\ntris_np = face_tri_ids_np.reshape((-1, 3))\nstretching_ids_np, bending_ids_np = find_constraint_indices(tris_np)\n\n# ============================================================================\n# Simulation Constants\n# ============================================================================\n\npaused = True\ngravity = ti.Vector([0.0, -9.8, 0.0])\ndt = 1.0 / 60.0\nnum_substeps = 15\nsdt = dt / num_substeps\nsolver_iterations = 1 # can increase\n\nexport_enabled = False\nexport_frame_count = 0\nusd_exporter = None\n\nnum_particles = len(verts_np)\nnum_tris = len(tris_np)\nnum_stretching_constraints = len(stretching_ids_np)\nnum_bending_constraints = len(bending_ids_np)\n\nstretching_compliance = 0.0\nbending_compliance = 1.0\n\n# ============================================================================\n# Taichi Field Allocations\n# ============================================================================\n\n# Simulation fields\npos = ti.Vector.field(3, dtype=ti.f64, shape=num_particles)\nprev_pos = ti.Vector.field(3, dtype=ti.f64, shape=num_particles)\nvel = ti.Vector.field(3, dtype=ti.f64, shape=num_particles)\ninv_mass = ti.field(dtype=ti.f64, shape=num_particles)\noriginal_inv_mass = ti.field(dtype=ti.f64, shape=num_particles)\n\n# Mesh topology fields\ntri_ids = ti.field(ti.i32, shape=num_tris * 3)\nstretching_ids = ti.field(ti.i32, shape=(num_stretching_constraints, 2))\nbending_ids = ti.field(ti.i32, shape=(num_bending_constraints, 2))\n\n# Constraint rest lengths\nstretching_lengths = ti.field(dtype=ti.f64, shape=num_stretching_constraints)\nbending_lengths = ti.field(dtype=ti.f64, shape=num_bending_constraints)\n\n# XPBD accumulated lambdas (one per constraint, reset each substep)\nstretching_lambdas = ti.field(dtype=ti.f64, shape=num_stretching_constraints)\nbending_lambdas = ti.field(dtype=ti.f64, shape=num_bending_constraints)\n\n# Visualization fields\nground_vertices = ti.Vector.field(3, dtype=ti.f64, shape=4)\nground_indices = ti.field(ti.i32, shape=6)\ngrab_indicator_pos = ti.Vector.field(3, dtype=ti.f64, shape=1)\nvertex_colors = ti.Vector.field(3, dtype=ti.f64, shape=num_particles)\n\n# ============================================================================\n# Initialize Fields from Mesh Data\n# ============================================================================\n\npos.from_numpy(verts_np)\ntri_ids.from_numpy(tris_np.flatten())\nstretching_ids.from_numpy(stretching_ids_np)\nbending_ids.from_numpy(bending_ids_np)\nground_vertices.from_numpy(np.array([[-10, 0, -10], [10, 0, -10], [10, 0, 10], [-10, 0, 10]], dtype=np.float64))\nground_indices.from_numpy(np.array([0, 1, 2, 0, 2, 3], dtype=np.int32))\n\n# ============================================================================\n# Simulation Substep Function\n# ============================================================================\n\n@ti.kernel\ndef reset_constraint_lambdas(\n    num_s: ti.i32, num_b: ti.i32,\n    s_lambdas: ti.template(), b_lambdas: ti.template()\n):\n    for i in range(num_s):\n        s_lambdas[i] = 0.0\n    for i in range(num_b):\n        b_lambdas[i] = 0.0\n\n\ndef substep(grab_id, grab_x, grab_y, grab_z):\n    \"\"\"Perform one simulation substep.\"\"\"\n    pre_solve(sdt, num_particles, gravity, pos, prev_pos, vel, inv_mass)\n    # XPBD: reset lambdas once per substep (they accumulate across solver iterations)\n    reset_constraint_lambdas(\n        num_stretching_constraints, num_bending_constraints,\n        stretching_lambdas, bending_lambdas\n    )\n    for _ in range(solver_iterations):\n        solve_stretching_constraints(stretching_compliance, sdt, num_stretching_constraints, pos, stretching_ids, stretching_lengths, inv_mass, stretching_lambdas)\n        solve_bending_constraints(bending_compliance, sdt, num_bending_constraints, pos, bending_ids, bending_lengths, inv_mass, bending_lambdas)\n    apply_grab(grab_id, grab_x, grab_y, grab_z, pos, vel, grab_indicator_pos)\n    post_solve(sdt, num_particles, pos, prev_pos, vel, inv_mass)\n\n\n# ============================================================================\n# Initialize Simulation\n# ============================================================================\n\ninit_physics(num_particles, num_tris, num_stretching_constraints, num_bending_constraints,\n             pos, prev_pos, vel, inv_mass, original_inv_mass,\n             tri_ids, stretching_ids, bending_ids, stretching_lengths, bending_lengths)\npin_top_vertices(num_particles, pos, inv_mass)\ninitialize_colors(num_particles, pos, vertex_colors)\n\n# ============================================================================\n# Setup UI and Camera\n# ============================================================================\n\nwindow = ti.ui.Window(\"Taichi XPBD Cloth\", (1024, 1024), vsync=True)\ncanvas = window.get_canvas()\nscene = window.get_scene()\ncamera = ti.ui.Camera()\ncamera.position(0, 1.0, 3.0)\ncamera.lookat(0, 0.5, 0)\n\n# ============================================================================\n# Animation State\n# ============================================================================\n\nis_grabbing = False\ngrabbed_particle_id = -1\ngrab_distance = 0.0\nbottom_corner_id = find_bottom_corner(pos.to_numpy())\n\nis_animating = False\nanimation_start_time = 0.0\nanimation_duration = 2.0\noriginal_corner_pos = None\ntarget_corner_pos = None\nstart_time = time.time()\n\n# ============================================================================\n# Main Simulation and Rendering Loop\n# ============================================================================\n\nwhile window.running:\n    gui = window.GUI\n    with gui.sub_window(\"Controls\", 0.05, 0.05, 0.3, 0.4):\n        paused = gui.checkbox(\"Paused\", paused)\n        bending_compliance = gui.slider_float(\"Bending Compliance\", bending_compliance, 0.0, 10.0)\n        \n        gui.text(\"Bottom Corner Control:\")\n        if paused:\n            gui.text(\"(Unpause simulation to control corner)\")\n        else:\n            if gui.button(\"Animate Corner\"):\n                if not is_animating and not is_grabbing:\n                    is_animating = True\n                    is_grabbing = True\n                    grabbed_particle_id = bottom_corner_id\n                    inv_mass[grabbed_particle_id] = 0.0\n                    \n                    original_corner_pos = pos[grabbed_particle_id]\n                    target_corner_pos = ti.Vector([original_corner_pos.x - 0.3, original_corner_pos.y + 0.5, original_corner_pos.z + 0.2])\n                    animation_start_time = 0.0\n            \n            if gui.button(\"Release Corner\"):\n                if is_grabbing and grabbed_particle_id != -1:\n                    inv_mass[grabbed_particle_id] = original_inv_mass[grabbed_particle_id]\n                is_grabbing = False\n                is_animating = False\n                grabbed_particle_id = -1\n        \n        if is_animating:\n            current_time = time.time()\n            elapsed_time = current_time - animation_start_time\n            progress = min(1.0, elapsed_time / animation_duration)\n            gui.text(f\"Animation Progress: {progress:.1%}\")\n        \n        gui.text(\"Export:\")\n        export_enabled = gui.checkbox(\"Export Animation\", export_enabled)\n        \n        if export_enabled and usd_exporter is None:\n            usd_exporter = USDExporter(\"cloth_animation.usd\", fps=60, scale=10.0)\n            print(\"USD exporter initialized!\")\n            \n        gui.text(f\"Exported Frames: {export_frame_count}\")\n        if usd_exporter:\n            gui.text(f\"USD File: {usd_exporter.output_path}\")\n        \n        if gui.button(\"Reset\"):\n            pos.from_numpy(verts_np)\n            init_physics(num_particles, num_tris, num_stretching_constraints, num_bending_constraints,\n                        pos, prev_pos, vel, inv_mass, original_inv_mass,\n                        tri_ids, stretching_ids, bending_ids, stretching_lengths, bending_lengths)\n            pin_top_vertices(num_particles, pos, inv_mass)\n            is_grabbing = False\n            is_animating = False\n            grabbed_particle_id = -1\n\n    grab_target_position = ti.Vector([0.0, 0.0, 0.0])\n    \n    if is_animating and grabbed_particle_id != -1:\n        if animation_start_time == 0.0:\n            animation_start_time = time.time()\n        \n        current_time = time.time()\n        elapsed_time = current_time - animation_start_time\n        \n        if elapsed_time < animation_duration:\n            t = elapsed_time / animation_duration\n            t = max(0.0, min(1.0, t))\n            \n            grab_target_position = calculate_quadratic_path_pos(original_corner_pos, target_corner_pos, t)\n        else:\n            grab_target_position = target_corner_pos\n            is_animating = False\n    \n    elif is_grabbing and grabbed_particle_id != -1:\n        grab_target_position = pos[grabbed_particle_id]\n    \n    if not paused:\n        for _ in range(num_substeps):\n            substep(grabbed_particle_id, grab_target_position.x, grab_target_position.y, grab_target_position.z)\n\n    if export_enabled and usd_exporter:\n        particle_positions = pos.to_numpy()\n        triangle_indices = tri_ids.to_numpy()\n        usd_exporter.export_frame(particle_positions, triangle_indices)\n        export_frame_count += 1\n\n    camera.track_user_inputs(window, movement_speed=0.03, hold_key=ti.ui.RMB)\n    scene.set_camera(camera)\n    scene.ambient_light((0.5, 0.5, 0.5))\n    scene.point_light(pos=(2, 3, 4), color=(1, 1, 1))\n    \n    scene.mesh(pos, indices=tri_ids, per_vertex_color=vertex_colors, two_sided=True)\n    scene.mesh(ground_vertices, indices=ground_indices, color=(0.8, 0.8, 0.8))\n\n    if is_grabbing:\n        scene.particles(grab_indicator_pos, radius=0.01, color=(1.0, 1.0, 0.0))\n\n    canvas.scene(scene)\n    window.show()\n\nif usd_exporter and export_frame_count > 0:\n    usd_exporter.save()\n    print(f\"\\nAnimation export complete!\")\n    print(f\"Total frames exported: {export_frame_count}\")\n    print(f\"USD file: {usd_exporter.output_path}\")\n"
  },
  {
    "path": "12_pbd_cloth/utils/__init__.py",
    "content": "from .mesh_loader import load_cloth_data_from_json, create_cloth_mesh_data\nfrom .constraint_finder import find_constraint_indices, find_bottom_corner, calculate_quadratic_path_pos\nfrom .cloth_utils import pin_top_vertices, apply_grab, initialize_colors\n\n__all__ = [\n    'load_cloth_data_from_json',\n    'create_cloth_mesh_data',\n    'find_constraint_indices',\n    'find_bottom_corner',\n    'calculate_quadratic_path_pos',\n    'pin_top_vertices',\n    'apply_grab',\n    'initialize_colors',\n]\n"
  },
  {
    "path": "12_pbd_cloth/utils/cloth_utils.py",
    "content": "import taichi as ti\n\n\n@ti.kernel\ndef pin_top_vertices(\n    num_particles: ti.i32,\n    pos: ti.template(), inv_mass: ti.template()\n):\n \n    max_y = -1e9\n    for i in range(num_particles):\n        if pos[i].y > max_y:\n            max_y = pos[i].y\n    for i in range(num_particles):\n        if pos[i].y >= max_y - 1e-6:\n            inv_mass[i] = 0.0\n\n\n@ti.kernel\ndef initialize_colors(\n    num_particles: ti.i32,\n    pos: ti.template(), vertex_colors: ti.template()\n):\n  \n    for i in range(num_particles):\n        x_coord = int((pos[i].x + 1.0) * 8) % 2\n        y_coord = int((pos[i].y + 1.0) * 8) % 2\n        \n        if (x_coord + y_coord) % 2 == 0:\n            vertex_colors[i] = ti.Vector([0.15, 0.35, 0.75])  # deep blue\n        else:\n            vertex_colors[i] = ti.Vector([0.95, 0.92, 0.85])  # light cream\n\n\n@ti.kernel\ndef apply_grab(\n    particle_idx: ti.i32, target_x: ti.f64, target_y: ti.f64, target_z: ti.f64,\n    pos: ti.template(), vel: ti.template(), grab_indicator_pos: ti.template()\n):\n \n    if particle_idx != -1:\n        target_pos = ti.Vector([target_x, target_y, target_z])\n        pos[particle_idx] = target_pos\n        vel[particle_idx] = ti.Vector([0.0, 0.0, 0.0])\n        grab_indicator_pos[0] = target_pos\n"
  },
  {
    "path": "12_pbd_cloth/utils/constraint_finder.py",
    "content": "import numpy as np\n\n\ndef find_constraint_indices(tri_ids_np):\n  \n    edge_to_tri_map = {}\n    \n    # Build a map from edges to triangles\n    for i, tri in enumerate(tri_ids_np):\n        for j in range(3):\n            v0_idx, v1_idx = tri[j], tri[(j + 1) % 3]\n            edge = tuple(sorted((v0_idx, v1_idx)))\n            if edge not in edge_to_tri_map:\n                edge_to_tri_map[edge] = []\n            edge_to_tri_map[edge].append(i)\n    \n    # All edges are stretching constraints\n    stretching_ids = list(edge_to_tri_map.keys())\n    \n    # Bending constraints: diagonals between triangles sharing an edge\n    bending_ids = []\n    for edge, tris in edge_to_tri_map.items():\n        if len(tris) == 2:  # Edge shared by exactly two triangles\n            tri0_idx, tri1_idx = tris[0], tris[1]\n            # Find the vertices not on the shared edge\n            p2 = [v for v in tri_ids_np[tri0_idx] if v not in edge][0]\n            p3 = [v for v in tri_ids_np[tri1_idx] if v not in edge][0]\n            bending_ids.append([p2, p3])\n    \n    return np.array(stretching_ids, dtype=np.int32), np.array(bending_ids, dtype=np.int32)\n\n\ndef find_bottom_corner(pos_np):\n   \n    min_y = float('inf')\n    min_x = float('inf')\n    corner_idx = -1\n    \n    # Find minimum y\n    for i in range(len(pos_np)):\n        if pos_np[i, 1] < min_y:\n            min_y = pos_np[i, 1]\n    \n    # Find minimum x among particles with minimum y\n    for i in range(len(pos_np)):\n        if abs(pos_np[i, 1] - min_y) < 1e-6:\n            if pos_np[i, 0] < min_x:\n                min_x = pos_np[i, 0]\n                corner_idx = i\n    \n    print(f\"Found bottom corner particle: {corner_idx} at position ({min_x:.3f}, {min_y:.3f})\")\n    return corner_idx\n\n\ndef calculate_quadratic_path_pos(start_pos, end_pos, t):\n  \n    t_squared = t * t\n    scaled_displacement = (end_pos - start_pos) * 0.3\n    return start_pos + scaled_displacement * t_squared\n"
  },
  {
    "path": "12_pbd_cloth/utils/mesh_loader.py",
    "content": "import json\nimport numpy as np\n\n\ndef load_cloth_data_from_json(filepath=\"cloth_data.json\"):\n    \"\"\"\n    Load cloth mesh data from a JSON file.\n    \n    Expected JSON format:\n    {\n        \"vertices\": [[x, y, z], ...],\n        \"faceTriIds\": [i0, i1, i2, ...]\n    }\n    \n    \"\"\"\n    try:\n        with open(filepath, 'r') as f:\n            data = json.load(f)\n        vertices = np.array(data['vertices'], dtype=np.float64).reshape((-1, 3))\n        face_tri_ids = np.array(data['faceTriIds'], dtype=np.int32)\n        print(f\"Loaded cloth data: {len(vertices)} vertices, {len(face_tri_ids)//3} triangles\")\n        return vertices, face_tri_ids\n    except Exception as e:\n        print(f\"Error loading cloth data from {filepath}: {e}\")\n        print(\"Falling back to procedural cloth generation...\")\n        verts_np, tris_np = create_cloth_mesh_data()\n        return verts_np, tris_np.flatten()\n\n\ndef create_cloth_mesh_data(width=20, height=15, spacing=0.1):\n\n    num_particles = width * height\n    verts = np.zeros((num_particles, 3), dtype=np.float64)\n    offset_x = - (width - 1) * spacing / 2.0\n    offset_y = - (height - 1) * spacing / 2.0 + (height * spacing * 0.8)\n    \n    for y in range(height):\n        for x in range(width):\n            idx = y * width + x\n            verts[idx] = [x * spacing + offset_x, y * spacing + offset_y, 0]\n    \n    num_tris = 2 * (width - 1) * (height - 1)\n    tri_ids = np.zeros((num_tris, 3), dtype=np.int32)\n    tri_idx = 0\n    \n    for y in range(height - 1):\n        for x in range(width - 1):\n            p0, p1, p2, p3 = y*width+x, y*width+x+1, (y+1)*width+x, (y+1)*width+x+1\n            tri_ids[tri_idx], tri_idx = [p0, p1, p2], tri_idx + 1\n            tri_ids[tri_idx], tri_idx = [p1, p3, p2], tri_idx + 1\n    \n    return verts, tri_ids\n"
  },
  {
    "path": "12_pbd_cloth/xpbd_base.py",
    "content": "\"\"\"\nThis module contains: \n- Time integration (pre_solve, post_solve)\n- Physics initialization (init_physics)\n\"\"\"\n\nimport taichi as ti\n\n\n@ti.kernel\ndef init_physics(\n    num_particles: ti.i32, num_tris: ti.i32,\n    num_stretching_constraints: ti.i32, num_bending_constraints: ti.i32,\n    pos: ti.template(), prev_pos: ti.template(), vel: ti.template(),\n    inv_mass: ti.template(), original_inv_mass: ti.template(),\n    tri_ids: ti.template(), stretching_ids: ti.template(), bending_ids: ti.template(),\n    stretching_lengths: ti.template(), bending_lengths: ti.template()\n):\n    \"\"\"\n    1. Initialize previous positions and velocities\n    2. Compute inverse masses from triangle areas\n    3. Compute rest lengths for stretching and bending constraints\n    4. Store original inverse masses for later restoration\n    \"\"\"\n    for i in range(num_particles):\n        prev_pos[i] = pos[i]\n        vel[i] = ti.Vector([0.0, 0.0, 0.0])\n    \n    inv_mass.fill(0.0)\n    for i in range(num_tris):\n        id0, id1, id2 = tri_ids[i * 3], tri_ids[i * 3 + 1], tri_ids[i * 3 + 2]\n        p0, p1, p2 = pos[id0], pos[id1], pos[id2]\n        area = 0.5 * (p1 - p0).cross(p2 - p0).norm()\n        p_inv_mass = 1.0 / (area / 3.0) if area > 0 else 0.0\n        inv_mass[id0] += p_inv_mass\n        inv_mass[id1] += p_inv_mass\n        inv_mass[id2] += p_inv_mass\n    \n    for i in range(num_stretching_constraints):\n        id0, id1 = stretching_ids[i, 0], stretching_ids[i, 1]\n        stretching_lengths[i] = (pos[id0] - pos[id1]).norm()\n    \n    for i in range(num_bending_constraints):\n        id0, id1 = bending_ids[i, 0], bending_ids[i, 1]\n        bending_lengths[i] = (pos[id0] - pos[id1]).norm()\n    \n    for i in range(num_particles):\n        original_inv_mass[i] = inv_mass[i]\n\n\n@ti.kernel\ndef pre_solve(\n    dt: ti.f64, num_particles: ti.i32,\n    gravity: ti.template(),\n    pos: ti.template(), prev_pos: ti.template(), vel: ti.template(), inv_mass: ti.template()\n):\n    \"\"\"\n    1. Apply gravity to velocities\n    2. Save current positions\n    3. Integrate positions forward\n    4. Handle ground collision (simple reflection at y=0)\n    \"\"\"\n    for i in range(num_particles):\n        if inv_mass[i] == 0.0: continue\n        vel[i] += gravity * dt\n        prev_pos[i] = pos[i]\n        pos[i] += vel[i] * dt\n        if pos[i].y < 0.0:\n            pos[i] = prev_pos[i]\n            pos[i].y = 0.0\n\n\n@ti.kernel\ndef post_solve(\n    dt: ti.f64, num_particles: ti.i32,\n    pos: ti.template(), prev_pos: ti.template(), vel: ti.template(), inv_mass: ti.template()\n):\n    for i in range(num_particles):\n        if inv_mass[i] == 0.0: continue\n        vel[i] = (pos[i] - prev_pos[i]) / dt\n"
  },
  {
    "path": "13_pbd_mesh/constraints/__init__.py",
    "content": "\"\"\"\nConstraints Package\n\nThis package contains all constraint solvers for the XPBD mesh simulation:\n- edge: Edge length constraints for structural stability\n- volume: Volume constraints for tetrahedra to prevent collapse\n\"\"\"\n\nfrom .edge import solve_edges\nfrom .volume import solve_volumes\n\n__all__ = [\n    'solve_edges',\n    'solve_volumes',\n]\n"
  },
  {
    "path": "13_pbd_mesh/constraints/edge.py",
    "content": "import taichi as ti\n\n\n@ti.kernel\ndef solve_edges(\n    compliance: ti.f64, dt: ti.f64, num_edges: ti.i32,\n    pos: ti.template(), edge_ids: ti.template(), edge_lengths: ti.template(),\n    inv_mass: ti.template(), lambdas: ti.template()\n):\n    alpha = compliance / (dt * dt)\n    for i in range(num_edges):\n        id0, id1 = edge_ids[i, 0], edge_ids[i, 1]\n        w0, w1 = inv_mass[id0], inv_mass[id1]\n        w_sum = w0 + w1\n        if w_sum == 0.0: continue\n        delta = pos[id0] - pos[id1]\n        dist = delta.norm()\n        if dist == 0.0: continue\n        grad = delta / dist\n        C = dist - edge_lengths[i]\n        dlambda = -(C + alpha * lambdas[i]) / (w_sum + alpha)\n        lambdas[i] += dlambda\n        pos[id0] += dlambda * w0 * grad\n        pos[id1] -= dlambda * w1 * grad\n"
  },
  {
    "path": "13_pbd_mesh/constraints/volume.py",
    "content": "import taichi as ti\nimport sys\nimport os\n# Add parent directory to path to import xpbd_base\n_parent_dir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nif _parent_dir not in sys.path:\n    sys.path.insert(0, _parent_dir)\nfrom xpbd_base import get_tet_volume\n\n\n@ti.kernel\ndef solve_volumes(\n    compliance: ti.f64, dt: ti.f64, num_tets: ti.i32,\n    pos: ti.template(), tet_ids: ti.template(), rest_vol: ti.template(), inv_mass: ti.template(),\n    vol_id_order: ti.template(), lambdas: ti.template()\n):\n    alpha = compliance / (dt * dt)\n    for i in range(num_tets):\n        p_indices = ti.Vector([tet_ids[i, 0], tet_ids[i, 1], tet_ids[i, 2], tet_ids[i, 3]])\n        w_sum = 0.0\n        grads = ti.Matrix.zero(ti.f64, 4, 3)\n        for j in ti.static(range(4)):\n            ids = ti.Vector([p_indices[vol_id_order[j, c]] for c in range(3)])\n            p0, p1, p2 = pos[ids[0]], pos[ids[1]], pos[ids[2]]\n            grad = (p1 - p0).cross(p2 - p0) / 6.0\n            grads[j, :] = grad\n            w_sum += inv_mass[p_indices[j]] * grad.norm_sqr()\n        if w_sum == 0.0: continue\n        C = get_tet_volume(p_indices, pos) - rest_vol[i]\n        dlambda = -(C + alpha * lambdas[i]) / (w_sum + alpha)\n        lambdas[i] += dlambda\n        for j in ti.static(range(4)):\n            pos[p_indices[j]] += dlambda * inv_mass[p_indices[j]] * grads[j, :]\n"
  },
  {
    "path": "13_pbd_mesh/dragon_data.json",
    "content": "\n{\n    \"verts\" : [\n-0.067935,  1.288305, -0.082477,  0.003506,  1.248151, -0.070033,  0.001571,  1.244475, -0.167807, -0.082122,  1.289001, -0.158913, \n0.075577,  1.205556, -0.085262,  0.086003,  1.196606, -0.169586, -0.000598,  1.241600, -0.265073, -0.075249,  1.280443, -0.233302, \n0.072027,  1.200585, -0.252378, -0.181908,  1.304366, -0.112030, -0.133853,  1.321139, -0.019623,  0.128278,  1.171134, -0.319993, \n-0.008263,  1.234653, -0.372647,  0.002688,  1.257620,  0.033030, -0.174918,  1.282726, -0.218455,  0.136393,  1.188153, -0.019390, \n0.179567,  1.156401, -0.169651,  0.103378,  1.359907, -0.076255,  0.054315,  1.421892, -0.080737,  0.104871,  1.371044, -0.172360, \n0.038392,  1.432074, -0.161453,  0.153649,  1.296934, -0.099417,  0.164369,  1.298177, -0.184921,  0.097664,  1.371062, -0.267377, \n0.046405,  1.427282, -0.235312,  0.145656,  1.303384, -0.261465, -0.018426,  1.540807, -0.155760,  0.007153,  1.485969, -0.012746, \n0.196154,  1.285770, 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-0.239054, -0.355019,  1.987958, -0.218115, -0.231851,  1.809961, -0.156157, -0.229655,  1.791259, -0.209656, \n-0.265450,  1.872129, -0.156965, -0.278477,  1.883849, -0.202584, -0.249736,  1.812189, -0.269500, -0.278294,  1.870008, -0.251976, \n-0.157419,  1.840701, -0.192166, -0.155527,  1.824586, -0.238263, -0.186369,  1.894268, -0.192861, -0.197594,  1.904366, -0.232169, \n-0.172830,  1.842621, -0.289827, -0.197436,  1.892440, -0.274728, -0.088877,  1.879210, -0.224357, -0.087338,  1.866112, -0.261828, \n-0.112409,  1.922753, -0.224922, -0.121534,  1.930962, -0.256874, -0.101403,  1.880771, -0.303743, -0.121405,  1.921268, -0.291469, \n-0.005016,  1.938426, -0.272145, -0.004284,  1.932194, -0.289974, -0.016213,  1.959145, -0.272414, -0.020555,  1.963051, -0.287617, \n-0.010976,  1.939169, -0.309918, -0.020494,  1.958438, -0.304078, -0.235657,  1.482269, -0.354519, -0.311173,  1.478340, -0.383676, \n-0.220749,  1.580119, -0.372853, -0.304255,  1.589198, -0.407754, -0.257143,  1.671165, -0.327515, -0.337475,  1.669567, -0.357897, \n-0.340432,  1.752723, -0.297254, -0.397379,  1.752027, -0.320563, -0.381580,  1.784705, -0.288781, -0.482284,  1.815994, -0.297580, \n-0.418682,  1.598247, -0.385624, -0.462596,  1.595175, -0.364133, -0.443574,  1.652777, -0.365897, -0.485030,  1.639512, -0.347000, \n-0.483010,  1.710376, -0.338505, -0.518619,  1.690785, -0.323372, -0.526085,  1.754547, -0.318661, -0.538853,  1.724944, -0.308700, \n-0.361714,  1.630437, -0.401060, -0.391051,  1.672439, -0.380057, -0.465445,  1.745199, -0.356638, -0.505952,  1.783021, -0.336281, \n-0.384771,  1.806392, -0.323836, -0.403839,  1.793230, -0.342988, -0.398372,  1.830163, -0.312201, -0.447822,  1.845106, -0.324431, \n-0.472811,  1.825094, -0.351638, -0.456603,  1.803627, -0.360269, -0.369945,  1.832066, -0.348766, -0.382180,  1.825206, -0.363641, \n-0.377783,  1.849332, -0.341686, -0.408198,  1.864335, -0.354082, -0.424307,  1.853498, -0.375050, -0.414782,  1.837508, -0.379827, \n-0.203019,  1.612761, -0.376444, -0.255069,  1.617073, -0.426230, -0.237903,  1.686575, -0.351574, -0.282462,  1.692255, -0.392562, \n-0.284350,  1.757008, -0.341328, -0.322153,  1.767123, -0.371753, -0.305907,  1.697302, -0.412438, -0.288897,  1.662178, -0.423850, \n-0.340966,  1.765011, -0.392760, -0.185162,  1.641927, -0.407919, -0.203824,  1.635811, -0.427870, -0.192150,  1.677370, -0.398565, \n-0.208392,  1.684142, -0.413583, -0.226533,  1.683118, -0.433909, -0.220758,  1.662031, -0.436028, -0.207475,  1.747180, -0.401046, \n-0.212448,  1.740988, -0.420762, -0.217124,  1.768198, -0.393857, -0.229373,  1.776849, -0.411475, -0.235024,  1.775081, -0.425552, \n-0.219968,  1.745843, -0.432219, -0.303126,  1.159700, -0.146851, -0.315364,  1.168176, -0.200909, -0.243315,  1.251629, -0.181745, \n-0.245862,  1.256281, -0.216783, -0.193333,  1.360323, -0.177638, -0.199342,  1.351720, -0.232844, -0.183250,  1.479429, -0.202880, \n-0.191723,  1.476408, -0.237475, -0.173252,  1.564945, -0.206386, -0.184226,  1.562824, -0.242513, -0.198529,  1.678659, -0.196926, \n-0.209159,  1.679416, -0.226669, -0.291517,  1.757451, -0.185293, -0.309513,  1.756183, -0.224338, -0.296402,  1.582637,  0.043769, \n-0.209789,  1.593744, -0.007833, -0.314577,  1.646383,  0.039223, -0.264866,  1.671860, -0.007617, -0.368320,  1.713544,  0.046490, \n-0.280003,  1.749997,  0.004662, -0.416223,  1.758006,  0.061844, -0.367750,  1.806139,  0.040032, -0.457209,  1.828056, -0.017492, \n-0.417318,  1.826629, -0.014055, -0.275877,  1.499083,  0.022547, -0.189713,  1.492837, -0.024779, -0.177127,  1.589953, -0.103622, \n-0.224345,  1.694967, -0.106810, -0.176843,  1.594339, -0.026451, -0.220057,  1.691055, -0.020035, -0.275335,  1.768685, -0.073124, \n-0.250510,  1.768917, -0.007057, -0.344714,  1.814445, -0.057369, -0.330066,  1.820805,  0.033237, -0.398909,  1.831208, -0.035006, \n-0.377811,  1.841501,  0.010845, -0.148478,  1.472089, -0.087203, -0.144082,  1.490044, -0.044022, -0.255188,  1.840626, -0.050387, \n-0.282408,  1.864384, -0.044227, -0.245036,  1.839366, -0.022054, -0.276332,  1.866347, -0.005482, -0.304974,  1.874958, -0.035132, \n-0.295699,  1.878140, -0.015454, -0.115934,  1.536853, -0.085969, -0.109236,  1.540295, -0.053553, -0.111010,  1.486371, -0.078724, \n-0.107697,  1.493573, -0.060531, -0.076019,  1.729601, -0.111860, -0.088841,  1.771242, -0.096758, -0.075412,  1.728518, -0.070139, \n-0.087140,  1.766435, -0.064428, -0.082589,  1.602400, -0.110502, -0.083029,  1.669789, -0.110758, -0.076403,  1.603632, -0.065720, \n-0.076058,  1.665504, -0.060537, -0.231240,  1.483415, -0.404736, -0.263135,  1.481755, -0.417050, -0.224943,  1.524743, -0.412479, \n-0.260213,  1.528577, -0.427220, -0.178381,  1.337394, -0.139442, -0.175073,  1.327155, -0.189794, -0.030360,  1.553008, -0.184191, \n-0.019796,  1.546447, -0.230715,  0.202285,  1.644248, -0.171367,  0.209754,  1.644888, -0.221304,  0.430427,  1.626671, -0.147212, \n0.439749,  1.624666, -0.205838,  0.593171,  1.525774, -0.110018,  0.607500,  1.526855, -0.188342,  0.681288,  1.378977, -0.114069, \n0.697556,  1.387882, -0.206391,  0.775100,  1.458657, -0.103302,  0.785488,  1.436024, -0.138109,  0.836248,  1.508391, -0.102501, \n0.853436,  1.481346, -0.137697,  0.785481,  1.445862, -0.058266,  0.827052,  1.494028, -0.051581,  0.905071,  1.507110, -0.062274, \n0.922145,  1.500188, -0.093569,  0.901133,  1.476639, -0.027774],\n    \"tetIds\" : [\n    1,0,2,521,522,0,521,2,522,2,521,523,524,522,523,3,523,2,3,522,\n2,0,3,522,2,3,1,19,20,3,19,1,20,1,19,17,18,20,17,0,\n17,1,0,20,1,3,0,20,4,1,5,525,521,1,525,5,521,5,525,526,\n523,521,526,2,526,5,2,521,5,1,2,521,5,2,4,22,19,2,22,4,\n19,4,22,21,17,19,21,1,21,4,1,19,4,2,1,19,3,0,9,524,\n522,0,524,9,522,9,524,530,531,522,530,10,530,9,10,522,9,0,10,522,\n9,10,3,26,27,10,26,3,27,3,26,20,18,27,20,0,20,3,0,27,\n3,10,0,27,8,6,11,529,527,6,529,11,527,11,529,532,533,527,532,12,\n532,11,12,527,11,6,12,527,11,12,8,28,29,12,28,8,29,8,28,25,\n23,29,25,6,25,8,6,29,8,12,6,29,0,1,10,522,521,1,522,10,\n521,10,522,531,534,521,531,13,531,10,13,521,10,1,13,521,10,13,0,27,\n30,13,27,0,30,0,27,18,17,30,18,1,18,0,1,30,0,13,1,30,\n6,7,12,527,528,7,527,12,528,12,527,533,535,528,533,14,533,12,14,528,\n12,7,14,528,12,14,6,29,31,14,29,6,31,6,29,23,24,31,23,7,\n23,6,7,31,6,14,7,31,7,3,14,528,524,3,528,14,524,14,528,535,\n530,524,535,9,535,14,9,524,14,3,9,524,14,9,7,31,26,9,31,7,\n26,7,31,24,20,26,24,3,24,7,3,26,7,9,3,26,4,5,15,525,\n526,5,525,15,526,15,525,536,537,526,536,16,536,15,16,526,15,5,16,526,\n15,16,4,32,33,16,32,4,33,4,32,21,22,33,21,5,21,4,5,33,\n4,16,5,33,1,4,13,521,525,4,521,13,525,13,521,534,536,525,534,15,\n534,13,15,525,13,4,15,525,13,15,1,30,32,15,30,1,32,1,30,17,\n21,32,17,4,17,1,4,32,1,15,4,32,19,20,17,36,37,20,36,17,\n37,17,36,34,35,37,34,18,34,17,18,37,17,20,18,37,22,19,21,39,\n36,19,39,21,36,21,39,38,34,36,38,17,38,21,17,36,21,19,17,36,\n23,24,19,40,41,24,40,19,41,19,40,36,37,41,36,20,36,19,20,41,\n19,24,20,41,25,23,22,42,40,23,42,22,40,22,42,39,36,40,39,19,\n39,22,19,40,22,23,19,40,26,27,20,43,44,27,43,20,44,20,43,37,\n35,44,37,18,37,20,18,44,20,27,18,44,28,29,25,45,46,29,45,25,\n46,25,45,42,40,46,42,23,42,25,23,46,25,29,23,46,27,30,18,44,\n47,30,44,18,47,18,44,35,34,47,35,17,35,18,17,47,18,30,17,47,\n29,31,23,46,48,31,46,23,48,23,46,40,41,48,40,24,40,23,24,48,\n23,31,24,48,26,31,9,1215,1216,31,1215,9,1216,9,1215,1213,1214,1216,1213,14,\n1213,9,14,1216,9,31,14,1216,31,26,24,48,43,26,48,24,43,24,48,41,\n37,43,41,20,41,24,20,43,24,26,20,43,32,33,21,49,50,33,49,21,\n50,21,49,38,39,50,38,22,38,21,22,50,21,33,22,50,30,32,17,47,\n49,32,47,17,49,17,47,34,38,49,34,21,34,17,21,49,17,32,21,49,\n33,28,22,50,45,28,50,22,45,22,50,39,42,45,39,25,39,22,25,45,\n22,28,25,45,36,37,34,53,54,37,53,34,54,34,53,51,52,54,51,35,\n51,34,35,54,34,37,35,54,39,36,38,56,53,36,56,38,53,38,56,55,\n51,53,55,34,55,38,34,53,38,36,34,53,40,41,36,57,58,41,57,36,\n58,36,57,53,54,58,53,37,53,36,37,58,36,41,37,58,42,40,39,59,\n57,40,59,39,57,39,59,56,53,57,56,36,56,39,36,57,39,40,36,57,\n43,44,37,60,61,44,60,37,61,37,60,54,52,61,54,35,54,37,35,61,\n37,44,35,61,45,46,42,62,63,46,62,42,63,42,62,59,57,63,59,40,\n59,42,40,63,42,46,40,63,44,47,35,61,64,47,61,35,64,35,61,52,\n51,64,52,34,52,35,34,64,35,47,34,64,46,48,40,63,65,48,63,40,\n65,40,63,57,58,65,57,41,57,40,41,65,40,48,41,65,43,48,26,1217,\n1218,48,1217,26,1218,26,1217,1215,1216,1218,1215,31,1215,26,31,1218,26,48,31,1218,\n48,43,41,65,60,43,65,41,60,41,65,58,54,60,58,37,58,41,37,60,\n41,43,37,60,49,50,38,66,67,50,66,38,67,38,66,55,56,67,55,39,\n55,38,39,67,38,50,39,67,47,49,34,64,66,49,64,34,66,34,64,51,\n55,66,51,38,51,34,38,66,34,49,38,66,50,45,39,67,62,45,67,39,\n62,39,67,56,59,62,56,42,56,39,42,62,39,45,42,62,53,54,51,70,\n71,54,70,51,71,51,70,68,69,71,68,52,68,51,52,71,51,54,52,71,\n56,53,55,73,70,53,73,55,70,55,73,72,68,70,72,51,72,55,51,70,\n55,53,51,70,57,58,53,74,75,58,74,53,75,53,74,70,71,75,70,54,\n70,53,54,75,53,58,54,75,59,57,56,76,74,57,76,56,74,56,76,73,\n70,74,73,53,73,56,53,74,56,57,53,74,60,61,54,77,78,61,77,54,\n78,54,77,71,69,78,71,52,71,54,52,78,54,61,52,78,62,63,59,79,\n80,63,79,59,80,59,79,76,74,80,76,57,76,59,57,80,59,63,57,80,\n61,64,52,78,81,64,78,52,81,52,78,69,68,81,69,51,69,52,51,81,\n52,64,51,81,63,65,57,80,82,65,80,57,82,57,80,74,75,82,74,58,\n74,57,58,82,57,65,58,82,60,65,43,1219,1220,65,1219,43,1220,43,1219,1217,\n1218,1220,1217,48,1217,43,48,1220,43,65,48,1220,65,60,58,82,77,60,82,58,\n77,58,82,75,71,77,75,54,75,58,54,77,58,60,54,77,66,67,55,83,\n84,67,83,55,84,55,83,72,73,84,72,56,72,55,56,84,55,67,56,84,\n64,66,51,81,83,66,81,51,83,51,81,68,72,83,68,55,68,51,55,83,\n51,66,55,83,67,62,56,84,79,62,84,56,79,56,84,73,76,79,73,59,\n73,56,59,79,56,62,59,79,70,71,68,87,88,71,87,68,88,68,87,85,\n86,88,85,69,85,68,69,88,68,71,69,88,73,70,72,90,87,70,90,72,\n87,72,90,89,85,87,89,68,89,72,68,87,72,70,68,87,74,75,70,91,\n92,75,91,70,92,70,91,87,88,92,87,71,87,70,71,92,70,75,71,92,\n76,74,73,93,91,74,93,73,91,73,93,90,87,91,90,70,90,73,70,91,\n73,74,70,91,77,78,71,94,95,78,94,71,95,71,94,88,86,95,88,69,\n88,71,69,95,71,78,69,95,79,80,76,96,97,80,96,76,97,76,96,93,\n91,97,93,74,93,76,74,97,76,80,74,97,78,81,69,95,98,81,95,69,\n98,69,95,86,85,98,86,68,86,69,68,98,69,81,68,98,80,82,74,97,\n99,82,97,74,99,74,97,91,92,99,91,75,91,74,75,99,74,82,75,99,\n77,82,60,1221,1222,82,1221,60,1222,60,1221,1219,1220,1222,1219,65,1219,60,65,1222,\n60,82,65,1222,82,77,75,99,94,77,99,75,94,75,99,92,88,94,92,71,\n92,75,71,94,75,77,71,94,83,84,72,100,101,84,100,72,101,72,100,89,\n90,101,89,73,89,72,73,101,72,84,73,101,81,83,68,98,100,83,98,68,\n100,68,98,85,89,100,85,72,85,68,72,100,68,83,72,100,84,79,73,101,\n96,79,101,73,96,73,101,90,93,96,90,76,90,73,76,96,73,79,76,96,\n87,88,85,104,105,88,104,85,105,85,104,102,103,105,102,86,102,85,86,105,\n85,88,86,105,90,87,89,107,104,87,107,89,104,89,107,106,102,104,106,85,\n106,89,85,104,89,87,85,104,91,92,87,108,109,92,108,87,109,87,108,104,\n105,109,104,88,104,87,88,109,87,92,88,109,93,91,90,110,108,91,110,90,\n108,90,110,107,104,108,107,87,107,90,87,108,90,91,87,108,94,95,88,111,\n112,95,111,88,112,88,111,105,103,112,105,86,105,88,86,112,88,95,86,112,\n96,97,93,113,114,97,113,93,114,93,113,110,108,114,110,91,110,93,91,114,\n93,97,91,114,95,98,86,112,115,98,112,86,115,86,112,103,102,115,103,85,\n103,86,85,115,86,98,85,115,97,99,91,114,116,99,114,91,116,91,114,108,\n109,116,108,92,108,91,92,116,91,99,92,116,94,99,77,1223,1224,99,1223,77,\n1224,77,1223,1221,1222,1224,1221,82,1221,77,82,1224,77,99,82,1224,99,94,92,116,\n111,94,116,92,111,92,116,109,105,111,109,88,109,92,88,111,92,94,88,111,\n100,101,89,117,118,101,117,89,118,89,117,106,107,118,106,90,106,89,90,118,\n89,101,90,118,98,100,85,115,117,100,115,85,117,85,115,102,106,117,102,89,\n102,85,89,117,85,100,89,117,101,96,90,118,113,96,118,90,113,90,118,107,\n110,113,107,93,107,90,93,113,90,96,93,113,104,105,102,121,122,105,121,102,\n122,102,121,119,120,122,119,103,119,102,103,122,102,105,103,122,107,104,106,124,\n121,104,124,106,121,106,124,123,119,121,123,102,123,106,102,121,106,104,102,121,\n108,109,104,125,126,109,125,104,126,104,125,121,122,126,121,105,121,104,105,126,\n104,109,105,126,110,108,107,127,125,108,127,107,125,107,127,124,121,125,124,104,\n124,107,104,125,107,108,104,125,111,112,105,128,129,112,128,105,129,105,128,122,\n120,129,122,103,122,105,103,129,105,112,103,129,113,114,110,130,131,114,130,110,\n131,110,130,127,125,131,127,108,127,110,108,131,110,114,108,131,112,115,103,129,\n132,115,129,103,132,103,129,120,119,132,120,102,120,103,102,132,103,115,102,132,\n114,116,108,131,133,116,131,108,133,108,131,125,126,133,125,109,125,108,109,133,\n108,116,109,133,116,111,109,133,128,111,133,109,128,109,133,126,122,128,126,105,\n126,109,105,128,109,111,105,128,117,118,106,134,135,118,134,106,135,106,134,123,\n124,135,123,107,123,106,107,135,106,118,107,135,115,117,102,132,134,117,132,102,\n134,102,132,119,123,134,119,106,119,102,106,134,102,117,106,134,118,113,107,135,\n130,113,135,107,130,107,135,124,127,130,124,110,124,107,110,130,107,113,110,130,\n121,122,119,138,139,122,138,119,139,119,138,136,137,139,136,120,136,119,120,139,\n119,122,120,139,124,121,123,141,138,121,141,123,138,123,141,140,136,138,140,119,\n140,123,119,138,123,121,119,138,125,126,121,142,143,126,142,121,143,121,142,138,\n139,143,138,122,138,121,122,143,121,126,122,143,127,125,124,144,142,125,144,124,\n142,124,144,141,138,142,141,121,141,124,121,142,124,125,121,142,128,129,122,145,\n146,129,145,122,146,122,145,139,137,146,139,120,139,122,120,146,122,129,120,146,\n130,131,127,147,148,131,147,127,148,127,147,144,142,148,144,125,144,127,125,148,\n127,131,125,148,129,132,120,146,149,132,146,120,149,120,146,137,136,149,137,119,\n137,120,119,149,120,132,119,149,131,133,125,148,150,133,148,125,150,125,148,142,\n143,150,142,126,142,125,126,150,125,133,126,150,133,128,126,150,145,128,150,126,\n145,126,150,143,139,145,143,122,143,126,122,145,126,128,122,145,134,135,123,151,\n152,135,151,123,152,123,151,140,141,152,140,124,140,123,124,152,123,135,124,152,\n132,134,119,149,151,134,149,119,151,119,149,136,140,151,136,123,136,119,123,151,\n119,134,123,151,135,130,124,152,147,130,152,124,147,124,152,141,144,147,141,127,\n141,124,127,147,124,130,127,147,138,139,136,155,156,139,155,136,156,136,155,153,\n154,156,153,137,153,136,137,156,136,139,137,156,141,138,140,158,155,138,158,140,\n155,140,158,157,153,155,157,136,157,140,136,155,140,138,136,155,142,143,138,159,\n160,143,159,138,160,138,159,155,156,160,155,139,155,138,139,160,138,143,139,160,\n144,142,141,161,159,142,161,141,159,141,161,158,155,159,158,138,158,141,138,159,\n141,142,138,159,145,146,139,162,163,146,162,139,163,139,162,156,154,163,156,137,\n156,139,137,163,139,146,137,163,147,148,144,164,165,148,164,144,165,144,164,161,\n159,165,161,142,161,144,142,165,144,148,142,165,146,149,137,163,166,149,163,137,\n166,137,163,154,153,166,154,136,154,137,136,166,137,149,136,166,148,150,142,165,\n167,150,165,142,167,142,165,159,160,167,159,143,159,142,143,167,142,150,143,167,\n150,145,143,167,162,145,167,143,162,143,167,160,156,162,160,139,160,143,139,162,\n143,145,139,162,151,152,140,168,169,152,168,140,169,140,168,157,158,169,157,141,\n157,140,141,169,140,152,141,169,149,151,136,166,168,151,166,136,168,136,166,153,\n157,168,153,140,153,136,140,168,136,151,140,168,152,147,141,169,164,147,169,141,\n164,141,169,158,161,164,158,144,158,141,144,164,141,147,144,164,155,156,153,172,\n173,156,172,153,173,153,172,170,171,173,170,154,170,153,154,173,153,156,154,173,\n158,155,157,175,172,155,175,157,172,157,175,174,170,172,174,153,174,157,153,172,\n157,155,153,172,159,160,155,176,177,160,176,155,177,155,176,172,173,177,172,156,\n172,155,156,177,155,160,156,177,161,159,158,178,176,159,178,158,176,158,178,175,\n172,176,175,155,175,158,155,176,158,159,155,176,162,163,156,179,180,163,179,156,\n180,156,179,173,171,180,173,154,173,156,154,180,156,163,154,180,164,165,161,181,\n182,165,181,161,182,161,181,178,176,182,178,159,178,161,159,182,161,165,159,182,\n163,166,154,180,183,166,180,154,183,154,180,171,170,183,171,153,171,154,153,183,\n154,166,153,183,165,167,159,182,184,167,182,159,184,159,182,176,177,184,176,160,\n176,159,160,184,159,167,160,184,167,162,160,184,179,162,184,160,179,160,184,177,\n173,179,177,156,177,160,156,179,160,162,156,179,168,169,157,185,186,169,185,157,\n186,157,185,174,175,186,174,158,174,157,158,186,157,169,158,186,166,168,153,183,\n185,168,183,153,185,153,183,170,174,185,170,157,170,153,157,185,153,168,157,185,\n169,164,158,186,181,164,186,158,181,158,186,175,178,181,175,161,175,158,161,181,\n158,164,161,181,172,173,170,189,190,173,189,170,190,170,189,187,188,190,187,171,\n187,170,171,190,170,173,171,190,175,172,174,192,189,172,192,174,189,174,192,191,\n187,189,191,170,191,174,170,189,174,172,170,189,176,177,172,193,194,177,193,172,\n194,172,193,189,190,194,189,173,189,172,173,194,172,177,173,194,178,176,175,195,\n193,176,195,175,193,175,195,192,189,193,192,172,192,175,172,193,175,176,172,193,\n179,180,173,196,197,180,196,173,197,173,196,190,188,197,190,171,190,173,171,197,\n173,180,171,197,181,182,178,198,199,182,198,178,199,178,198,195,193,199,195,176,\n195,178,176,199,178,182,176,199,183,180,166,406,407,180,406,166,407,166,406,404,\n405,407,404,163,404,166,163,407,166,180,163,407,180,183,171,197,200,183,197,171,\n200,171,197,188,187,200,188,170,188,171,170,200,171,183,170,200,182,184,176,199,\n201,184,199,176,201,176,199,193,194,201,193,177,193,176,177,201,176,184,177,201,\n184,179,177,201,196,179,201,177,196,177,201,194,190,196,194,173,194,177,173,196,\n177,179,173,196,185,186,174,202,203,186,202,174,203,174,202,191,192,203,191,175,\n191,174,175,203,174,186,175,203,185,183,168,409,406,183,409,168,406,168,409,408,\n404,406,408,166,408,168,166,406,168,183,166,406,183,185,170,200,202,185,200,170,\n202,170,200,187,191,202,187,174,187,170,174,202,170,185,174,202,186,181,175,203,\n198,181,203,175,198,175,203,192,195,198,192,178,192,175,178,198,175,181,178,198,\n189,190,187,206,207,190,206,187,207,187,206,204,205,207,204,188,204,187,188,207,\n187,190,188,207,192,189,191,209,206,189,209,191,206,191,209,208,204,206,208,187,\n208,191,187,206,191,189,187,206,193,194,189,210,211,194,210,189,211,189,210,206,\n207,211,206,190,206,189,190,211,189,194,190,211,195,193,192,212,210,193,212,192,\n210,192,212,209,206,210,209,189,209,192,189,210,192,193,189,210,197,196,180,240,\n241,196,240,180,241,180,240,238,239,241,238,179,238,180,179,241,180,196,179,241,\n196,197,190,213,214,197,213,190,214,190,213,207,205,214,207,188,207,190,188,214,\n190,197,188,214,199,198,182,384,385,198,384,182,385,182,384,382,383,385,382,181,\n382,182,181,385,182,198,181,385,198,199,195,215,216,199,215,195,216,195,215,212,\n210,216,212,193,212,195,193,216,195,199,193,216,200,197,183,410,411,197,410,183,\n411,183,410,406,407,411,406,180,406,183,180,411,183,197,180,411,197,200,188,214,\n217,200,214,188,217,188,214,205,204,217,205,187,205,188,187,217,188,200,187,217,\n201,199,184,387,384,199,387,184,384,184,387,386,382,384,386,182,386,184,182,384,\n184,199,182,384,199,201,193,216,218,201,216,193,218,193,216,210,211,218,210,194,\n210,193,194,218,193,201,194,218,196,201,179,241,243,201,241,179,243,179,241,239,\n242,243,239,184,239,179,184,243,179,201,184,243,201,196,194,218,213,196,218,194,\n213,194,218,211,207,213,211,190,211,194,190,213,194,196,190,213,202,203,191,219,\n220,203,219,191,220,191,219,208,209,220,208,192,208,191,192,220,191,203,192,220,\n202,200,185,412,410,200,412,185,410,185,412,409,406,410,409,183,409,185,183,410,\n185,200,183,410,200,202,187,217,219,202,217,187,219,187,217,204,208,219,204,191,\n204,187,191,219,187,202,191,219,198,203,181,385,389,203,385,181,389,181,385,383,\n388,389,383,186,383,181,186,389,181,203,186,389,203,198,192,220,215,198,220,192,\n215,192,220,209,212,215,209,195,209,192,195,215,192,198,195,215,206,207,204,223,\n224,207,223,204,224,204,223,221,222,224,221,205,221,204,205,224,204,207,205,224,\n209,206,208,226,223,206,226,208,223,208,226,225,221,223,225,204,225,208,204,223,\n208,206,204,223,210,211,206,227,228,211,227,206,228,206,227,223,224,228,223,207,\n223,206,207,228,206,211,207,228,212,210,209,229,227,210,229,209,227,209,229,226,\n223,227,226,206,226,209,206,227,209,210,206,227,214,213,197,244,245,213,244,197,\n245,197,244,240,241,245,240,196,240,197,196,245,197,213,196,245,213,214,207,230,\n231,214,230,207,231,207,230,224,222,231,224,205,224,207,205,231,207,214,205,231,\n216,215,199,390,391,215,390,199,391,199,390,384,385,391,384,198,384,199,198,391,\n199,215,198,391,215,216,212,232,233,216,232,212,233,212,232,229,227,233,229,210,\n229,212,210,233,212,216,210,233,217,214,200,413,414,214,413,200,414,200,413,410,\n411,414,410,197,410,200,197,414,200,214,197,414,214,217,205,231,234,217,231,205,\n234,205,231,222,221,234,222,204,222,205,204,234,205,217,204,234,218,216,201,392,\n390,216,392,201,390,201,392,387,384,390,387,199,387,201,199,390,201,216,199,390,\n216,218,210,233,235,218,233,210,235,210,233,227,228,235,227,211,227,210,211,235,\n210,218,211,235,213,218,196,245,246,218,245,196,246,196,245,241,243,246,241,201,\n241,196,201,246,196,218,201,246,218,213,211,235,230,213,235,211,230,211,235,228,\n224,230,228,207,228,211,207,230,211,213,207,230,219,220,208,236,237,220,236,208,\n237,208,236,225,226,237,225,209,225,208,209,237,208,220,209,237,219,217,202,415,\n413,217,415,202,413,202,415,412,410,413,412,200,412,202,200,413,202,217,200,413,\n217,219,204,234,236,219,234,204,236,204,234,221,225,236,221,208,221,204,208,236,\n204,219,208,236,215,220,198,391,393,220,391,198,393,198,391,385,389,393,385,203,\n385,198,203,393,198,220,203,393,220,215,209,237,232,215,237,209,232,209,237,226,\n229,232,226,212,226,209,212,232,209,215,212,232,231,230,214,247,248,230,247,214,\n248,214,247,244,245,248,244,213,244,214,213,248,214,230,213,248,234,231,217,416,\n417,231,416,217,417,217,416,413,414,417,413,214,413,217,214,417,217,231,214,417,\n230,235,213,248,249,235,248,213,249,213,248,245,246,249,245,218,245,213,218,249,\n213,235,218,249,240,238,197,418,419,238,418,197,419,197,418,411,407,419,411,180,\n411,197,180,419,197,238,180,419,240,241,238,252,253,241,252,238,253,238,252,250,\n251,253,250,239,250,238,239,253,238,241,239,253,241,243,239,253,255,243,253,239,\n255,239,253,251,254,255,251,242,251,239,242,255,239,243,242,255,244,240,214,420,\n418,240,420,214,418,214,420,414,411,418,414,197,414,214,197,418,214,240,197,418,\n244,245,240,256,257,245,256,240,257,240,256,252,253,257,252,241,252,240,241,257,\n240,245,241,257,245,246,241,257,258,246,257,241,258,241,257,253,255,258,253,243,\n253,241,243,258,241,246,243,258,247,244,231,422,420,244,422,231,420,231,422,417,\n414,420,417,214,417,231,214,420,231,244,214,420,247,248,244,259,260,248,259,244,\n260,244,259,256,257,260,256,245,256,244,245,260,244,248,245,260,248,249,245,260,\n261,249,260,245,261,245,260,257,258,261,257,246,257,245,246,261,245,249,246,261,\n252,253,250,264,265,253,264,250,265,250,264,262,263,265,262,251,262,250,251,265,\n250,253,251,265,253,255,251,265,267,255,265,251,267,251,265,263,266,267,263,254,\n263,251,254,267,251,255,254,267,256,257,252,268,269,257,268,252,269,252,268,264,\n265,269,264,253,264,252,253,269,252,257,253,269,257,258,253,269,270,258,269,253,\n270,253,269,265,267,270,265,255,265,253,255,270,253,258,255,270,259,260,256,271,\n272,260,271,256,272,256,271,268,269,272,268,257,268,256,257,272,256,260,257,272,\n260,261,257,272,273,261,272,257,273,257,272,269,270,273,269,258,269,257,258,273,\n257,261,258,273,264,265,262,276,277,265,276,262,277,262,276,274,275,277,274,263,\n274,262,263,277,262,265,263,277,265,267,263,277,279,267,277,263,279,263,277,275,\n278,279,275,266,275,263,266,279,263,267,266,279,268,269,264,280,281,269,280,264,\n281,264,280,276,277,281,276,265,276,264,265,281,264,269,265,281,269,270,265,281,\n282,270,281,265,282,265,281,277,279,282,277,267,277,265,267,282,265,270,267,282,\n271,272,268,283,284,272,283,268,284,268,283,280,281,284,280,269,280,268,269,284,\n268,272,269,284,272,273,269,284,285,273,284,269,285,269,284,281,282,285,281,270,\n281,269,270,285,269,273,270,285,276,277,274,288,289,277,288,274,289,274,288,286,\n287,289,286,275,286,274,275,289,274,277,275,289,277,279,275,289,291,279,289,275,\n291,275,289,287,290,291,287,278,287,275,278,291,275,279,278,291,280,281,276,292,\n293,281,292,276,293,276,292,288,289,293,288,277,288,276,277,293,276,281,277,293,\n281,282,277,293,294,282,293,277,294,277,293,289,291,294,289,279,289,277,279,294,\n277,282,279,294,283,284,280,295,296,284,295,280,296,280,295,292,293,296,292,281,\n292,280,281,296,280,284,281,296,284,285,281,296,297,285,296,281,297,281,296,293,\n294,297,293,282,293,281,282,297,281,285,282,297,288,289,286,300,301,289,300,286,\n301,286,300,298,299,301,298,287,298,286,287,301,286,289,287,301,289,291,287,301,\n303,291,301,287,303,287,301,299,302,303,299,290,299,287,290,303,287,291,290,303,\n292,293,288,304,305,293,304,288,305,288,304,300,301,305,300,289,300,288,289,305,\n288,293,289,305,293,294,289,305,306,294,305,289,306,289,305,301,303,306,301,291,\n301,289,291,306,289,294,291,306,295,296,292,307,308,296,307,292,308,292,307,304,\n305,308,304,293,304,292,293,308,292,296,293,308,296,297,293,308,309,297,308,293,\n309,293,308,305,306,309,305,294,305,293,294,309,293,297,294,309,300,301,298,312,\n313,301,312,298,313,298,312,310,311,313,310,299,310,298,299,313,298,301,299,313,\n301,303,299,313,315,303,313,299,315,299,313,311,314,315,311,302,311,299,302,315,\n299,303,302,315,304,305,300,316,317,305,316,300,317,300,316,312,313,317,312,301,\n312,300,301,317,300,305,301,317,305,306,301,317,318,306,317,301,318,301,317,313,\n315,318,313,303,313,301,303,318,301,306,303,318,307,308,304,319,320,308,319,304,\n320,304,319,316,317,320,316,305,316,304,305,320,304,308,305,320,308,309,305,320,\n321,309,320,305,321,305,320,317,318,321,317,306,317,305,306,321,305,309,306,321,\n312,313,310,324,325,313,324,310,325,310,324,322,323,325,322,311,322,310,311,325,\n310,313,311,325,313,315,311,325,327,315,325,311,327,311,325,323,326,327,323,314,\n323,311,314,327,311,315,314,327,316,317,312,328,329,317,328,312,329,312,328,324,\n325,329,324,313,324,312,313,329,312,317,313,329,317,318,313,329,330,318,329,313,\n330,313,329,325,327,330,325,315,325,313,315,330,313,318,315,330,319,320,316,331,\n332,320,331,316,332,316,331,328,329,332,328,317,328,316,317,332,316,320,317,332,\n320,321,317,332,333,321,332,317,333,317,332,329,330,333,329,318,329,317,318,333,\n317,321,318,333,324,325,322,336,337,325,336,322,337,322,336,334,335,337,334,323,\n334,322,323,337,322,325,323,337,325,327,323,337,339,327,337,323,339,323,337,335,\n338,339,335,326,335,323,326,339,323,327,326,339,328,329,324,340,341,329,340,324,\n341,324,340,336,337,341,336,325,336,324,325,341,324,329,325,341,329,330,325,341,\n342,330,341,325,342,325,341,337,339,342,337,327,337,325,327,342,325,330,327,342,\n331,332,328,343,344,332,343,328,344,328,343,340,341,344,340,329,340,328,329,344,\n328,332,329,344,332,333,329,344,345,333,344,329,345,329,344,341,342,345,341,330,\n341,329,330,345,329,333,330,345,336,337,334,348,349,337,348,334,349,334,348,346,\n347,349,346,335,346,334,335,349,334,337,335,349,337,339,335,349,351,339,349,335,\n351,335,349,347,350,351,347,338,347,335,338,351,335,339,338,351,340,341,336,352,\n353,341,352,336,353,336,352,348,349,353,348,337,348,336,337,353,336,341,337,353,\n341,342,337,353,354,342,353,337,354,337,353,349,351,354,349,339,349,337,339,354,\n337,342,339,354,343,344,340,355,356,344,355,340,356,340,355,352,353,356,352,341,\n352,340,341,356,340,344,341,356,344,345,341,356,357,345,356,341,357,341,356,353,\n354,357,353,342,353,341,342,357,341,345,342,357,346,347,334,1227,347,1228,1227,334,\n1228,334,1227,1225,1226,1228,1225,335,1225,334,335,1228,334,347,335,1228,348,346,336,1230,\n1227,346,1230,336,1227,336,1230,1229,1225,1227,1229,334,1229,336,334,1227,336,346,334,1227,\n348,349,346,360,361,349,360,346,361,346,360,358,359,361,358,347,358,346,347,361,\n346,349,347,361,349,351,347,361,363,351,361,347,363,347,361,359,362,363,359,350,\n359,347,350,363,347,351,350,363,352,353,348,364,365,353,364,348,365,348,364,360,\n361,365,360,349,360,348,349,365,348,353,349,365,353,354,349,365,366,354,365,349,\n366,349,365,361,363,366,361,351,361,349,351,366,349,354,351,366,355,356,352,367,\n368,356,367,352,368,352,367,364,365,368,364,353,364,352,353,368,352,356,353,368,\n356,357,353,368,369,357,368,353,369,353,368,365,366,369,365,354,365,353,354,369,\n353,357,354,369,358,359,346,1231,1232,359,1231,346,1232,346,1231,1227,1228,1232,1227,347,\n1227,346,347,1232,346,359,347,1232,360,358,348,1233,1231,358,1233,348,1231,348,1233,1230,\n1227,1231,1230,346,1230,348,346,1231,348,358,346,1231,360,361,358,372,373,361,372,358,\n373,358,372,370,371,373,370,359,370,358,359,373,358,361,359,373,361,363,359,373,\n375,363,373,359,375,359,373,371,374,375,371,362,371,359,362,375,359,363,362,375,\n364,365,360,376,377,365,376,360,377,360,376,372,373,377,372,361,372,360,361,377,\n360,365,361,377,365,366,361,377,378,366,377,361,378,361,377,373,375,378,373,363,\n373,361,363,378,361,366,363,378,367,368,364,379,380,368,379,364,380,364,379,376,\n377,380,376,365,376,364,365,380,364,368,365,380,368,369,365,380,381,369,380,365,\n381,365,380,377,378,381,377,366,377,365,366,381,365,369,366,381,384,385,382,396,\n397,385,396,382,397,382,396,394,395,397,394,383,394,382,383,397,382,385,383,397,\n385,389,383,397,399,389,397,383,399,383,397,395,398,399,395,388,395,383,388,399,\n383,389,388,399,390,391,384,400,401,391,400,384,401,384,400,396,397,401,396,385,\n396,384,385,401,384,391,385,401,391,393,385,401,402,393,401,385,402,385,401,397,\n399,402,397,389,397,385,389,402,385,393,389,402,163,180,403,405,407,180,405,403,\n407,403,405,421,419,407,421,238,421,403,238,407,403,180,238,407,406,407,404,425,\n426,407,425,404,426,404,425,423,424,426,423,405,423,404,405,426,404,407,405,426,\n410,411,406,427,428,411,427,406,428,406,427,425,426,428,425,407,425,406,407,428,\n406,411,407,428,412,410,409,430,427,410,430,409,427,409,430,429,425,427,429,406,\n429,409,406,427,409,410,406,427,413,414,410,431,432,414,431,410,432,410,431,427,\n428,432,427,411,427,410,411,432,410,414,411,432,415,413,412,433,431,413,433,412,\n431,412,433,430,427,431,430,410,430,412,410,431,412,413,410,431,416,417,413,434,\n435,417,434,413,435,413,434,431,432,435,431,414,431,413,414,435,413,417,414,435,\n419,418,238,443,444,418,443,238,444,238,443,441,444,442,441,240,441,238,240,444,\n238,418,240,444,418,419,411,436,437,419,436,411,437,411,436,428,426,437,428,407,\n428,411,407,437,411,419,407,437,420,418,414,438,436,418,438,414,436,414,438,432,\n428,436,432,411,432,414,411,436,414,418,411,436,421,419,403,446,443,419,446,403,\n443,403,446,445,441,443,445,238,445,403,238,443,403,419,238,443,405,421,163,478,\n479,421,478,163,479,163,478,476,477,479,476,403,476,163,403,479,163,421,403,479,\n405,407,421,424,426,407,424,421,426,421,424,439,437,426,439,419,439,421,419,426,\n421,407,419,426,417,422,414,435,440,422,435,414,440,414,435,432,438,440,432,420,\n432,414,420,440,414,422,420,440,427,428,425,452,453,428,452,425,453,425,452,450,\n451,453,450,426,450,425,426,453,425,428,426,453,430,427,429,455,452,427,455,429,\n452,429,455,454,450,452,454,425,454,429,425,452,429,427,425,452,431,432,427,456,\n457,432,456,427,457,427,456,452,453,457,452,428,452,427,428,457,427,432,428,457,\n433,431,430,458,456,431,458,430,456,430,458,455,452,456,455,427,455,430,427,456,\n430,431,427,456,434,435,431,459,460,435,459,431,460,431,459,456,457,460,456,432,\n456,431,432,460,431,435,432,460,437,436,419,447,448,436,447,419,448,419,447,443,\n444,448,443,418,443,419,418,448,419,436,418,448,439,437,421,449,447,437,449,421,\n447,421,449,446,443,447,446,419,446,421,419,447,421,437,419,447,424,439,405,480,\n481,439,480,405,481,405,480,478,479,481,478,421,478,405,421,481,405,439,421,481,\n446,445,421,482,483,445,482,421,483,421,482,479,477,483,479,403,479,421,403,483,\n421,445,403,483,449,446,439,484,482,446,484,439,482,439,484,481,479,482,481,421,\n481,439,421,482,439,446,421,482,452,453,450,463,464,453,463,450,464,450,463,461,\n462,464,461,451,461,450,451,464,450,453,451,464,455,452,454,466,463,452,466,454,\n463,454,466,465,461,463,465,450,465,454,450,463,454,452,450,463,456,457,452,467,\n468,457,467,452,468,452,467,463,464,468,463,453,463,452,453,468,452,457,453,468,\n458,456,455,475,467,456,475,455,467,455,475,466,463,467,466,452,466,455,452,467,\n455,456,452,467,463,464,461,471,472,464,471,461,472,461,471,469,470,472,469,462,\n469,461,462,472,461,464,462,472,467,468,463,473,474,468,473,463,474,463,473,471,\n472,474,471,464,471,463,464,474,463,468,464,474,478,479,476,487,488,479,487,476,\n488,476,487,485,486,488,485,477,485,476,477,488,476,479,477,488,480,481,478,489,\n490,481,489,478,490,478,489,487,488,490,487,479,487,478,479,490,478,481,479,490,\n482,483,479,491,492,483,491,479,492,479,491,488,486,492,488,477,488,479,477,492,\n479,483,477,492,484,482,481,493,491,482,493,481,491,481,493,490,488,491,490,479,\n490,481,479,491,481,482,479,491,487,488,485,496,497,488,496,485,497,485,496,494,\n495,497,494,486,494,485,486,497,485,488,486,497,489,490,487,498,499,490,498,487,\n499,487,498,496,497,499,496,488,496,487,488,499,487,490,488,499,491,492,488,500,\n501,492,500,488,501,488,500,497,495,501,497,486,497,488,486,501,488,492,486,501,\n493,491,490,502,500,491,502,490,500,490,502,499,497,500,499,488,499,490,488,500,\n490,491,488,500,496,497,494,505,506,497,505,494,506,494,505,503,504,506,503,495,\n503,494,495,506,494,497,495,506,498,499,496,507,508,499,507,496,508,496,507,505,\n506,508,505,497,505,496,497,508,496,499,497,508,500,501,497,509,510,501,509,497,\n510,497,509,506,504,510,506,495,506,497,495,510,497,501,495,510,502,500,499,511,\n509,500,511,499,509,499,511,508,506,509,508,497,508,499,497,509,499,500,497,509,\n505,506,503,514,515,506,514,503,515,503,514,512,513,515,512,504,512,503,504,515,\n503,506,504,515,507,508,505,516,517,508,516,505,517,505,516,514,515,517,514,506,\n514,505,506,517,505,508,506,517,509,510,506,518,519,510,518,506,519,506,518,515,\n513,519,515,504,515,506,504,519,506,510,504,519,511,509,508,520,518,509,520,508,\n518,508,520,517,515,518,517,506,517,508,506,518,508,509,506,518,525,521,526,542,\n538,521,542,526,538,526,542,543,540,538,543,523,543,526,523,538,526,521,523,538,\n524,522,530,541,539,522,541,530,539,530,541,547,548,539,547,531,547,530,531,539,\n530,522,531,539,529,527,532,546,544,527,546,532,544,532,546,549,550,544,549,533,\n549,532,533,544,532,527,533,544,522,521,531,539,538,521,539,531,538,531,539,548,\n551,538,548,534,548,531,534,538,531,521,534,538,527,528,533,544,545,528,544,533,\n545,533,544,550,552,545,550,535,550,533,535,545,533,528,535,545,528,524,535,545,\n541,524,545,535,541,535,545,552,547,541,552,530,552,535,530,541,535,524,530,541,\n525,526,536,542,543,526,542,536,543,536,542,553,554,543,553,537,553,536,537,543,\n536,526,537,543,521,525,534,538,542,525,538,534,542,534,538,551,553,542,551,536,\n551,534,536,542,534,525,536,542,538,539,540,555,556,539,555,540,556,540,555,557,\n558,556,557,541,557,540,541,556,540,539,541,556,542,538,543,559,555,538,559,543,\n555,543,559,560,557,555,560,540,560,543,540,555,543,538,540,555,541,539,547,558,\n556,539,558,547,556,547,558,564,565,556,564,548,564,547,548,556,547,539,548,556,\n546,544,549,563,561,544,563,549,561,549,563,566,567,561,566,550,566,549,550,561,\n549,544,550,561,539,538,548,556,555,538,556,548,555,548,556,565,568,555,565,551,\n565,548,551,555,548,538,551,555,544,545,550,561,562,545,561,550,562,550,561,567,\n569,562,567,552,567,550,552,562,550,545,552,562,545,541,552,562,558,541,562,552,\n558,552,562,569,564,558,569,547,569,552,547,558,552,541,547,558,542,543,553,559,\n560,543,559,553,560,553,559,570,571,560,570,554,570,553,554,560,553,543,554,560,\n538,542,551,555,559,542,555,551,559,551,555,568,570,559,568,553,568,551,553,559,\n551,542,553,559,559,555,560,576,572,555,576,560,572,560,576,577,574,572,577,557,\n577,560,557,572,560,555,557,572,558,556,564,575,573,556,575,564,573,564,575,581,\n582,573,581,565,581,564,565,573,564,556,565,573,563,561,566,580,578,561,580,566,\n578,566,580,583,584,578,583,567,583,566,567,578,566,561,567,578,556,555,565,573,\n572,555,573,565,572,565,573,582,585,572,582,568,582,565,568,572,565,555,568,572,\n561,562,567,578,579,562,578,567,579,567,578,584,586,579,584,569,584,567,569,579,\n567,562,569,579,562,558,569,579,575,558,579,569,575,569,579,586,581,575,586,564,\n586,569,564,575,569,558,564,575,559,560,570,576,577,560,576,570,577,570,576,587,\n588,577,587,571,587,570,571,577,570,560,571,577,555,559,568,572,576,559,572,568,\n576,568,572,585,587,576,585,570,585,568,570,576,568,559,570,576,560,563,571,577,\n580,563,577,571,580,571,577,588,583,580,588,566,588,571,566,580,571,563,566,580,\n576,572,577,593,589,572,593,577,589,577,593,594,591,589,594,574,594,577,574,589,\n577,572,574,589,565,564,582,623,624,564,623,582,624,582,623,625,626,624,625,581,\n625,582,581,624,582,564,581,624,575,573,581,592,590,573,592,581,590,581,592,598,\n599,590,598,582,598,581,582,590,581,573,582,590,580,578,583,597,595,578,597,583,\n595,583,597,600,601,595,600,584,600,583,584,595,583,578,584,595,568,565,585,647,\n623,565,647,585,623,585,647,648,625,623,648,582,648,585,582,623,585,565,582,623,\n573,572,582,590,589,572,590,582,589,582,590,599,602,589,599,585,599,582,585,589,\n582,572,585,589,569,567,586,635,636,567,635,586,636,586,635,637,638,636,637,584,\n637,586,584,636,586,567,584,636,578,579,584,595,596,579,595,584,596,584,595,601,\n603,596,601,586,601,584,586,596,584,579,586,596,564,569,581,624,627,569,624,581,\n627,581,624,626,628,627,626,586,626,581,586,627,581,569,586,627,579,575,586,596,\n592,575,596,586,592,586,596,603,598,592,603,581,603,586,581,592,586,575,581,592,\n576,577,587,593,594,577,593,587,594,587,593,604,605,594,604,588,604,587,588,594,\n587,577,588,594,570,568,587,665,666,568,665,587,666,587,665,667,668,666,667,585,\n667,587,585,666,587,568,585,666,572,576,585,589,593,576,589,585,593,585,589,602,\n604,593,602,587,602,585,587,593,585,576,587,593,577,580,588,594,597,580,594,588,\n597,588,594,605,600,597,605,583,605,588,583,597,588,580,583,597,589,590,591,606,\n607,590,606,591,607,591,606,608,609,607,608,592,608,591,592,607,591,590,592,607,\n593,589,594,610,606,589,610,594,606,594,610,611,608,606,611,591,611,594,591,606,\n594,589,591,606,582,581,599,625,626,581,625,599,626,599,625,629,630,626,629,598,\n629,599,598,626,599,581,598,626,592,590,598,609,607,590,609,598,607,598,609,615,\n616,607,615,599,615,598,599,607,598,590,599,607,597,595,600,614,612,595,614,600,\n612,600,614,617,618,612,617,601,617,600,601,612,600,595,601,612,585,582,602,648,\n625,582,648,602,625,602,648,649,629,625,649,599,649,602,599,625,602,582,599,625,\n590,589,599,607,606,589,607,599,606,599,607,616,619,606,616,602,616,599,602,606,\n599,589,602,606,586,584,603,637,638,584,637,603,638,603,637,639,640,638,639,601,\n639,603,601,638,603,584,601,638,595,596,601,612,613,596,612,601,613,601,612,618,\n620,613,618,603,618,601,603,613,601,596,603,613,581,586,598,626,628,586,626,598,\n628,598,626,630,631,628,630,603,630,598,603,628,598,586,603,628,596,592,603,613,\n609,592,613,603,609,603,613,620,615,609,620,598,620,603,598,609,603,592,598,609,\n593,594,604,610,611,594,610,604,611,604,610,621,622,611,621,605,621,604,605,611,\n604,594,605,611,587,585,604,667,668,585,667,604,668,604,667,669,670,668,669,602,\n669,604,602,668,604,585,602,668,589,593,602,606,610,593,606,602,610,602,606,619,\n621,610,619,604,619,602,604,610,602,593,604,610,594,597,605,611,614,597,611,605,\n614,605,611,622,617,614,622,600,622,605,600,614,605,597,600,614,599,598,616,629,\n630,598,629,616,630,616,629,632,633,630,632,615,632,616,615,630,616,598,615,630,\n602,599,619,649,629,599,649,619,629,619,649,650,632,629,650,616,650,619,616,629,\n619,599,616,629,603,601,620,639,640,601,639,620,640,620,639,641,642,640,641,618,\n641,620,618,640,620,601,618,640,598,603,615,630,631,603,630,615,631,615,630,633,\n634,631,633,620,633,615,620,631,615,603,620,631,604,602,621,669,670,602,669,621,\n670,621,669,671,672,670,671,619,671,621,619,670,621,602,619,670,623,624,625,680,\n681,624,680,625,681,625,680,682,683,681,682,626,682,625,626,681,625,624,626,681,\n569,586,627,635,637,586,635,627,637,627,635,643,644,637,643,628,643,627,628,637,\n627,586,628,637,624,627,626,681,684,627,681,626,684,626,681,683,685,684,683,628,\n683,626,628,684,626,627,628,684,625,626,629,682,683,626,682,629,683,629,682,686,\n687,683,686,630,686,629,630,683,629,626,630,683,586,603,628,637,639,603,637,628,\n639,628,637,644,645,639,644,631,644,628,631,639,628,603,631,639,626,628,630,683,\n685,628,683,630,685,630,683,687,688,685,687,631,687,630,631,685,630,628,631,685,\n629,630,632,686,687,630,686,632,687,632,686,689,690,687,689,633,689,632,633,687,\n632,630,633,687,603,620,631,639,641,620,639,631,641,631,639,645,646,641,645,634,\n645,631,634,641,631,620,634,641,630,631,633,687,688,631,687,633,688,633,687,690,\n691,688,690,634,690,633,634,688,633,631,634,688,628,627,644,685,684,627,685,644,\n684,644,685,692,693,684,692,643,692,644,643,684,644,627,643,684,631,628,645,688,\n685,628,688,645,685,645,688,694,692,685,694,644,694,645,644,685,645,628,644,685,\n634,631,646,691,688,631,691,646,688,646,691,695,694,688,695,645,695,646,645,688,\n646,631,645,688,647,648,568,679,673,648,679,568,673,568,679,666,668,673,666,585,\n666,568,585,673,568,648,585,673,625,648,623,651,652,648,651,623,652,623,651,653,\n654,652,653,647,653,623,647,652,623,648,647,652,648,649,585,673,674,649,673,585,\n674,585,673,668,670,674,668,602,668,585,602,674,585,649,602,674,629,649,625,655,\n656,649,655,625,656,625,655,651,652,656,651,648,651,625,648,656,625,649,648,656,\n650,619,649,675,672,619,675,649,672,649,675,674,670,672,674,602,674,649,602,672,\n649,619,602,672,650,649,632,657,656,649,657,632,656,632,657,658,655,656,658,629,\n658,632,629,656,632,649,629,656,623,625,653,680,682,625,680,653,682,653,680,696,\n697,682,696,651,696,653,651,682,653,625,651,682,625,629,651,682,686,629,682,651,\n686,651,682,697,698,686,697,655,697,651,655,686,651,629,655,686,649,648,656,674,\n673,648,674,656,673,656,674,676,677,673,676,652,676,656,652,673,656,648,652,673,\n655,656,651,661,662,656,661,651,662,651,661,659,660,662,659,652,659,651,652,662,\n651,656,652,662,650,649,657,675,674,649,675,657,674,657,675,678,676,674,678,656,\n678,657,656,674,657,649,656,674,629,632,655,686,689,632,686,655,689,655,686,698,\n699,689,698,658,698,655,658,689,655,632,658,689,657,656,658,663,662,656,663,658,\n662,658,663,664,661,662,664,655,664,658,655,662,658,656,655,662,651,655,659,697,\n698,655,697,659,698,659,697,700,701,698,700,661,700,659,661,698,659,655,661,698,\n655,658,661,698,699,658,698,661,699,661,698,701,702,699,701,664,701,661,664,699,\n661,658,664,699,623,624,680,723,724,624,723,680,724,680,723,725,726,724,725,681,\n725,680,681,724,680,624,681,724,680,681,682,703,704,681,703,682,704,682,703,705,\n706,704,705,683,705,682,683,704,682,681,683,704,624,627,681,724,727,627,724,681,\n727,681,724,726,728,727,726,684,726,681,684,727,681,627,684,727,681,684,683,704,\n707,684,704,683,707,683,704,706,708,707,706,685,706,683,685,707,683,684,685,707,\n682,683,686,705,706,683,705,686,706,686,705,709,710,706,709,687,709,686,687,706,\n686,683,687,706,683,685,687,706,708,685,706,687,708,687,706,710,711,708,710,688,\n710,687,688,708,687,685,688,708,686,687,689,709,710,687,709,689,710,689,709,712,\n713,710,712,690,712,689,690,710,689,687,690,710,687,688,690,710,711,688,710,690,\n711,690,710,713,714,711,713,691,713,690,691,711,690,688,691,711,691,688,695,714,\n711,688,714,695,711,695,714,715,716,711,715,694,715,695,694,711,695,688,694,711,\n680,681,703,725,726,681,725,703,726,703,725,729,730,726,729,704,729,703,704,726,\n703,681,704,726,703,704,705,717,718,704,717,705,718,705,717,719,720,718,719,706,\n719,705,706,718,705,704,706,718,681,684,704,726,728,684,726,704,728,704,726,730,\n731,728,730,707,730,704,707,728,704,684,707,728,704,707,706,718,721,707,718,706,\n721,706,718,720,722,721,720,708,720,706,708,721,706,707,708,721,703,704,717,729,\n730,704,729,717,730,717,729,732,733,730,732,718,732,717,718,730,717,704,718,730,\n704,707,718,730,731,707,730,718,731,718,730,733,734,731,733,721,733,718,721,731,\n718,707,721,731,723,724,725,735,736,724,735,725,736,725,735,737,738,736,737,726,\n737,725,726,736,725,724,726,736,724,727,726,736,739,727,736,726,739,726,736,738,\n740,739,738,728,738,726,728,739,726,727,728,739,725,726,729,737,738,726,737,729,\n738,729,737,741,742,738,741,730,741,729,730,738,729,726,730,738,726,728,730,738,\n740,728,738,730,740,730,738,742,743,740,742,731,742,730,731,740,730,728,731,740,\n729,730,732,741,742,730,741,732,742,732,741,744,745,742,744,733,744,732,733,742,\n732,730,733,742,730,731,733,742,743,731,742,733,743,733,742,745,746,743,745,734,\n745,733,734,743,733,731,734,743,735,736,737,747,748,736,747,737,748,737,747,749,\n750,748,749,738,749,737,738,748,737,736,738,748,736,739,738,748,751,739,748,738,\n751,738,748,750,752,751,750,740,750,738,740,751,738,739,740,751,737,738,741,749,\n750,738,749,741,750,741,749,753,754,750,753,742,753,741,742,750,741,738,742,750,\n738,740,742,750,752,740,750,742,752,742,750,754,755,752,754,743,754,742,743,752,\n742,740,743,752,741,742,744,753,754,742,753,744,754,744,753,756,757,754,756,745,\n756,744,745,754,744,742,745,754,742,743,745,754,755,743,754,745,755,745,754,757,\n758,755,757,746,757,745,746,755,745,743,746,755,747,748,749,759,760,748,759,749,\n760,749,759,761,762,760,761,750,761,749,750,760,749,748,750,760,736,739,748,1153,\n1154,739,1153,748,1154,748,1153,1155,1156,1154,1155,751,1155,748,751,1154,748,739,751,1154,\n748,751,750,760,763,751,760,750,763,750,760,762,764,763,762,752,762,750,752,763,\n750,751,752,763,749,750,753,761,762,750,761,753,762,753,761,765,766,762,765,754,\n765,753,754,762,753,750,754,762,750,752,754,762,764,752,762,754,764,754,762,766,\n767,764,766,755,766,754,755,764,754,752,755,764,753,754,756,765,766,754,765,756,\n766,756,765,768,769,766,768,757,768,756,757,766,756,754,757,766,754,755,757,766,\n767,755,766,757,767,757,766,769,770,767,769,758,769,757,758,767,757,755,758,767,\n759,760,761,771,772,760,771,761,772,761,771,773,774,772,773,762,773,761,762,772,\n761,760,762,772,748,751,760,1155,1156,751,1155,760,1156,760,1155,1157,1158,1156,1157,763,\n1157,760,763,1156,760,751,763,1156,760,763,762,772,775,763,772,762,775,762,772,774,\n776,775,774,764,774,762,764,775,762,763,764,775,761,762,765,773,774,762,773,765,\n774,765,773,777,778,774,777,766,777,765,766,774,765,762,766,774,762,764,766,774,\n776,764,774,766,776,766,774,778,779,776,778,767,778,766,767,776,766,764,767,776,\n765,766,768,777,778,766,777,768,778,768,777,780,781,778,780,769,780,768,769,778,\n768,766,769,778,766,767,769,778,779,767,778,769,779,769,778,781,782,779,781,770,\n781,769,770,779,769,767,770,779,771,772,773,783,784,772,783,773,784,773,783,785,\n786,784,785,774,785,773,774,784,773,772,774,784,760,763,772,1157,1158,763,1157,772,\n1158,772,1157,1159,1160,1158,1159,775,1159,772,775,1158,772,763,775,1158,772,775,774,784,\n787,775,784,774,787,774,784,786,788,787,786,776,786,774,776,787,774,775,776,787,\n773,774,777,785,786,774,785,777,786,777,785,789,790,786,789,778,789,777,778,786,\n777,774,778,786,774,776,778,786,788,776,786,778,788,778,786,790,791,788,790,779,\n790,778,779,788,778,776,779,788,768,765,780,843,844,765,843,780,844,780,843,845,\n846,844,845,777,845,780,777,844,780,765,777,844,769,768,781,847,843,768,847,781,\n843,781,847,848,845,843,848,780,848,781,780,843,781,768,780,843,777,778,780,789,\n790,778,789,780,790,780,789,792,793,790,792,781,792,780,781,790,780,778,781,790,\n770,769,782,849,847,769,849,782,847,782,849,850,848,847,850,781,850,782,781,847,\n782,769,781,847,778,779,781,790,791,779,790,781,791,781,790,793,794,791,793,782,\n793,781,782,791,781,779,782,791,773,771,785,1177,1178,771,1177,785,1178,785,1177,1167,\n1168,1178,1167,783,1167,785,783,1178,785,771,783,1178,783,784,785,795,796,784,795,785,\n796,785,795,797,798,796,797,786,797,785,786,796,785,784,786,796,772,775,784,1159,\n1160,775,1159,784,1160,784,1159,1161,1162,1160,1161,787,1161,784,787,1160,784,775,787,1160,\n775,776,787,1098,1099,776,1098,787,1099,787,1098,1100,1101,1099,1100,788,1100,787,788,1099,\n787,776,788,1099,784,787,786,796,799,787,796,786,799,786,796,798,800,799,798,788,\n798,786,788,799,786,787,788,799,785,786,789,797,798,786,797,789,798,789,797,801,\n802,798,801,790,801,789,790,798,789,786,790,798,786,788,790,798,800,788,798,790,\n800,790,798,802,803,800,802,791,802,790,791,800,790,788,791,800,780,777,792,845,\n846,777,845,792,846,792,845,851,852,846,851,789,851,792,789,846,792,777,789,846,\n781,780,793,848,845,780,848,793,845,793,848,853,851,845,853,792,853,793,792,845,\n793,780,792,845,789,790,792,801,802,790,801,792,802,792,801,804,805,802,804,793,\n804,792,793,802,792,790,793,802,782,781,794,850,848,781,850,794,848,794,850,854,\n853,848,854,793,854,794,793,848,794,781,793,848,790,791,793,802,803,791,802,793,\n803,793,802,805,806,803,805,794,805,793,794,803,793,791,794,803,785,783,797,1167,\n1168,783,1167,797,1168,797,1167,1169,1170,1168,1169,795,1169,797,795,1168,797,783,795,1168,\n795,796,797,807,808,796,807,797,808,797,807,809,810,808,809,798,809,797,798,808,\n797,796,798,808,784,787,796,1161,1162,787,1161,796,1162,796,1161,1163,1164,1162,1163,799,\n1163,796,799,1162,796,787,799,1162,787,788,799,1100,1101,788,1100,799,1101,799,1100,1102,\n1103,1101,1102,800,1102,799,800,1101,799,788,800,1101,796,799,798,808,811,799,808,798,\n811,798,808,810,812,811,810,800,810,798,800,811,798,799,800,811,797,798,801,809,\n810,798,809,801,810,801,809,813,814,810,813,802,813,801,802,810,801,798,802,810,\n788,791,800,1108,1109,791,1108,800,1109,800,1108,1110,1111,1109,1110,803,1110,800,803,1109,\n800,791,803,1109,798,800,802,810,812,800,810,802,812,802,810,814,815,812,814,803,\n814,802,803,812,802,800,803,812,792,789,804,851,852,789,851,804,852,804,851,855,\n856,852,855,801,855,804,801,852,804,789,801,852,793,792,805,853,851,792,853,805,\n851,805,853,857,855,851,857,804,857,805,804,851,805,792,804,851,801,802,804,813,\n814,802,813,804,814,804,813,816,817,814,816,805,816,804,805,814,804,802,805,814,\n794,793,806,854,853,793,854,806,853,806,854,858,857,853,858,805,858,806,805,853,\n806,793,805,853,802,803,805,814,815,803,814,805,815,805,814,817,818,815,817,806,\n817,805,806,815,805,803,806,815,797,795,809,1169,1170,795,1169,809,1170,809,1169,1171,\n1172,1170,1171,807,1171,809,807,1170,809,795,807,1170,807,808,809,819,820,808,819,809,\n820,809,819,821,822,820,821,810,821,809,810,820,809,808,810,820,796,799,808,1163,\n1164,799,1163,808,1164,808,1163,1165,1166,1164,1165,811,1165,808,811,1164,808,799,811,1164,\n799,800,811,1102,1103,800,1102,811,1103,811,1102,1104,1105,1103,1104,812,1104,811,812,1103,\n811,800,812,1103,808,811,810,820,823,811,820,810,823,810,820,822,824,823,822,812,\n822,810,812,823,810,811,812,823,809,810,813,821,822,810,821,813,822,813,821,825,\n826,822,825,814,825,813,814,822,813,810,814,822,800,803,812,1110,1111,803,1110,812,\n1111,812,1110,1112,1113,1111,1112,815,1112,812,815,1111,812,803,815,1111,810,812,814,822,\n824,812,822,814,824,814,822,826,827,824,826,815,826,814,815,824,814,812,815,824,\n804,801,816,979,980,801,979,816,980,816,979,981,982,980,981,813,981,816,813,980,\n816,801,813,980,805,804,817,983,979,804,983,817,979,817,983,984,981,979,984,816,\n984,817,816,979,817,804,816,979,813,814,816,825,826,814,825,816,826,816,825,828,\n829,826,828,817,828,816,817,826,816,814,817,826,806,805,818,985,983,805,985,818,\n983,818,985,986,984,983,986,817,986,818,817,983,818,805,817,983,814,815,817,826,\n827,815,826,817,827,817,826,829,830,827,829,818,829,817,818,827,817,815,818,827,\n807,808,819,1059,1060,808,1059,819,1060,819,1059,1061,1062,1060,1061,820,1061,819,820,1060,\n819,808,820,1060,809,807,821,1171,1172,807,1171,821,1172,821,1171,1173,1174,1172,1173,819,\n1173,821,819,1172,821,807,819,1172,819,820,821,831,832,820,831,821,832,821,831,833,\n834,832,833,822,833,821,822,832,821,820,822,832,808,811,820,1060,1063,811,1060,820,\n1063,820,1060,1062,1064,1063,1062,823,1062,820,823,1063,820,811,823,1063,811,812,823,1104,\n1105,812,1104,823,1105,823,1104,1106,1107,1105,1106,824,1106,823,824,1105,823,812,824,1105,\n820,823,822,832,835,823,832,822,835,822,832,834,836,835,834,824,834,822,824,835,\n822,823,824,835,821,822,825,833,834,822,833,825,834,825,833,837,838,834,837,826,\n837,825,826,834,825,822,826,834,812,815,824,1112,815,1113,1112,824,1113,824,1112,1114,\n1115,1113,1114,827,1114,824,827,1113,824,815,827,1113,822,824,826,834,836,824,834,826,\n836,826,834,838,839,836,838,827,838,826,827,836,826,824,827,836,816,813,828,981,\n982,813,981,828,982,828,981,987,988,982,987,825,987,828,825,982,828,813,825,982,\n817,816,829,984,981,816,984,829,981,829,984,989,987,981,989,828,989,829,828,981,\n829,816,828,981,818,817,830,986,984,817,986,830,984,830,986,990,989,984,990,829,\n990,830,829,984,830,817,829,984,826,827,829,838,839,827,838,829,839,829,838,841,\n842,839,841,830,841,829,830,839,829,827,830,839,819,820,831,1061,1062,820,1061,831,\n1062,831,1061,1065,1066,1062,1065,832,1065,831,832,1062,831,820,832,1062,821,819,833,1173,\n1174,819,1173,833,1174,833,1173,1175,1176,1174,1175,831,1175,833,831,1174,833,819,831,1174,\n820,823,832,1062,1064,823,1062,832,1064,832,1062,1066,1067,1064,1066,835,1066,832,835,1064,\n832,823,835,1064,828,825,840,987,988,825,987,840,988,840,987,991,992,988,991,837,\n991,840,837,988,840,825,837,988,830,829,842,990,989,829,990,842,989,842,990,994,\n993,989,994,841,994,842,841,989,842,829,841,989,843,844,845,859,860,844,859,845,\n860,845,859,861,862,860,861,846,861,845,846,860,845,844,846,860,847,843,848,863,\n859,843,863,848,859,848,863,864,861,859,864,845,864,848,845,859,848,843,845,859,\n849,847,850,865,863,847,865,850,863,850,865,866,864,863,866,848,866,850,848,863,\n850,847,848,863,845,846,851,861,862,846,861,851,862,851,861,867,868,862,867,852,\n867,851,852,862,851,846,852,862,848,845,853,864,861,845,864,853,861,853,864,869,\n867,861,869,851,869,853,851,861,853,845,851,861,850,848,854,866,864,848,866,854,\n864,854,866,870,869,864,870,853,870,854,853,864,854,848,853,864,851,852,855,867,\n868,852,867,855,868,855,867,871,872,868,871,856,871,855,856,868,855,852,856,868,\n853,851,857,869,867,851,869,857,867,857,869,873,871,867,873,855,873,857,855,867,\n857,851,855,867,854,853,858,870,869,853,870,858,869,858,870,874,873,869,874,857,\n874,858,857,869,858,853,857,869,859,860,861,875,876,860,875,861,876,861,875,877,\n878,876,877,862,877,861,862,876,861,860,862,876,863,859,864,879,875,859,879,864,\n875,864,879,880,877,875,880,861,880,864,861,875,864,859,861,875,865,863,866,881,\n879,863,881,866,879,866,881,882,880,879,882,864,882,866,864,879,866,863,864,879,\n861,862,867,877,878,862,877,867,878,867,877,883,884,878,883,868,883,867,868,878,\n867,862,868,878,864,861,869,880,877,861,880,869,877,869,880,885,883,877,885,867,\n885,869,867,877,869,861,867,877,866,864,870,882,880,864,882,870,880,870,882,886,\n885,880,886,869,886,870,869,880,870,864,869,880,867,868,871,883,884,868,883,871,\n884,871,883,887,888,884,887,872,887,871,872,884,871,868,872,884,869,867,873,885,\n883,867,885,873,883,873,885,889,887,883,889,871,889,873,871,883,873,867,871,883,\n870,869,874,886,885,869,886,874,885,874,886,890,889,885,890,873,890,874,873,885,\n874,869,873,885,875,876,877,891,892,876,891,877,892,877,891,893,894,892,893,878,\n893,877,878,892,877,876,878,892,879,875,880,895,891,875,895,880,891,880,895,896,\n893,891,896,877,896,880,877,891,880,875,877,891,881,879,882,897,895,879,897,882,\n895,882,897,898,896,895,898,880,898,882,880,895,882,879,880,895,877,878,883,893,\n894,878,893,883,894,883,893,899,900,894,899,884,899,883,884,894,883,878,884,894,\n880,877,885,896,893,877,896,885,893,885,896,901,899,893,901,883,901,885,883,893,\n885,877,883,893,882,880,886,898,896,880,898,886,896,886,898,902,901,896,902,885,\n902,886,885,896,886,880,885,896,883,884,887,899,900,884,899,887,900,887,899,903,\n904,900,903,888,903,887,888,900,887,884,888,900,885,883,889,901,899,883,901,889,\n899,889,901,905,903,899,905,887,905,889,887,899,889,883,887,899,886,885,890,902,\n901,885,902,890,901,890,902,906,905,901,906,889,906,890,889,901,890,885,889,901,\n891,892,893,907,908,892,907,893,908,893,907,909,910,908,909,894,909,893,894,908,\n893,892,894,908,895,891,896,911,907,891,911,896,907,896,911,912,909,907,912,893,\n912,896,893,907,896,891,893,907,897,895,898,913,911,895,913,898,911,898,913,914,\n912,911,914,896,914,898,896,911,898,895,896,911,893,894,899,909,910,894,909,899,\n910,899,909,915,916,910,915,900,915,899,900,910,899,894,900,910,896,893,901,912,\n909,893,912,901,909,901,912,917,915,909,917,899,917,901,899,909,901,893,899,909,\n898,896,902,914,912,896,914,902,912,902,914,918,917,912,918,901,918,902,901,912,\n902,896,901,912,899,900,903,915,916,900,915,903,916,903,915,919,920,916,919,904,\n919,903,904,916,903,900,904,916,901,899,905,917,915,899,917,905,915,905,917,921,\n919,915,921,903,921,905,903,915,905,899,903,915,902,901,906,918,917,901,918,906,\n917,906,918,922,921,917,922,905,922,906,905,917,906,901,905,917,907,908,909,923,\n924,908,923,909,924,909,923,925,926,924,925,910,925,909,910,924,909,908,910,924,\n911,907,912,927,923,907,927,912,923,912,927,928,925,923,928,909,928,912,909,923,\n912,907,909,923,913,911,914,929,927,911,929,914,927,914,929,930,928,927,930,912,\n930,914,912,927,914,911,912,927,909,910,915,925,926,910,925,915,926,915,925,931,\n932,926,931,916,931,915,916,926,915,910,916,926,912,909,917,928,925,909,928,917,\n925,917,928,933,931,925,933,915,933,917,915,925,917,909,915,925,914,912,918,930,\n928,912,930,918,928,918,930,934,933,928,934,917,934,918,917,928,918,912,917,928,\n915,916,919,931,932,916,931,919,932,919,931,935,936,932,935,920,935,919,920,932,\n919,916,920,932,917,915,921,933,931,915,933,921,931,921,933,937,935,931,937,919,\n937,921,919,931,921,915,919,931,918,917,922,934,933,917,934,922,933,922,934,938,\n937,933,938,921,938,922,921,933,922,917,921,933,923,924,925,939,940,924,939,925,\n940,925,939,941,942,940,941,926,941,925,926,940,925,924,926,940,927,923,928,943,\n939,923,943,928,939,928,943,944,941,939,944,925,944,928,925,939,928,923,925,939,\n929,927,930,945,943,927,945,930,943,930,945,946,944,943,946,928,946,930,928,943,\n930,927,928,943,925,926,931,941,942,926,941,931,942,931,941,947,948,942,947,932,\n947,931,932,942,931,926,932,942,928,925,933,944,941,925,944,933,941,933,944,949,\n947,941,949,931,949,933,931,941,933,925,931,941,930,928,934,946,944,928,946,934,\n944,934,946,950,949,944,950,933,950,934,933,944,934,928,933,944,931,932,935,947,\n948,932,947,935,948,935,947,951,952,948,951,936,951,935,936,948,935,932,936,948,\n933,931,937,949,947,931,949,937,947,937,949,953,951,947,953,935,953,937,935,947,\n937,931,935,947,934,933,938,950,949,933,950,938,949,938,950,954,953,949,954,937,\n954,938,937,949,938,933,937,949,939,940,941,955,956,940,955,941,956,941,955,957,\n958,956,957,942,957,941,942,956,941,940,942,956,943,939,944,959,955,939,959,944,\n955,944,959,960,957,955,960,941,960,944,941,955,944,939,941,955,945,943,946,961,\n959,943,961,946,959,946,961,962,960,959,962,944,962,946,944,959,946,943,944,959,\n941,942,947,957,958,942,957,947,958,947,957,963,964,958,963,948,963,947,948,958,\n947,942,948,958,944,941,949,960,957,941,960,949,957,949,960,965,963,957,965,947,\n965,949,947,957,949,941,947,957,946,944,950,962,960,944,962,950,960,950,962,966,\n965,960,966,949,966,950,949,960,950,944,949,960,947,948,951,963,964,948,963,951,\n964,951,963,967,968,964,967,952,967,951,952,964,951,948,952,964,949,947,953,965,\n963,947,965,953,963,953,965,969,967,963,969,951,969,953,951,963,953,947,951,963,\n950,949,954,966,965,949,966,954,965,954,966,970,969,965,970,953,970,954,953,965,\n954,949,953,965,965,963,969,971,972,963,971,969,972,969,971,973,974,972,973,967,\n973,969,967,972,969,963,967,972,971,972,973,975,976,972,975,973,976,973,975,977,\n978,976,977,974,977,973,974,976,973,972,974,976,979,980,981,995,996,980,995,981,\n996,981,995,997,998,996,997,982,997,981,982,996,981,980,982,996,983,979,984,999,\n995,979,999,984,995,984,999,1000,997,995,1000,981,1000,984,981,995,984,979,981,995,\n985,983,986,1001,999,983,1001,986,999,986,1001,1002,1000,999,1002,984,1002,986,984,999,\n986,983,984,999,981,982,987,997,998,982,997,987,998,987,997,1003,1004,998,1003,988,\n1003,987,988,998,987,982,988,998,984,981,989,1000,997,981,1000,989,997,989,1000,1005,\n1003,997,1005,987,1005,989,987,997,989,981,987,997,986,984,990,1002,1000,984,1002,990,\n1000,990,1002,1006,1005,1000,1006,989,1006,990,989,1000,990,984,989,1000,987,988,991,1003,\n1004,988,1003,991,1004,991,1003,1007,1008,1004,1007,992,1007,991,992,1004,991,988,992,1004,\n989,987,993,1005,1003,987,1005,993,1003,993,1005,1009,1007,1003,1009,991,1009,993,991,1003,\n993,987,991,1003,990,989,994,1006,1005,989,1006,994,1005,994,1006,1010,1009,1005,1010,993,\n1010,994,993,1005,994,989,993,1005,995,996,997,1011,1012,996,1011,997,1012,997,1011,1013,\n1014,1012,1013,998,1013,997,998,1012,997,996,998,1012,999,995,1000,1015,1011,995,1015,1000,\n1011,1000,1015,1016,1013,1011,1016,997,1016,1000,997,1011,1000,995,997,1011,1001,999,1002,1017,\n1015,999,1017,1002,1015,1002,1017,1018,1016,1015,1018,1000,1018,1002,1000,1015,1002,999,1000,1015,\n997,998,1003,1013,1014,998,1013,1003,1014,1003,1013,1019,1020,1014,1019,1004,1019,1003,1004,1014,\n1003,998,1004,1014,1000,997,1005,1016,1013,997,1016,1005,1013,1005,1016,1021,1019,1013,1021,1003,\n1021,1005,1003,1013,1005,997,1003,1013,1002,1000,1006,1018,1016,1000,1018,1006,1016,1006,1018,1022,\n1021,1016,1022,1005,1022,1006,1005,1016,1006,1000,1005,1016,1003,1004,1007,1019,1020,1004,1019,1007,\n1020,1007,1019,1023,1024,1020,1023,1008,1023,1007,1008,1020,1007,1004,1008,1020,1005,1003,1009,1021,\n1019,1003,1021,1009,1019,1009,1021,1025,1023,1019,1025,1007,1025,1009,1007,1019,1009,1003,1007,1019,\n1006,1005,1010,1022,1021,1005,1022,1010,1021,1010,1022,1026,1025,1021,1026,1009,1026,1010,1009,1021,\n1010,1005,1009,1021,1011,1012,1013,1027,1028,1012,1027,1013,1028,1013,1027,1029,1030,1028,1029,1014,\n1029,1013,1014,1028,1013,1012,1014,1028,1015,1011,1016,1031,1027,1011,1031,1016,1027,1016,1031,1032,\n1029,1027,1032,1013,1032,1016,1013,1027,1016,1011,1013,1027,1017,1015,1018,1033,1031,1015,1033,1018,\n1031,1018,1033,1034,1032,1031,1034,1016,1034,1018,1016,1031,1018,1015,1016,1031,1013,1014,1019,1029,\n1030,1014,1029,1019,1030,1019,1029,1035,1036,1030,1035,1020,1035,1019,1020,1030,1019,1014,1020,1030,\n1016,1013,1021,1032,1029,1013,1032,1021,1029,1021,1032,1037,1035,1029,1037,1019,1037,1021,1019,1029,\n1021,1013,1019,1029,1018,1016,1022,1034,1032,1016,1034,1022,1032,1022,1034,1038,1037,1032,1038,1021,\n1038,1022,1021,1032,1022,1016,1021,1032,1019,1020,1023,1035,1036,1020,1035,1023,1036,1023,1035,1039,\n1040,1036,1039,1024,1039,1023,1024,1036,1023,1020,1024,1036,1021,1019,1025,1037,1035,1019,1037,1025,\n1035,1025,1037,1041,1039,1035,1041,1023,1041,1025,1023,1035,1025,1019,1023,1035,1022,1021,1026,1038,\n1037,1021,1038,1026,1037,1026,1038,1042,1041,1037,1042,1025,1042,1026,1025,1037,1026,1021,1025,1037,\n1027,1028,1029,1043,1044,1028,1043,1029,1044,1029,1043,1045,1046,1044,1045,1030,1045,1029,1030,1044,\n1029,1028,1030,1044,1031,1027,1032,1047,1043,1027,1047,1032,1043,1032,1047,1048,1045,1043,1048,1029,\n1048,1032,1029,1043,1032,1027,1029,1043,1033,1031,1034,1049,1047,1031,1049,1034,1047,1034,1049,1050,\n1048,1047,1050,1032,1050,1034,1032,1047,1034,1031,1032,1047,1029,1030,1035,1045,1046,1030,1045,1035,\n1046,1035,1045,1051,1052,1046,1051,1036,1051,1035,1036,1046,1035,1030,1036,1046,1032,1029,1037,1048,\n1045,1029,1048,1037,1045,1037,1048,1053,1051,1045,1053,1035,1053,1037,1035,1045,1037,1029,1035,1045,\n1034,1032,1038,1050,1048,1032,1050,1038,1048,1038,1050,1054,1053,1048,1054,1037,1054,1038,1037,1048,\n1038,1032,1037,1048,1035,1036,1039,1051,1052,1036,1051,1039,1052,1039,1051,1055,1056,1052,1055,1040,\n1055,1039,1040,1052,1039,1036,1040,1052,1037,1035,1041,1053,1051,1035,1053,1041,1051,1041,1053,1057,\n1055,1051,1057,1039,1057,1041,1039,1051,1041,1035,1039,1051,1038,1037,1042,1054,1053,1037,1054,1042,\n1053,1042,1054,1058,1057,1053,1058,1041,1058,1042,1041,1053,1042,1037,1041,1053,1059,1060,1061,1074,\n1075,1060,1074,1061,1075,1061,1074,1076,1077,1075,1076,1062,1076,1061,1062,1075,1061,1060,1062,1075,\n1060,1063,1062,1075,1078,1063,1075,1062,1078,1062,1075,1077,1079,1078,1077,1064,1077,1062,1064,1078,\n1062,1063,1064,1078,1061,1062,1065,1068,1069,1062,1068,1065,1069,1065,1068,1070,1071,1069,1070,1066,\n1070,1065,1066,1069,1065,1062,1066,1069,1062,1064,1066,1069,1072,1064,1069,1066,1072,1066,1069,1071,\n1073,1072,1071,1067,1071,1066,1067,1072,1066,1064,1067,1072,1074,1075,1076,1080,1081,1075,1080,1076,\n1081,1076,1080,1082,1083,1081,1082,1077,1082,1076,1077,1081,1076,1075,1077,1081,1075,1078,1077,1081,\n1084,1078,1081,1077,1084,1077,1081,1083,1085,1084,1083,1079,1083,1077,1079,1084,1077,1078,1079,1084,\n1080,1081,1082,1086,1087,1081,1086,1082,1087,1082,1086,1088,1089,1087,1088,1083,1088,1082,1083,1087,\n1082,1081,1083,1087,1081,1084,1083,1087,1090,1084,1087,1083,1090,1083,1087,1089,1091,1090,1089,1085,\n1089,1083,1085,1090,1083,1084,1085,1090,1086,1087,1088,1092,1093,1087,1092,1088,1093,1088,1092,1094,\n1095,1093,1094,1089,1094,1088,1089,1093,1088,1087,1089,1093,1087,1090,1089,1093,1096,1090,1093,1089,\n1096,1089,1093,1095,1097,1096,1095,1091,1095,1089,1091,1096,1089,1090,1091,1096,1098,1099,1100,1209,\n1210,1099,1209,1100,1210,1100,1209,1211,1212,1210,1211,1101,1211,1100,1101,1210,1100,1099,1101,1210,\n788,800,1101,1108,1110,800,1108,1101,1110,1101,1108,1116,1117,1110,1116,1103,1116,1101,1103,1110,\n1101,800,1103,1110,1100,1101,1102,1132,1133,1101,1132,1102,1133,1102,1132,1134,1135,1133,1134,1103,\n1134,1102,1103,1133,1102,1101,1103,1133,800,812,1103,1110,1112,812,1110,1103,1112,1103,1110,1117,\n1118,1112,1117,1105,1117,1103,1105,1112,1103,812,1105,1112,1102,1103,1104,1134,1135,1103,1134,1104,\n1135,1104,1134,1136,1137,1135,1136,1105,1136,1104,1105,1135,1104,1103,1105,1135,812,824,1105,1112,\n1114,824,1112,1105,1114,1105,1112,1118,1119,1114,1118,1107,1118,1105,1107,1114,1105,824,1107,1114,\n1104,1105,1106,1120,1121,1105,1120,1106,1121,1106,1120,1122,1123,1121,1122,1107,1122,1106,1107,1121,\n1106,1105,1107,1121,1103,1101,1117,1135,1133,1101,1135,1117,1133,1117,1135,1138,1139,1133,1138,1116,\n1138,1117,1116,1133,1117,1101,1116,1133,1105,1103,1118,1137,1135,1103,1137,1118,1135,1118,1137,1140,\n1138,1135,1140,1117,1140,1118,1117,1135,1118,1103,1117,1135,1107,1105,1119,1123,1121,1105,1123,1119,\n1121,1119,1123,1124,1125,1121,1124,1118,1124,1119,1118,1121,1119,1105,1118,1121,1120,1121,1122,1126,\n1127,1121,1126,1122,1127,1122,1126,1128,1129,1127,1128,1123,1128,1122,1123,1127,1122,1121,1123,1127,\n1123,1121,1124,1129,1127,1121,1129,1124,1127,1124,1129,1130,1131,1127,1130,1125,1130,1124,1125,1127,\n1124,1121,1125,1127,1132,1133,1134,1141,1142,1133,1141,1134,1142,1134,1141,1143,1144,1142,1143,1135,\n1143,1134,1135,1142,1134,1133,1135,1142,1134,1135,1136,1147,1148,1135,1147,1136,1148,1136,1147,1149,\n1150,1148,1149,1137,1149,1136,1137,1148,1136,1135,1137,1148,1135,1133,1138,1144,1142,1133,1144,1138,\n1142,1138,1144,1145,1146,1142,1145,1139,1145,1138,1139,1142,1138,1133,1139,1142,1137,1135,1140,1150,\n1148,1135,1150,1140,1148,1140,1150,1151,1152,1148,1151,1138,1151,1140,1138,1148,1140,1135,1138,1148,\n783,795,1168,1179,1180,795,1179,1168,1180,1168,1179,1181,1182,1180,1181,1170,1181,1168,1170,1180,\n1168,795,1170,1180,795,807,1170,1180,1183,807,1180,1170,1183,1170,1180,1182,1184,1183,1182,1172,\n1182,1170,1172,1183,1170,807,1172,1183,807,819,1172,1183,1185,819,1183,1172,1185,1172,1183,1184,\n1186,1185,1184,1174,1184,1172,1174,1185,1172,819,1174,1185,819,831,1174,1185,1187,831,1185,1174,\n1187,1174,1185,1186,1188,1187,1186,1176,1186,1174,1176,1187,1174,831,1176,1187,783,1168,771,1179,\n1181,1168,1179,771,1181,771,1179,1189,1190,1181,1189,1178,1189,771,1178,1181,771,1168,1178,1181,\n1179,1180,1181,1205,1206,1180,1205,1181,1206,1181,1205,1207,1208,1206,1207,1182,1207,1181,1182,1206,\n1181,1180,1182,1206,1180,1183,1182,1201,1202,1183,1201,1182,1202,1182,1201,1203,1204,1202,1203,1184,\n1203,1182,1184,1202,1182,1183,1184,1202,1183,1185,1184,1191,1192,1185,1191,1184,1192,1184,1191,1193,\n1194,1192,1193,1186,1193,1184,1186,1192,1184,1185,1186,1192,1185,1187,1186,1192,1195,1187,1192,1186,\n1195,1186,1192,1194,1196,1195,1194,1188,1194,1186,1188,1195,1186,1187,1188,1195,1179,1181,1189,1197,\n1198,1181,1197,1189,1198,1189,1197,1199,1200,1198,1199,1190,1199,1189,1190,1198,1189,1181,1190,1198],\n    \"edgeIds\" : [\n    0, 30, 0, 13, 0, 27, 0, 10, 0, 524, 0, 9, 0, 17, 0, 20, 0, 18, 0, 3, \n0, 522, 0, 521, 0, 2, 0, 1, 1, 32, 1, 15, 1, 18, 1, 30, 1, 13, 1, 522, \n1, 10, 1, 21, 1, 525, 1, 5, 1, 4, 1, 17, 1, 20, 1, 19, 1, 3, 1, 521, \n1, 2, 2, 22, 2, 4, 2, 5, 2, 526, 2, 19, 2, 3, 2, 523, 2, 522, 2, 521, \n3, 24, 3, 528, 3, 14, 3, 7, 3, 27, 3, 26, 3, 10, 3, 9, 3, 20, 3, 19, \n3, 523, 3, 522, 3, 524, 4, 17, 4, 521, 4, 13, 4, 33, 4, 32, 4, 16, 4, 15, \n4, 21, 4, 19, 4, 22, 4, 525, 4, 5, 5, 21, 5, 33, 5, 16, 5, 15, 5, 22, \n5, 526, 5, 521, 5, 525, 6, 31, 6, 14, 6, 7, 6, 25, 6, 29, 6, 23, 6, 12, \n6, 527, 6, 529, 6, 11, 6, 8, 7, 26, 7, 9, 7, 23, 7, 31, 7, 24, 7, 14, \n7, 528, 7, 527, 7, 12, 8, 25, 8, 29, 8, 28, 8, 12, 8, 529, 8, 11, 9, 1213, \n9, 1216, 9, 1215, 9, 31, 9, 14, 9, 535, 9, 26, 9, 10, 9, 530, 9, 522, 9, 524, \n10, 13, 10, 521, 10, 27, 10, 26, 10, 530, 10, 522, 10, 531, 11, 28, 11, 12, 11, 532, \n11, 527, 11, 529, 12, 14, 12, 528, 12, 29, 12, 28, 12, 532, 12, 527, 12, 533, 13, 15, \n13, 525, 13, 30, 13, 27, 13, 531, 13, 521, 13, 534, 14, 1213, 14, 1216, 14, 1214, 14, 524, \n14, 31, 14, 29, 14, 533, 14, 528, 14, 535, 15, 30, 15, 534, 15, 32, 15, 16, 15, 536, \n15, 526, 15, 525, 16, 33, 16, 32, 16, 536, 16, 526, 16, 537, 17, 49, 17, 35, 17, 47, \n17, 38, 17, 34, 17, 37, 17, 36, 17, 32, 17, 30, 17, 21, 17, 18, 17, 19, 17, 20, \n18, 47, 18, 44, 18, 34, 18, 37, 18, 35, 18, 30, 18, 27, 18, 20, 19, 41, 19, 40, \n19, 23, 19, 24, 19, 39, 19, 36, 19, 21, 19, 22, 19, 20, 20, 44, 20, 43, 20, 41, \n20, 37, 20, 36, 20, 24, 20, 26, 20, 27, 21, 34, 21, 50, 21, 49, 21, 38, 21, 36, \n21, 39, 21, 32, 21, 33, 21, 22, 22, 45, 22, 28, 22, 38, 22, 50, 22, 40, 22, 42, \n22, 25, 22, 23, 22, 39, 22, 33, 23, 48, 23, 46, 23, 42, 23, 40, 23, 24, 23, 31, \n23, 25, 23, 29, 24, 43, 24, 48, 24, 41, 24, 40, 24, 26, 24, 31, 25, 39, 25, 46, \n25, 45, 25, 42, 25, 28, 25, 29, 26, 1218, 26, 1217, 26, 48, 26, 1215, 26, 43, 26, 31, \n26, 27, 27, 44, 27, 43, 27, 30, 28, 50, 28, 33, 28, 45, 28, 29, 29, 46, 29, 45, \n29, 31, 30, 47, 30, 44, 30, 32, 31, 1218, 31, 1216, 31, 1215, 31, 48, 31, 46, 32, 47, \n32, 49, 32, 33, 33, 50, 33, 49, 34, 66, 34, 52, 34, 64, 34, 55, 34, 51, 34, 54, \n34, 53, 34, 49, 34, 47, 34, 38, 34, 35, 34, 36, 34, 37, 35, 64, 35, 61, 35, 51, \n35, 54, 35, 52, 35, 47, 35, 44, 35, 37, 36, 58, 36, 57, 36, 56, 36, 53, 36, 40, \n36, 41, 36, 38, 36, 39, 36, 37, 37, 61, 37, 60, 37, 58, 37, 54, 37, 53, 37, 43, \n37, 44, 37, 41, 38, 51, 38, 67, 38, 66, 38, 55, 38, 53, 38, 56, 38, 49, 38, 50, \n38, 39, 39, 62, 39, 55, 39, 67, 39, 57, 39, 59, 39, 56, 39, 45, 39, 50, 39, 42, \n39, 40, 40, 65, 40, 63, 40, 59, 40, 57, 40, 48, 40, 46, 40, 42, 40, 41, 41, 60, \n41, 65, 41, 58, 41, 57, 41, 43, 41, 48, 42, 56, 42, 63, 42, 62, 42, 59, 42, 45, \n42, 46, 43, 1220, 43, 1219, 43, 65, 43, 1217, 43, 60, 43, 48, 43, 44, 44, 61, 44, 60, \n44, 47, 45, 67, 45, 62, 45, 50, 45, 46, 46, 63, 46, 62, 46, 48, 47, 64, 47, 61, \n47, 49, 48, 1220, 48, 1218, 48, 1217, 48, 65, 48, 63, 49, 64, 49, 66, 49, 50, 50, 67, \n50, 66, 51, 83, 51, 69, 51, 81, 51, 72, 51, 68, 51, 71, 51, 70, 51, 66, 51, 64, \n51, 55, 51, 52, 51, 53, 51, 54, 52, 81, 52, 78, 52, 68, 52, 71, 52, 69, 52, 64, \n52, 61, 52, 54, 53, 75, 53, 74, 53, 73, 53, 70, 53, 57, 53, 58, 53, 55, 53, 56, \n53, 54, 54, 78, 54, 77, 54, 75, 54, 71, 54, 70, 54, 60, 54, 61, 54, 58, 55, 68, \n55, 84, 55, 83, 55, 72, 55, 70, 55, 73, 55, 66, 55, 67, 55, 56, 56, 79, 56, 72, \n56, 84, 56, 74, 56, 76, 56, 73, 56, 62, 56, 67, 56, 59, 56, 57, 57, 82, 57, 80, \n57, 76, 57, 74, 57, 65, 57, 63, 57, 59, 57, 58, 58, 77, 58, 82, 58, 75, 58, 74, \n58, 60, 58, 65, 59, 73, 59, 80, 59, 79, 59, 76, 59, 62, 59, 63, 60, 1222, 60, 1221, \n60, 82, 60, 1219, 60, 77, 60, 65, 60, 61, 61, 78, 61, 77, 61, 64, 62, 84, 62, 79, \n62, 67, 62, 63, 63, 80, 63, 79, 63, 65, 64, 81, 64, 78, 64, 66, 65, 1222, 65, 1220, \n65, 1219, 65, 82, 65, 80, 66, 81, 66, 83, 66, 67, 67, 84, 67, 83, 68, 100, 68, 86, \n68, 98, 68, 89, 68, 85, 68, 88, 68, 87, 68, 83, 68, 81, 68, 72, 68, 69, 68, 70, \n68, 71, 69, 98, 69, 95, 69, 85, 69, 88, 69, 86, 69, 81, 69, 78, 69, 71, 70, 92, \n70, 91, 70, 90, 70, 87, 70, 74, 70, 75, 70, 72, 70, 73, 70, 71, 71, 95, 71, 94, \n71, 92, 71, 88, 71, 87, 71, 77, 71, 78, 71, 75, 72, 85, 72, 101, 72, 100, 72, 89, \n72, 87, 72, 90, 72, 83, 72, 84, 72, 73, 73, 96, 73, 89, 73, 101, 73, 91, 73, 93, \n73, 90, 73, 79, 73, 84, 73, 76, 73, 74, 74, 99, 74, 97, 74, 93, 74, 91, 74, 82, \n74, 80, 74, 76, 74, 75, 75, 94, 75, 99, 75, 92, 75, 91, 75, 77, 75, 82, 76, 90, \n76, 97, 76, 96, 76, 93, 76, 79, 76, 80, 77, 1224, 77, 1223, 77, 99, 77, 1221, 77, 94, \n77, 82, 77, 78, 78, 95, 78, 94, 78, 81, 79, 101, 79, 96, 79, 84, 79, 80, 80, 97, \n80, 96, 80, 82, 81, 98, 81, 95, 81, 83, 82, 1224, 82, 1222, 82, 1221, 82, 99, 82, 97, \n83, 98, 83, 100, 83, 84, 84, 101, 84, 100, 85, 117, 85, 103, 85, 115, 85, 106, 85, 102, \n85, 105, 85, 104, 85, 100, 85, 98, 85, 89, 85, 86, 85, 87, 85, 88, 86, 115, 86, 112, \n86, 102, 86, 105, 86, 103, 86, 98, 86, 95, 86, 88, 87, 109, 87, 108, 87, 107, 87, 104, \n87, 91, 87, 92, 87, 89, 87, 90, 87, 88, 88, 112, 88, 111, 88, 109, 88, 105, 88, 104, \n88, 94, 88, 95, 88, 92, 89, 102, 89, 118, 89, 117, 89, 106, 89, 104, 89, 107, 89, 100, \n89, 101, 89, 90, 90, 113, 90, 106, 90, 118, 90, 108, 90, 110, 90, 107, 90, 96, 90, 101, \n90, 93, 90, 91, 91, 116, 91, 114, 91, 110, 91, 108, 91, 99, 91, 97, 91, 93, 91, 92, \n92, 111, 92, 116, 92, 109, 92, 108, 92, 94, 92, 99, 93, 107, 93, 114, 93, 113, 93, 110, \n93, 96, 93, 97, 94, 116, 94, 1223, 94, 111, 94, 99, 94, 95, 95, 112, 95, 111, 95, 98, \n96, 118, 96, 113, 96, 101, 96, 97, 97, 114, 97, 113, 97, 99, 98, 115, 98, 112, 98, 100, \n99, 1224, 99, 1223, 99, 116, 99, 114, 100, 115, 100, 117, 100, 101, 101, 118, 101, 117, 102, 134, \n102, 120, 102, 132, 102, 123, 102, 119, 102, 122, 102, 121, 102, 117, 102, 115, 102, 106, 102, 103, \n102, 104, 102, 105, 103, 132, 103, 129, 103, 119, 103, 122, 103, 120, 103, 115, 103, 112, 103, 105, \n104, 126, 104, 125, 104, 124, 104, 121, 104, 108, 104, 109, 104, 106, 104, 107, 104, 105, 105, 129, \n105, 128, 105, 126, 105, 122, 105, 121, 105, 111, 105, 112, 105, 109, 106, 119, 106, 135, 106, 134, \n106, 123, 106, 121, 106, 124, 106, 117, 106, 118, 106, 107, 107, 130, 107, 123, 107, 135, 107, 125, \n107, 127, 107, 124, 107, 113, 107, 118, 107, 110, 107, 108, 108, 133, 108, 131, 108, 127, 108, 125, \n108, 116, 108, 114, 108, 110, 108, 109, 109, 128, 109, 133, 109, 126, 109, 125, 109, 111, 109, 116, \n110, 124, 110, 131, 110, 130, 110, 127, 110, 113, 110, 114, 111, 133, 111, 128, 111, 116, 111, 112, \n112, 129, 112, 128, 112, 115, 113, 135, 113, 130, 113, 118, 113, 114, 114, 131, 114, 130, 114, 116, \n115, 132, 115, 129, 115, 117, 116, 133, 116, 131, 117, 132, 117, 134, 117, 118, 118, 135, 118, 134, \n119, 151, 119, 137, 119, 149, 119, 140, 119, 136, 119, 139, 119, 138, 119, 134, 119, 132, 119, 123, \n119, 120, 119, 121, 119, 122, 120, 149, 120, 146, 120, 136, 120, 139, 120, 137, 120, 132, 120, 129, \n120, 122, 121, 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383, 394, \n383, 397, 383, 395, 383, 388, 383, 389, 383, 385, 384, 401, 384, 400, 384, 396, 384, 390, 384, 391, \n384, 386, 384, 387, 384, 385, 385, 402, 385, 401, 385, 397, 385, 396, 385, 393, 385, 391, 385, 389, \n386, 387, 387, 392, 387, 390, 388, 395, 388, 399, 388, 398, 388, 389, 389, 402, 389, 399, 389, 397, \n389, 393, 390, 400, 390, 392, 390, 391, 391, 401, 391, 400, 391, 393, 393, 402, 393, 401, 394, 395, \n394, 396, 394, 397, 395, 398, 395, 399, 395, 397, 396, 400, 396, 401, 396, 397, 397, 402, 397, 401, \n397, 399, 398, 399, 399, 402, 400, 401, 401, 402, 403, 483, 403, 476, 403, 479, 403, 477, 403, 445, \n403, 443, 403, 446, 403, 419, 403, 421, 403, 407, 403, 405, 404, 423, 404, 426, 404, 425, 404, 408, \n404, 405, 404, 406, 404, 407, 405, 481, 405, 480, 405, 439, 405, 478, 405, 423, 405, 426, 405, 424, \n405, 421, 405, 407, 406, 429, 406, 428, 406, 427, 406, 425, 406, 410, 406, 411, 406, 408, 406, 409, \n406, 407, 407, 424, 407, 437, 407, 428, 407, 426, 407, 425, 407, 421, 407, 419, 407, 411, 408, 409, \n409, 429, 409, 427, 409, 430, 409, 412, 409, 410, 410, 432, 410, 431, 410, 430, 410, 427, 410, 413, \n410, 414, 410, 412, 410, 411, 411, 437, 411, 436, 411, 432, 411, 428, 411, 427, 411, 418, 411, 419, \n411, 414, 412, 431, 412, 433, 412, 430, 412, 415, 412, 413, 413, 435, 413, 434, 413, 433, 413, 431, \n413, 416, 413, 417, 413, 415, 413, 414, 414, 440, 414, 422, 414, 436, 414, 438, 414, 435, 414, 432, \n414, 431, 414, 420, 414, 418, 414, 417, 415, 433, 416, 434, 416, 417, 417, 435, 417, 434, 417, 422, \n417, 420, 418, 448, 418, 438, 418, 436, 418, 444, 418, 443, 418, 420, 418, 419, 419, 448, 419, 447, \n419, 439, 419, 426, 419, 446, 419, 437, 419, 436, 419, 443, 419, 421, 420, 432, 420, 440, 420, 438, \n420, 422, 421, 483, 421, 482, 421, 445, 421, 481, 421, 447, 421, 449, 421, 437, 421, 439, 421, 426, \n421, 424, 421, 479, 421, 478, 421, 446, 422, 440, 422, 435, 423, 424, 423, 425, 423, 426, 424, 480, \n424, 439, 424, 426, 425, 454, 425, 450, 425, 453, 425, 452, 425, 429, 425, 427, 425, 428, 425, 426, \n426, 450, 426, 453, 426, 451, 426, 439, 426, 437, 426, 428, 427, 457, 427, 456, 427, 455, 427, 452, \n427, 431, 427, 432, 427, 429, 427, 430, 427, 428, 428, 457, 428, 453, 428, 452, 428, 436, 428, 437, \n428, 432, 429, 454, 429, 452, 429, 455, 429, 430, 430, 456, 430, 458, 430, 455, 430, 433, 430, 431, \n431, 460, 431, 459, 431, 458, 431, 456, 431, 434, 431, 435, 431, 433, 431, 432, 432, 460, 432, 457, \n432, 456, 432, 440, 432, 438, 432, 436, 432, 435, 433, 458, 434, 459, 434, 435, 435, 460, 435, 459, \n435, 440, 436, 448, 436, 447, 436, 438, 436, 437, 437, 449, 437, 447, 437, 439, 438, 440, 439, 482, \n439, 484, 439, 446, 439, 481, 439, 480, 439, 449, 441, 445, 441, 442, 441, 443, 441, 444, 442, 444, \n443, 447, 443, 448, 443, 445, 443, 446, 443, 444, 444, 448, 445, 483, 445, 482, 445, 446, 446, 484, \n446, 482, 446, 449, 446, 447, 447, 449, 447, 448, 449, 484, 450, 465, 450, 461, 450, 464, 450, 463, \n450, 454, 450, 451, 450, 452, 450, 453, 451, 461, 451, 464, 451, 462, 451, 453, 452, 468, 452, 467, \n452, 466, 452, 463, 452, 456, 452, 457, 452, 454, 452, 455, 452, 453, 453, 468, 453, 464, 453, 463, \n453, 457, 454, 465, 454, 463, 454, 466, 454, 455, 455, 467, 455, 475, 455, 466, 455, 458, 455, 456, \n456, 475, 456, 467, 456, 459, 456, 460, 456, 458, 456, 457, 457, 468, 457, 467, 457, 460, 458, 475, \n459, 460, 461, 469, 461, 472, 461, 471, 461, 465, 461, 462, 461, 463, 461, 464, 462, 469, 462, 472, \n462, 470, 462, 464, 463, 474, 463, 473, 463, 471, 463, 467, 463, 468, 463, 465, 463, 466, 463, 464, \n464, 474, 464, 472, 464, 471, 464, 468, 465, 466, 466, 475, 466, 467, 467, 473, 467, 475, 467, 468, \n468, 474, 468, 473, 469, 470, 469, 471, 469, 472, 470, 472, 471, 473, 471, 474, 471, 472, 472, 474, \n473, 474, 476, 485, 476, 488, 476, 487, 476, 477, 476, 478, 476, 479, 477, 492, 477, 485, 477, 488, \n477, 486, 477, 483, 477, 479, 478, 490, 478, 489, 478, 487, 478, 480, 478, 481, 478, 479, 479, 492, \n479, 491, 479, 490, 479, 488, 479, 487, 479, 482, 479, 483, 479, 481, 480, 489, 480, 481, 481, 491, \n481, 493, 481, 490, 481, 489, 481, 484, 481, 482, 482, 493, 482, 491, 482, 484, 482, 483, 483, 492, \n483, 491, 484, 493, 485, 494, 485, 497, 485, 496, 485, 486, 485, 487, 485, 488, 486, 501, 486, 494, \n486, 497, 486, 495, 486, 492, 486, 488, 487, 499, 487, 498, 487, 496, 487, 489, 487, 490, 487, 488, \n488, 501, 488, 500, 488, 499, 488, 497, 488, 496, 488, 491, 488, 492, 488, 490, 489, 498, 489, 490, \n490, 500, 490, 502, 490, 499, 490, 498, 490, 493, 490, 491, 491, 502, 491, 500, 491, 493, 491, 492, \n492, 501, 492, 500, 493, 502, 494, 503, 494, 506, 494, 505, 494, 495, 494, 496, 494, 497, 495, 510, \n495, 503, 495, 506, 495, 504, 495, 501, 495, 497, 496, 508, 496, 507, 496, 505, 496, 498, 496, 499, \n496, 497, 497, 510, 497, 509, 497, 508, 497, 506, 497, 505, 497, 500, 497, 501, 497, 499, 498, 507, \n498, 499, 499, 509, 499, 511, 499, 508, 499, 507, 499, 502, 499, 500, 500, 511, 500, 509, 500, 502, \n500, 501, 501, 510, 501, 509, 502, 511, 503, 512, 503, 515, 503, 514, 503, 504, 503, 505, 503, 506, \n504, 519, 504, 512, 504, 515, 504, 513, 504, 510, 504, 506, 505, 517, 505, 516, 505, 514, 505, 507, \n505, 508, 505, 506, 506, 519, 506, 518, 506, 517, 506, 515, 506, 514, 506, 509, 506, 510, 506, 508, \n507, 516, 507, 508, 508, 518, 508, 520, 508, 517, 508, 516, 508, 511, 508, 509, 509, 520, 509, 518, \n509, 511, 509, 510, 510, 519, 510, 518, 511, 520, 512, 513, 512, 514, 512, 515, 513, 519, 513, 515, \n514, 516, 514, 517, 514, 515, 515, 518, 515, 519, 515, 517, 516, 517, 517, 520, 517, 518, 518, 520, \n518, 519, 521, 539, 521, 538, 521, 542, 521, 534, 521, 531, 521, 526, 521, 525, 521, 523, 521, 522, \n522, 539, 522, 541, 522, 531, 522, 530, 522, 524, 522, 523, 523, 543, 523, 538, 523, 540, 523, 526, \n523, 524, 524, 545, 524, 541, 524, 535, 524, 528, 524, 530, 525, 538, 525, 542, 525, 534, 525, 536, \n525, 526, 526, 543, 526, 538, 526, 542, 526, 537, 526, 536, 527, 544, 527, 546, 527, 528, 527, 533, \n527, 532, 527, 529, 528, 545, 528, 544, 528, 535, 528, 533, 529, 546, 529, 532, 530, 552, 530, 547, \n530, 539, 530, 541, 530, 535, 530, 531, 531, 538, 531, 547, 531, 539, 531, 548, 531, 534, 532, 549, \n532, 544, 532, 546, 532, 533, 533, 545, 533, 549, 533, 544, 533, 550, 533, 535, 534, 542, 534, 548, \n534, 538, 534, 551, 534, 536, 535, 541, 535, 550, 535, 545, 535, 552, 536, 551, 536, 553, 536, 543, \n536, 542, 536, 537, 537, 553, 537, 543, 537, 554, 538, 556, 538, 559, 538, 555, 538, 551, 538, 548, \n538, 539, 538, 540, 538, 543, 538, 542, 539, 558, 539, 556, 539, 555, 539, 540, 539, 548, 539, 547, \n539, 541, 540, 560, 540, 541, 540, 557, 540, 556, 540, 555, 540, 543, 541, 562, 541, 557, 541, 556, \n541, 558, 541, 552, 541, 545, 541, 547, 542, 555, 542, 559, 542, 551, 542, 553, 542, 543, 543, 560, \n543, 555, 543, 559, 543, 554, 543, 553, 544, 561, 544, 563, 544, 545, 544, 550, 544, 549, 544, 546, \n545, 562, 545, 561, 545, 552, 545, 550, 546, 563, 546, 549, 547, 569, 547, 564, 547, 556, 547, 558, \n547, 552, 547, 548, 548, 555, 548, 564, 548, 556, 548, 565, 548, 551, 549, 566, 549, 561, 549, 563, \n549, 550, 550, 562, 550, 566, 550, 561, 550, 567, 550, 552, 551, 559, 551, 565, 551, 555, 551, 568, \n551, 553, 552, 558, 552, 567, 552, 562, 552, 569, 553, 568, 553, 570, 553, 560, 553, 559, 553, 554, \n554, 570, 554, 560, 554, 571, 555, 573, 555, 572, 555, 576, 555, 568, 555, 565, 555, 560, 555, 559, \n555, 557, 555, 556, 556, 573, 556, 575, 556, 565, 556, 564, 556, 558, 556, 557, 557, 577, 557, 572, \n557, 574, 557, 560, 557, 558, 558, 579, 558, 575, 558, 569, 558, 562, 558, 564, 559, 572, 559, 576, \n559, 568, 559, 570, 559, 560, 560, 563, 560, 577, 560, 572, 560, 576, 560, 571, 560, 570, 561, 578, \n561, 580, 561, 562, 561, 567, 561, 566, 561, 563, 562, 579, 562, 578, 562, 569, 562, 567, 563, 577, \n563, 571, 563, 580, 563, 566, 564, 624, 564, 623, 564, 582, 564, 586, 564, 581, 564, 573, 564, 575, \n564, 569, 564, 565, 565, 647, 565, 585, 565, 623, 565, 572, 565, 581, 565, 573, 565, 582, 565, 568, \n566, 571, 566, 588, 566, 583, 566, 578, 566, 580, 566, 567, 567, 636, 567, 635, 567, 586, 567, 579, \n567, 583, 567, 578, 567, 584, 567, 569, 568, 673, 568, 679, 568, 648, 568, 666, 568, 665, 568, 587, \n568, 647, 568, 576, 568, 582, 568, 572, 568, 585, 568, 570, 569, 627, 569, 624, 569, 581, 569, 635, \n569, 575, 569, 584, 569, 579, 569, 586, 570, 665, 570, 585, 570, 587, 570, 577, 570, 576, 570, 571, \n571, 580, 571, 587, 571, 577, 571, 588, 572, 590, 572, 589, 572, 593, 572, 585, 572, 582, 572, 573, \n572, 574, 572, 577, 572, 576, 573, 590, 573, 592, 573, 582, 573, 581, 573, 575, 574, 594, 574, 589, \n574, 591, 574, 577, 575, 596, 575, 592, 575, 586, 575, 579, 575, 581, 576, 589, 576, 593, 576, 585, \n576, 587, 576, 577, 577, 594, 577, 589, 577, 593, 577, 580, 577, 588, 577, 587, 578, 595, 578, 597, \n578, 579, 578, 584, 578, 583, 578, 580, 579, 596, 579, 595, 579, 586, 579, 584, 580, 594, 580, 597, \n580, 588, 580, 583, 581, 599, 581, 603, 581, 627, 581, 598, 581, 590, 581, 592, 581, 625, 581, 624, \n581, 626, 581, 586, 581, 582, 582, 602, 582, 589, 582, 648, 582, 598, 582, 590, 582, 599, 582, 625, \n582, 624, 582, 623, 582, 585, 583, 605, 583, 600, 583, 595, 583, 597, 583, 588, 583, 584, 584, 603, \n584, 596, 584, 637, 584, 636, 584, 638, 584, 600, 584, 595, 584, 601, 584, 586, 585, 674, 585, 649, \n585, 673, 585, 604, 585, 593, 585, 667, 585, 666, 585, 668, 585, 599, 585, 589, 585, 602, 585, 648, \n585, 623, 585, 647, 585, 587, 586, 598, 586, 592, 586, 626, 586, 627, 586, 628, 586, 601, 586, 596, \n586, 603, 586, 637, 586, 636, 586, 635, 587, 602, 587, 667, 587, 666, 587, 665, 587, 604, 587, 594, \n587, 593, 587, 588, 588, 597, 588, 604, 588, 594, 588, 605, 589, 607, 589, 610, 589, 606, 589, 602, \n589, 599, 589, 590, 589, 591, 589, 594, 589, 593, 590, 609, 590, 607, 590, 606, 590, 591, 590, 599, \n590, 598, 590, 592, 591, 611, 591, 592, 591, 608, 591, 607, 591, 606, 591, 594, 592, 613, 592, 608, \n592, 607, 592, 609, 592, 603, 592, 596, 592, 598, 593, 606, 593, 610, 593, 602, 593, 604, 593, 594, \n594, 611, 594, 606, 594, 610, 594, 597, 594, 605, 594, 604, 595, 612, 595, 614, 595, 596, 595, 601, \n595, 600, 595, 597, 596, 613, 596, 612, 596, 603, 596, 601, 597, 611, 597, 614, 597, 605, 597, 600, \n598, 616, 598, 620, 598, 628, 598, 615, 598, 607, 598, 609, 598, 629, 598, 626, 598, 630, 598, 603, \n598, 599, 599, 619, 599, 606, 599, 649, 599, 615, 599, 607, 599, 616, 599, 629, 599, 626, 599, 625, \n599, 602, 600, 622, 600, 617, 600, 612, 600, 614, 600, 605, 600, 601, 601, 620, 601, 613, 601, 639, \n601, 638, 601, 640, 601, 617, 601, 612, 601, 618, 601, 603, 602, 672, 602, 674, 602, 621, 602, 610, \n602, 669, 602, 668, 602, 670, 602, 616, 602, 606, 602, 619, 602, 649, 602, 625, 602, 648, 602, 604, \n603, 615, 603, 609, 603, 630, 603, 628, 603, 631, 603, 618, 603, 613, 603, 620, 603, 639, 603, 638, \n603, 637, 604, 619, 604, 669, 604, 668, 604, 667, 604, 621, 604, 611, 604, 610, 604, 605, 605, 614, \n605, 621, 605, 611, 605, 622, 606, 619, 606, 616, 606, 611, 606, 610, 606, 608, 606, 607, 607, 616, \n607, 615, 607, 609, 607, 608, 608, 611, 608, 609, 609, 620, 609, 613, 609, 615, 610, 619, 610, 621, \n610, 611, 611, 614, 611, 622, 611, 621, 612, 613, 612, 618, 612, 617, 612, 614, 613, 620, 613, 618, \n614, 622, 614, 617, 615, 631, 615, 632, 615, 630, 615, 633, 615, 620, 615, 616, 616, 650, 616, 632, \n616, 630, 616, 629, 616, 619, 617, 622, 617, 618, 618, 641, 618, 640, 618, 642, 618, 620, 619, 675, \n619, 671, 619, 670, 619, 672, 619, 650, 619, 629, 619, 649, 619, 621, 620, 633, 620, 631, 620, 634, \n620, 641, 620, 640, 620, 639, 621, 671, 621, 670, 621, 669, 621, 622, 623, 723, 623, 653, 623, 652, \n623, 651, 623, 680, 623, 648, 623, 647, 623, 625, 623, 624, 624, 724, 624, 723, 624, 681, 624, 680, \n624, 627, 624, 626, 624, 625, 625, 653, 625, 656, 625, 655, 625, 651, 625, 682, 625, 681, 625, 680, \n625, 649, 625, 629, 625, 648, 625, 626, 626, 684, 626, 682, 626, 681, 626, 683, 626, 630, 626, 629, \n626, 628, 626, 627, 627, 727, 627, 724, 627, 685, 627, 644, 627, 684, 627, 681, 627, 643, 627, 637, \n627, 635, 627, 628, 628, 688, 628, 645, 628, 639, 628, 683, 628, 684, 628, 685, 628, 643, 628, 637, \n628, 644, 628, 631, 628, 630, 629, 651, 629, 658, 629, 656, 629, 655, 629, 686, 629, 683, 629, 682, \n629, 650, 629, 632, 629, 649, 629, 630, 630, 685, 630, 686, 630, 683, 630, 687, 630, 633, 630, 632, \n630, 631, 631, 691, 631, 646, 631, 641, 631, 687, 631, 685, 631, 688, 631, 644, 631, 639, 631, 645, \n631, 634, 631, 633, 632, 655, 632, 658, 632, 656, 632, 657, 632, 649, 632, 689, 632, 687, 632, 686, \n632, 650, 632, 633, 633, 688, 633, 689, 633, 687, 633, 690, 633, 634, 634, 690, 634, 688, 634, 691, \n634, 645, 634, 641, 634, 646, 635, 643, 635, 637, 635, 636, 636, 638, 636, 637, 637, 644, 637, 643, \n637, 639, 637, 638, 638, 640, 638, 639, 639, 645, 639, 644, 639, 641, 639, 640, 640, 642, 640, 641, \n641, 646, 641, 645, 641, 642, 643, 692, 643, 684, 643, 693, 643, 644, 644, 694, 644, 692, 644, 684, \n644, 685, 644, 645, 645, 695, 645, 694, 645, 685, 645, 688, 645, 646, 646, 695, 646, 688, 646, 691, \n647, 653, 647, 652, 647, 654, 647, 679, 647, 648, 648, 674, 648, 656, 648, 652, 648, 651, 648, 673, \n648, 679, 648, 649, 649, 657, 649, 672, 649, 675, 649, 656, 649, 655, 649, 674, 649, 673, 649, 650, \n650, 657, 650, 675, 651, 659, 651, 662, 651, 661, 651, 686, 651, 696, 651, 682, 651, 697, 651, 655, \n651, 656, 651, 653, 651, 652, 652, 659, 652, 662, 652, 660, 652, 676, 652, 673, 652, 677, 652, 656, \n652, 654, 652, 653, 653, 696, 653, 682, 653, 680, 653, 654, 655, 659, 655, 664, 655, 662, 655, 689, \n655, 661, 655, 697, 655, 686, 655, 698, 655, 658, 655, 656, 656, 663, 656, 678, 656, 662, 656, 661, \n656, 676, 656, 673, 656, 674, 656, 658, 656, 657, 657, 663, 657, 678, 657, 674, 657, 675, 657, 658, \n658, 661, 658, 664, 658, 662, 658, 663, 658, 698, 658, 689, 658, 699, 659, 700, 659, 698, 659, 697, \n659, 660, 659, 661, 659, 662, 660, 662, 661, 699, 661, 700, 661, 698, 661, 701, 661, 664, 661, 662, \n662, 664, 662, 663, 663, 664, 664, 701, 664, 699, 664, 702, 665, 667, 665, 666, 666, 679, 666, 673, \n666, 668, 666, 667, 667, 669, 667, 668, 668, 674, 668, 673, 668, 670, 668, 669, 669, 671, 669, 670, \n670, 674, 670, 672, 670, 671, 671, 672, 672, 674, 672, 675, 673, 677, 673, 676, 673, 674, 673, 679, \n674, 678, 674, 676, 674, 675, 675, 678, 676, 678, 676, 677, 680, 703, 680, 725, 680, 724, 680, 723, \n680, 696, 680, 682, 680, 681, 681, 727, 681, 704, 681, 703, 681, 725, 681, 724, 681, 726, 681, 684, \n681, 683, 681, 682, 682, 705, 682, 704, 682, 703, 682, 697, 682, 696, 682, 686, 682, 683, 683, 707, \n683, 705, 683, 704, 683, 706, 683, 687, 683, 686, 683, 685, 683, 684, 684, 707, 684, 704, 684, 726, \n684, 727, 684, 728, 684, 693, 684, 692, 684, 685, 685, 706, 685, 707, 685, 708, 685, 694, 685, 692, \n685, 688, 685, 687, 686, 709, 686, 706, 686, 705, 686, 698, 686, 697, 686, 689, 686, 687, 687, 708, \n687, 709, 687, 706, 687, 710, 687, 690, 687, 689, 687, 688, 688, 714, 688, 710, 688, 708, 688, 711, \n688, 695, 688, 694, 688, 691, 688, 690, 689, 712, 689, 710, 689, 709, 689, 699, 689, 698, 689, 690, \n690, 711, 690, 712, 690, 710, 690, 713, 690, 691, 691, 713, 691, 711, 691, 714, 691, 695, 692, 694, \n692, 693, 694, 715, 694, 711, 694, 716, 694, 695, 695, 715, 695, 711, 695, 714, 696, 697, 697, 700, \n697, 698, 698, 701, 698, 700, 698, 699, 699, 702, 699, 701, 700, 701, 701, 702, 703, 717, 703, 729, \n703, 726, 703, 725, 703, 705, 703, 704, 704, 728, 704, 718, 704, 717, 704, 729, 704, 726, 704, 730, \n704, 707, 704, 706, 704, 705, 705, 719, 705, 718, 705, 717, 705, 709, 705, 706, 706, 721, 706, 719, \n706, 718, 706, 720, 706, 710, 706, 709, 706, 708, 706, 707, 707, 721, 707, 718, 707, 730, 707, 728, \n707, 731, 707, 708, 708, 720, 708, 721, 708, 722, 708, 711, 708, 710, 709, 712, 709, 710, 710, 713, \n710, 712, 710, 711, 711, 716, 711, 715, 711, 714, 711, 713, 712, 713, 713, 714, 714, 715, 715, 716, \n717, 732, 717, 730, 717, 729, 717, 719, 717, 718, 718, 731, 718, 732, 718, 730, 718, 733, 718, 721, \n718, 720, 718, 719, 719, 720, 720, 722, 720, 721, 721, 733, 721, 731, 721, 734, 721, 722, 723, 735, \n723, 725, 723, 724, 724, 736, 724, 735, 724, 727, 724, 726, 724, 725, 725, 737, 725, 736, 725, 735, \n725, 729, 725, 726, 726, 739, 726, 737, 726, 736, 726, 738, 726, 730, 726, 729, 726, 728, 726, 727, \n727, 739, 727, 736, 727, 728, 728, 738, 728, 739, 728, 740, 728, 731, 728, 730, 729, 741, 729, 738, \n729, 737, 729, 732, 729, 730, 730, 740, 730, 741, 730, 738, 730, 742, 730, 733, 730, 732, 730, 731, \n731, 742, 731, 740, 731, 743, 731, 734, 731, 733, 732, 744, 732, 742, 732, 741, 732, 733, 733, 743, \n733, 744, 733, 742, 733, 745, 733, 734, 734, 745, 734, 743, 734, 746, 735, 747, 735, 737, 735, 736, \n736, 1153, 736, 748, 736, 747, 736, 739, 736, 738, 736, 737, 737, 749, 737, 748, 737, 747, 737, 741, \n737, 738, 738, 751, 738, 749, 738, 748, 738, 750, 738, 742, 738, 741, 738, 740, 738, 739, 739, 1154, \n739, 1153, 739, 751, 739, 748, 739, 740, 740, 750, 740, 751, 740, 752, 740, 743, 740, 742, 741, 753, \n741, 750, 741, 749, 741, 744, 741, 742, 742, 752, 742, 753, 742, 750, 742, 754, 742, 745, 742, 744, \n742, 743, 743, 754, 743, 752, 743, 755, 743, 746, 743, 745, 744, 756, 744, 754, 744, 753, 744, 745, \n745, 755, 745, 756, 745, 754, 745, 757, 745, 746, 746, 757, 746, 755, 746, 758, 747, 759, 747, 749, \n747, 748, 748, 1155, 748, 1154, 748, 1153, 748, 760, 748, 759, 748, 751, 748, 750, 748, 749, 749, 761, \n749, 760, 749, 759, 749, 753, 749, 750, 750, 763, 750, 761, 750, 760, 750, 762, 750, 754, 750, 753, \n750, 752, 750, 751, 751, 763, 751, 760, 751, 1155, 751, 1154, 751, 1156, 751, 752, 752, 762, 752, 763, \n752, 764, 752, 755, 752, 754, 753, 765, 753, 762, 753, 761, 753, 756, 753, 754, 754, 764, 754, 765, \n754, 762, 754, 766, 754, 757, 754, 756, 754, 755, 755, 766, 755, 764, 755, 767, 755, 758, 755, 757, \n756, 768, 756, 766, 756, 765, 756, 757, 757, 767, 757, 768, 757, 766, 757, 769, 757, 758, 758, 769, \n758, 767, 758, 770, 759, 771, 759, 761, 759, 760, 760, 1157, 760, 1156, 760, 1155, 760, 772, 760, 771, \n760, 763, 760, 762, 760, 761, 761, 773, 761, 772, 761, 771, 761, 765, 761, 762, 762, 775, 762, 773, \n762, 772, 762, 774, 762, 766, 762, 765, 762, 764, 762, 763, 763, 775, 763, 772, 763, 1157, 763, 1156, \n763, 1158, 763, 764, 764, 774, 764, 775, 764, 776, 764, 767, 764, 766, 765, 844, 765, 843, 765, 780, \n765, 777, 765, 774, 765, 773, 765, 768, 765, 766, 766, 776, 766, 777, 766, 774, 766, 778, 766, 769, \n766, 768, 766, 767, 767, 778, 767, 776, 767, 779, 767, 770, 767, 769, 768, 847, 768, 781, 768, 843, \n768, 780, 768, 778, 768, 777, 768, 769, 769, 849, 769, 782, 769, 847, 769, 779, 769, 780, 769, 778, \n769, 781, 769, 770, 770, 849, 770, 781, 770, 779, 770, 782, 771, 1189, 771, 1181, 771, 1179, 771, 1168, \n771, 1178, 771, 1177, 771, 785, 771, 783, 771, 773, 771, 772, 772, 1159, 772, 1158, 772, 1157, 772, 784, \n772, 783, 772, 775, 772, 774, 772, 773, 773, 1177, 773, 785, 773, 784, 773, 783, 773, 777, 773, 774, \n774, 787, 774, 785, 774, 784, 774, 786, 774, 778, 774, 777, 774, 776, 774, 775, 775, 1098, 775, 787, \n775, 784, 775, 1159, 775, 1158, 775, 1160, 775, 776, 776, 1099, 776, 1098, 776, 786, 776, 787, 776, 788, \n776, 779, 776, 778, 777, 792, 777, 845, 777, 844, 777, 846, 777, 789, 777, 786, 777, 785, 777, 780, \n777, 778, 778, 788, 778, 789, 778, 786, 778, 790, 778, 781, 778, 780, 778, 779, 779, 790, 779, 788, \n779, 791, 779, 782, 779, 781, 780, 793, 780, 792, 780, 790, 780, 789, 780, 848, 780, 845, 780, 844, \n780, 843, 780, 781, 781, 794, 781, 791, 781, 850, 781, 792, 781, 790, 781, 793, 781, 848, 781, 843, \n781, 847, 781, 782, 782, 793, 782, 791, 782, 794, 782, 850, 782, 847, 782, 849, 783, 1179, 783, 797, \n783, 795, 783, 1167, 783, 1178, 783, 1168, 783, 785, 783, 784, 784, 1161, 784, 1160, 784, 1159, 784, 796, \n784, 795, 784, 787, 784, 786, 784, 785, 785, 797, 785, 796, 785, 795, 785, 1167, 785, 1178, 785, 1177, \n785, 789, 785, 786, 786, 799, 786, 797, 786, 796, 786, 798, 786, 790, 786, 789, 786, 788, 786, 787, \n787, 799, 787, 796, 787, 1100, 787, 1099, 787, 1098, 787, 1161, 787, 1160, 787, 1162, 787, 788, 788, 1108, \n788, 798, 788, 799, 788, 800, 788, 1100, 788, 1099, 788, 1101, 788, 791, 788, 790, 789, 804, 789, 851, \n789, 846, 789, 852, 789, 801, 789, 798, 789, 797, 789, 792, 789, 790, 790, 800, 790, 801, 790, 798, \n790, 802, 790, 793, 790, 792, 790, 791, 791, 1109, 791, 1108, 791, 802, 791, 800, 791, 803, 791, 794, \n791, 793, 792, 805, 792, 804, 792, 802, 792, 801, 792, 853, 792, 851, 792, 846, 792, 845, 792, 793, \n793, 806, 793, 803, 793, 854, 793, 804, 793, 802, 793, 805, 793, 853, 793, 845, 793, 848, 793, 794, \n794, 805, 794, 803, 794, 806, 794, 854, 794, 848, 794, 850, 795, 1180, 795, 1179, 795, 809, 795, 807, \n795, 1169, 795, 1168, 795, 1170, 795, 797, 795, 796, 796, 1163, 796, 1162, 796, 1161, 796, 808, 796, 807, \n796, 799, 796, 798, 796, 797, 797, 809, 797, 808, 797, 807, 797, 1169, 797, 1168, 797, 1167, 797, 801, \n797, 798, 798, 811, 798, 809, 798, 808, 798, 810, 798, 802, 798, 801, 798, 800, 798, 799, 799, 811, \n799, 808, 799, 1102, 799, 1101, 799, 1100, 799, 1163, 799, 1162, 799, 1164, 799, 800, 800, 1110, 800, 1109, \n800, 1108, 800, 810, 800, 811, 800, 812, 800, 1102, 800, 1101, 800, 1103, 800, 803, 800, 802, 801, 980, \n801, 979, 801, 816, 801, 855, 801, 852, 801, 856, 801, 813, 801, 810, 801, 809, 801, 804, 801, 802, \n802, 812, 802, 813, 802, 810, 802, 814, 802, 805, 802, 804, 802, 803, 803, 814, 803, 812, 803, 815, \n803, 1110, 803, 1109, 803, 1111, 803, 806, 803, 805, 804, 983, 804, 817, 804, 979, 804, 816, 804, 814, \n804, 813, 804, 857, 804, 855, 804, 852, 804, 851, 804, 805, 805, 985, 805, 818, 805, 983, 805, 815, \n805, 858, 805, 816, 805, 814, 805, 817, 805, 857, 805, 851, 805, 853, 805, 806, 806, 985, 806, 817, \n806, 815, 806, 818, 806, 858, 806, 853, 806, 854, 807, 1183, 807, 1180, 807, 821, 807, 1059, 807, 819, \n807, 1171, 807, 1170, 807, 1172, 807, 809, 807, 808, 808, 1060, 808, 1059, 808, 1165, 808, 1164, 808, 1163, \n808, 820, 808, 819, 808, 811, 808, 810, 808, 809, 809, 821, 809, 820, 809, 819, 809, 1171, 809, 1170, \n809, 1169, 809, 813, 809, 810, 810, 823, 810, 821, 810, 820, 810, 822, 810, 814, 810, 813, 810, 812, \n810, 811, 811, 1063, 811, 1060, 811, 823, 811, 820, 811, 1104, 811, 1103, 811, 1102, 811, 1165, 811, 1164, \n811, 1166, 811, 812, 812, 1112, 812, 1111, 812, 1110, 812, 822, 812, 823, 812, 824, 812, 1104, 812, 1103, \n812, 1105, 812, 815, 812, 814, 813, 828, 813, 981, 813, 980, 813, 982, 813, 825, 813, 822, 813, 821, \n813, 816, 813, 814, 814, 824, 814, 825, 814, 822, 814, 826, 814, 817, 814, 816, 814, 815, 815, 826, \n815, 824, 815, 827, 815, 1112, 815, 1111, 815, 1113, 815, 818, 815, 817, 816, 829, 816, 828, 816, 826, \n816, 825, 816, 984, 816, 981, 816, 980, 816, 979, 816, 817, 817, 830, 817, 827, 817, 986, 817, 828, \n817, 826, 817, 829, 817, 984, 817, 979, 817, 983, 817, 818, 818, 829, 818, 827, 818, 830, 818, 986, \n818, 983, 818, 985, 819, 1185, 819, 1183, 819, 833, 819, 831, 819, 1173, 819, 1172, 819, 1174, 819, 1061, \n819, 1060, 819, 1059, 819, 821, 819, 820, 820, 1063, 820, 832, 820, 831, 820, 1061, 820, 1060, 820, 1062, \n820, 823, 820, 822, 820, 821, 821, 833, 821, 832, 821, 831, 821, 1173, 821, 1172, 821, 1171, 821, 825, \n821, 822, 822, 835, 822, 833, 822, 832, 822, 834, 822, 826, 822, 825, 822, 824, 822, 823, 823, 835, \n823, 832, 823, 1106, 823, 1105, 823, 1104, 823, 1062, 823, 1063, 823, 1064, 823, 824, 824, 1114, 824, 1113, \n824, 1112, 824, 834, 824, 835, 824, 836, 824, 1106, 824, 1105, 824, 1107, 824, 827, 824, 826, 825, 840, \n825, 987, 825, 982, 825, 988, 825, 837, 825, 834, 825, 833, 825, 828, 825, 826, 826, 836, 826, 837, \n826, 834, 826, 838, 826, 829, 826, 828, 826, 827, 827, 838, 827, 836, 827, 839, 827, 1114, 827, 1113, \n827, 1115, 827, 830, 827, 829, 828, 840, 828, 989, 828, 987, 828, 982, 828, 981, 828, 829, 829, 842, \n829, 841, 829, 839, 829, 838, 829, 990, 829, 989, 829, 981, 829, 984, 829, 830, 830, 841, 830, 839, \n830, 842, 830, 990, 830, 984, 830, 986, 831, 1187, 831, 1185, 831, 1175, 831, 1174, 831, 1176, 831, 1065, \n831, 1062, 831, 1061, 831, 833, 831, 832, 832, 1064, 832, 1065, 832, 1062, 832, 1066, 832, 835, 832, 834, \n832, 833, 833, 1175, 833, 1174, 833, 1173, 833, 837, 833, 834, 834, 838, 834, 837, 834, 836, 834, 835, \n835, 1066, 835, 1064, 835, 1067, 835, 836, 836, 839, 836, 838, 837, 840, 837, 991, 837, 988, 837, 992, \n837, 838, 838, 841, 838, 839, 839, 842, 839, 841, 840, 991, 840, 988, 840, 987, 841, 994, 841, 989, \n841, 993, 841, 842, 842, 994, 842, 989, 842, 990, 843, 863, 843, 859, 843, 848, 843, 847, 843, 845, \n843, 844, 844, 860, 844, 859, 844, 846, 844, 845, 845, 864, 845, 861, 845, 860, 845, 859, 845, 853, \n845, 851, 845, 848, 845, 846, 846, 861, 846, 860, 846, 862, 846, 852, 846, 851, 847, 865, 847, 863, \n847, 850, 847, 849, 847, 848, 848, 866, 848, 864, 848, 859, 848, 863, 848, 854, 848, 853, 848, 850, \n849, 865, 849, 850, 850, 866, 850, 863, 850, 865, 850, 854, 851, 869, 851, 867, 851, 862, 851, 861, \n851, 857, 851, 855, 851, 853, 851, 852, 852, 867, 852, 862, 852, 868, 852, 856, 852, 855, 853, 870, \n853, 869, 853, 861, 853, 864, 853, 858, 853, 857, 853, 854, 854, 870, 854, 864, 854, 866, 854, 858, \n855, 873, 855, 871, 855, 868, 855, 867, 855, 857, 855, 856, 856, 871, 856, 868, 856, 872, 857, 874, \n857, 873, 857, 867, 857, 869, 857, 858, 858, 874, 858, 869, 858, 870, 859, 879, 859, 875, 859, 864, \n859, 863, 859, 861, 859, 860, 860, 876, 860, 875, 860, 862, 860, 861, 861, 880, 861, 877, 861, 876, \n861, 875, 861, 869, 861, 867, 861, 864, 861, 862, 862, 877, 862, 876, 862, 878, 862, 868, 862, 867, \n863, 881, 863, 879, 863, 866, 863, 865, 863, 864, 864, 882, 864, 880, 864, 875, 864, 879, 864, 870, \n864, 869, 864, 866, 865, 881, 865, 866, 866, 882, 866, 879, 866, 881, 866, 870, 867, 885, 867, 883, \n867, 878, 867, 877, 867, 873, 867, 871, 867, 869, 867, 868, 868, 883, 868, 878, 868, 884, 868, 872, \n868, 871, 869, 886, 869, 885, 869, 877, 869, 880, 869, 874, 869, 873, 869, 870, 870, 886, 870, 880, \n870, 882, 870, 874, 871, 889, 871, 887, 871, 884, 871, 883, 871, 873, 871, 872, 872, 887, 872, 884, \n872, 888, 873, 890, 873, 889, 873, 883, 873, 885, 873, 874, 874, 890, 874, 885, 874, 886, 875, 895, \n875, 891, 875, 880, 875, 879, 875, 877, 875, 876, 876, 892, 876, 891, 876, 878, 876, 877, 877, 896, \n877, 893, 877, 892, 877, 891, 877, 885, 877, 883, 877, 880, 877, 878, 878, 893, 878, 892, 878, 894, \n878, 884, 878, 883, 879, 897, 879, 895, 879, 882, 879, 881, 879, 880, 880, 898, 880, 896, 880, 891, \n880, 895, 880, 886, 880, 885, 880, 882, 881, 897, 881, 882, 882, 898, 882, 895, 882, 897, 882, 886, \n883, 901, 883, 899, 883, 894, 883, 893, 883, 889, 883, 887, 883, 885, 883, 884, 884, 899, 884, 894, \n884, 900, 884, 888, 884, 887, 885, 902, 885, 901, 885, 893, 885, 896, 885, 890, 885, 889, 885, 886, \n886, 902, 886, 896, 886, 898, 886, 890, 887, 905, 887, 903, 887, 900, 887, 899, 887, 889, 887, 888, \n888, 903, 888, 900, 888, 904, 889, 906, 889, 905, 889, 899, 889, 901, 889, 890, 890, 906, 890, 901, \n890, 902, 891, 911, 891, 907, 891, 896, 891, 895, 891, 893, 891, 892, 892, 908, 892, 907, 892, 894, \n892, 893, 893, 912, 893, 909, 893, 908, 893, 907, 893, 901, 893, 899, 893, 896, 893, 894, 894, 909, \n894, 908, 894, 910, 894, 900, 894, 899, 895, 913, 895, 911, 895, 898, 895, 897, 895, 896, 896, 914, \n896, 912, 896, 907, 896, 911, 896, 902, 896, 901, 896, 898, 897, 913, 897, 898, 898, 914, 898, 911, \n898, 913, 898, 902, 899, 917, 899, 915, 899, 910, 899, 909, 899, 905, 899, 903, 899, 901, 899, 900, \n900, 915, 900, 910, 900, 916, 900, 904, 900, 903, 901, 918, 901, 917, 901, 909, 901, 912, 901, 906, \n901, 905, 901, 902, 902, 918, 902, 912, 902, 914, 902, 906, 903, 921, 903, 919, 903, 916, 903, 915, \n903, 905, 903, 904, 904, 919, 904, 916, 904, 920, 905, 922, 905, 921, 905, 915, 905, 917, 905, 906, \n906, 922, 906, 917, 906, 918, 907, 927, 907, 923, 907, 912, 907, 911, 907, 909, 907, 908, 908, 924, \n908, 923, 908, 910, 908, 909, 909, 928, 909, 925, 909, 924, 909, 923, 909, 917, 909, 915, 909, 912, \n909, 910, 910, 925, 910, 924, 910, 926, 910, 916, 910, 915, 911, 929, 911, 927, 911, 914, 911, 913, \n911, 912, 912, 930, 912, 928, 912, 923, 912, 927, 912, 918, 912, 917, 912, 914, 913, 929, 913, 914, \n914, 930, 914, 927, 914, 929, 914, 918, 915, 933, 915, 931, 915, 926, 915, 925, 915, 921, 915, 919, \n915, 917, 915, 916, 916, 931, 916, 926, 916, 932, 916, 920, 916, 919, 917, 934, 917, 933, 917, 925, \n917, 928, 917, 922, 917, 921, 917, 918, 918, 934, 918, 928, 918, 930, 918, 922, 919, 937, 919, 935, \n919, 932, 919, 931, 919, 921, 919, 920, 920, 935, 920, 932, 920, 936, 921, 938, 921, 937, 921, 931, \n921, 933, 921, 922, 922, 938, 922, 933, 922, 934, 923, 943, 923, 939, 923, 928, 923, 927, 923, 925, \n923, 924, 924, 940, 924, 939, 924, 926, 924, 925, 925, 944, 925, 941, 925, 940, 925, 939, 925, 933, \n925, 931, 925, 928, 925, 926, 926, 941, 926, 940, 926, 942, 926, 932, 926, 931, 927, 945, 927, 943, \n927, 930, 927, 929, 927, 928, 928, 946, 928, 944, 928, 939, 928, 943, 928, 934, 928, 933, 928, 930, \n929, 945, 929, 930, 930, 946, 930, 943, 930, 945, 930, 934, 931, 949, 931, 947, 931, 942, 931, 941, \n931, 937, 931, 935, 931, 933, 931, 932, 932, 947, 932, 942, 932, 948, 932, 936, 932, 935, 933, 950, \n933, 949, 933, 941, 933, 944, 933, 938, 933, 937, 933, 934, 934, 950, 934, 944, 934, 946, 934, 938, \n935, 953, 935, 951, 935, 948, 935, 947, 935, 937, 935, 936, 936, 951, 936, 948, 936, 952, 937, 954, \n937, 953, 937, 947, 937, 949, 937, 938, 938, 954, 938, 949, 938, 950, 939, 959, 939, 955, 939, 944, \n939, 943, 939, 941, 939, 940, 940, 956, 940, 955, 940, 942, 940, 941, 941, 960, 941, 957, 941, 956, \n941, 955, 941, 949, 941, 947, 941, 944, 941, 942, 942, 957, 942, 956, 942, 958, 942, 948, 942, 947, \n943, 961, 943, 959, 943, 946, 943, 945, 943, 944, 944, 962, 944, 960, 944, 955, 944, 959, 944, 950, \n944, 949, 944, 946, 945, 961, 945, 946, 946, 962, 946, 959, 946, 961, 946, 950, 947, 965, 947, 963, \n947, 958, 947, 957, 947, 953, 947, 951, 947, 949, 947, 948, 948, 963, 948, 958, 948, 964, 948, 952, \n948, 951, 949, 966, 949, 965, 949, 957, 949, 960, 949, 954, 949, 953, 949, 950, 950, 966, 950, 960, \n950, 962, 950, 954, 951, 969, 951, 967, 951, 964, 951, 963, 951, 953, 951, 952, 952, 967, 952, 964, \n952, 968, 953, 970, 953, 969, 953, 963, 953, 965, 953, 954, 954, 970, 954, 965, 954, 966, 955, 960, \n955, 959, 955, 957, 955, 956, 956, 958, 956, 957, 957, 965, 957, 963, 957, 960, 957, 958, 958, 964, \n958, 963, 959, 962, 959, 961, 959, 960, 960, 966, 960, 965, 960, 962, 961, 962, 962, 966, 963, 972, \n963, 971, 963, 969, 963, 967, 963, 965, 963, 964, 964, 968, 964, 967, 965, 971, 965, 970, 965, 969, \n965, 966, 966, 970, 967, 973, 967, 972, 967, 974, 967, 969, 967, 968, 969, 973, 969, 972, 969, 971, \n969, 970, 971, 975, 971, 973, 971, 972, 972, 976, 972, 975, 972, 974, 972, 973, 973, 977, 973, 976, \n973, 975, 973, 974, 974, 977, 974, 976, 974, 978, 975, 977, 975, 976, 976, 978, 976, 977, 977, 978, \n979, 999, 979, 995, 979, 984, 979, 983, 979, 981, 979, 980, 980, 996, 980, 995, 980, 982, 980, 981, \n981, 1000, 981, 997, 981, 996, 981, 995, 981, 989, 981, 987, 981, 984, 981, 982, 982, 997, 982, 996, \n982, 998, 982, 988, 982, 987, 983, 1001, 983, 999, 983, 986, 983, 985, 983, 984, 984, 1002, 984, 1000, \n984, 995, 984, 999, 984, 990, 984, 989, 984, 986, 985, 1001, 985, 986, 986, 1002, 986, 999, 986, 1001, \n986, 990, 987, 993, 987, 1005, 987, 1003, 987, 998, 987, 997, 987, 991, 987, 989, 987, 988, 988, 1003, \n988, 998, 988, 1004, 988, 992, 988, 991, 989, 1006, 989, 1005, 989, 997, 989, 1000, 989, 993, 989, 994, \n989, 990, 990, 1006, 990, 1000, 990, 1002, 990, 994, 991, 993, 991, 1009, 991, 1007, 991, 1004, 991, 1003, \n991, 992, 992, 1007, 992, 1004, 992, 1008, 993, 1010, 993, 1009, 993, 1003, 993, 1005, 993, 994, 994, 1010, \n994, 1005, 994, 1006, 995, 1015, 995, 1011, 995, 1000, 995, 999, 995, 997, 995, 996, 996, 1012, 996, 1011, \n996, 998, 996, 997, 997, 1016, 997, 1013, 997, 1012, 997, 1011, 997, 1005, 997, 1003, 997, 1000, 997, 998, \n998, 1013, 998, 1012, 998, 1014, 998, 1004, 998, 1003, 999, 1017, 999, 1015, 999, 1002, 999, 1001, 999, 1000, \n1000, 1018, 1000, 1016, 1000, 1011, 1000, 1015, 1000, 1006, 1000, 1005, 1000, 1002, 1001, 1017, 1001, 1002, 1002, 1018, \n1002, 1015, 1002, 1017, 1002, 1006, 1003, 1021, 1003, 1019, 1003, 1014, 1003, 1013, 1003, 1009, 1003, 1007, 1003, 1005, \n1003, 1004, 1004, 1019, 1004, 1014, 1004, 1020, 1004, 1008, 1004, 1007, 1005, 1022, 1005, 1021, 1005, 1013, 1005, 1016, \n1005, 1010, 1005, 1009, 1005, 1006, 1006, 1022, 1006, 1016, 1006, 1018, 1006, 1010, 1007, 1025, 1007, 1023, 1007, 1020, \n1007, 1019, 1007, 1009, 1007, 1008, 1008, 1023, 1008, 1020, 1008, 1024, 1009, 1026, 1009, 1025, 1009, 1019, 1009, 1021, \n1009, 1010, 1010, 1026, 1010, 1021, 1010, 1022, 1011, 1031, 1011, 1027, 1011, 1016, 1011, 1015, 1011, 1013, 1011, 1012, \n1012, 1028, 1012, 1027, 1012, 1014, 1012, 1013, 1013, 1032, 1013, 1029, 1013, 1028, 1013, 1027, 1013, 1021, 1013, 1019, \n1013, 1016, 1013, 1014, 1014, 1029, 1014, 1028, 1014, 1030, 1014, 1020, 1014, 1019, 1015, 1033, 1015, 1031, 1015, 1018, \n1015, 1017, 1015, 1016, 1016, 1034, 1016, 1032, 1016, 1027, 1016, 1031, 1016, 1022, 1016, 1021, 1016, 1018, 1017, 1033, \n1017, 1018, 1018, 1034, 1018, 1031, 1018, 1033, 1018, 1022, 1019, 1037, 1019, 1035, 1019, 1030, 1019, 1029, 1019, 1025, \n1019, 1023, 1019, 1021, 1019, 1020, 1020, 1035, 1020, 1030, 1020, 1036, 1020, 1024, 1020, 1023, 1021, 1038, 1021, 1037, \n1021, 1029, 1021, 1032, 1021, 1026, 1021, 1025, 1021, 1022, 1022, 1038, 1022, 1032, 1022, 1034, 1022, 1026, 1023, 1041, \n1023, 1039, 1023, 1036, 1023, 1035, 1023, 1025, 1023, 1024, 1024, 1039, 1024, 1036, 1024, 1040, 1025, 1042, 1025, 1041, \n1025, 1035, 1025, 1037, 1025, 1026, 1026, 1042, 1026, 1037, 1026, 1038, 1027, 1047, 1027, 1043, 1027, 1032, 1027, 1031, \n1027, 1029, 1027, 1028, 1028, 1044, 1028, 1043, 1028, 1030, 1028, 1029, 1029, 1048, 1029, 1045, 1029, 1044, 1029, 1043, \n1029, 1037, 1029, 1035, 1029, 1032, 1029, 1030, 1030, 1045, 1030, 1044, 1030, 1046, 1030, 1036, 1030, 1035, 1031, 1049, \n1031, 1047, 1031, 1034, 1031, 1033, 1031, 1032, 1032, 1050, 1032, 1048, 1032, 1043, 1032, 1047, 1032, 1038, 1032, 1037, \n1032, 1034, 1033, 1049, 1033, 1034, 1034, 1050, 1034, 1047, 1034, 1049, 1034, 1038, 1035, 1053, 1035, 1051, 1035, 1046, \n1035, 1045, 1035, 1041, 1035, 1039, 1035, 1037, 1035, 1036, 1036, 1051, 1036, 1046, 1036, 1052, 1036, 1040, 1036, 1039, \n1037, 1054, 1037, 1053, 1037, 1045, 1037, 1048, 1037, 1042, 1037, 1041, 1037, 1038, 1038, 1054, 1038, 1048, 1038, 1050, \n1038, 1042, 1039, 1057, 1039, 1055, 1039, 1052, 1039, 1051, 1039, 1041, 1039, 1040, 1040, 1055, 1040, 1052, 1040, 1056, \n1041, 1058, 1041, 1057, 1041, 1051, 1041, 1053, 1041, 1042, 1042, 1058, 1042, 1053, 1042, 1054, 1043, 1048, 1043, 1047, \n1043, 1045, 1043, 1044, 1044, 1046, 1044, 1045, 1045, 1053, 1045, 1051, 1045, 1048, 1045, 1046, 1046, 1052, 1046, 1051, \n1047, 1050, 1047, 1049, 1047, 1048, 1048, 1054, 1048, 1053, 1048, 1050, 1049, 1050, 1050, 1054, 1051, 1057, 1051, 1055, \n1051, 1053, 1051, 1052, 1052, 1056, 1052, 1055, 1053, 1058, 1053, 1057, 1053, 1054, 1054, 1058, 1055, 1057, 1055, 1056, \n1057, 1058, 1059, 1074, 1059, 1061, 1059, 1060, 1060, 1075, 1060, 1074, 1060, 1063, 1060, 1062, 1060, 1061, 1061, 1068, \n1061, 1076, 1061, 1075, 1061, 1074, 1061, 1065, 1061, 1062, 1062, 1069, 1062, 1068, 1062, 1078, 1062, 1076, 1062, 1075, \n1062, 1077, 1062, 1066, 1062, 1065, 1062, 1064, 1062, 1063, 1063, 1078, 1063, 1075, 1063, 1064, 1064, 1072, 1064, 1069, \n1064, 1077, 1064, 1078, 1064, 1079, 1064, 1067, 1064, 1066, 1065, 1070, 1065, 1069, 1065, 1068, 1065, 1066, 1066, 1072, \n1066, 1070, 1066, 1069, 1066, 1071, 1066, 1067, 1067, 1071, 1067, 1072, 1067, 1073, 1068, 1070, 1068, 1069, 1069, 1072, \n1069, 1071, 1069, 1070, 1070, 1071, 1071, 1073, 1071, 1072, 1072, 1073, 1074, 1080, 1074, 1076, 1074, 1075, 1075, 1081, \n1075, 1080, 1075, 1078, 1075, 1077, 1075, 1076, 1076, 1082, 1076, 1081, 1076, 1080, 1076, 1077, 1077, 1084, 1077, 1082, \n1077, 1081, 1077, 1083, 1077, 1079, 1077, 1078, 1078, 1084, 1078, 1081, 1078, 1079, 1079, 1083, 1079, 1084, 1079, 1085, \n1080, 1086, 1080, 1082, 1080, 1081, 1081, 1087, 1081, 1086, 1081, 1084, 1081, 1083, 1081, 1082, 1082, 1088, 1082, 1087, \n1082, 1086, 1082, 1083, 1083, 1090, 1083, 1088, 1083, 1087, 1083, 1089, 1083, 1085, 1083, 1084, 1084, 1090, 1084, 1087, \n1084, 1085, 1085, 1089, 1085, 1090, 1085, 1091, 1086, 1092, 1086, 1088, 1086, 1087, 1087, 1093, 1087, 1092, 1087, 1090, \n1087, 1089, 1087, 1088, 1088, 1094, 1088, 1093, 1088, 1092, 1088, 1089, 1089, 1096, 1089, 1094, 1089, 1093, 1089, 1095, \n1089, 1091, 1089, 1090, 1090, 1096, 1090, 1093, 1090, 1091, 1091, 1095, 1091, 1096, 1091, 1097, 1092, 1094, 1092, 1093, \n1093, 1096, 1093, 1095, 1093, 1094, 1094, 1095, 1095, 1097, 1095, 1096, 1096, 1097, 1098, 1209, 1098, 1100, 1098, 1099, \n1099, 1210, 1099, 1209, 1099, 1101, 1099, 1100, 1100, 1132, 1100, 1211, 1100, 1210, 1100, 1209, 1100, 1102, 1100, 1101, \n1101, 1135, 1101, 1117, 1101, 1133, 1101, 1132, 1101, 1116, 1101, 1110, 1101, 1108, 1101, 1211, 1101, 1210, 1101, 1212, \n1101, 1103, 1101, 1102, 1102, 1134, 1102, 1133, 1102, 1132, 1102, 1104, 1102, 1103, 1103, 1137, 1103, 1118, 1103, 1112, \n1103, 1134, 1103, 1133, 1103, 1135, 1103, 1116, 1103, 1110, 1103, 1117, 1103, 1105, 1103, 1104, 1104, 1120, 1104, 1136, \n1104, 1135, 1104, 1134, 1104, 1106, 1104, 1105, 1105, 1123, 1105, 1119, 1105, 1121, 1105, 1120, 1105, 1114, 1105, 1136, \n1105, 1135, 1105, 1137, 1105, 1117, 1105, 1112, 1105, 1118, 1105, 1107, 1105, 1106, 1106, 1122, 1106, 1121, 1106, 1120, \n1106, 1107, 1107, 1122, 1107, 1121, 1107, 1123, 1107, 1118, 1107, 1114, 1107, 1119, 1108, 1116, 1108, 1110, 1108, 1109, \n1109, 1111, 1109, 1110, 1110, 1117, 1110, 1116, 1110, 1112, 1110, 1111, 1111, 1113, 1111, 1112, 1112, 1118, 1112, 1117, \n1112, 1114, 1112, 1113, 1113, 1115, 1113, 1114, 1114, 1119, 1114, 1118, 1114, 1115, 1116, 1138, 1116, 1133, 1116, 1139, \n1116, 1117, 1117, 1140, 1117, 1138, 1117, 1133, 1117, 1135, 1117, 1118, 1118, 1124, 1118, 1121, 1118, 1125, 1118, 1140, \n1118, 1135, 1118, 1137, 1118, 1119, 1119, 1124, 1119, 1121, 1119, 1123, 1120, 1126, 1120, 1122, 1120, 1121, 1121, 1129, \n1121, 1127, 1121, 1126, 1121, 1125, 1121, 1124, 1121, 1123, 1121, 1122, 1122, 1128, 1122, 1127, 1122, 1126, 1122, 1123, \n1123, 1128, 1123, 1127, 1123, 1129, 1123, 1124, 1124, 1130, 1124, 1127, 1124, 1129, 1124, 1125, 1125, 1130, 1125, 1127, \n1125, 1131, 1126, 1128, 1126, 1127, 1127, 1131, 1127, 1130, 1127, 1129, 1127, 1128, 1128, 1129, 1129, 1130, 1130, 1131, \n1132, 1141, 1132, 1134, 1132, 1133, 1133, 1144, 1133, 1142, 1133, 1141, 1133, 1139, 1133, 1138, 1133, 1135, 1133, 1134, \n1134, 1147, 1134, 1143, 1134, 1142, 1134, 1141, 1134, 1136, 1134, 1135, 1135, 1150, 1135, 1148, 1135, 1147, 1135, 1143, \n1135, 1142, 1135, 1144, 1135, 1140, 1135, 1138, 1135, 1137, 1135, 1136, 1136, 1149, 1136, 1148, 1136, 1147, 1136, 1137, \n1137, 1149, 1137, 1148, 1137, 1150, 1137, 1140, 1138, 1151, 1138, 1148, 1138, 1152, 1138, 1145, 1138, 1142, 1138, 1144, \n1138, 1140, 1138, 1139, 1139, 1145, 1139, 1142, 1139, 1146, 1140, 1151, 1140, 1148, 1140, 1150, 1141, 1143, 1141, 1142, \n1142, 1146, 1142, 1145, 1142, 1144, 1142, 1143, 1143, 1144, 1144, 1145, 1145, 1146, 1147, 1149, 1147, 1148, 1148, 1152, \n1148, 1151, 1148, 1150, 1148, 1149, 1149, 1150, 1150, 1151, 1151, 1152, 1153, 1155, 1153, 1154, 1154, 1156, 1154, 1155, \n1155, 1157, 1155, 1156, 1156, 1158, 1156, 1157, 1157, 1159, 1157, 1158, 1158, 1160, 1158, 1159, 1159, 1161, 1159, 1160, \n1160, 1162, 1160, 1161, 1161, 1163, 1161, 1162, 1162, 1164, 1162, 1163, 1163, 1165, 1163, 1164, 1164, 1166, 1164, 1165, \n1165, 1166, 1167, 1169, 1167, 1168, 1167, 1177, 1167, 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0.765719, 1.374749, -0.155456, \n0.666374, 1.380577, -0.155543, -0.701021, 1.398482, -0.156623, -0.718793, 1.401026, -0.156877, -0.695034, 1.402011, -0.156406, \n-0.724593, 1.404713, -0.158404, 0.642613, 1.413218, -0.157760, -0.741574, 1.427223, -0.155288, -0.090797, 1.414188, -0.155526, \n0.644542, 1.421885, -0.158526, 0.642810, 1.431076, -0.158000, 0.639809, 1.433481, -0.155270, 0.638586, 1.437172, -0.158785, \n-0.027621, 1.463773, -0.156087, -0.012371, 1.474275, -0.159778, 0.024331, 1.507082, -0.156332, 0.569994, 1.514648, -0.157984, \n0.566269, 1.520320, -0.157119, 0.502553, 1.530317, -0.154964, 0.427059, 1.570354, -0.155733, -0.691560, 1.568441, -0.156705, \n0.433774, 1.581958, -0.158880, 0.414741, 1.570533, -0.153549, 0.425753, 1.580913, -0.157746, -0.615428, 1.599309, -0.155098, \n-0.615751, 1.601117, -0.153084, -0.618291, 1.601776, -0.151957, -0.817293, 1.631940, -0.155697, -0.325005, 1.760136, -0.154043, \n-0.338174, 1.860747, -0.150143, -0.740574, 0.610234, -0.162874, -0.725501, 0.605773, -0.162744, -0.751832, 0.615096, -0.162689, \n-0.763578, 0.623579, -0.162315, -0.775384, 0.633093, -0.164792, -0.781218, 0.642573, -0.166053, 0.595041, 1.051551, -0.161354, \n0.704670, 1.170354, -0.149340, -0.233920, 1.193358, -0.156339, -0.226555, 1.204661, -0.156598, -0.159720, 1.312357, -0.156951, \n0.642305, 1.427899, -0.154836, -0.036464, 1.458193, -0.155659, 0.486206, 1.551749, -0.153919, -0.616408, 1.601819, -0.152135, \n-0.614925, 1.603648, -0.150057, -0.777235, 0.663098, -0.160673, -0.777580, 0.674254, -0.160922, -0.358936, 1.129845, -0.155179],\n\"triIds\" : [\n29395, 28844, 23750,  29214, 4608, 28843,  29040, 23750, 28844,  \n29748, 25329, 29672,  23353, 5174, 12696,  29748, 19319, 25329,  \n1235, 9063, 21799,  29669, 16248, 29748,  29525, 6615, 29209,  \n10811, 21381, 29379,  29397, 23353, 29399,  29748, 23861, 19319,  \n29667, 29399, 23353,  29733, 10811, 29379,  6615, 4608, 29214,  \n20729, 20728, 10208,  29519, 29733, 29379,  20852, 15492, 1236,  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29, 16,  \n27, 35, 26,  26, 25, 29,  4, 34, 14,  \n11, 17, 30,  8036, 22, 21885,  12, 8443, 4,  \n28607, 47, 48,  25, 104, 16,  27807, 37, 43,  \n37, 27021, 44,  48, 28601, 28607,  28601, 48, 46,  \n46, 28384, 28601,  51, 28409, 52,  40, 28427, 54,  \n54, 55, 40,  29673, 133, 29545,  43, 58, 59,  \n37, 58, 43,  45, 37, 44,  46, 48, 61,  \n62, 47, 38,  30, 17, 18,  49, 50, 65,  \n49, 65, 64,  50, 28409, 51,  52, 28424, 53,  \n40, 53, 28424,  53, 40, 55,  67, 53, 55,  \n54, 28427, 56,  69, 55, 54,  71, 57, 42,  \n36, 43, 42,  58, 37, 45,  38, 28395, 28003,  \n38, 47, 28395,  47, 28607, 28395,  61, 48, 72,  \n48, 47, 72,  62, 72, 47,  73, 72, 62,  \n50, 51, 65,  75, 65, 51,  76, 51, 66,  \n66, 52, 53,  66, 53, 67,  66, 51, 52,  \n68, 67, 55,  28226, 56, 28427,  93, 69, 54,  \n69, 68, 55,  77, 68, 69,  71, 70, 57,  \n78, 58, 45,  80, 45, 44,  45, 80, 79,  \n60, 28384, 81,  82, 72, 73,  63, 39, 83,  \n38, 28003, 83,  83, 28003, 63,  74, 83, 39,  \n39, 49, 74,  74, 49, 64,  64, 65, 85,  \n84, 64, 85,  86, 87, 85,  51, 76, 75,  \n75, 85, 65,  76, 88, 75,  66, 89, 76,  \n67, 90, 66,  41, 104, 25,  91, 92, 93,  \n92, 77, 69,  69, 93, 92,  16, 29, 25,  \n43, 59, 42,  45, 79, 78,  95, 79, 80,  \n95, 44, 96,  95, 80, 44,  44, 60, 96,  \n28384, 46, 81,  97, 61, 98,  61, 72, 98,  \n82, 98, 72,  73, 62, 38,  99, 38, 83,  \n100, 64, 84,  87, 100, 84,  87, 84, 85,  \n86, 85, 75,  86, 75, 88,  101, 86, 88,  \n66, 90, 89,  76, 89, 88,  90, 67, 68,  \n68, 102, 90,  102, 68, 77,  91, 93, 103,  \n103, 93, 28642,  57, 70, 105,  106, 105, 70,  \n108, 71, 42,  107, 71, 108,  109, 59, 58,  \n109, 58, 78,  110, 78, 79,  79, 95, 111,  \n111, 95, 96,  96, 60, 81,  61, 81, 46,  \n112, 81, 61,  73, 113, 82,  73, 38, 99,  \n99, 83, 74,  99, 74, 114,  114, 74, 64,  \n64, 115, 114,  116, 88, 89,  116, 101, 88,  \n117, 89, 90,  117, 116, 89,  90, 102, 117,  \n77, 118, 102,  92, 119, 120,  92, 120, 77,  \n93, 54, 56,  109, 108, 59,  108, 42, 59,  \n111, 110, 79,  112, 96, 81,  61, 97, 112,  \n82, 124, 98,  113, 124, 82,  99, 125, 113,  \n73, 99, 113,  115, 64, 100,  115, 100, 148,  \n148, 100, 126,  126, 100, 87,  126, 87, 127,  \n86, 127, 87,  86, 101, 127,  117, 128, 116,  \n128, 129, 116,  129, 130, 101,  128, 117, 131,  \n131, 102, 132,  131, 117, 102,  118, 132, 102,  \n119, 92, 91,  77, 120, 118,  103, 133, 91,  \n29787, 29186, 94,  29787, 94, 155,  134, 94, 105,  \n70, 135, 106,  71, 107, 135,  70, 71, 135,  \n137, 135, 107,  108, 137, 107,  78, 110, 139,  \n123, 110, 111,  123, 111, 140,  111, 96, 141,  \n112, 97, 142,  98, 143, 97,  144, 98, 124,  \n145, 144, 124,  146, 124, 113,  114, 115, 148,  \n148, 126, 149,  127, 149, 126,  127, 101, 150,  \n128, 151, 129,  116, 129, 101,  153, 152, 131,  \n128, 131, 152,  153, 131, 132,  154, 153, 132,  \n154, 132, 118,  120, 154, 118,  133, 122, 91,  \n133, 121, 122,  91, 122, 119,  106, 135, 136,  \n138, 137, 108,  109, 78, 156,  78, 139, 156,  \n141, 140, 111,  141, 96, 112,  141, 112, 158,  \n112, 142, 158,  142, 97, 143,  98, 144, 143,  \n146, 159, 124,  159, 145, 124,  147, 159, 146,  \n113, 125, 146,  125, 147, 146,  99, 160, 125,  \n147, 125, 160,  160, 99, 114,  148, 161, 114,  \n161, 160, 114,  161, 148, 149,  149, 162, 161,  \n162, 149, 127,  163, 162, 127,  127, 150, 163,  \n101, 130, 150,  151, 128, 164,  129, 165, 130,  \n164, 128, 152,  166, 152, 153,  167, 166, 153,  \n153, 154, 167,  168, 167, 154,  121, 29673, 170,  \n121, 133, 29673,  154, 120, 168,  171, 119, 122,  \n120, 119, 171,  155, 94, 134,  135, 137, 136,  \n138, 194, 137,  139, 110, 177,  110, 123, 177,  \n178, 157, 140,  178, 140, 179,  158, 179, 141,  \n180, 142, 143,  144, 180, 143,  144, 181, 180,  \n145, 181, 144,  183, 159, 147,  182, 183, 160,  \n183, 147, 160,  184, 160, 161,  184, 182, 160,  \n184, 161, 185,  162, 185, 161,  186, 185, 162,  \n186, 162, 163,  163, 150, 130,  165, 129, 151,  \n164, 152, 187,  166, 187, 152,  167, 188, 166,  \n168, 188, 167,  29673, 169, 170,  170, 189, 121,  \n122, 121, 171,  168, 120, 171,  134, 173, 155,  \n155, 173, 17442,  174, 134, 175,  105, 175, 134,  \n175, 105, 106,  190, 106, 191,  191, 106, 192,  \n136, 192, 106,  193, 192, 136,  137, 193, 136,  \n194, 176, 137,  108, 109, 138,  156, 138, 109,  \n123, 195, 177,  157, 195, 123,  157, 123, 140,  \n179, 197, 196,  140, 141, 179,  178, 179, 196,  \n158, 198, 179,  198, 158, 199,  199, 158, 142,  \n199, 142, 180,  200, 199, 180,  181, 200, 180,  \n201, 181, 145,  145, 159, 201,  183, 202, 159,  \n183, 182, 203,  184, 204, 182,  185, 204, 184,  \n185, 205, 204,  186, 205, 185,  206, 205, 186,  \n186, 163, 206,  163, 130, 206,  130, 165, 206,  \n164, 208, 151,  209, 211, 187,  210, 211, 209,  \n164, 187, 208,  212, 209, 166,  166, 209, 187,  \n212, 166, 188,  188, 213, 214,  189, 215, 121,  \n215, 171, 121,  168, 171, 213,  29, 3, 27,  \n134, 174, 173,  190, 175, 106,  176, 193, 137,  \n216, 176, 194,  138, 217, 194,  138, 156, 217,  \n156, 139, 177,  157, 218, 195,  218, 157, 178,  \n179, 198, 197,  219, 197, 198,  220, 198, 199,  \n221, 220, 199,  200, 221, 199,  222, 221, 200,  \n222, 200, 181,  201, 222, 181,  223, 201, 159,  \n202, 223, 159,  203, 224, 183,  225, 203, 182,  \n204, 226, 225,  204, 225, 182,  228, 227, 204,  \n204, 205, 228,  205, 206, 228,  206, 229, 228,  \n246, 207, 208,  207, 151, 208,  165, 207, 206,  \n187, 211, 208,  151, 207, 165,  212, 188, 214,  \n189, 231, 215,  189, 230, 231,  171, 215, 213,  \n213, 188, 168,  3, 21885, 27,  192, 232, 191,  \n232, 192, 193,  216, 193, 176,  233, 216, 194,  \n217, 233, 194,  234, 217, 156,  177, 234, 156,  \n235, 234, 177,  195, 235, 177,  218, 235, 195,  \n218, 178, 236,  236, 178, 196,  219, 198, 238,  \n239, 238, 220,  238, 198, 220,  221, 241, 220,  \n241, 240, 220,  222, 241, 221,  242, 222, 201,  \n242, 201, 223,  223, 202, 243,  223, 243, 242,  \n183, 224, 202,  224, 203, 225,  204, 227, 226,  \n244, 245, 210,  210, 245, 211,  208, 211, 246,  \n206, 207, 229,  247, 244, 248,  248, 244, 209,  \n209, 244, 210,  248, 209, 212,  212, 214, 250,  \n212, 250, 248,  249, 230, 9516,  250, 213, 231,  \n213, 250, 214,  230, 189, 9516,  215, 231, 213,  \n2, 23, 15,  253, 20649, 252,  20649, 173, 252,  \n254, 252, 255,  173, 174, 252,  255, 174, 175,  \n256, 255, 175,  175, 190, 256,  256, 190, 191,  \n191, 257, 256,  191, 258, 257,  191, 232, 258,  \n232, 193, 216,  233, 217, 259,  260, 259, 234,  \n259, 217, 234,  260, 234, 235,  236, 196, 237,  \n196, 197, 237,  220, 240, 239,  222, 261, 241,  \n261, 222, 242,  243, 224, 262,  224, 225, 262,  \n202, 224, 243,  265, 264, 226,  12, 226, 264,  \n226, 12, 225,  225, 12, 14,  266, 227, 267,  \n268, 267, 228,  267, 227, 228,  269, 211, 245,  \n229, 207, 268,  229, 268, 228,  246, 270, 207,  \n271, 248, 250,  249, 231, 230,  249, 271, 231,  \n231, 271, 250,  5538, 11, 20369,  253, 252, 17,  \n252, 174, 255,  272, 254, 255,  272, 255, 256,  \n256, 273, 272,  257, 273, 256,  274, 257, 258,  \n232, 274, 258,  275, 274, 276,  232, 216, 274,  \n233, 259, 104,  19, 104, 259,  19, 259, 260,  \n235, 277, 260,  277, 8, 260,  277, 218, 278,  \n235, 218, 277,  278, 218, 236,  197, 219, 237,  \n238, 239, 31,  238, 31, 219,  261, 240, 241,  \n261, 279, 240,  280, 279, 261,  242, 280, 261,  \n13, 263, 262,  243, 263, 280,  243, 280, 242,  \n262, 263, 243,  14512, 12, 264,  262, 225, 14,  \n265, 226, 266,  266, 226, 227,  211, 269, 246,  \n269, 270, 246,  266, 270, 269,  268, 270, 266,  \n266, 267, 268,  270, 268, 207,  271, 247, 248,  \n11, 253, 17,  11, 0, 20369,  0, 18970, 20369,  \n17, 252, 32,  32, 252, 254,  272, 251, 254,  \n251, 273, 27,  272, 273, 251,  257, 281, 273,  \n281, 257, 282,  282, 257, 274,  275, 282, 274,  \n274, 216, 276,  216, 233, 276,  275, 276, 41,  \n233, 41, 276,  41, 233, 104,  7, 19, 8,  \n260, 8, 19,  277, 283, 8,  278, 283, 277,  \n278, 237, 284,  278, 284, 283,  278, 236, 237,  \n284, 24, 23,  237, 219, 284,  284, 219, 24,  \n219, 31, 24,  33, 31, 239,  239, 279, 33,  \n240, 279, 239,  263, 21, 280,  280, 21, 279,  \n262, 14, 13,  285, 14512, 264,  264, 265, 285,  \n266, 286, 265,  286, 269, 172,  286, 266, 269,  \n254, 22, 32,  18, 17, 32,  254, 251, 22,  \n21885, 251, 27,  251, 21885, 22,  27, 273, 281,  \n35, 27, 281,  282, 35, 281,  275, 26, 35,  \n282, 275, 35,  275, 25, 26,  41, 25, 275,  \n104, 19, 16,  6, 8, 283,  23, 6, 283,  \n284, 23, 283,  5, 33, 21,  21, 33, 279,  \n12, 4, 14,  13, 34, 263,  34, 21, 263,  \n285, 265, 286,  288, 10001, 3047,  20335, 14265, 289,  \n294, 20527, 295,  287, 290, 297,  297, 291, 287,  \n4713, 298, 299,  291, 297, 300,  308, 309, 310,  \n309, 308, 311,  313, 10389, 314,  321, 308, 310,  \n311, 308, 287,  8064, 7987, 323,  308, 321, 287,  \n296, 311, 287,  334, 311, 296,  337, 11940, 338,  \n287, 321, 290,  296, 287, 291,  343, 344, 345,  \n346, 347, 348,  321, 310, 290,  296, 291, 352,  \n353, 354, 355,  16982, 356, 357,  352, 291, 300,  \n368, 297, 290,  847, 369, 370,  375, 376, 377,  \n300, 297, 368,  352, 300, 381,  393, 394, 11071,  \n397, 401, 368,  401, 300, 368,  381, 300, 401,  \n404, 405, 406,  412, 399, 400,  14523, 4532, 13753,  \n401, 422, 381,  409, 381, 434,  381, 422, 434,  \n436, 437, 438,  443, 444, 14776,  448, 449, 450,  \n311, 451, 309,  334, 451, 311,  445, 310, 309,  \n19250, 7201, 465,  479, 480, 481,  492, 493, 494,  \n296, 495, 334,  496, 497, 498,  502, 503, 504,  \n485, 290, 310,  19819, 8609, 507,  495, 296, 352,  \n14872, 3475, 518,  519, 520, 521,  16062, 529, 530,  \n522, 538, 539,  485, 541, 290,  543, 544, 545,  \n546, 19814, 547,  368, 290, 397,  541, 397, 290,  \n555, 556, 557,  15021, 5324, 331,  352, 381, 495,  \n562, 563, 564,  495, 381, 409,  581, 582, 583,  \n585, 586, 587,  590, 7127, 591,  597, 598, 599,  \n593, 409, 434,  620, 621, 622,  18570, 623, 624,  \n401, 605, 422,  633, 634, 635,  638, 639, 640,  \n648, 649, 650,  654, 655, 656,  434, 422, 658,  \n658, 647, 434,  674, 675, 676,  677, 422, 605,  \n658, 422, 677,  658, 685, 647,  688, 15768, 6913,  \n451, 699, 309,  309, 699, 697,  21579, 702, 703,  \n309, 697, 445,  451, 334, 714,  699, 451, 714,  \n445, 717, 310,  727, 728, 729,  310, 717, 485,  \n730, 7536, 731,  733, 734, 735,  742, 12830, 396,  \n15926, 463, 748,  485, 749, 528,  783, 784, 785,  \n15705, 794, 795,  541, 485, 528,  800, 801, 802,  \n806, 807, 808,  810, 811, 812,  409, 593, 495,  \n829, 1575, 12913,  834, 835, 836,  838, 9403, 839,  \n842, 843, 844,  605, 401, 397,  849, 3771, 22317,  \n851, 16613, 852,  605, 397, 855,  647, 593, 434,  \n856, 11498, 857,  593, 647, 841,  647, 862, 841,  \n668, 8270, 631,  13504, 874, 875,  878, 879, 880,  \n873, 605, 855,  605, 873, 677,  888, 889, 890,  \n891, 892, 893,  907, 11840, 758,  914, 677, 873,  \n3485, 6545, 16510,  914, 658, 677,  917, 658, 914,  \n685, 917, 920,  685, 658, 917,  925, 917, 914,  \n697, 927, 445,  928, 929, 930,  938, 939, 940,  \n945, 790, 791,  724, 714, 334,  950, 951, 952,  \n724, 334, 955,  957, 958, 959,  960, 961, 962,  \n485, 717, 749,  955, 334, 495,  976, 17669, 977,  \n495, 984, 955,  4358, 985, 986,  1976, 8237, 987,  \n988, 989, 990,  991, 992, 993,  999, 911, 1000,  \n984, 495, 593,  1003, 14841, 916,  1004, 1005, 1006,  \n841, 1012, 593,  1016, 11106, 12414,  541, 1022, 397,  \n459, 1025, 1026,  1040, 991, 1041,  616, 1045, 2867,  \n1046, 1050, 20109,  1022, 855, 397,  1055, 1056, 15453,  \n647, 685, 862,  1067, 862, 685,  1060, 1061, 1062,  \n1069, 1061, 1060,  920, 1067, 685,  5649, 1073, 1074,  \n855, 1076, 873,  18553, 9502, 1077,  1078, 1079, 8780,  \n1084, 925, 873,  914, 873, 925,  1087, 16017, 1088,  \n925, 1090, 917,  917, 1090, 920,  927, 1098, 445,  \n1099, 927, 697,  699, 1099, 697,  1099, 699, 1101,  \n1101, 714, 942,  1098, 1102, 717,  717, 445, 1098,  \n1102, 1108, 717,  13166, 12592, 1113,  1114, 1115, 1116,  \n9416, 1117, 1118,  1125, 1126, 1127,  8285, 16428, 1128,  \n13857, 1129, 1130,  971, 717, 1108,  749, 717, 971,  \n1134, 8880, 424,  1142, 1143, 1144,  21159, 14433, 1154,  \n1159, 1160, 1161,  1169, 1170, 1171,  1172, 1173, 1174,  \n1175, 1176, 1177,  9009, 1190, 23622,  1191, 1192, 10075,  \n1201, 1202, 1203,  1204, 14780, 1111,  1205, 1206, 2958,  \n1209, 1210, 1930,  1012, 841, 1211,  541, 528, 1208,  \n1212, 1213, 17130,  6339, 8317, 8318,  1219, 1220, 1221,  \n1223, 1224, 1225,  16035, 9719, 1228,  1229, 1230, 1231,  \n1232, 1233, 1234,  1235, 1236, 1237,  841, 862, 1222,  \n2662, 15161, 1250,  1532, 7059, 1252,  1222, 862, 1067,  \n1254, 13853, 1255,  7493, 1263, 1264,  1076, 855, 1022,  \n1261, 1067, 920,  22862, 649, 11238,  873, 1076, 1084,  \n14104, 23938, 1277,  1090, 1280, 920,  11682, 1281, 407,  \n920, 1280, 1261,  1285, 925, 1084,  925, 1285, 1090,  \n18831, 18614, 785,  1298, 1098, 927,  1298, 927, 1099,  \n1298, 1099, 1299,  1101, 1299, 1099,  1101, 699, 714,  \n1306, 12440, 1307,  1315, 942, 714,  714, 724, 1315,  \n9590, 1321, 1322,  465, 1323, 14914,  10719, 1324, 4115,  \n1333, 1334, 1335,  955, 984, 1164,  1347, 1348, 1349,  \n1012, 984, 593,  6100, 1374, 1375,  1378, 1379, 1380,  \n1383, 8114, 15051,  1389, 1390, 2445,  1393, 1394, 1395,  \n6098, 1402, 1333,  1403, 1404, 1405,  541, 1208, 1022,  \n1407, 1408, 1409,  1425, 1426, 14216,  1428, 1222, 1067,  \n1392, 1435, 1436,  9071, 1452, 1453,  1461, 1462, 19281,  \n1463, 1464, 16719,  1467, 1090, 1285,  1300, 1301, 1471,  \n1473, 1474, 1475,  1482, 1102, 1098,  7257, 17107, 12946,  \n1298, 1482, 1098,  1299, 1101, 1490,  1490, 1101, 942,  \n10989, 1493, 1413,  1494, 1495, 1496,  23549, 1502, 1503,  \n1505, 942, 1315,  1482, 1108, 1102,  1315, 724, 1515,  \n955, 1164, 724,  1164, 1515, 724,  1519, 1520, 15982,  \n1521, 1522, 1523,  1526, 1527, 1528,  1531, 2260, 1532,  \n1108, 1514, 971,  11946, 1534, 1535,  10788, 3088, 1536,  \n1529, 1164, 984,  1541, 984, 1012,  9666, 15421, 1560,  \n1561, 528, 749,  749, 971, 1561,  1561, 1208, 528,  \n1579, 1580, 1581,  841, 1222, 1211,  1590, 1591, 4651,  \n18420, 1594, 1595,  1597, 1067, 1598,  1599, 1600, 1601,  \n1597, 1428, 1067,  1606, 1607, 1608,  1615, 1616, 12300,  \n1067, 1261, 1598,  1623, 1624, 1625,  1626, 1627, 3719,  \n1620, 1084, 1076,  1489, 1629, 1630,  16327, 1635, 1636,  \n5668, 620, 1637,  1090, 1467, 1643,  1650, 1651, 1652,  \n1482, 1298, 1654,  1299, 1654, 1298,  1654, 1299, 1657,  \n1661, 1662, 1663,  1490, 1657, 1299,  1664, 1665, 19445,  \n1482, 1654, 1508,  4394, 1669, 1670,  1672, 13782, 15441,  \n1682, 1683, 1684,  1690, 1490, 942,  1690, 942, 1505,  \n1505, 1315, 1515,  1514, 1108, 1482,  1514, 1482, 1508,  \n17603, 1696, 1697,  1515, 1164, 1529,  1704, 1514, 1508,  \n1529, 984, 1541,  1713, 1714, 1715,  1717, 1718, 1719,  \n1721, 1722, 1723,  1725, 1726, 14405,  1728, 1729, 7422,  \n1730, 10873, 1731,  1211, 1541, 1012,  1736, 1737, 16456,  \n1361, 1561, 971,  1720, 1541, 1211,  6587, 1740, 3642,  \n1743, 1744, 1745,  1746, 1747, 1748,  1578, 1211, 1222,  \n1167, 17563, 5819,  1755, 1756, 10185,  1758, 17590, 16884,  \n1208, 2009, 1022,  1759, 18446, 908,  2610, 1620, 2009,  \n1076, 1022, 1620,  1771, 16610, 1772,  1776, 1777, 1778,  \n1084, 1620, 1780,  607, 1781, 1782,  1598, 1261, 1280,  \n1780, 1285, 1084,  1789, 1790, 1791,  1792, 6608, 1793,  \n1794, 1795, 3576,  1780, 1801, 1285,  974, 1804, 562,  \n1807, 1808, 1809,  1816, 1817, 1818,  1090, 1643, 1280,  \n1822, 13763, 1823,  1827, 1828, 4325,  15494, 1836, 1837,  \n1838, 2070, 1826,  1839, 1840, 1838,  1843, 28211, 1844,  \n1826, 1833, 1842,  1848, 1849, 1850,  1838, 1826, 1839,  \n1851, 2102, 1840,  1826, 1842, 1839,  11406, 9232, 1856,  \n1840, 1839, 1855,  2102, 1838, 1840,  1865, 1840, 1855,  \n1855, 1839, 1842,  1872, 1840, 1865,  1842, 1860, 1871,  \n1874, 1350, 5087,  1855, 1842, 1871,  1879, 14829, 1880,  \n1855, 1871, 1865,  1885, 1871, 1860,  1891, 1871, 1885,  \n1891, 1865, 1871,  1897, 1654, 1657,  1897, 1657, 1903,  \n1011, 13408, 1904,  1905, 1906, 1907,  1903, 1657, 1490,  \n1910, 1490, 1690,  1654, 1897, 1508,  1929, 1930, 2853,  \n1645, 1934, 1935,  1936, 1937, 1938,  1505, 1515, 1941,  \n1529, 1942, 1515,  1950, 1951, 1954,  1897, 1903, 1953,  \n1541, 1942, 1529,  1508, 1897, 1704,  1897, 1953, 1704,  \n1621, 11266, 1966,  1968, 1704, 1953,  406, 1972, 404,  \n1704, 1968, 1514,  1514, 1361, 971,  1968, 1361, 1514,  \n1984, 1720, 1578,  5348, 8941, 11426,  13339, 1995, 1996,  \n1999, 2000, 2001,  2002, 2003, 2004,  1208, 1561, 1994,  \n29382, 2006, 11326,  2010, 2011, 4014,  2012, 2013, 1222,  \n1578, 1222, 2013,  2016, 2017, 2018,  2012, 1222, 1428,  \n2020, 2021, 2022,  1620, 1022, 2009,  2026, 2027, 2028,  \n2034, 2035, 2036,  1780, 2330, 1801,  1285, 1801, 1467,  \n4179, 2066, 3418,  1467, 2054, 1643,  21015, 2067, 2068,  \n2074, 2075, 1826,  2076, 2077, 2078,  2084, 2070, 2085,  \n2086, 2087, 2088,  1693, 2091, 2092,  2096, 396, 12830,  \n2085, 2070, 1838,  2102, 2085, 1838,  2075, 2103, 1833,  \n2104, 2105, 2106,  2107, 2108, 1767,  1826, 2075, 1833,  \n6261, 2111, 2112,  2115, 7686, 9947,  5958, 2122, 2123,  \n1842, 1833, 2126,  14992, 2139, 2140,  2126, 1860, 1842,  \n1872, 1851, 1840,  6506, 2149, 2150,  2152, 1860, 2126,  \n2162, 2163, 2164,  1885, 1860, 2152,  2971, 3660, 9902,  \n1885, 2152, 2176,  1885, 2176, 1891,  2181, 2182, 2183,  \n2191, 2192, 2193,  2196, 2197, 2198,  1903, 1490, 2199,  \n2199, 1490, 1910,  2199, 1910, 1690,  1690, 1505, 1941,  \n8453, 2210, 2211,  2214, 2215, 10518,  2221, 7328, 2222,  \n2225, 1942, 1541,  2228, 1953, 1903,  2225, 1541, 1720,  \n2233, 2234, 2235,  2239, 2240, 2105,  2243, 2244, 423,  \n10099, 2250, 1884,  2251, 2252, 2253,  1968, 1953, 2256,  \n2256, 1953, 2228,  1720, 1211, 1578,  1968, 2256, 1361,  \n2256, 2259, 1361,  2261, 1984, 1578,  1361, 2259, 1561,  \n2259, 2265, 1561,  2265, 1994, 1561,  2273, 2274, 2275,  \n19351, 2276, 2277,  2278, 2279, 2280,  21513, 13067, 2281,  \n1208, 1994, 2009,  2231, 15300, 2282,  2261, 1578, 2013,  \n2290, 2294, 8800,  2297, 4645, 2298,  2299, 2300, 2301,  \n20388, 5155, 2305,  2306, 2307, 1874,  2318, 2319, 2320,  \n14451, 2321, 2322,  1280, 2044, 1598,  1780, 1620, 2330,  \n1280, 1643, 2340,  2044, 1280, 2340,  1801, 2342, 2343,  \n2346, 7006, 2347,  2348, 2349, 3505,  2359, 941, 2360,  \n2361, 2070, 2071,  2362, 2361, 2071,  2364, 2365, 2366,  \n2368, 2369, 2370,  2361, 2376, 2358,  2358, 2074, 2070,  \n2379, 2380, 2381,  2361, 2358, 2070,  2080, 2081, 2382,  \n2071, 2070, 2084,  299, 11912, 2388,  2373, 2075, 2074,  \n462, 1530, 2401,  2404, 3715, 2405,  2070, 2074, 1826,  \n2102, 2391, 2085,  2407, 2075, 2373,  2395, 2409, 13242,  \n2103, 2075, 2407,  2414, 2415, 10851,  2418, 2103, 2407,  \n2432, 2433, 20657,  2103, 2418, 2126,  1833, 2103, 2126,  \n2102, 1851, 2391,  616, 615, 2444,  2453, 2454, 2455,  \n2460, 2461, 2462,  3775, 2468, 2469,  2478, 2479, 2480,  \n2463, 2152, 2126,  1872, 1865, 2477,  14306, 19682, 2487,  \n2152, 2490, 2176,  1891, 2496, 1865,  1865, 2496, 2477,  \n2176, 2499, 1891,  2499, 2496, 1891,  2506, 2507, 2534,  \n898, 2512, 2513,  2515, 2516, 2517,  2519, 2520, 2521,  \n2524, 1690, 1941,  2547, 14481, 2525,  2528, 2529, 2530,  \n2532, 1515, 1942,  1941, 1515, 2532,  2537, 20480, 16221,  \n2228, 1903, 2538,  2539, 6376, 9804,  1903, 2199, 2538,  \n2541, 2284, 968,  2546, 2547, 2548,  2549, 1942, 2225,  \n2550, 2551, 2552,  2553, 15713, 2554,  289, 2565, 2566,  \n2577, 2256, 2228,  2568, 2569, 2570,  2562, 2563, 2571,  \n2572, 2573, 2282,  2577, 2578, 2256,  2579, 11818, 1952,  \n21347, 10550, 2588,  2596, 3486, 2597,  2602, 2603, 2604,  \n2607, 2608, 2609,  2009, 2295, 2610,  2012, 1428, 2613,  \n11436, 2617, 467,  2613, 1428, 1597,  2624, 1620, 2610,  \n2634, 1713, 2635,  535, 2637, 2638,  2330, 1620, 2624,  \n2643, 2644, 11222,  2646, 2647, 2648,  2652, 2330, 2624,  \n2653, 4556, 2654,  2657, 2658, 2659,  13829, 2672, 2673,  \n2676, 2677, 12947,  2675, 2376, 3017,  2681, 2682, 2683,  \n2684, 2330, 2685,  2685, 2330, 2652,  2684, 1801, 2330,  \n2054, 1467, 2343,  2690, 9405, 2691,  629, 2234, 2694,  \n2698, 2699, 2700,  2376, 2675, 2074,  2376, 2074, 2358,  \n2707, 2708, 2709,  2718, 2719, 9609,  2724, 2725, 2726,  \n2730, 2731, 2732,  2734, 1770, 2735,  2750, 2751, 2752,  \n2675, 2717, 2373,  2675, 2373, 2074,  1239, 1240, 2761,  \n2768, 5402, 9895,  12267, 2772, 2773,  2776, 21210, 2777,  \n727, 2780, 728,  2781, 2782, 2783,  2745, 2085, 2391,  \n2745, 2084, 2085,  2786, 2407, 2717,  2373, 2717, 2407,  \n1623, 2787, 346,  582, 2788, 2789,  2407, 2786, 2790,  \n16631, 2799, 12402,  2808, 1451, 1450,  6008, 2809, 14312,  \n2810, 2811, 2812,  2814, 2813, 10509,  2816, 14140, 13720,  \n2407, 2790, 2418,  1851, 2795, 2391,  11351, 6843, 2821,  \n2790, 2823, 2418,  21076, 2829, 2830,  2838, 1077, 2839,  \n2126, 2418, 2823,  1851, 1872, 2795,  735, 2848, 7030,  \n2463, 2126, 2823,  2862, 19838, 2863,  2864, 2865, 2866,  \n12964, 2875, 2379,  2878, 2879, 11172,  2463, 2490, 2152,  \n2891, 2892, 2893,  2901, 7124, 8557,  15490, 2833, 15491,  \n2477, 2496, 2888,  2913, 2176, 2490,  2176, 2913, 2499,  \n2499, 2916, 2496,  2532, 2524, 1941,  2924, 2925, 2926,  \n2538, 2199, 2927,  2929, 395, 396,  2199, 2524, 2927,  \n2524, 2199, 1690,  2930, 2931, 20772,  2532, 1942, 2549,  \n2940, 8163, 2941,  1720, 1984, 2225,  1984, 2943, 2225,  \n2946, 2947, 2948,  2950, 2951, 2952,  2964, 2505, 2965,  \n2578, 2259, 2256,  2972, 2242, 2189,  2259, 2578, 2265,  \n2979, 2265, 2578,  2265, 2982, 1994,  2265, 2979, 2982,  \n2598, 2261, 2013,  2009, 1994, 2982,  2988, 2989, 2990,  \n2365, 1978, 16650,  2994, 2995, 2807,  2012, 2598, 2013,  \n1408, 2998, 2999,  3001, 3002, 16022,  2624, 2610, 3381,  \n24596, 3005, 3006,  2636, 1597, 1598,  3017, 3018, 3019,  \n3021, 3022, 3319,  3023, 3024, 1932,  3028, 3029, 3030,  \n3031, 3032, 3033,  3038, 1066, 3039,  3019, 3040, 3041,  \n3019, 3041, 3042,  3017, 3019, 3042,  2807, 3046, 2808,  \n3034, 2652, 2624,  3048, 2076, 3049,  3017, 3042, 2675,  \n3051, 5800, 3052,  3055, 3785, 3056,  3059, 3060, 3061,  \n2217, 3064, 2218,  779, 3067, 3068,  1055, 3071, 3072,  \n3075, 3042, 3041,  3079, 3080, 3081,  3086, 3087, 10241,  \n6660, 3094, 12179,  3110, 3111, 3112,  2652, 3034, 3107,  \n3107, 3116, 2652,  2652, 3116, 2685,  2684, 2342, 1801,  \n6796, 3119, 2374,  1467, 1801, 2343,  1643, 2054, 2340,  \n3042, 3075, 2717,  2717, 2675, 3042,  3097, 2361, 2362,  \n3137, 3138, 3139,  3142, 3143, 3144,  3145, 3146, 328,  \n3147, 3148, 3149,  2362, 2071, 3151,  3155, 3156, 3157,  \n3107, 2071, 2084,  3160, 14824, 1110,  3107, 2745, 3116,  \n3161, 1932, 3162,  3165, 2685, 3116,  3169, 6772, 3170,  \n3175, 1017, 13982,  3107, 2084, 2745,  3183, 567, 23549,  \n3116, 2745, 3165,  3185, 17393, 3186,  3187, 9583, 3188,  \n2766, 2767, 3192,  3193, 2745, 2391,  2745, 3193, 3165,  \n3196, 3197, 3198,  3075, 2786, 2717,  3206, 3207, 4867,  \n12071, 3208, 1223,  3193, 2391, 3214,  2786, 3213, 2790,  \n3214, 2391, 2795,  3224, 2755, 3225,  3226, 4203, 3227,  \n3228, 3229, 3230,  4312, 661, 13366,  3234, 3235, 3236,  \n3213, 3242, 2790,  3245, 2832, 2831,  3247, 3248, 3249,  \n2790, 3242, 2823,  3258, 3259, 3260,  11098, 2872, 2871,  \n2463, 2823, 3242,  2477, 2795, 1872,  9668, 3267, 3268,  \n3269, 3246, 3270,  18801, 3272, 3273,  7191, 2759, 3282,  \n3283, 4690, 778,  3284, 18287, 3285,  13146, 3296, 16192,  \n3299, 3300, 2490,  2913, 3301, 2499,  2532, 3309, 2524,  \n2917, 2524, 3309,  2917, 2927, 2524,  2532, 2549, 3315,  \n9414, 6211, 17347,  2943, 2549, 2225,  2927, 3330, 2538,  \n3331, 3332, 3333,  2538, 3330, 2228,  3335, 3336, 3337,  \n3339, 3340, 3341,  3122, 9140, 926,  2228, 3330, 2577,  \n3330, 2963, 2577,  3344, 2577, 2963,  3346, 3347, 3348,  \n3344, 2578, 2577,  3360, 3361, 13442,  2009, 2982, 2295,  \n3377, 12997, 13365,  13910, 3155, 3380,  3397, 3398, 3399,  \n1763, 14980, 10493,  3401, 2440, 3402,  8696, 7043, 3409,  \n3416, 3417, 3418,  2376, 3062, 3017,  3423, 18751, 3424,  \n2376, 2361, 3062,  3381, 3034, 2624,  3428, 3034, 3381,  \n2962, 5402, 2768,  3431, 3432, 9520,  3040, 3403, 3050,  \n3050, 3403, 3434,  3040, 3050, 3041,  3435, 3436, 3437,  \n3062, 3018, 3017,  3444, 778, 779,  13129, 6228, 3446,  \n3449, 3450, 1058,  2044, 2340, 3452,  1598, 2044, 3453,  \n1128, 3456, 3457,  1468, 18961, 1469,  6098, 1333, 1335,  \n3466, 1281, 3467,  1805, 3472, 10069,  3453, 2044, 3452,  \n3488, 1751, 3489,  3494, 3495, 3496,  3034, 3151, 3107,  \n3151, 2071, 3107,  4171, 3502, 3503,  22451, 18287, 21683,  \n3504, 8645, 3505,  490, 3512, 3513,  3075, 3050, 3518,  \n3075, 3041, 3050,  2685, 3165, 3527,  2684, 2685, 3527,  \n3536, 3537, 314,  988, 537, 3541,  6139, 3546, 2865,  \n3548, 3549, 16373,  3075, 3518, 2786,  2786, 3518, 3554,  \n4568, 3555, 3556,  3213, 2786, 3554,  3557, 3558, 3559,  \n3560, 3561, 3562,  3554, 3563, 3213,  3570, 11904, 3571,  \n11338, 3578, 3579,  3242, 3213, 3563,  7535, 3415, 3582,  \n3593, 13152, 4269,  2477, 3594, 2795,  3598, 3599, 3600,  \n9150, 1533, 3601,  3602, 3603, 3604,  3605, 3606, 3607,  \n2888, 3262, 2477,  3242, 2490, 2463,  2614, 3614, 6735,  \n3242, 3299, 2490,  15357, 3622, 16976,  2888, 2496, 2916,  \n3625, 15699, 3626,  2490, 3300, 2913,  2499, 3301, 2916,  \n19124, 3633, 20569,  3315, 3309, 2532,  3636, 3637, 353,  \n2927, 2917, 3651,  3315, 2549, 3656,  3656, 2549, 2943,  \n3657, 10016, 7459,  12530, 3662, 3663,  3671, 2943, 1984,  \n19020, 3673, 3674,  1984, 2261, 3345,  3680, 20811, 3681,  \n3344, 3686, 2578,  3686, 2979, 2578,  3686, 3689, 2979,  \n13123, 3690, 3691,  3689, 2982, 2979,  4270, 3695, 2261,  \n3699, 3700, 328,  3705, 3706, 3710,  3707, 2610, 2295,  \n3381, 2610, 3707,  2459, 3718, 3169,  3720, 3403, 3040,  \n3019, 3720, 3040,  3058, 3019, 3018,  3720, 3019, 3058,  \n3724, 3725, 3726,  3729, 3058, 3018,  3736, 3737, 3738,  \n3748, 3749, 3750,  3764, 3765, 3766,  3769, 3770, 1246,  \n3403, 3743, 3434,  3333, 3332, 17952,  3778, 3779, 2409,  \n1109, 3780, 3781,  3151, 3428, 2362,  3782, 3783, 3784,  \n3428, 3151, 3034,  3787, 3788, 3789,  3790, 3791, 3792,  \n17300, 3468, 2348,  2340, 2054, 3515,  3050, 3434, 3518,  \n3289, 5094, 3813,  2684, 3527, 2342,  1459, 1460, 3818,  \n3804, 2448, 6045,  3820, 3821, 3822,  9857, 3823, 8012,  \n3828, 3826, 3827,  3833, 3834, 497,  3310, 3311, 3842,  \n17489, 18043, 2793,  2526, 2527, 3859,  3863, 3864, 3563,  \n3868, 3869, 8285,  3870, 3871, 3872,  3589, 3242, 3563,  \n11535, 3268, 3879,  16680, 3884, 871,  9626, 1584, 3891,  \n1756, 20119, 12650,  15969, 15651, 3895,  3299, 3242, 3589,  \n3906, 3907, 3908,  2913, 3300, 3301,  3917, 3918, 3919,  \n9744, 3922, 3923,  3651, 2917, 3927,  3927, 2917, 3309,  \n3933, 3315, 3656,  3934, 13687, 18971,  4387, 4386, 1410,  \n570, 3937, 571,  3671, 3656, 2943,  3330, 3950, 2963,  \n2525, 3956, 2547,  3345, 3671, 1984,  3961, 3344, 2963,  \n3963, 3964, 3965,  10704, 19068, 15168,  21522, 3969, 3970,  \n22979, 3976, 3977,  3978, 494, 3152,  850, 14444, 3979,  \n3980, 3981, 3982,  3689, 3984, 2982,  2982, 3984, 2295,  \n3987, 19171, 3988,  2295, 3984, 3707,  3989, 3990, 2649,  \n3992, 2363, 4866,  3997, 3998, 3999,  8154, 3749, 4000,  \n2890, 4001, 1572,  4004, 4005, 9923,  3392, 3720, 3058,  \n3381, 3707, 3428,  4011, 13164, 4012,  4014, 11298, 16315,  \n4015, 9811, 7443,  4016, 3958, 3959,  4017, 7515, 4018,  \n4021, 3731, 3729,  4036, 4037, 4038,  4046, 17639, 1427,  \n13014, 4048, 4049,  18688, 4050, 4051,  3729, 3018, 3062,  \n3729, 3062, 3097,  4057, 7151, 4058,  2361, 3097, 3062,  \n10110, 11012, 4062,  3743, 4047, 3434,  1925, 4074, 2197,  \n4075, 21582, 4076,  4080, 13655, 4081,  4083, 4084, 4085,  \n4086, 1913, 5979,  22514, 4089, 4090,  4098, 823, 4099,  \n4109, 3527, 3165,  4110, 4111, 4112,  2342, 3527, 4366,  \n3820, 20860, 3821,  19870, 4115, 1324,  4116, 4117, 4118,  \n4119, 4120, 4121,  4122, 1899, 4123,  2343, 4124, 2054,  \n4130, 4131, 4132,  3515, 2054, 4124,  3554, 3434, 4105,  \n3518, 3434, 3554,  4139, 4140, 23940,  4142, 4143, 4144,  \n4145, 4742, 15034,  3193, 4141, 3165,  3193, 3214, 3553,  \n3563, 3554, 3863,  4161, 5993, 4162,  4166, 11302, 23711,  \n4172, 4173, 4174,  1656, 4185, 4186,  3299, 4193, 3300,  \n8383, 4200, 4201,  3301, 4202, 2916,  1875, 1876, 21665,  \n4208, 4209, 7090,  4215, 4216, 4217,  3330, 2927, 4223,  \n4226, 4227, 4228,  3451, 1562, 4242,  4246, 3686, 3344,  \n3345, 2261, 3695,  4251, 4252, 4253,  4257, 4258, 4259,  \n2261, 2598, 4270,  4266, 3689, 3686,  4268, 23668, 4269,  \n4266, 3984, 3689,  1828, 7554, 23025,  949, 4272, 4273,  \n4274, 4275, 6066,  4276, 4277, 2029,  3984, 4271, 3707,  \n17744, 4280, 4281,  4147, 8084, 4146,  4007, 3428, 4271,  \n3428, 3707, 4271,  3996, 2012, 2613,  3996, 2598, 2012,  \n7273, 4291, 4292,  4310, 4311, 4312,  3403, 4309, 3743,  \n3403, 3720, 4309,  3392, 3058, 3729,  3392, 3729, 3731,  \n4315, 4316, 4317,  3097, 4021, 3729,  17398, 3222, 4322,  \n4324, 4325, 12336,  3097, 4303, 4021,  2362, 4303, 3097,  \n4329, 4330, 4331,  4303, 2362, 4007,  2362, 3428, 4007,  \n4332, 15692, 4333,  2636, 2613, 1597,  4347, 2273, 2275,  \n4353, 4354, 4355,  5152, 4357, 1048,  4359, 1896, 21777,  \n3434, 4350, 4105,  14063, 4362, 4363,  3527, 4109, 4366,  \n4369, 2342, 4366,  21832, 4372, 3221,  4377, 4378, 4379,  \n3515, 4380, 2340,  4380, 3452, 2340,  4386, 4387, 4388,  \n4109, 3165, 4141,  4390, 4391, 4392,  16091, 1669, 4394,  \n664, 4399, 10213,  3553, 4141, 3193,  4105, 3863, 3554,  \n7538, 4407, 5400,  3890, 3596, 4409,  3512, 4410, 11955,  \n4413, 4414, 2805,  4415, 4416, 4909,  4417, 4418, 4419,  \n4420, 2991, 4421,  4423, 16543, 4424,  4426, 4427, 4428,  \n3214, 2795, 3553,  4158, 4486, 8581,  3563, 3864, 3589,  \n3864, 4169, 3589,  12782, 4435, 4436,  14550, 4437, 4438,  \n6024, 4450, 4451,  3589, 4175, 3299,  4193, 3299, 4175,  \n2916, 4461, 2888,  4462, 9257, 4463,  4464, 4465, 4466,  \n8298, 4470, 16530,  4474, 4475, 7334,  3309, 3315, 3933,  \n4479, 16694, 4480,  4481, 4482, 9745,  3927, 3309, 3933,  \n4223, 2927, 3651,  4491, 2781, 4492,  3330, 4223, 3950,  \n21462, 2479, 4500,  4512, 2172, 359,  3961, 4246, 3344,  \n4519, 4429, 4520,  4246, 4266, 3686,  4266, 4271, 3984,  \n4529, 4530, 4531,  4007, 4271, 4282,  2478, 2480, 1592,  \n4540, 4541, 4542,  4007, 4282, 4547,  4554, 3720, 3392,  \n19672, 4558, 28799,  4303, 4547, 4321,  4303, 4007, 4547,  \n4566, 4567, 4568,  4571, 4047, 4309,  4309, 4047, 3743,  \n4309, 3720, 4554,  4571, 4309, 4554,  4557, 4554, 3392,  \n4557, 4578, 5142,  4557, 3392, 3731,  3731, 4021, 4321,  \n4588, 4589, 4240,  4021, 4303, 4321,  4593, 3362, 387,  \n2562, 2571, 4594,  4047, 4350, 3434,  4596, 657, 4597,  \n3453, 2636, 1598,  4603, 3751, 4513,  4369, 2343, 2342,  \n4350, 4605, 4105,  2343, 4889, 4124,  3515, 4124, 4380,  \n4636, 4637, 4638,  14329, 4639, 4640,  4641, 4105, 4605,  \n4641, 3863, 4105,  4644, 4645, 4564,  4655, 4656, 4657,  \n4658, 3863, 4641,  4661, 4662, 4663,  4676, 4677, 4678,  \n3594, 2477, 3262,  4681, 14734, 6112,  4682, 3037, 15826,  \n4685, 4686, 4687,  4689, 10648, 4690,  2888, 4695, 3262,  \n4698, 16024, 11718,  2888, 4461, 4695,  2916, 4202, 4461,  \n4714, 4715, 5011,  4721, 4722, 19771,  4724, 4725, 4726,  \n4728, 4729, 4723,  4717, 4716, 4723,  11765, 4730, 8653,  \n4729, 4717, 4723,  4739, 18413, 15846,  4743, 13936, 21433,  \n17004, 4744, 4745,  4746, 3933, 3656,  4754, 23410, 4755,  \n4757, 16958, 4758,  3671, 4746, 3656,  4766, 4767, 4768,  \n3671, 3345, 3695,  4770, 4771, 4772,  4270, 4774, 3695,  \n4266, 4786, 4271,  4786, 4282, 4271,  4419, 4789, 4790,  \n4791, 4792, 19636,  4794, 4270, 2598,  3996, 4794, 2598,  \n4547, 4282, 4800,  4807, 11202, 4808,  1714, 4809, 4810,  \n4587, 4321, 4547,  4571, 4816, 4047,  4818, 4571, 4554,  \n4818, 4554, 4557,  13397, 4212, 4821,  4825, 4826, 4827,  \n3731, 4578, 4557,  3731, 4314, 4578,  4314, 3731, 4321,  \n4314, 4321, 4587,  4805, 2613, 2636,  4834, 4835, 4836,  \n6567, 4843, 4214,  4844, 4845, 4846,  4847, 17386, 7586,  \n4849, 4850, 4851,  4350, 4047, 4816,  13769, 4862, 11703,  \n4366, 4109, 4863,  910, 4864, 4865,  4867, 3207, 13889,  \n4358, 986, 1779,  4878, 3757, 16725,  4881, 4882, 4883,  \n16117, 9240, 11019,  4886, 4887, 4888,  4897, 4898, 4899,  \n4901, 4205, 4902,  4907, 4908, 15642,  4909, 4910, 4911,  \n5243, 4658, 4641,  4912, 4655, 4657,  4658, 3864, 3863,  \n2970, 2296, 4916,  4917, 1539, 1540,  3553, 2795, 3594,  \n4923, 4924, 4720,  3262, 4671, 3594,  1340, 4943, 1339,  \n4175, 4941, 4193,  18530, 4944, 12392,  15958, 5211, 4945,  \n4947, 4948, 4949,  4950, 4951, 4952,  2147, 4958, 4959,  \n4961, 4962, 4963,  4964, 4965, 4966,  4972, 9705, 4973,  \n1293, 4978, 1776,  4717, 4979, 4716,  4980, 4981, 4982,  \n4983, 4979, 4717,  4723, 4716, 4992,  4995, 4996, 14526,  \n4983, 4717, 4998,  4723, 4992, 5002,  5004, 5005, 10358,  \n4998, 4717, 4729,  5002, 4728, 4723,  3337, 5015, 5016,  \n5018, 19336, 7315,  4998, 5017, 5008,  4998, 4729, 5017,  \n5019, 2440, 3401,  1378, 11052, 5022,  4728, 5017, 4729,  \n5025, 5026, 5027,  4106, 5029, 5030,  5017, 4728, 5031,  \n415, 414, 12709,  12709, 414, 5042,  5057, 5058, 5059,  \n2232, 5061, 5062,  5057, 5063, 5058,  5065, 5066, 7828,  \n5069, 5070, 5071,  5076, 21724, 2025,  4756, 11565, 5080,  \n3961, 2963, 3950,  5088, 1456, 5089,  4774, 3671, 3695,  \n5091, 5092, 5093,  14739, 2204, 5095,  5097, 5098, 5099,  \n19261, 5102, 18398,  5103, 5104, 1035,  1736, 5112, 5113,  \n3867, 5114, 20060,  5115, 5116, 5117,  4282, 4786, 4800,  \n5122, 5123, 2544,  5125, 5126, 5127,  4571, 5130, 4816,  \n4800, 4587, 4547,  4805, 3996, 2613,  1610, 5138, 5139,  \n5130, 4571, 4818,  4818, 4557, 5142,  11997, 12718, 5145,  \n5146, 1029, 5147,  5148, 1209, 5149,  20128, 16258, 1228,  \n5153, 4314, 4587,  5155, 5156, 5157,  5144, 5143, 20130,  \n5166, 4578, 5167,  5166, 5142, 4578,  1464, 5171, 3000,  \n5172, 4187, 16153,  349, 5173, 9988,  5176, 5177, 5178,  \n4578, 4314, 4581,  4314, 5153, 4581,  5180, 5181, 5182,  \n5186, 4805, 2636,  4605, 4350, 4816,  518, 5201, 5202,  \n5204, 5205, 3857,  16934, 21916, 3288,  5207, 2828, 5208,  \n5206, 5209, 4605,  5210, 4836, 5211,  3453, 5186, 2636,  \n18488, 16337, 5214,  4187, 13769, 11703,  4366, 5221, 4369,  \n4366, 4863, 5221,  4369, 5221, 2343,  5223, 5224, 3454,  \n4141, 4863, 4109,  2343, 5221, 4889,  2229, 2230, 19694,  \n5233, 9664, 11521,  3452, 4380, 5234,  15127, 2553, 2554,  \n5234, 3453, 3452,  5238, 5239, 3530,  4605, 5209, 5243,  \n4605, 5243, 4641,  5249, 5250, 6397,  5264, 5265, 5266,  \n12295, 8169, 5267,  3553, 3594, 4906,  4946, 5269, 5270,  \n4169, 4175, 3589,  4941, 4175, 4169,  4695, 4938, 3262,  \n3300, 4193, 4941,  4957, 3300, 4941,  1756, 6096, 6098,  \n3301, 3300, 4957,  4957, 4711, 3301,  4979, 5312, 4975,  \n2945, 5317, 16016,  4975, 5320, 4992,  5321, 21195, 5322,  \n4975, 4992, 4716,  4975, 4716, 4979,  5326, 11868, 5327,  \n5333, 5334, 4410,  5341, 4905, 11902,  5337, 4983, 4998,  \n5337, 4998, 5343,  13032, 4821, 5345,  5343, 4998, 5008,  \n5343, 5008, 5349,  4728, 5002, 5366,  2628, 5372, 5373,  \n5374, 5017, 5031,  5376, 5377, 5378,  5774, 4728, 5366,  \n5774, 5031, 4728,  3290, 12299, 5382,  5385, 5386, 5387,  \n5394, 5388, 5389,  5394, 5393, 5388,  5395, 303, 5396,  \n5389, 5795, 5397,  5394, 5389, 5397,  5405, 5397, 5795,  \n7468, 921, 5406,  5394, 5397, 5409,  5411, 5397, 5405,  \n5412, 5413, 5414,  5411, 5409, 5397,  3933, 4746, 5423,  \n4223, 3651, 5428,  5286, 2609, 11489,  13504, 875, 5424,  \n5425, 5426, 5427,  5431, 5432, 5433,  4310, 5434, 5435,  \n14608, 5440, 5441,  5442, 3950, 4223,  5445, 6996, 5446,  \n4746, 3671, 4774,  5449, 5450, 5922,  9684, 5459, 6261,  \n5460, 5461, 474,  4246, 4786, 4266,  2875, 5468, 5469,  \n5105, 8502, 16284,  6624, 5475, 10330,  5478, 5479, 5480,  \n4794, 3996, 6401,  13418, 1921, 5498,  5500, 5501, 5502,  \n3996, 4805, 6401,  4922, 4139, 23940,  5510, 6594, 5511,  \n5130, 4818, 5514,  5514, 4818, 5142,  5515, 4646, 3604,  \n461, 5519, 460,  1243, 5521, 5522,  5526, 5514, 5142,  \n4647, 5532, 4648,  5540, 5541, 20179,  5545, 5546, 5547,  \n989, 3541, 1786,  5166, 5526, 5142,  5552, 4031, 5553,  \n5167, 4578, 5528,  5556, 9018, 5557,  19157, 1121, 3832,  \n4605, 4816, 5206,  4249, 5566, 22324,  3952, 5567, 14680,  \n5568, 5569, 5570,  5571, 5227, 5206,  5574, 5575, 1760,  \n5206, 5227, 5209,  4141, 5587, 4863,  11553, 5589, 5590,  \n5593, 11491, 8835,  5221, 5597, 4889,  8242, 2563, 2562,  \n5601, 5602, 5603,  5609, 5209, 5227,  5610, 5611, 3449,  \n2642, 13113, 21454,  5617, 882, 5618,  1386, 12150, 1387,  \n5627, 7503, 5628,  5768, 22248, 7598,  5243, 5209, 5609,  \n3553, 5629, 4141,  5633, 7191, 3993,  5638, 5639, 6462,  \n5645, 5646, 5647,  3594, 4671, 4906,  1053, 5657, 22437,  \n2308, 5660, 16296,  4938, 4671, 3262,  5666, 3794, 3793,  \n7322, 5671, 5672,  5674, 5675, 5676,  5677, 5678, 5679,  \n5681, 5682, 5683,  4711, 4202, 3301,  19745, 5690, 5691,  \n5320, 6151, 5699,  5701, 6395, 5702,  4975, 5312, 5704,  \n3687, 5711, 10444,  5717, 7882, 5718,  5722, 5721, 4979,  \n5721, 5312, 4979,  5722, 4979, 4983,  5699, 5712, 4992,  \n4992, 5320, 5699,  8523, 13597, 10482,  5722, 4983, 5337,  \n3411, 5731, 5732,  4992, 5712, 5734,  5735, 17338, 5736,  \n5002, 4992, 5734,  20184, 5744, 3840,  2648, 2647, 5745,  \n5366, 5002, 5352,  5752, 5753, 2753,  5766, 22733, 10654,  \n5366, 5773, 5774,  5777, 5778, 5779,  5386, 5385, 5780,  \n5782, 5783, 5784,  5374, 5031, 5788,  5788, 5031, 5774,  \n5796, 5388, 6259,  5388, 5801, 6259,  5796, 5389, 5388,  \n4311, 5807, 4312,  5393, 5813, 5388,  5814, 5802, 2992,  \n5796, 5795, 5389,  5820, 654, 5821,  5813, 5801, 5388,  \n4753, 5823, 2928,  5813, 5393, 5824,  3182, 5825, 3181,  \n5824, 5394, 5828,  5824, 5393, 5394,  16367, 5830, 2951,  \n5826, 5405, 5795,  2630, 29326, 5835,  5836, 5837, 5838,  \n5828, 5394, 5409,  5839, 5411, 5405,  5849, 5409, 5411,  \n3651, 3927, 5850,  5851, 5852, 10488,  5861, 3661, 11460,  \n7298, 5429, 5430,  3961, 3950, 5442,  5428, 5442, 4223,  \n5882, 5883, 5884,  6145, 5896, 5897,  3961, 5903, 4246,  \n5442, 5903, 3961,  4270, 5463, 4774,  10890, 5901, 5902,  \n4786, 4246, 5903,  4024, 5098, 17772,  5907, 4800, 4786,  \n5907, 4786, 5903,  3281, 5718, 5913,  5916, 4800, 5907,  \n15106, 5917, 5918,  5919, 10660, 5920,  5922, 5923, 5924,  \n5916, 4587, 4800,  3061, 15746, 5183,  5930, 5931, 5932,  \n5933, 5934, 5935,  5937, 4816, 5130,  5514, 5937, 5130,  \n4587, 5916, 5153,  5959, 5960, 3878,  17699, 5960, 5959,  \n20329, 5961, 4555,  1081, 5967, 5968,  5969, 4581, 5954,  \n1175, 4293, 5970,  5971, 5972, 5973,  5954, 4581, 5153,  \n4816, 5937, 5206,  5528, 4578, 4581,  5528, 4581, 5969,  \n1206, 1205, 5983,  5937, 5978, 5206,  3908, 5990, 5991,  \n5992, 5978, 5526,  5992, 5526, 5166,  5999, 6000, 6001,  \n5988, 6009, 6010,  5206, 5978, 5571,  5571, 5978, 5992,  \n5992, 5166, 5167,  6014, 5167, 5528,  6015, 6016, 6017,  \n5571, 5992, 5227,  5992, 5167, 6022,  6022, 5167, 6023,  \n6014, 6023, 5167,  5227, 5992, 6022,  6030, 6031, 6032,  \n6033, 6034, 6035,  5221, 4863, 6040,  828, 5785, 6043,  \n5221, 6040, 5597,  5609, 5227, 6022,  4141, 6056, 5587,  \n6061, 17458, 19019,  12119, 10367, 6065,  6056, 4141, 5629,  \n5956, 6069, 6070,  6071, 6072, 6073,  4124, 6076, 4380,  \n4124, 4889, 6076,  4784, 6082, 3523,  6083, 6084, 7916,  \n6086, 6087, 13493,  5629, 3553, 4906,  6092, 6106, 4658,  \n6096, 6097, 6098,  6106, 6107, 4169,  6108, 6109, 2594,  \n6110, 2796, 6111,  6112, 20926, 6113,  6114, 6102, 4671,  \n6115, 14159, 17567,  5408, 5407, 652,  6134, 6135, 15969,  \n6138, 4695, 4461,  4202, 4711, 6143,  8492, 6144, 6145,  \n4957, 5697, 4711,  6148, 3757, 6149,  6154, 23583, 6155,  \n6158, 6159, 6160,  6151, 6650, 5699,  6162, 23583, 6154,  \n6151, 5320, 5704,  5704, 5320, 4975,  1372, 6163, 6164,  \n6167, 6168, 9148,  5721, 5704, 5312,  1852, 1853, 6170,  \n2352, 9623, 6172,  5722, 6668, 5721,  817, 6178, 6179,  \n5807, 2120, 4312,  6184, 5722, 5337,  6187, 18142, 6188,  \n5582, 6190, 2456,  16803, 6191, 14983,  6192, 5337, 5343,  \n6192, 6184, 5337,  6196, 5343, 5349,  6196, 6192, 5343,  \n6786, 6787, 2922,  6199, 6200, 3118,  5352, 5002, 5734,  \n6204, 6205, 6206,  6212, 5352, 6213,  5764, 6220, 5008,  \n5764, 5008, 5017,  5374, 5764, 5017,  5773, 5366, 6212,  \n6223, 3538, 6224,  7708, 6238, 3962,  5374, 5788, 6241,  \n5374, 6241, 5764,  5788, 5774, 6243,  6243, 5774, 5773,  \n11122, 13955, 6247,  5796, 6254, 6255,  5795, 5796, 6255,  \n6259, 6254, 5796,  6264, 6265, 4317,  6270, 3073, 6271,  \n13342, 6274, 6275,  6279, 3899, 13656,  3899, 16463, 13656,  \n6285, 6286, 6287,  5824, 6296, 6295,  5405, 5826, 6297,  \n6296, 5824, 5828,  5289, 6300, 6301,  5405, 6297, 5839,  \n6314, 5828, 5409,  5098, 6315, 5099,  3829, 6316, 6317,  \n6320, 6321, 6322,  9986, 6323, 6324,  5839, 6319, 5411,  \n4289, 6326, 4288,  12384, 4856, 12382,  444, 826, 14775,  \n6329, 9213, 6330,  5411, 6331, 5849,  6333, 5849, 6331,  \n5849, 6314, 5409,  5849, 6333, 6314,  4255, 11697, 5608,  \n6331, 5411, 6319,  6338, 6333, 6331,  6340, 6341, 16961,  \n3927, 3933, 5850,  6288, 6347, 6348,  6351, 5850, 5423,  \n6359, 6360, 6361,  5889, 4746, 4774,  4911, 4415, 4909,  \n6366, 6367, 6368,  4774, 5463, 5889,  2270, 6374, 6375,  \n1775, 5228, 6378,  4270, 4794, 5463,  5463, 4794, 6386,  \n6387, 6388, 17896,  6394, 1161, 6395,  5250, 6396, 6397,  \n6393, 5907, 5903,  2492, 6405, 4743,  6408, 1265, 22211,  \n21777, 15052, 6412,  5916, 6885, 5153,  1757, 6419, 6420,  \n5954, 5153, 6431,  5954, 6431, 6432,  6431, 5153, 6885,  \n751, 6439, 750,  4506, 6469, 17223,  6456, 6079, 6080,  \n10657, 6460, 6461,  5937, 5514, 5978,  5514, 5526, 5978,  \n6465, 6466, 6467,  5859, 6473, 6474,  5186, 6457, 4805,  \n6129, 6130, 6480,  6484, 7516, 6485,  6497, 6498, 6499,  \n6495, 6500, 6496,  6472, 6014, 5528,  6512, 6111, 2796,  \n6040, 4863, 5587,  6516, 1253, 6517,  1605, 20015, 1604,  \n1634, 6524, 6525,  10951, 12668, 4488,  6533, 5974, 6534,  \n6535, 6040, 5587,  6535, 5597, 6040,  6167, 9602, 6168,  \n5609, 6023, 6541,  6022, 6023, 5609,  5505, 1080, 6542,  \n6546, 933, 6547,  6548, 1683, 6549,  6076, 6560, 4380,  \n5234, 4380, 6560,  5609, 6541, 6566,  3547, 6570, 6571,  \n6572, 6573, 6574,  17860, 6577, 6578,  5609, 6566, 5243,  \n6092, 5243, 6566,  6588, 6589, 6590,  4906, 6593, 5629,  \n5243, 6092, 4658,  6911, 13742, 2817,  4906, 6102, 6593,  \n6106, 3864, 4658,  6106, 4169, 3864,  4906, 4671, 6102,  \n1517, 10437, 6608,  11878, 6617, 20756,  10080, 6619, 6620,  \n7013, 6621, 4169,  6622, 8507, 6623,  6621, 4941, 4169,  \n6624, 17595, 6625,  6626, 6627, 6628,  4695, 6138, 4938,  \n6621, 6632, 4941,  4704, 6635, 1233,  18663, 3395, 4838,  \n4941, 6632, 4957,  5697, 4957, 6632,  4202, 6640, 4461,  \n1821, 6641, 17106,  6644, 6649, 6650,  6650, 6649, 6651,  \n6646, 6650, 6151,  6646, 6644, 6650,  6152, 6646, 5704,  \n6646, 6151, 5704,  2971, 6654, 3660,  29259, 6658, 6897,  \n14500, 6659, 2283,  6651, 5699, 6650,  6651, 6670, 5699,  \n5699, 6670, 5712,  6679, 6680, 11761,  6668, 5722, 6681,  \n6682, 6683, 6684,  6670, 6185, 5712,  6689, 6690, 1926,  \n6681, 5722, 6184,  6192, 6691, 6184,  5712, 6185, 5734,  \n15547, 3894, 2561,  6213, 5352, 5734,  6698, 2497, 6699,  \n5008, 6220, 5349,  6220, 6196, 5349,  6710, 6711, 6712,  \n6212, 5366, 5352,  6714, 6715, 6716,  5179, 6720, 6721,  \n6212, 6722, 5773,  6727, 6728, 6729,  6243, 5773, 6722,  \n6243, 6736, 5788,  6736, 6241, 5788,  6737, 6738, 14805,  \n7194, 7195, 6746,  16081, 16318, 11338,  6746, 6255, 6254,  \n6746, 7195, 6255,  6758, 6724, 6723,  5696, 6484, 5611,  \n6746, 6254, 6259,  3783, 4302, 6761,  2312, 6767, 15307,  \n6760, 6259, 5801,  5801, 6776, 6760,  6763, 5826, 6255,  \n5795, 6255, 5826,  5813, 6776, 5801,  6295, 6776, 5813,  \n6295, 5813, 5824,  6296, 6788, 6295,  5826, 6784, 6297,  \n6795, 6796, 10749,  6797, 5756, 5757,  6798, 6799, 6800,  \n4402, 2181, 2183,  6794, 6296, 5828,  5839, 6297, 6803,  \n6794, 5828, 6314,  6319, 5839, 6803,  6820, 6821, 6822,  \n6823, 6824, 6825,  6818, 6338, 6319,  6319, 6338, 6331,  \n3115, 20094, 22472,  6834, 6835, 6836,  5428, 3651, 5850,  \n5850, 3933, 5423,  6852, 6853, 6854,  23149, 6855, 6856,  \n10599, 6857, 2062,  6864, 1181, 5036,  1322, 6173, 5691,  \n19847, 2154, 6869,  6386, 4794, 6401,  11868, 5326, 11867,  \n6880, 6881, 6882,  6891, 1712, 3089,  2452, 6901, 6902,  \n6904, 4805, 6457,  5528, 5969, 6472,  6919, 6920, 4285,  \n6929, 6930, 7269,  6457, 5186, 3453,  5990, 6933, 5991,  \n6936, 6937, 6633,  13250, 6940, 6289,  5083, 13439, 6947,  \n10597, 3684, 1035,  6948, 6023, 6014,  6951, 2744, 6952,  \n17065, 14896, 20161,  6535, 6955, 5597,  6955, 4889, 5597,  \n6963, 11483, 6964,  6965, 12833, 6966,  6023, 6948, 6541,  \n15369, 6968, 20332,  5477, 13309, 3810,  6076, 4889, 6955,  \n6839, 6972, 6973,  6092, 6566, 6981,  9746, 1636, 6988,  \n6990, 4563, 3130,  6989, 6593, 6102,  6994, 3223, 6995,  \n6996, 6997, 6998,  2802, 776, 7002,  1763, 7011, 2386,  \n12243, 7012, 12511,  6114, 4671, 4938,  7013, 4169, 6107,  \n7016, 4938, 6138,  7023, 11136, 7024,  5543, 18089, 5606,  \n7032, 7033, 7034,  6621, 7037, 6632,  7038, 7039, 7040,  \n7041, 7042, 7043,  7047, 3409, 7043,  7048, 7049, 9320,  \n6632, 7037, 7050,  7050, 5697, 6632,  5697, 7053, 4711,  \n4711, 7053, 6143,  7058, 11394, 7059,  7064, 7065, 4500,  \n7073, 7071, 7074,  7073, 7067, 7071,  4101, 2671, 3801,  \n7075, 7071, 7067,  7076, 7077, 7078,  7074, 7071, 7079,  \n7083, 7084, 7085,  7584, 7071, 7086,  7089, 7090, 7091,  \n7584, 7079, 7071,  17887, 7092, 7093,  6644, 7097, 7095,  \n6646, 7098, 6644,  6644, 7098, 7097,  7095, 7096, 6649,  \n7101, 7102, 7103,  7095, 6649, 6644,  6646, 6152, 7098,  \n4089, 7111, 10739,  6152, 5704, 5721,  15579, 7115, 7116,  \n7117, 7118, 7119,  7121, 7122, 7123,  7124, 7125, 7126,  \n7135, 6668, 6681,  7133, 6185, 6670,  6184, 6691, 6681,  \n5965, 5966, 6863,  5735, 7150, 20346,  6192, 6196, 7155,  \n6713, 7155, 6220,  7155, 6196, 6220,  568, 7158, 7159,  \n7160, 6220, 5764,  7160, 6713, 6220,  5764, 6241, 7160,  \n7164, 7165, 7166,  7173, 4686, 7174,  6722, 7180, 6243,  \n7180, 6736, 6243,  5748, 7183, 5749,  7184, 7185, 3690,  \n7188, 7189, 17071,  6842, 7190, 7191,  7202, 6259, 6760,  \n7205, 7202, 6760,  7208, 6255, 7195,  7212, 7213, 7214,  \n3202, 7206, 13174,  2619, 7222, 17419,  7922, 7234, 7223,  \n7208, 6763, 6255,  7226, 7227, 7228,  21680, 7231, 3704,  \n7223, 7234, 7235,  5911, 4721, 7237,  6295, 7236, 6776,  \n7240, 1397, 7241,  6788, 7236, 6295,  1630, 1488, 1489,  \n7246, 6297, 6784,  6788, 6296, 6794,  8319, 6803, 7246,  \n6803, 6297, 7246,  7256, 15186, 7257,  7258, 7259, 16275,  \n7260, 6794, 6314,  7262, 6818, 6803,  6803, 6818, 6319,  \n7265, 7266, 7267,  6314, 6333, 7260,  6198, 4470, 7269,  \n6333, 6338, 7274,  7275, 19631, 7276,  5299, 2104, 447,  \n7285, 7286, 7287,  7289, 5423, 4746,  7289, 4746, 5889,  \n7302, 1396, 7303,  7244, 4684, 7310,  8098, 7311, 6959,  \n5707, 7315, 19336,  6141, 7316, 6142,  7313, 5907, 6393,  \n7317, 7318, 7319,  3091, 7321, 7322,  7325, 7326, 4787,  \n7331, 6401, 7330,  4570, 4569, 7347,  6325, 7357, 12061,  \n6014, 6472, 6948,  13448, 5096, 7362,  5587, 7363, 6535,  \n7369, 1059, 7370,  18043, 7371, 14795,  7373, 7374, 6373,  \n4524, 6088, 7376,  7363, 5587, 6056,  7380, 7381, 9440,  \n7390, 7391, 7392,  6566, 6541, 6981,  7393, 7394, 7395,  \n6981, 6541, 6948,  10131, 7401, 18722,  5877, 5876, 7402,  \n7403, 16880, 1870,  7404, 7405, 16659,  7411, 6092, 6981,  \n7420, 22066, 8338,  7422, 7423, 18143,  7424, 7425, 1511,  \n13473, 7430, 7431,  6107, 6106, 7414,  7438, 7439, 7440,  \n7446, 7447, 5274,  4938, 7016, 6114,  15507, 7605, 7449,  \n7013, 7453, 6621,  7455, 16892, 1499,  7035, 6621, 7453,  \n6621, 7035, 7037,  3295, 7459, 3294,  2835, 7461, 4586,  \n7050, 7053, 5697,  7471, 7472, 22082,  6640, 4202, 6143,  \n7035, 7475, 7037,  7476, 7037, 7477,  7478, 7479, 7480,  \n7476, 7050, 7037,  7481, 7053, 7476,  7476, 7053, 7050,  \n7723, 7482, 7483,  7484, 9457, 12739,  7490, 7477, 7491,  \n7477, 7475, 7486,  7477, 7486, 7491,  7475, 7485, 7486,  \n7493, 1264, 7494,  7496, 7490, 7491,  7486, 7485, 7499,  \n2313, 7500, 2312,  5628, 7503, 14715,  7491, 7486, 7499,  \n7496, 7491, 7506,  7508, 7496, 7506,  7499, 7502, 7509,  \n5171, 10203, 3000,  7524, 3079, 7394,  7491, 7527, 7506,  \n7528, 5974, 7529,  7499, 7509, 7531,  7534, 7535, 6556,  \n7491, 7499, 7531,  7491, 7531, 7527,  7538, 6487, 4407,  \n5333, 6587, 5947,  7543, 7067, 7073,  23025, 7554, 7555,  \n7558, 7559, 7560,  7553, 7073, 7074,  7561, 6176, 2856,  \n7553, 7074, 7562,  7563, 2099, 2098,  7565, 7075, 7547,  \n7067, 7547, 7075,  7074, 7079, 7562,  7573, 17485, 7574,  \n7576, 21946, 7577,  7075, 7086, 7071,  7578, 6676, 1372,  \n15468, 3747, 1218,  3830, 3829, 2820,  7583, 7584, 7086,  \n7585, 7586, 7587,  7079, 7584, 7590,  7584, 7583, 7590,  \n7593, 7594, 7097,  9147, 4464, 7597,  7097, 7594, 7095,  \n16246, 5768, 7598,  7095, 7594, 7096,  8131, 7097, 7098,  \n8131, 7098, 8140,  7096, 7600, 6649,  7611, 3383, 1342,  \n7613, 7098, 6152,  7614, 17400, 7615,  7522, 1369, 7523,  \n7616, 6649, 7600,  7616, 6651, 6649,  6670, 6651, 7616,  \n6668, 6152, 5721,  7616, 7133, 6670,  7629, 6668, 7135,  \n7636, 7135, 6681,  6691, 7636, 6681,  7633, 17585, 7632,  \n7636, 6691, 7638,  6192, 7638, 6691,  1834, 7644, 7718,  \n5615, 3133, 3134,  6192, 7645, 7638,  7643, 5734, 6185,  \n7651, 7652, 7653,  6213, 7643, 8193,  6213, 5734, 7643,  \n7645, 6192, 7155,  7671, 7672, 7673,  7675, 5136, 17897,  \n6212, 6213, 7676,  7677, 7678, 7679,  667, 7681, 5574,  \n4690, 7684, 7685,  6212, 7676, 7688,  7757, 7690, 7691,  \n6722, 6212, 7688,  6722, 7688, 7692,  10534, 9038, 7693,  \n7160, 6241, 7178,  568, 7159, 569,  1545, 8264, 4799,  \n7699, 6722, 7692,  7700, 13430, 7701,  7699, 7180, 6722,  \n22785, 2936, 7702,  13095, 7706, 7707,  7712, 2304, 20358,  \n7178, 6241, 6736,  7713, 12393, 7714,  6736, 7180, 7720,  \n7068, 7729, 7730,  7731, 7732, 7733,  7195, 7734, 8865,  \n7736, 7737, 7738,  7734, 7195, 7194,  7202, 8278, 7741,  \n14367, 7749, 3694,  7202, 6746, 6259,  6514, 6515, 7753,  \n7208, 7195, 8865,  7755, 7756, 20513,  6762, 7205, 6760,  \n6776, 6762, 6760,  342, 1534, 341,  6784, 5826, 6763,  \n5947, 7762, 5333,  7763, 7760, 7761,  6328, 6327, 822,  \n7765, 6776, 7236,  7775, 7236, 6788,  7776, 4854, 12349,  \n10754, 7777, 19269,  7781, 7118, 7117,  6332, 6368, 7782,  \n7789, 7790, 7791,  7775, 6794, 7792,  6788, 6794, 7775,  \n8319, 7262, 6803,  7792, 6794, 7260,  6704, 7804, 7805,  \n7807, 2560, 7808,  7809, 7810, 7811,  7274, 7260, 6333,  \n7820, 7821, 7822,  7826, 5892, 1304,  6351, 5423, 7289,  \n5442, 5428, 6849,  16220, 7840, 7841,  22004, 7851, 4847,  \n7852, 8224, 7853,  7854, 2106, 2240,  3237, 2192, 2191,  \n7855, 7856, 3095,  11563, 6263, 7857,  1075, 7858, 16185,  \n7860, 7861, 7862,  6879, 5907, 7313,  7331, 6386, 6401,  \n4509, 4510, 7866,  6885, 5916, 5907,  7867, 6885, 6879,  \n7869, 7870, 7871,  7330, 6401, 4805,  4805, 6904, 7330,  \n10015, 1380, 14083,  7885, 7886, 7887,  620, 622, 1637,  \n1378, 1380, 7889,  376, 7891, 7892,  376, 7893, 7891,  \n7858, 7894, 7895,  3453, 5234, 7897,  7363, 7898, 6535,  \n7899, 7900, 7901,  7898, 6955, 6535,  7898, 7904, 6955,  \n7761, 7907, 7908,  21750, 5562, 7910,  7890, 6981, 6948,  \n7913, 7914, 5267,  6955, 7904, 6076,  6076, 7917, 6560,  \n7904, 7917, 6076,  7919, 7920, 7921,  8446, 7923, 7924,  \n7925, 7926, 7927,  6092, 7414, 6106,  6092, 7411, 7414,  \n7935, 7936, 7937,  7938, 6107, 7414,  3090, 7384, 3089,  \n7913, 7940, 7914,  9945, 21579, 1470,  7016, 7955, 6114,  \n7955, 7016, 7961,  7953, 7453, 7013,  11940, 6683, 6682,  \n6138, 7961, 7016,  6138, 4461, 7961,  7966, 7035, 7453,  \n7035, 7966, 7475,  7053, 7972, 6143,  3828, 547, 7973,  \n7475, 7477, 7037,  7979, 7980, 1311,  6262, 7988, 7989,  \n7481, 7972, 7053,  7995, 15657, 1093,  1048, 16721, 4355,  \n7476, 7477, 7481,  8001, 8002, 5074,  5321, 2572, 3740,  \n8004, 4877, 8005,  7481, 7477, 7490,  7485, 7475, 7966,  \n1548, 8007, 8008,  8010, 8011, 10036,  7999, 7490, 7496,  \n7499, 7485, 7502,  8030, 8031, 8032,  8038, 8272, 8039,  \n7506, 8037, 7508,  8047, 7531, 7509,  7509, 8034, 8047,  \n2000, 8050, 8051,  8057, 8058, 8059,  1742, 1741, 8060,  \n7527, 7531, 8061,  8061, 7531, 8047,  6795, 8066, 2921,  \n7067, 7543, 8070,  8071, 6112, 8072,  7543, 8073, 8070,  \n7543, 8074, 8073,  8074, 7543, 7073,  7073, 8075, 8074,  \n7553, 8075, 7073,  8077, 8075, 7553,  8070, 7547, 7067,  \n1352, 8081, 20085,  8083, 8084, 8085,  8086, 2447, 8087,  \n8077, 7553, 7562,  5021, 8092, 8093,  1647, 8094, 20070,  \n2815, 8095, 8096,  19034, 8101, 7492,  8105, 8106, 8107,  \n7086, 7075, 8104,  28329, 17969, 9374,  7086, 8104, 7583,  \n2125, 5082, 5081,  8117, 8118, 7817,  8122, 13485, 8123,  \n11446, 8125, 8126,  8127, 8137, 7594,  7593, 8127, 7594,  \n7593, 7097, 8131,  7096, 7594, 8137,  24315, 8142, 8143,  \n7618, 12437, 743,  8137, 8138, 7600,  8137, 7600, 7096,  \n8148, 8149, 20009,  14608, 4920, 5440,  7613, 8140, 7098,  \n11604, 8155, 8156,  7613, 6152, 8158,  8159, 8160, 8161,  \n8158, 6152, 6668,  8184, 13646, 6928,  6804, 4299, 12464,  \n7133, 7643, 6185,  975, 8188, 8189,  7645, 8191, 7638,  \n1110, 14824, 8199,  8200, 8201, 8202,  8204, 3220, 8205,  \n8208, 7676, 6213,  8193, 8208, 6213,  7829, 1609, 7830,  \n6713, 8216, 7155,  7155, 8216, 7645,  12703, 8217, 8218,  \n8216, 6713, 7160,  1993, 17886, 8223,  5797, 8224, 15480,  \n8225, 7688, 7676,  7160, 7178, 8226,  7178, 8247, 8226,  \n8243, 7178, 6736,  8243, 8247, 7178,  5300, 8254, 8255,  \n8265, 8266, 7900,  8268, 7734, 7194,  2820, 3829, 6317,  \n8270, 8271, 631,  7741, 6746, 7202,  8273, 21571, 8274,  \n7741, 7194, 6746,  8279, 1843, 2476,  4445, 4444, 8281,  \n7205, 8278, 7202,  6763, 7208, 8284,  4897, 4899, 3341,  \n2800, 8291, 8292,  8293, 4065, 16190,  6763, 8284, 8294,  \n3595, 11492, 18036,  8299, 6762, 6776,  8303, 8299, 7765,  \n8299, 6776, 7765,  8294, 6784, 6763,  7236, 8303, 7765,  \n8309, 8303, 7775,  23236, 2993, 3841,  7236, 7775, 8303,  \n8317, 12251, 8318,  8319, 6784, 8313,  8320, 8321, 8322,  \n6784, 8319, 7246,  7129, 8323, 8324,  7806, 6818, 7262,  \n6818, 8337, 6338,  7806, 8337, 6818,  6338, 8337, 7274,  \n7274, 8337, 8341,  8342, 8343, 7192,  7260, 7274, 8341,  \n7792, 7260, 8341,  8346, 22116, 2907,  7311, 8098, 698,  \n8347, 8348, 8349,  8348, 8350, 8349,  7752, 6626, 8354,  \n8350, 8355, 8356,  8360, 8361, 8362,  728, 4777, 10652,  \n8365, 8178, 8366,  8349, 8359, 8347,  8348, 8347, 8372,  \n8348, 8372, 8355,  7808, 8373, 8374,  8377, 8355, 8372,  \n8384, 3508, 2967,  8385, 8355, 8377,  8372, 8347, 8387,  \n8377, 8372, 8386,  8372, 8387, 8386,  4538, 4539, 8390,  \n7619, 8391, 8392,  6351, 7825, 5850,  6122, 15384, 18509,  \n8399, 8400, 3184,  8401, 8402, 14137,  5903, 5442, 6849,  \n6386, 5889, 5463,  5889, 6386, 7305,  5903, 6849, 6393,  \n21472, 5551, 3347,  18794, 2960, 3448,  8414, 8415, 2587,  \n6885, 5907, 6879,  8420, 8421, 8422,  8426, 5954, 6432,  \n6472, 5969, 5954,  3453, 7875, 6457,  5530, 20585, 2091,  \n5234, 6560, 7897,  7890, 6472, 8426,  7897, 7875, 3453,  \n8440, 8441, 7945,  14512, 12154, 8443,  8444, 6981, 7890,  \n6948, 6472, 7890,  6056, 8450, 7363,  3675, 4133, 4134,  \n8450, 7898, 7363,  8455, 6552, 8456,  8461, 1205, 2958,  \n8463, 8464, 8465,  6560, 8470, 7897,  6560, 7917, 8470,  \n5629, 8476, 6056,  6981, 8444, 7411,  6593, 6989, 8476,  \n5010, 5011, 4715,  7512, 2133, 7633,  8491, 18129, 7186,  \n8496, 6107, 7938,  8496, 7013, 6107,  7953, 7013, 8496,  \n8507, 8684, 8508,  8509, 8510, 8511,  7966, 7453, 7962,  \n7953, 7962, 7453,  7854, 8515, 6081,  4461, 6640, 7961,  \n8516, 7147, 1915,  21343, 14545, 19200,  19108, 21427, 8517,  \n8518, 5896, 8519,  8521, 8522, 5736,  6640, 6143, 7972,  \n4018, 8352, 6915,  7966, 8528, 7485,  7972, 7481, 7999,  \n3290, 8538, 1492,  7481, 7490, 7999,  1882, 5325, 1509,  \n8544, 4397, 4398,  7502, 7485, 8528,  5339, 8547, 3000,  \n12254, 696, 8549,  8550, 11242, 10067,  7999, 7496, 7508,  \n13742, 13666, 2817,  6859, 6858, 8555,  8560, 8561, 7508,  \n8563, 8564, 8565,  7508, 8037, 8560,  4810, 2056, 2055,  \n5454, 11388, 5453,  1282, 6451, 8574,  8575, 8576, 1708,  \n8577, 4701, 7109,  7506, 7527, 8037,  8580, 8581, 12816,  \n16227, 8582, 8583,  8584, 11602, 4368,  7353, 8585, 8586,  \n8587, 8037, 7527,  4526, 8599, 20680,  8587, 7527, 8061,  \n8605, 8047, 8596,  8605, 8061, 8047,  8611, 8612, 8613,  \n7830, 1609, 8614,  8615, 8616, 2417,  8620, 1384, 22364,  \n3758, 2607, 2609,  8077, 8623, 8075,  8623, 8077, 8630,  \n339, 11352, 340,  8630, 8077, 7562,  8634, 8630, 7562,  \n8505, 8636, 4665,  7079, 8640, 7562,  8642, 7227, 14062,  \n8640, 8634, 7562,  8643, 2163, 8644,  8646, 7942, 8647,  \n7075, 7565, 8104,  7590, 8640, 7079,  8655, 8656, 8657,  \n8660, 6026, 8661,  8104, 8664, 7583,  9150, 3601, 8668,  \n8669, 7590, 7583,  8675, 7583, 8664,  4535, 5746, 19603,  \n7583, 8675, 8669,  8676, 8680, 8127,  8676, 8127, 7593,  \n8676, 7593, 8131,  8680, 8685, 8137,  2398, 8687, 6924,  \n8127, 8680, 8137,  8138, 8137, 8685,  14658, 10361, 687,  \n8699, 13857, 1130,  15166, 1537, 3774,  18583, 6577, 17860,  \n8715, 15578, 15709,  689, 8721, 8722,  7629, 8158, 6668,  \n3179, 6845, 921,  8731, 22724, 3439,  8180, 7133, 7616,  \n8732, 7629, 7135,  7769, 8734, 5005,  7643, 7133, 8180,  \n7638, 7135, 7636,  8743, 359, 358,  8746, 8193, 8740,  \n7643, 8740, 8193,  8710, 2003, 8493,  8193, 8746, 8747,  \n3885, 13864, 8748,  18366, 8761, 8762,  8766, 8767, 8768,  \n8208, 8225, 7676,  8770, 8216, 7160,  8772, 8092, 8773,  \n8777, 8770, 8226,  8226, 8770, 7160,  8779, 8780, 8781,  \n8787, 8788, 8782,  3938, 8790, 10956,  8771, 7692, 7688,  \n8794, 8795, 2756,  414, 415, 8796,  8782, 8783, 8248,  \n8782, 8248, 9539,  8782, 9539, 8787,  5123, 6652, 2544,  \n8812, 8799, 8248,  8813, 7977, 8814,  8815, 6749, 7813,  \n8252, 7699, 7692,  5055, 8818, 8819,  7720, 7180, 7699,  \n1097, 8822, 6733,  8824, 8825, 7786,  8830, 8831, 1516,  \n8248, 8783, 8829,  8832, 8812, 8248,  8836, 8837, 8838,  \n8839, 6736, 7720,  8840, 5750, 5087,  8829, 8832, 8248,  \n8829, 8851, 8832,  8852, 20047, 1006,  8855, 8672, 8856,  \n3576, 8190, 1794,  1494, 484, 408,  8867, 8868, 8869,  \n8864, 8865, 8870,  23933, 8871, 6696,  8865, 7734, 8870,  \n8870, 7734, 8268,  8571, 8572, 19971,  8875, 8876, 8877,  \n22752, 2386, 1476,  4782, 11213, 8879,  8881, 2221, 2222,  \n8268, 7194, 7741,  4468, 8888, 8889,  8890, 3985, 3986,  \n8891, 8892, 8893,  8898, 7205, 6762,  6762, 8903, 8898,  \n8299, 8903, 6762,  8303, 8903, 8299,  6598, 8912, 1399,  \n8930, 8931, 8932,  2020, 6129, 6739,  8943, 8944, 2079,  \n7792, 8947, 8309,  7775, 7792, 8309,  8949, 8950, 7806,  \n7262, 8319, 8933,  11192, 13331, 8952,  7792, 8341, 8947,  \n10931, 8955, 8956,  8957, 4276, 2029,  8961, 6741, 7368,  \n8353, 8349, 8350,  8351, 8963, 8350,  8964, 8965, 8966,  \n8963, 8353, 8350,  8969, 8970, 1964,  8359, 8349, 8353,  \n8967, 8359, 8353,  10946, 3429, 8983,  8350, 8348, 8355,  \n13842, 4845, 8987,  8997, 3380, 8988,  8994, 8995, 8996,  \n8998, 8356, 8355,  8379, 8359, 8991,  8347, 8359, 8379,  \n9009, 9010, 9011,  1835, 1153, 7843,  6939, 2010, 6938,  \n9014, 9015, 9016,  9018, 9019, 13744,  9021, 4830, 9022,  \n8998, 8355, 8385,  8379, 8991, 9006,  5355, 15835, 19649,  \n9033, 4167, 9034,  8998, 8385, 9037,  9047, 8385, 8377,  \n8387, 8347, 8379,  9059, 2412, 17608,  9062, 3856, 6420,  \n8379, 9053, 9066,  8379, 9006, 9053,  4666, 5164, 9074,  \n9075, 9076, 3886,  8385, 9047, 9049,  9080, 806, 15088,  \n9083, 9084, 9085,  8386, 8387, 9088,  1586, 1224, 3208,  \n2447, 9092, 8087,  9093, 9047, 8377,  7665, 9095, 9096,  \n477, 4464, 9147,  8387, 8379, 9066,  8377, 8386, 9093,  \n9047, 9093, 9103,  8386, 9108, 9093,  5041, 9110, 2016,  \n9049, 9047, 9103,  18691, 3216, 9114,  8598, 9115, 9116,  \n5428, 5850, 9118,  9124, 9125, 9126,  9133, 9134, 7112,  \n8322, 9137, 9138,  4573, 7386, 7628,  9108, 8386, 9088,  \n6849, 5428, 9118,  5889, 7305, 7289,  6303, 7939, 3114,  \n9156, 5189, 9157,  9103, 9093, 9158,  3738, 14622, 3992,  \n9161, 3460, 3461,  7313, 6393, 9179,  328, 327, 3145,  \n9188, 4765, 9189,  9191, 9192, 9193,  9195, 8163, 2940,  \n5928, 4856, 4855,  9197, 9198, 9199,  9200, 7331, 7330,  \n6885, 7867, 6431,  12328, 7019, 9201,  7330, 6904, 9200,  \n6904, 6457, 9205,  9207, 7513, 2509,  6457, 7876, 9205,  \n6272, 5175, 8803,  6472, 5954, 8426,  1392, 15631, 9210,  \n9212, 7875, 7897,  9220, 9213, 6329,  9222, 12632, 9223,  \n9228, 9229, 3693,  8476, 8450, 6056,  4165, 9231, 1155,  \n5582, 317, 2837,  9236, 9237, 9238,  4752, 9240, 4753,  \n7411, 8444, 9243,  5629, 6593, 8476,  11218, 9245, 9246,  \n9243, 7414, 7411,  7938, 7414, 9243,  9247, 9248, 4147,  \n6102, 9250, 6989,  7938, 10059, 8496,  9253, 5021, 9254,  \n5896, 9255, 9256,  8496, 7962, 7953,  9257, 9258, 9259,  \n9250, 6102, 6114,  1387, 9265, 10248,  7962, 9275, 7966,  \n9281, 9282, 9283,  6640, 10101, 7961,  9295, 1214, 9296,  \n9275, 8528, 7966,  21513, 9297, 20062,  1604, 8122, 5419,  \n9298, 2238, 9299,  9305, 10213, 4399,  9303, 7972, 7999,  \n7336, 6320, 8477,  6085, 6218, 6219,  9312, 858, 9313,  \n7509, 11641, 8034,  5324, 15021, 9320,  5670, 5877, 7402,  \n9324, 9329, 8034,  9331, 9332, 9333,  9336, 7005, 9337,  \n8034, 9329, 8047,  7789, 3150, 3966,  9339, 8037, 8587,  \n9341, 8596, 9329,  8596, 8047, 9329,  8111, 9346, 793,  \n7524, 9448, 8088,  9355, 9052, 9356,  9359, 8073, 8074,  \n10421, 9360, 9361,  9359, 8074, 9362,  8075, 9362, 8074,  \n8073, 10173, 8070,  8573, 13166, 11261,  9362, 8075, 8623,  \n2025, 9367, 5076,  9377, 8623, 8630,  9384, 8630, 8634,  \n9526, 8900, 9387,  9389, 2482, 9390,  8640, 9399, 8634,  \n9403, 9404, 9405,  8640, 7590, 10210,  9407, 9408, 1433,  \n9410, 8664, 8104,  9413, 20467, 3094,  9410, 8675, 8664,  \n9434, 9425, 8676,  9425, 9426, 8680,  9425, 8680, 8676,  \n7380, 9440, 20415,  1103, 9442, 1104,  8088, 9448, 4493,  \n8680, 9426, 8685,  9451, 9452, 9453,  4953, 2852, 14827,  \n8685, 10258, 9460,  9463, 8138, 9460,  8138, 8685, 9460,  \n6517, 9122, 6516,  10298, 3987, 3988,  9472, 9473, 4055,  \n9463, 7600, 8138,  9476, 9477, 9478,  9479, 9480, 9481,  \n1008, 9483, 9484,  9482, 7616, 7600,  9495, 5473, 8460,  \n7629, 8723, 8158,  6345, 6344, 19471,  8723, 7629, 8732,  \n9501, 9502, 2640,  8732, 7135, 9503,  2569, 10843, 9504,  \n7638, 9503, 7135,  9503, 7638, 9506,  9508, 5437, 9509,  \n9511, 18159, 9512,  7638, 8191, 9506,  17786, 249, 9513,  \n8951, 9518, 9519,  3717, 6110, 9522,  8747, 8208, 8193,  \n1322, 9527, 6173,  19312, 11206, 11208,  2802, 7002, 9533,  \n9076, 3291, 9534,  1923, 1924, 2132,  8022, 8010, 9535,  \n8225, 9538, 9539,  9542, 9543, 8929,  9546, 20480, 2537,  \n4627, 9547, 9548,  8787, 9552, 8788,  13202, 9554, 9555,  \n9556, 3615, 2820,  9538, 8787, 9539,  8929, 21619, 9560,  \n9567, 8783, 8782,  9571, 15528, 9572,  3808, 21256, 7217,  \n9577, 9578, 9579,  8225, 9539, 9580,  7688, 8225, 9580,  \n9583, 9584, 24898,  9580, 9539, 8799,  7688, 9580, 8771,  \n9585, 9586, 9587,  9589, 17581, 5225,  3771, 9590, 9591,  \n9592, 22043, 20182,  8247, 8243, 9595,  8247, 9595, 8226,  \n8783, 9597, 9598,  9599, 9600, 5022,  9601, 9269, 3948,  \n8771, 9580, 9604,  8771, 9604, 9605,  6279, 3900, 3899,  \n7692, 8771, 9605,  9608, 9268, 9609,  7692, 9607, 8252,  \n6736, 9617, 8243,  9539, 8248, 8799,  9580, 8799, 9604,  \n8252, 7720, 7699,  9630, 3175, 13982,  9633, 9634, 808,  \n8829, 9598, 9632,  8851, 8829, 9632,  9604, 8799, 8812,  \n9604, 8812, 9605,  8832, 9652, 9653,  9652, 8851, 9655,  \n15264, 9656, 16389,  9661, 2858, 4637,  10451, 8870, 8268,  \n8284, 9670, 9671,  11235, 8268, 7741,  8881, 9678, 2221,  \n8865, 8284, 7208,  9681, 12638, 7270,  8857, 7990, 7332,  \n9691, 7971, 9692,  9688, 8278, 7205,  8898, 9688, 7205,  \n10475, 8898, 8903,  9699, 9700, 9701,  9705, 4972, 9706,  \n7317, 901, 9709,  8303, 8309, 8903,  9710, 8282, 10930,  \n9713, 19518, 9714,  6784, 8294, 8313,  2942, 9715, 3685,  \n9719, 9720, 1391,  3617, 9809, 3616,  7262, 8942, 8949,  \n7262, 8949, 7806,  11966, 9475, 9730,  10508, 8337, 8950,  \n8337, 7806, 8950,  2169, 9744, 3923,  8337, 10508, 8341,  \n2694, 2234, 9749,  9755, 10689, 9756,  9757, 671, 14995,  \n8980, 8351, 8350,  14587, 17874, 9762,  9751, 8353, 8963,  \n9751, 8967, 8353,  9116, 9115, 14363,  8350, 8356, 8980,  \n8980, 8356, 8979,  8536, 9772, 8535,  3470, 9773, 9774,  \n9775, 9776, 9777,  9781, 9782, 9783,  8991, 8967, 9784,  \n8967, 8991, 8359,  9006, 8991, 9784,  9789, 9790, 9791,  \n6460, 6052, 6053,  9794, 9795, 9796,  9799, 9800, 9801,  \n7354, 769, 9802,  12191, 9803, 3763,  3602, 9805, 3603,  \n9806, 431, 15113,  9037, 8385, 9049,  7333, 9813, 8677,  \n17090, 9815, 909,  9817, 11108, 9818,  9829, 9830, 1880,  \n9832, 9833, 5912,  9049, 9834, 9037,  9836, 9837, 9838,  \n9532, 7648, 16834,  9842, 8255, 9843,  9846, 9847, 6569,  \n7494, 5673, 7493,  9834, 9049, 9850,  1677, 2754, 9851,  \n7825, 9118, 5850,  4788, 9852, 8884,  2444, 9853, 616,  \n5391, 9857, 9858,  17662, 9862, 9863,  9864, 12949, 9865,  \n7825, 6351, 9120,  9867, 9868, 22958,  9869, 9870, 4443,  \n16859, 3741, 9873,  4156, 8260, 19233,  9878, 20924, 9879,  \n9850, 9049, 9103,  9882, 7289, 7305,  9886, 8387, 9066,  \n9887, 4261, 4260,  10178, 5085, 4170,  21539, 9892, 9893,  \n9313, 858, 859,  9897, 8115, 8116,  6309, 17033, 17107,  \n9088, 8387, 9886,  11854, 6825, 9900,  9088, 9901, 9108,  \n9850, 9158, 9907,  9850, 9103, 9158,  9908, 9909, 9910,  \n7400, 9911, 9912,  9914, 7305, 6386,  11066, 9915, 9916,  \n9920, 11668, 9921,  9088, 9160, 9901,  9925, 9926, 9927,  \n13070, 1979, 1866,  9907, 9935, 9850,  9886, 9941, 9088,  \n9942, 9943, 9944,  23164, 9945, 9946,  9158, 9093, 9146,  \n12857, 9951, 9326,  15576, 9952, 5989,  9907, 9158, 9953,  \n2734, 4200, 9956,  9000, 9958, 10375,  5962, 9933, 7303,  \n5203, 614, 9930,  9963, 9964, 9965,  9953, 9158, 9973,  \n9975, 24870, 9976,  18189, 2313, 2312,  18194, 9978, 2037,  \n17647, 3046, 9980,  9851, 10360, 7661,  9141, 3143, 3142,  \n538, 522, 9992,  4288, 9993, 7834,  15060, 20758, 9785,  \n9953, 10002, 9907,  10003, 6431, 7867,  9200, 6904, 9205,  \n9953, 10006, 10002,  9953, 9973, 10006,  1533, 19062, 10008,  \n4518, 21832, 20755,  10006, 9973, 10011,  4112, 10014, 10015,  \n7875, 7876, 6457,  10016, 4680, 10017,  9525, 10026, 10027,  \n7890, 8426, 9214,  10031, 5899, 10032,  7897, 8470, 9212,  \n3979, 14444, 10033,  18238, 10039, 10040,  10030, 7904, 7898,  \n10041, 1334, 1333,  10042, 3714, 2705,  7904, 10043, 7917,  \n10044, 2194, 6404,  7917, 10043, 8470,  9214, 10047, 8444,  \n9214, 8444, 7890,  3419, 10053, 3420,  19565, 4631, 17926,  \n10054, 10055, 10056,  10050, 8450, 8476,  8444, 10047, 9243,  \n9243, 10059, 7938,  10047, 10059, 9243,  6989, 9250, 8476,  \n10064, 8212, 10065,  611, 9373, 610,  6491, 10068, 6492,  \n1269, 10069, 10070,  7962, 8496, 10071,  10074, 10075, 10076,  \n10077, 11328, 10532,  7962, 10071, 9275,  8691, 10081, 10082,  \n7955, 7961, 10091,  7955, 10091, 10092,  1537, 643, 3774,  \n8683, 10094, 10095,  9229, 9228, 10097,  10098, 10099, 10100,  \n8528, 9275, 10085,  6640, 7972, 10106,  11655, 948, 11085,  \n9306, 7502, 8528,  2584, 20968, 10115,  7999, 7508, 8561,  \n7509, 7502, 9306,  7509, 9306, 11641,  8560, 10118, 8561,  \n11641, 9324, 8034,  19208, 10129, 11531,  10131, 10132, 7401,  \n8560, 8037, 9339,  3582, 1796, 1970,  5552, 8069, 4030,  \n9334, 9335, 1119,  7749, 820, 10137,  1830, 9350, 10139,  \n10140, 10141, 10142,  4022, 10143, 4023,  10147, 10148, 3538,  \n9341, 10149, 8596,  10149, 8605, 8596,  10150, 8513, 8512,  \n10153, 8587, 10154,  10154, 8587, 8061,  8587, 10153, 9339,  \n8605, 10154, 8061,  5924, 10158, 9676,  10161, 10162, 5723,  \n11680, 8073, 9359,  3156, 16766, 10167,  10170, 10168, 9362,  \n10171, 19221, 10172,  10174, 1579, 1581,  19032, 8633, 4775,  \n10170, 9362, 8623,  9377, 10170, 8623,  10189, 9816, 10053,  \n8630, 9384, 9377,  7547, 8070, 10192,  9392, 7565, 7547,  \n9392, 10193, 7565,  9056, 2875, 10196,  9384, 8634, 9399,  \n9612, 10199, 12702,  10201, 8104, 10193,  8104, 7565, 10193,  \n8640, 10210, 9399,  8669, 10210, 7590,  9410, 8104, 10201,  \n2308, 16296, 10214,  13861, 9977, 4758,  8427, 11308, 7737,  \n9417, 10210, 8669,  10039, 9465, 10220,  9425, 10226, 11000,  \n10227, 7190, 6842,  9425, 10228, 10226,  1454, 14465, 10229,  \n9425, 11000, 9426,  10228, 9425, 9434,  1712, 6891, 1018,  \n10243, 10244, 19746,  10245, 10246, 10247,  9434, 8676, 9447,  \n9447, 8676, 8131,  10254, 21968, 13002,  10256, 10257, 17661,  \n10255, 5144, 20130,  10258, 8685, 9426,  8140, 9447, 8131,  \n10263, 10264, 10265,  2534, 2966, 2533,  7613, 10279, 8140,  \n6778, 9466, 8708,  10281, 10282, 3814,  963, 10283, 10284,  \n14250, 10287, 19261,  10288, 10289, 10290,  16398, 10291, 10292,  \n10294, 8044, 924,  1827, 1977, 10296,  7613, 8158, 10293,  \n10303, 10293, 8158,  10306, 7800, 10307,  10308, 10102, 16434,  \n10303, 8158, 8723,  10310, 7015, 7014,  8180, 9482, 10312,  \n7616, 9482, 8180,  1477, 1478, 5758,  9503, 10313, 8732,  \n10313, 8723, 8732,  6677, 9547, 10320,  8740, 8180, 10312,  \n8740, 7643, 8180,  4318, 473, 4319,  10331, 15473, 10332,  \n10333, 10334, 6048,  22854, 10335, 15882,  10325, 8746, 8740,  \n6020, 8745, 10336,  10337, 10055, 4638,  7645, 9506, 8191,  \n4768, 10342, 4654,  5039, 10344, 7558,  10346, 9563, 10347,  \n8225, 8208, 8747,  10351, 10352, 10353,  7241, 1397, 1398,  \n10362, 4196, 10363,  924, 7268, 7204,  10357, 9567, 8788,  \n8788, 9567, 8782,  7293, 7951, 7952,  10369, 9571, 9572,  \n1415, 22011, 10371,  5266, 5265, 1426,  10375, 10376, 15936,  \n8783, 9567, 9597,  10379, 10380, 10381,  10382, 10383, 10384,  \n8226, 9595, 8777,  10389, 10393, 10390,  8829, 8783, 9598,  \n10389, 1124, 10393,  9617, 9595, 8243,  8015, 8016, 2454,  \n9607, 7692, 9605,  4722, 5912, 22298,  8252, 10402, 7720,  \n2650, 4305, 15083,  10217, 10406, 10407,  8839, 9617, 6736,  \n10409, 10410, 10411,  3377, 660, 2429,  7272, 756, 16466,  \n10420, 890, 10421,  10423, 10424, 3989,  10427, 4528, 10428,  \n10429, 10430, 10431,  9605, 8812, 9653,  9655, 9632, 10435,  \n9632, 9655, 8851,  8832, 8851, 9652,  10439, 10440, 10441,  \n8832, 9653, 8812,  6956, 8900, 8899,  8864, 10450, 10447,  \n8870, 10451, 8864,  2226, 3550, 5715,  438, 10453, 1527,  \n10454, 2466, 10455,  9670, 8865, 10447,  8864, 10447, 8865,  \n614, 6985, 10459,  8268, 11235, 10451,  11235, 7741, 10460,  \n6905, 9707, 6906,  10460, 7741, 10461,  8278, 10461, 7741,  \n10468, 10461, 8278,  8284, 8865, 9670,  10468, 8278, 9688,  \n9671, 8294, 8284,  10473, 9688, 8898,  10475, 10473, 8898,  \n10475, 8903, 10478,  13639, 3874, 3873,  5470, 10479, 7018,  \n10476, 8313, 8294,  10478, 8903, 8309,  10467, 10485, 3557,  \n7756, 7755, 10486,  10487, 13917, 10488,  10489, 8933, 10484,  \n8319, 8313, 10484,  8933, 8319, 10484,  1676, 5417, 7140,  \n8578, 10495, 10496,  8942, 8933, 10494,  8947, 10491, 8309,  \n10492, 10501, 10493,  7262, 8933, 8942,  8741, 10503, 5703,  \n8341, 10508, 8947,  10511, 10512, 10513,  10514, 10515, 3580,  \n10519, 3714, 6177,  10520, 10379, 10381,  10532, 10533, 10534,  \n8633, 15649, 3631,  9751, 10524, 8967,  3161, 10543, 10544,  \n10545, 5523, 2184,  10546, 10547, 10548,  10551, 8979, 8356,  \n9784, 8967, 10524,  10565, 10566, 10567,  8356, 10569, 10551,  \n10569, 8356, 8998,  10575, 10576, 9784,  1203, 1202, 9759,  \n10576, 9006, 9784,  10569, 8998, 9037,  10569, 9037, 10582,  \n7070, 2848, 10583,  10584, 10585, 10586,  10576, 9053, 9006,  \n4415, 4363, 4416,  13898, 10594, 5664,  10597, 2707, 10598,  \n10603, 10604, 1232,  10582, 9037, 9834,  5275, 364, 18775,  \n16322, 10607, 10608,  10609, 10610, 9834,  652, 5407, 6513,  \n5616, 3227, 4203,  1548, 20644, 10614,  10606, 10615, 9066,  \n10618, 10619, 10620,  7289, 9882, 6351,  10630, 18411, 10631,  \n9850, 9935, 10609,  9696, 10231, 10640,  2051, 4625, 10641,  \n10644, 10645, 7434,  8902, 7684, 10648,  10615, 9886, 9066,  \n6548, 6978, 6979,  10659, 10660, 5919,  10662, 10663, 10052,  \n10665, 9941, 9886,  10671, 9088, 9941,  9160, 9088, 10671,  \n10680, 10681, 684,  9093, 9108, 9146,  4387, 5231, 1144,  \n7943, 6898, 5878,  6393, 6849, 9179,  6386, 7331, 10678,  \n5989, 4609, 10691,  10692, 10693, 5906,  6372, 11455, 10696,  \n10698, 4894, 4893,  10699, 9797, 10700,  613, 4119, 612,  \n10709, 10710, 10711,  9106, 3159, 2007,  5856, 10712, 10713,  \n4082, 8809, 10701,  14658, 687, 10714,  5955, 20667, 6180,  \n9200, 10678, 7331,  10636, 10718, 10719,  732, 10413, 10414,  \n9901, 9160, 10706,  9108, 9901, 10705,  9108, 10705, 10721,  \n10721, 9146, 9108,  706, 5882, 10725,  9973, 9146, 9996,  \n9973, 9158, 9146,  9935, 9907, 10726,  16526, 10731, 10732,  \n9146, 10721, 9996,  9143, 10734, 10735,  6773, 10737, 6774,  \n5876, 13622, 3047,  10726, 9907, 10002,  10760, 10742, 10743,  \n10744, 6431, 10003,  10745, 6613, 23408,  3841, 10748, 12716,  \n10751, 10752, 1150,  10753, 10754, 19269,  3311, 4842, 4841,  \n10011, 9973, 9996,  8426, 6432, 10744,  2895, 10763, 2894,  \n10011, 9996, 10787,  9817, 15320, 6771,  8187, 18657, 1371,  \n10778, 10779, 10006,  10778, 10006, 10011,  14994, 10780, 10781,  \n10002, 10006, 10779,  10788, 2974, 10789,  7898, 8450, 10030,  \n10030, 10043, 7904,  1202, 1201, 1232,  10798, 10799, 5545,  \n7982, 9736, 4942,  7432, 11383, 10803,  10810, 13747, 20584,  \n8590, 8237, 9156,  3673, 4787, 10814,  10816, 7949, 2442,  \n8476, 9250, 10050,  10819, 4263, 7489,  5028, 10827, 10889,  \n10071, 8496, 10059,  7955, 10832, 6114,  10833, 9275, 10071,  \n9275, 10833, 10085,  10837, 1931, 3857,  10838, 10839, 1258,  \n5357, 5356, 5645,  7961, 10096, 10091,  18759, 4066, 4065,  \n10101, 6640, 10106,  6550, 15717, 12928,  10104, 10106, 7972,  \n9306, 8528, 10853,  656, 655, 5503,  10861, 7748, 10862,  \n10863, 7999, 8561,  10864, 10853, 10865,  10853, 10864, 9306,  \n7976, 7977, 6318,  7235, 7234, 10867,  1920, 13418, 10870,  \n10877, 10878, 10879,  9324, 9341, 9329,  3678, 8773, 9253,  \n10893, 9339, 10153,  4296, 10894, 20161,  9341, 10892, 10149,  \n10149, 10899, 8605,  13861, 4758, 10901,  10154, 10902, 10153,  \n774, 14195, 1727,  11680, 10173, 8073,  10910, 2046, 1734,  \n10909, 9359, 9362,  10909, 9362, 10168,  10168, 10170, 10914,  \n10915, 10914, 10170,  8070, 10173, 10916,  10917, 10916, 10173,  \n10919, 16942, 10920,  9377, 10915, 10170,  10929, 6147, 19082,  \n18800, 10930, 10931,  10915, 9377, 10943,  8035, 5872, 5871,  \n10121, 10935, 10936,  10943, 9377, 9384,  8070, 10916, 10192,  \n303, 10940, 10941,  3157, 10947, 10948,  10949, 10943, 10950,  \n9384, 9399, 10943,  6840, 10963, 10966,  8293, 10968, 10969,  \n10210, 10970, 9399,  10971, 15769, 5936,  10974, 9410, 10201,  \n6993, 9293, 9294,  10975, 8669, 8675,  10976, 5489, 7488,  \n4604, 3472, 10983,  10984, 9069, 10985,  9417, 8669, 10975,  \n10226, 11004, 11000,  11008, 10694, 9279,  18032, 8162, 5763,  \n11014, 555, 557,  17160, 3670, 11018,  11001, 11009, 11000,  \n3135, 11019, 4752,  9426, 11000, 11009,  9426, 11009, 10252,  \n9870, 11025, 11026,  11028, 11029, 11030,  9768, 11029, 11028,  \n10272, 9447, 8140,  7231, 2419, 3704,  10258, 9426, 10252,  \n11048, 9460, 10258,  385, 11049, 384,  11048, 11053, 9460,  \n11055, 11056, 9484,  9460, 11053, 9463,  11053, 11059, 9463,  \n24631, 5210, 5211,  11062, 7560, 8164,  9463, 9482, 7600,  \n9463, 11059, 9482,  11067, 11068, 20044,  6494, 5793, 2149,  \n6282, 11071, 11072,  18575, 6688, 7165,  19139, 11074, 11075,  \n11076, 11077, 11078,  4334, 11079, 11080,  9503, 9506, 10322,  \n11095, 11096, 11097,  11099, 11100, 11101,  11102, 11103, 11104,  \n8187, 8626, 13850,  6446, 2863, 11109,  8747, 8746, 10343,  \n11111, 11112, 11113,  8216, 9506, 7645,  15596, 11123, 11124,  \n5830, 8907, 2952,  8225, 8747, 9538,  11141, 8216, 8770,  \n9501, 4390, 18717,  9332, 11135, 6523,  9169, 11142, 9170,  \n11143, 9567, 10357,  11146, 11147, 11148,  11134, 10357, 8788,  \n9538, 9552, 8787,  11154, 5244, 11155,  11162, 11163, 11164,  \n1506, 11168, 11169,  11141, 8770, 8777,  8777, 9595, 10394,  \n9617, 11174, 9595,  9595, 11174, 10394,  6157, 8256, 11175,  \n11177, 9607, 9605,  9607, 10402, 8252,  4233, 4532, 14523,  \n8839, 7720, 10402,  3289, 8538, 3290,  11183, 9632, 9598,  \n11186, 10402, 9607,  8133, 17616, 11190,  11177, 9605, 11194,  \n8579, 11198, 11199,  21856, 3858, 11200,  24005, 13543, 11205,  \n11206, 11207, 11208,  11210, 22571, 11211,  10429, 11212, 10430,  \n4561, 11213, 3687,  9653, 11194, 9605,  11218, 9311, 1241,  \n11219, 2112, 9465,  16369, 11225, 344,  11231, 9670, 10447,  \n9749, 2234, 2233,  7708, 8459, 6238,  10451, 10450, 8864,  \n16520, 11234, 15015,  9811, 7283, 11238,  9732, 7929, 16401,  \n11241, 15446, 15887,  10014, 4112, 16560,  9670, 11231, 9671,  \n6363, 6362, 1207,  9671, 11965, 10472,  10460, 10461, 11253,  \n11253, 10461, 10468,  11255, 10468, 9688,  10473, 11255, 9688,  \n8294, 9671, 10472,  10476, 8294, 10472,  5634, 9631, 4039,  \n10478, 8309, 10491,  11278, 11279, 11280,  4367, 11285, 8696,  \n7589, 11291, 3440,  10489, 10494, 8933,  12840, 10491, 10508,  \n10491, 8947, 10508,  11294, 19585, 20056,  22671, 11119, 7388,  \n4652, 4651, 11297,  8950, 8949, 10508,  11298, 9889, 965,  \n11302, 11303, 11304,  672, 3443, 16669,  1292, 18746, 11311,  \n2560, 2756, 10259,  20101, 11317, 11318,  9056, 9055, 2875,  \n3314, 11326, 588,  6072, 6071, 19306,  18521, 20068, 15501,  \n19928, 12215, 11340,  11342, 11343, 11344,  10575, 9784, 11332,  \n11348, 5634, 4039,  11356, 10569, 10582,  11358, 11357, 10575,  \n10576, 10575, 11357,  2020, 4709, 11359,  11360, 2953, 11361,  \n11364, 9388, 4935,  394, 11366, 11367,  11372, 11373, 11374,  \n9834, 11356, 10582,  10606, 9053, 10576,  12871, 11377, 1110,  \n10606, 10576, 11357,  9066, 9053, 10606,  11379, 11380, 11381,  \n17071, 7189, 13406,  9834, 9850, 10609,  7042, 17837, 7043,  \n9882, 11389, 6351,  9120, 6351, 11389,  11343, 11342, 10984,  \n11849, 11393, 6467,  11394, 11395, 7059,  11400, 25158, 11401,  \n11404, 7305, 9914,  24786, 9232, 11406,  11409, 11410, 7574,  \n9914, 6386, 10678,  11415, 11416, 8918,  3906, 1038, 3907,  \n11419, 12100, 8874,  10665, 9886, 10615,  11425, 9941, 10665,  \n2392, 15200, 5062,  11432, 3354, 3355,  11433, 7868, 9515,  \n10686, 9941, 11425,  9941, 10686, 10671,  11435, 11436, 11437,  \n10671, 11442, 9160,  11445, 11446, 8126,  9527, 1647, 6173,  \n11447, 8203, 4474,  15161, 6312, 1250,  1709, 11449, 12103,  \n6750, 14494, 11453,  9160, 11442, 10706,  10705, 9901, 10706,  \n10726, 11431, 9935,  10737, 897, 6774,  11465, 2939, 11466,  \n11472, 9200, 9205,  2721, 11473, 11474,  6873, 11475, 6674,  \n11478, 11479, 7302,  6432, 6431, 10744,  11476, 3627, 3912,  \n11485, 10963, 8003,  3811, 11486, 3810,  4181, 3955, 15280,  \n9645, 5286, 11489,  20812, 8328, 20313,  4764, 23979, 11496,  \n11497, 3592, 1456,  7875, 11519, 7876,  11562, 11500, 11501,  \n11431, 10726, 10002,  11506, 10705, 11507,  11508, 15248, 5693,  \n1491, 3307, 3308,  11509, 11431, 10002,  472, 11517, 11518,  \n7875, 9212, 11519,  11520, 11521, 11522,  2732, 6441, 6442,  \n11523, 16040, 11524,  9737, 21854, 11526,  11527, 6523, 11135,  \n10779, 11509, 10002,  11529, 11530, 15453,  11531, 11532, 11533,  \n3879, 11534, 11535,  11538, 7003, 7004,  9214, 8426, 10806,  \n11546, 11536, 8470,  11536, 9212, 8470,  10847, 21404, 10846,  \n10778, 10011, 10787,  10087, 11552, 3350,  11557, 17738, 3975,  \n8450, 10050, 11559,  8450, 11559, 10030,  6043, 5785, 11561,  \n13264, 11562, 14101,  10043, 11546, 8470,  11563, 11181, 7952,  \n7369, 11567, 1059,  11568, 10737, 6773,  1396, 11569, 4218,  \n18274, 787, 7340,  11571, 11546, 10043,  10779, 10778, 11573,  \n11578, 10047, 9214,  10806, 11578, 9214,  11579, 10050, 9250,  \n11580, 19228, 5890,  11040, 11581, 10317,  11588, 2994, 2807,  \n10047, 11589, 10059,  11578, 11589, 10047,  10059, 11589, 10071,  \n10232, 3146, 11593,  10071, 11589, 10833,  9250, 6114, 10832,  \n6285, 2099, 9979,  625, 18473, 11600,  1575, 829, 18797,  \n11597, 9250, 10832,  10833, 11601, 10085,  10935, 7787, 10936,  \n11609, 9464, 20014,  4180, 4976, 15143,  10101, 10096, 7961,  \n11234, 11613, 3628,  3331, 10836, 19901,  8528, 11601, 12446,  \n8528, 10085, 11601,  8528, 12446, 11617,  3994, 11245, 1198,  \n8528, 11617, 10853,  9107, 5563, 11619,  10104, 7972, 9303,  \n11376, 11623, 11624,  1777, 11625, 7474,  11617, 10865, 10853,  \n478, 8894, 11248,  12065, 11632, 2438,  11633, 11401, 1459,  \n10864, 10865, 11631,  8706, 11605, 11635,  11634, 8561, 10118,  \n8960, 23629, 8959,  11637, 9866, 3146,  17047, 11639, 6878,  \n6235, 10530, 10529,  9731, 11640, 10549,  3940, 3374, 3941,  \n11631, 11638, 10864,  11641, 10864, 11638,  11641, 9306, 10864,  \n11646, 19950, 11647,  11650, 1980, 1981,  11649, 9324, 11641,  \n1912, 1911, 11652,  8560, 11653, 10118,  11649, 11654, 9324,  \n11653, 8560, 9339,  9324, 11654, 9341,  2156, 11192, 11657,  \n10054, 10056, 17159,  11658, 22413, 11659,  10892, 9341, 11654,  \n9222, 11003, 12632,  4857, 11666, 11667,  3669, 5569, 11668,  \n11669, 2194, 2195,  10899, 10149, 10892,  11673, 11674, 1565,  \n8605, 10899, 11676,  8605, 11676, 10154,  11677, 11678, 3998,  \n10154, 11676, 10902,  11680, 9359, 10909,  10168, 10914, 11685,  \n11685, 10909, 10168,  11688, 11689, 19976,  11691, 11692, 11693,  \n11696, 10858, 11697,  9392, 7547, 10192,  6586, 11698, 3291,  \n10949, 10915, 10943,  11701, 7426, 9486,  11702, 11703, 11704,  \n4513, 2097, 4603,  11710, 10949, 10950,  10943, 9399, 10950,  \n11712, 11713, 11714,  11715, 11710, 10950,  11719, 11720, 11721,  \n9399, 10970, 11715,  9399, 11715, 10950,  443, 14776, 6029,  \n11723, 17563, 11724,  11722, 10201, 10193,  11726, 11727, 11728,  \n11729, 10970, 9417,  10210, 9417, 10970,  11732, 11733, 4880,  \n11129, 1973, 11741,  11742, 9059, 6412,  13305, 8675, 9410,  \n9069, 2727, 11745,  11748, 8165, 8166,  19070, 11750, 11751,  \n11746, 11001, 11000,  11746, 11000, 11004,  10661, 1895, 11753,  \n10228, 11749, 10226,  11754, 9676, 11755,  10769, 8931, 9613,  \n10228, 9434, 11749,  11758, 11759, 17196,  2553, 11760, 15713,  \n1256, 10260, 11761,  21185, 6886, 15966,  11778, 11779, 11780,  \n10820, 7443, 5081,  11790, 8468, 11997,  11219, 11791, 4871,  \n7176, 11792, 11793,  11794, 7694, 8827,  17456, 5688, 11798,  \n10272, 8140, 10279,  11803, 11804, 11805,  10252, 11048, 10258,  \n7613, 10293, 10279,  19938, 11786, 16197,  5743, 3753, 3754,  \n2385, 8240, 2384,  7703, 11816, 11817,  18011, 11311, 6499,  \n17451, 11821, 11822,  4472, 11058, 10005,  6781, 11824, 11324,  \n1883, 1884, 11827,  2122, 3797, 11829,  11831, 11832, 11833,  \n11834, 11823, 10293,  11398, 11840, 11399,  11842, 3413, 3412,  \n10312, 9482, 11059,  11846, 4857, 11667,  10313, 10303, 8723,  \n4334, 11080, 11851,  11423, 11852, 14789,  1622, 1291, 4352,  \n3802, 377, 7892,  11850, 8740, 10312,  1674, 5348, 18071,  \n4999, 11853, 7382,  9503, 10322, 10313,  1089, 11855, 11856,  \n11850, 10325, 8740,  10325, 11850, 10343,  12755, 11860, 540,  \n6365, 10321, 11861,  10325, 10343, 8746,  1064, 1063, 6868,  \n8327, 11866, 8328,  3287, 4267, 3286,  11875, 10789, 11876,  \n11877, 6617, 11878,  5034, 11879, 11880,  1271, 11885, 11886,  \n7439, 13620, 7440,  11890, 11891, 4627,  9567, 11143, 11907,  \n13403, 11143, 10357,  7359, 7358, 1484,  11134, 8788, 9552,  \n12717, 9552, 9538,  1501, 4078, 8848,  11913, 4341, 5120,  \n11915, 6858, 11916,  9567, 11907, 9597,  11919, 11920, 11201,  \n9598, 9597, 11183,  11927, 9632, 11183,  11928, 9617, 8839,  \n12234, 10599, 11929,  11930, 11931, 4994,  9607, 11177, 11186,  \n8839, 10402, 11928,  10416, 9632, 11927,  9483, 1008, 4532,  \n4892, 11940, 7114,  11941, 709, 4878,  4878, 709, 708,  \n9632, 10416, 10435,  11947, 11948, 11949,  3071, 11530, 11950,  \n5636, 8099, 2481,  11953, 9652, 9655,  11956, 9652, 11953,  \n9653, 9652, 11956,  9653, 11958, 11194,  11953, 11231, 11956,  \n11961, 5687, 8482,  11962, 9980, 11963,  11956, 11958, 9653,  \n11953, 11965, 11231,  11956, 10447, 10450,  11231, 10447, 11956,  \n10450, 10451, 11967,  11231, 11965, 9671,  850, 9051, 610,  \n11969, 11970, 11971,  11958, 11956, 10450,  11235, 11967, 10451,  \n6871, 6870, 1138,  3701, 11973, 2180,  11974, 11630, 11975,  \n11978, 11235, 10460,  11977, 11235, 11978,  2113, 11982, 9175,  \n7946, 8441, 2531,  8823, 16791, 5061,  11978, 10460, 11253,  \n6555, 7421, 14027,  11255, 11253, 10468,  1044, 1043, 10138,  \n11990, 11991, 11992,  10475, 11988, 10473,  11993, 3648, 4927,  \n11994, 6437, 20966,  15462, 12000, 12001,  12003, 12004, 15030,  \n12009, 7820, 7683,  17190, 10464, 10465,  10476, 10484, 8313,  \n1699, 1698, 18999,  12015, 17210, 12016,  12022, 11457, 12023,  \n12025, 12026, 12027,  1070, 12028, 12029,  12030, 4006, 12031,  \n12039, 1238, 8795,  3693, 4236, 12040,  537, 12043, 12044,  \n2443, 4385, 6077,  5842, 11051, 3730,  12049, 12050, 12051,  \n12055, 12056, 17280,  12059, 8678, 9381,  12064, 6218, 1247,  \n23938, 12065, 867,  12068, 12069, 12070,  7967, 9112, 5998,  \n9751, 11319, 12075,  9751, 12075, 12077,  4999, 12080, 11853,  \n9751, 12077, 10524,  8979, 10551, 29620,  11280, 12086, 9611,  \n12088, 9294, 12089,  9784, 10524, 11332,  3313, 17073, 17260,  \n8527, 22064, 491,  4291, 6059, 5315,  10551, 10569, 10571,  \n5060, 12792, 1184,  12109, 12110, 10574,  11332, 11358, 10575,  \n12112, 12113, 12114,  12122, 11357, 11358,  845, 9520, 8714,  \n12123, 11356, 9834,  6335, 12130, 12131,  10650, 12132, 12133,  \n12683, 5683, 5682,  12136, 10606, 11357,  12122, 12136, 11357,  \n1888, 1887, 2400,  12141, 10606, 12136,  12148, 12197, 12149,  \n12152, 12149, 12153,  8632, 5995, 5996,  12149, 12155, 12148,  \n4444, 329, 330,  4651, 9319, 1590,  9120, 12168, 7825,  \n5412, 8176, 5413,  5061, 9208, 17134,  12153, 12149, 12197,  \n12174, 11127, 12175,  12176, 12177, 12178,  10606, 12141, 11397,  \n513, 1876, 8472,  11010, 12189, 11973,  2465, 22822, 2466,  \n10615, 10606, 11397,  9179, 6849, 9118,  12193, 6467, 11393,  \n1700, 13686, 5047,  11404, 9882, 7305,  2125, 9810, 12799,  \n11413, 12197, 12198,  12153, 11413, 11412,  13421, 5738, 1729,  \n12152, 11412, 12200,  12152, 12153, 11412,  12207, 929, 928,  \n11413, 12153, 12197,  12214, 12200, 11412,  12216, 4787, 10109,  \n11414, 10609, 9935,  9914, 10678, 12218,  4622, 4621, 12220,  \n12202, 10615, 11397,  9468, 4022, 4023,  11859, 12227, 16472,  \n12197, 12219, 12198,  11412, 11413, 12214,  12231, 15783, 12232,  \n2877, 3119, 12233,  11414, 9935, 11431,  12236, 11531, 11533,  \n2915, 6791, 10602,  10403, 12238, 18820,  10176, 10891, 12241,  \n3758, 2609, 4447,  18204, 11272, 5711,  12248, 12249, 4911,  \n9200, 11461, 10678,  12252, 2588, 12253,  10073, 8419, 14836,  \n12198, 12219, 12242,  12256, 12214, 12257,  6039, 12260, 11489,  \n17363, 12263, 10380,  10686, 12264, 10671,  4615, 5207, 13012,  \n12265, 7256, 7257,  10255, 2143, 8868,  12242, 11413, 12198,  \n5630, 6783, 12254,  12214, 11413, 12257,  3279, 5516, 4188,  \n11442, 13022, 10706,  12273, 12274, 23770,  12242, 12219, 12278,  \n12257, 11413, 12242,  12287, 7174, 4686,  5718, 4652, 5913,  \n4891, 7113, 12292,  10825, 7462, 8807,  12302, 6976, 17161,  \n12303, 17161, 6976,  10706, 11507, 10705,  12305, 12306, 12307,  \n12311, 9205, 7876,  7876, 11519, 12311,  12312, 12313, 8110,  \n8426, 10744, 10806,  10721, 10705, 11506,  3704, 22290, 21680,  \n6611, 10044, 6404,  11506, 9996, 10721,  10787, 9996, 11506,  \n11519, 9212, 12326,  12327, 12328, 12329,  12332, 8306, 4168,  \n12333, 12334, 7670,  12335, 10537, 1016,  12336, 12337, 6481,  \n12326, 9212, 11536,  2946, 10268, 8249,  10169, 1215, 11986,  \n12348, 13574, 12316,  12353, 12354, 12355,  12364, 11536, 11546,  \n12347, 11536, 12364,  3161, 13227, 10543,  10030, 11559, 11571,  \n10043, 10030, 11571,  12374, 3547, 12375,  12376, 967, 12377,  \n12380, 7232, 12699,  10806, 12344, 11578,  3703, 6727, 2360,  \n6043, 11561, 17309,  12387, 12388, 10152,  10779, 12386, 12352,  \n5188, 12391, 5189,  20645, 12393, 8007,  3337, 10499, 5015,  \n5848, 5862, 12396,  10050, 11579, 11559,  10779, 11573, 12405,  \n10833, 11589, 12409,  10563, 4460, 7444,  6116, 4820, 12418,  \n12386, 10779, 12405,  13808, 11579, 11597,  11597, 11579, 9250,  \n12409, 12424, 10833,  12427, 5617, 5618,  12432, 12405, 11573,  \n7764, 12433, 8847,  10833, 12424, 11601,  10832, 7955, 10092,  \n1094, 4261, 5316,  12446, 11601, 12424,  6231, 3939, 11797,  \n11468, 19447, 10601,  10092, 10091, 10096,  9658, 8088, 2612,  \n12445, 12446, 12424,  10096, 10101, 10106,  12487, 5814, 6816,  \n11617, 12446, 12449,  9637, 12456, 14879,  12463, 11617, 12449,  \n12466, 12467, 4834,  12472, 12473, 12474,  12463, 10865, 11617,  \n12477, 5725, 5724,  11631, 12463, 12478,  9303, 7999, 10863,  \n7245, 897, 896,  12463, 11631, 10865,  12485, 18320, 12486,  \n3180, 12487, 6816,  8561, 11634, 10863,  8024, 20711, 12490,  \n7717, 3228, 7000,  1546, 2580, 11178,  11631, 12496, 12497,  \n10772, 10773, 12498,  4456, 8269, 1195,  10118, 12500, 11634,  \n12501, 12497, 12496,  2731, 11610, 3551,  12502, 12503, 7457,  \n12504, 11286, 11287,  12506, 8082, 12507,  12497, 11638, 11631,  \n12512, 12513, 12501,  12513, 12497, 12501,  12513, 11638, 12497,  \n12516, 6754, 6755,  2082, 12521, 12522,  12523, 2802, 12904,  \n12513, 11641, 11638,  3286, 5617, 12427,  12513, 11649, 11641,  \n12531, 11654, 11649,  12532, 3028, 1583,  12533, 12534, 12535,  \n12536, 11054, 12537,  11653, 9339, 10893,  1018, 13145, 5973,  \n12540, 12541, 8442,  10892, 12539, 10899,  10153, 10902, 12546,  \n12549, 11676, 10899,  11676, 12551, 10902,  10909, 11685, 11680,  \n8129, 17683, 28689,  12558, 12557, 10173,  11680, 12556, 10173,  \n12558, 10173, 12556,  12560, 11130, 8625,  15697, 16809, 6782,  \n12557, 10917, 10173,  10967, 10989, 5390,  12567, 10914, 10915,  \n22914, 4133, 3675,  12444, 12572, 12573,  2097, 12579, 4603,  \n4290, 6131, 6132,  12587, 11710, 11715,  12587, 12586, 11710,  \n9028, 12592, 11153,  12602, 11269, 10782,  16479, 12603, 538,  \n12604, 11465, 11466,  11094, 373, 6410,  12610, 10974, 10201,  \n12611, 12612, 12613,  9994, 6939, 6938,  1618, 12617, 6035,  \n2995, 12618, 12619,  12620, 12621, 3560,  12624, 11004, 10226,  \n12627, 3681, 12628,  9430, 13906, 12629,  12624, 10226, 11749,  \n11957, 6342, 12633,  12636, 12637, 2251,  11001, 11746, 11762,  \n12636, 12641, 12637,  12642, 12643, 20799,  11763, 11749, 9434,  \n9447, 11763, 9434,  1509, 5325, 12645,  14313, 12115, 12648,  \n1836, 15730, 12649,  12653, 13243, 14293,  9316, 10012, 9315,  \n12657, 10272, 10279,  1665, 14826, 12659,  2842, 12666, 12667,  \n16431, 3458, 12669,  11009, 12665, 10252,  8801, 3559, 1286,  \n10293, 11823, 10279,  13795, 9771, 12676,  10252, 12673, 11048,  \n12673, 10252, 12665,  3149, 20358, 2304,  12684, 18950, 8371,  \n4313, 14153, 8567,  10303, 11834, 10293,  11059, 12697, 10312,  \n12698, 11844, 10313,  10313, 11844, 10303,  8581, 2573, 2572,  \n11850, 10312, 12697,  8418, 12704, 12705,  13948, 12712, 12713,  \n5879, 2398, 6924,  12717, 9538, 10343,  8747, 10343, 9538,  \n6372, 572, 2679,  12722, 12678, 12723,  2282, 15299, 3465,  \n3621, 12729, 12730,  2698, 8023, 5347,  11134, 13403, 10357,  \n2947, 2946, 14606,  11134, 9552, 12717,  10829, 4422, 10093,  \n12738, 11308, 1523,  8777, 12740, 11141,  8777, 10394, 12740,  \n1847, 8330, 411,  9617, 11928, 11174,  10402, 13445, 11928,  \n9364, 1834, 12017,  11186, 11177, 12751,  12752, 2416, 2417,  \n11194, 12751, 11177,  12756, 11186, 12751,  12757, 10435, 10416,  \n4127, 12760, 12761,  7009, 11428, 12763,  12764, 8512, 16284,  \n12765, 11953, 10435,  11953, 9655, 10435,  1680, 9431, 12169,  \n11965, 11953, 12765,  11194, 11958, 12766,  11967, 12766, 11958,  \n12524, 3086, 11129,  10450, 11967, 11958,  14885, 11797, 12776,  \n12775, 12774, 4253,  11967, 11235, 11977,  1950, 12783, 12784,  \n12787, 1841, 5272,  12788, 12789, 11978,  12794, 997, 3358,  \n12795, 12796, 8199,  11255, 12793, 11253,  12799, 9810, 15281,  \n2681, 8020, 2682,  10473, 12793, 11255,  10374, 701, 700,  \n12805, 4512, 8860,  10478, 11988, 10475,  10484, 10476, 12806,  \n12812, 12813, 12814,  10484, 12815, 10489,  12818, 10659, 21073,  \n12820, 6358, 12821,  10491, 12822, 10478,  6232, 2641, 1638,  \n12825, 18221, 12826,  8292, 12827, 12828,  10494, 10489, 12829,  \n12830, 12831, 12832,  12840, 12822, 10491,  12143, 3356, 7975,  \n12840, 10508, 13496,  12841, 2167, 7948,  6812, 6811, 12845,  \n8949, 13496, 10508,  12853, 12854, 12855,  474, 11624, 12860,  \n10362, 5619, 12862,  8189, 12865, 12866,  12444, 12872, 9711,  \n11858, 12227, 11859,  12874, 6821, 1960,  9038, 3790, 11880,  \n19143, 8095, 3698,  12314, 10250, 452,  12077, 12878, 10524,  \n12878, 11332, 10524,  10340, 17377, 12886,  11777, 17913, 12889,  \n12890, 3342, 3343,  10164, 7127, 15262,  11332, 12878, 12891,  \n6263, 11563, 12894,  732, 12895, 1530,  10571, 10569, 11356,  \n12899, 11358, 11332,  12891, 12899, 11332,  11711, 12869, 12910,  \n12911, 2770, 8481,  11358, 12899, 12915,  12916, 12917, 12918,  \n12919, 12155, 12149,  12149, 12922, 12919,  12152, 12922, 12149,  \n12122, 12915, 12140,  17231, 12924, 14942,  6384, 2266, 5805,  \n12122, 11358, 12915,  1600, 12932, 1601,  12136, 12122, 12141,  \n11058, 4472, 4086,  29485, 12935, 12936,  7724, 7725, 12937,  \n9933, 5963, 12938,  3845, 2844, 13747,  7825, 12168, 12944,  \n12200, 12945, 12152,  7936, 12438, 11424,  12953, 2458, 12954,  \n12945, 12939, 12152,  12122, 12140, 12141,  11397, 12141, 12202,  \n9179, 9118, 12944,  12961, 11404, 9914,  12962, 11079, 12429,  \n12148, 12963, 12197,  9295, 12965, 12966,  15301, 6928, 13487,  \n10935, 5531, 12968,  3195, 12969, 4205,  12970, 4778, 12583,  \n9914, 12218, 12961,  12197, 12972, 12219,  12214, 12973, 12200,  \n4220, 12974, 3100,  12975, 12973, 12214,  11461, 12218, 10678,  \n12978, 18259, 7844,  12985, 7313, 9179,  10021, 7988, 12498,  \n1790, 10707, 1791,  12992, 11425, 10665,  11504, 11505, 12994,  \n10734, 12801, 10735,  12999, 12219, 13000,  12702, 2798, 13001,  \n13004, 13005, 11996,  13006, 7838, 13734,  13008, 12810, 13009,  \n13010, 15708, 13011,  13164, 8276, 13013,  3968, 13015, 11783,  \n11442, 10671, 12264,  12219, 12999, 12278,  13025, 8833, 8369,  \n16756, 1799, 8866,  12257, 12242, 12278,  1817, 13878, 13487,  \n10706, 13022, 13028,  8275, 1454, 3741,  8065, 13033, 5811,  \n5550, 5551, 4194,  6105, 13034, 7931,  8012, 8013, 12290,  \n12278, 13035, 12257,  12256, 12257, 13035,  13036, 9966, 417,  \n12720, 13038, 12719,  13040, 9153, 20574,  4071, 7931, 13042,  \n12117, 13043, 5309,  13045, 11431, 11509,  13395, 13046, 9728,  \n5909, 8046, 15940,  13051, 13049, 11507,  11506, 11507, 13049,  \n13057, 13058, 12326,  2421, 13059, 2422,  11506, 13049, 13063,  \n12352, 11509, 10779,  3970, 3969, 13069,  12347, 12326, 11536,  \n9296, 13074, 13075,  11355, 12104, 13082,  13083, 12344, 12356,  \n12185, 12873, 3022,  13084, 6174, 20684,  16105, 16106, 1343,  \n8646, 13086, 7942,  13088, 13089, 5475,  13090, 12347, 12364,  \n10787, 11506, 13063,  13091, 3826, 13092,  13097, 13098, 14385,  \n10487, 10488, 13099,  9419, 13102, 6013,  11546, 11571, 13104,  \n12364, 11546, 13104,  13063, 13106, 10787,  13107, 12344, 13083,  \n2338, 7804, 6703,  13111, 4919, 13112,  8442, 10223, 17417,  \n919, 8290, 2174,  13114, 10632, 13115,  919, 2174, 918,  \n13117, 13118, 13119,  9791, 12390, 13120,  12308, 13121, 9717,  \n11514, 19926, 7106,  11578, 13107, 11589,  13107, 11578, 12344,  \n804, 13125, 13126,  3909, 20504, 13127,  11513, 13129, 11514,  \n12409, 11589, 13107,  13132, 12293, 13133,  13106, 13134, 10787,  \n10778, 10787, 13134,  12424, 12409, 13140,  6892, 8156, 13141,  \n13142, 8646, 11669,  12424, 13140, 12445,  12409, 13107, 13140,  \n13148, 11597, 10832,  11573, 10778, 13134,  13152, 14032, 11612,  \n13154, 17833, 13155,  4552, 12394, 1878,  12195, 16278, 13160,  \n13134, 13161, 12432,  2208, 13162, 13163,  13164, 8277, 8276,  \n10092, 10096, 13168,  7066, 3524, 4790,  13171, 16463, 3124,  \n11573, 13134, 12432,  12451, 12452, 4456,  13179, 23157, 12230,  \n4067, 4068, 10942,  13183, 10106, 10104,  3008, 14843, 9582,  \n12463, 12449, 13186,  12463, 13186, 12478,  2728, 13193, 5707,  \n13194, 14219, 13195,  9303, 10863, 10104,  13199, 13200, 13201,  \n8433, 1341, 13205,  13206, 12496, 12478,  11631, 12478, 12496,  \n10690, 8142, 10674,  2423, 10912, 8364,  13208, 12501, 12496,  \n4762, 5015, 13212,  5280, 12518, 12578,  4568, 13224, 13225,  \n12512, 13226, 12513,  12513, 13226, 12531,  12513, 12531, 11649,  \n10543, 13227, 13232,  11654, 12539, 10892,  12539, 11654, 12531,  \n12546, 10893, 10153,  2891, 13236, 13237,  10902, 12551, 12546,  \n13245, 12556, 11680,  11685, 13245, 11680,  13247, 3709, 12172,  \n13250, 5594, 5595,  10914, 13252, 11685,  1375, 412, 781,  \n1035, 2707, 10597,  13263, 16425, 1879,  13252, 10914, 12567,  \n3888, 13264, 3887,  4772, 4771, 21131,  13267, 13268, 8532,  \n13269, 21347, 2588,  7487, 7426, 13270,  20298, 13273, 4281,  \n13274, 7334, 13275,  8058, 13276, 5425,  13280, 12567, 10915,  \n10949, 13280, 10915,  13280, 10949, 12586,  7663, 13281, 13349,  \n13282, 13283, 4815,  11710, 12586, 10949,  13285, 1846, 8378,  \n13286, 13287, 9392,  10192, 13286, 9392,  11722, 10193, 13288,  \n10970, 11729, 11715,  13293, 13294, 15061,  13295, 10201, 11722,  \n13298, 8675, 13305,  10975, 11729, 9417,  13299, 4126, 13300,  \n10201, 13295, 12610,  9218, 13302, 12787,  10975, 8675, 13298,  \n10300, 13309, 5477,  2453, 8015, 2454,  10974, 13305, 9410,  \n9013, 9012, 5481,  12630, 13313, 11004,  11762, 11746, 13316,  \n13317, 4955, 7038,  13313, 11746, 11004,  12630, 11004, 12624,  \n13322, 13323, 7625,  864, 14763, 863,  13327, 13322, 7625,  \n5154, 4798, 13328,  3781, 13334, 1109,  4033, 20404, 7754,  \n4811, 4812, 4184,  11001, 11762, 11009,  1088, 13341, 13342,  \n3558, 3557, 10485,  10777, 3636, 1798,  853, 10782, 13343,  \n9441, 13347, 21221,  3816, 11658, 11659,  12839, 13351, 16265,  \n12657, 10279, 11823,  13354, 12665, 11009,  11834, 14051, 11823,  \n13361, 1955, 13362,  12665, 13363, 12673,  11844, 11834, 10303,  \n15462, 13368, 13369,  13364, 3503, 13370,  13371, 12673, 13363,  \n13372, 2414, 10851,  11053, 11048, 13371,  5431, 9545, 5432,  \n13374, 4881, 13375,  12697, 11053, 13377,  12697, 11059, 11053,  \n12697, 13377, 11850,  1890, 1889, 13379,  4831, 13381, 5219,  \n5931, 5930, 1226,  12698, 10313, 10322,  3053, 10808, 13384,  \n11850, 12707, 10343,  9506, 13388, 10322,  21741, 13394, 13395,  \n13388, 9506, 15802,  12707, 12717, 10343,  951, 13724, 953,  \n9506, 8216, 15802,  12910, 12270, 11711,  13405, 13406, 9196,  \n9459, 9353, 13413,  13414, 11134, 12717,  3735, 8221, 8222,  \n13426, 13427, 13428,  13431, 13432, 12642,  11183, 9597, 13434,  \n13438, 12740, 10394,  11928, 13438, 11174,  22357, 5222, 12310,  \n13442, 9995, 7592,  13438, 10394, 11174,  13443, 10444, 9345,  \n11186, 13445, 10402,  12675, 10564, 10563,  11186, 12756, 13445,  \n9127, 5997, 13448,  5948, 10058, 5236,  13449, 4532, 1008,  \n9402, 6346, 9380,  8798, 302, 6851,  5935, 13453, 5933,  \n13454, 4000, 3749,  12766, 12751, 11194,  13458, 20629, 4898,  \n12766, 11967, 13460,  13461, 13462, 10051,  11965, 12765, 13463,  \n13460, 11967, 11977,  11977, 11978, 13460,  11978, 12789, 13460,  \n1555, 13465, 12835,  11253, 12788, 11978,  13466, 12789, 12788,  \n3607, 13467, 10077,  5658, 9735, 5659,  12793, 12788, 11253,  \n13466, 12788, 12793,  13471, 1836, 15494,  13463, 12807, 10472,  \n13472, 6353, 11490,  11988, 12793, 10473,  13478, 7641, 4466,  \n12807, 10476, 10472,  10476, 12807, 13480,  9742, 13485, 13486,  \n13487, 1818, 1817,  13489, 6349, 13490,  13491, 10478, 12822,  \n12829, 10489, 12815,  12434, 725, 6719,  11002, 10037, 10029,  \n3832, 9374, 17969,  12782, 6335, 4435,  13502, 17825, 7091,  \n3776, 3232, 18698,  7460, 13518, 9921,  4708, 6227, 11365,  \n7239, 1987, 13521,  13522, 12077, 12075,  11992, 13984, 13525,  \n14196, 13526, 13527,  12077, 13522, 13523,  29620, 10551, 12879,  \n2345, 21226, 13530,  11129, 16602, 12524,  4691, 6813, 10550,  \n10571, 12879, 10551,  8737, 7539, 12559,  3340, 13537, 12074,  \n5985, 11994, 8652,  818, 13540, 3932,  13543, 13544, 13545,  \n13536, 12891, 12878,  19221, 3803, 10172,  12123, 13549, 11356,  \n4383, 13553, 4384,  16015, 13554, 4446,  12907, 15863, 16718,  \n13563, 9003, 13561,  12123, 9834, 10610,  13569, 6315, 13570,  \n4158, 8581, 2572,  13574, 13575, 13576,  13315, 17518, 5586,  \n13580, 12899, 12891,  10991, 13576, 10992,  12155, 12919, 13577,  \n4718, 3491, 1248,  12919, 12922, 13585,  12922, 12152, 13585,  \n9791, 9790, 12390,  12155, 13589, 12148,  13591, 11390, 1427,  \n12939, 13585, 12152,  17019, 7151, 13606,  713, 3390, 8674,  \n12963, 12972, 12197,  13610, 13611, 10289,  4933, 13612, 17455,  \n12140, 13613, 13614,  10401, 13616, 13617,  13618, 18019, 13619,  \n9118, 7825, 12944,  13625, 8705, 7957,  12537, 11054, 3822,  \n12627, 12628, 4507,  12945, 12200, 12973,  7650, 13637, 13937,  \n4933, 17455, 4934,  12140, 12915, 13613,  13642, 4269, 1136,  \n7798, 2278, 13644,  5271, 13647, 2848,  926, 6337, 18794,  \n7078, 13651, 13652,  12140, 12202, 12141,  14240, 10119, 4505,  \n16463, 14848, 13656,  6487, 8168, 4407,  2150, 2149, 13660,  \n13662, 10086, 13663,  16542, 13664, 3545,  10615, 12202, 13675,  \n10615, 13675, 10665,  13000, 12219, 12972,  4599, 13686, 13687,  \n10087, 3350, 13688,  13675, 12992, 10665,  10127, 12051, 12050,  \n13684, 12975, 12214,  9740, 5981, 6588,  3840, 19944, 18655,  \n1660, 13697, 15196,  12999, 13000, 13698,  13701, 13702, 5194,  \n13703, 6120, 13704,  12577, 628, 13705,  3827, 3826, 13708,  \n4492, 13710, 13711,  11442, 12264, 13022,  5335, 13712, 14262,  \n1105, 1106, 4544,  11472, 11461, 9200,  13713, 13714, 19707,  \n13716, 13717, 13718,  13684, 12214, 12256,  3556, 13720, 4568,  \n12264, 13721, 13022,  953, 13724, 954,  9897, 12680, 8115,  \n11507, 10706, 13028,  13045, 11414, 11431,  12728, 13734, 13735,  \n13736, 10670, 11568,  3907, 1038, 1039,  3777, 18698, 1805,  \n12999, 13741, 12278,  2379, 2381, 13743,  13741, 13035, 12278,  \n9368, 10821, 13747,  4633, 11219, 4871,  13746, 12256, 13035,  \n674, 13754, 13755,  13757, 7899, 13758,  20472, 7087, 6994,  \n7362, 5096, 5667,  13759, 9601, 9616,  13051, 11507, 13028,  \n13590, 6316, 3829,  13761, 10806, 10744,  11519, 13058, 12311,  \n13779, 12344, 13761,  13283, 13780, 13662,  13049, 13051, 13063,  \n5327, 5846, 13782,  11509, 12352, 13777,  12356, 12344, 13779,  \n577, 17088, 7041,  13058, 11519, 12326,  10356, 13783, 13784,  \n13785, 13786, 17021,  6471, 8524, 13787,  6207, 13790, 6208,  \n12326, 13791, 13057,  12326, 12347, 13791,  5051, 18076, 13553,  \n21695, 8218, 4647,  13791, 12347, 13090,  1114, 13804, 7787,  \n21249, 10969, 13805,  4628, 4279, 4629,  11571, 11559, 13808,  \n11571, 13808, 13104,  13090, 12364, 13104,  8305, 8306, 22249,  \n13107, 13083, 13815,  11559, 11579, 13808,  16276, 8652, 12411,  \n3143, 18211, 13821,  13819, 8435, 13820,  13090, 13822, 13791,  \n12386, 13797, 12352,  13140, 13107, 13815,  13134, 13106, 14464,  \n13832, 13833, 13140,  13841, 3934, 13842,  16925, 9527, 1322,  \n13833, 12445, 13140,  11597, 13148, 13847,  11452, 13848, 11409,  \n11597, 13847, 13808,  13134, 14464, 13849,  12405, 13840, 12386,  \n10682, 10683, 13852,  13856, 13181, 13833,  13181, 12445, 13833,  \n7715, 9356, 9052,  13181, 12446, 12445,  13858, 2394, 1358,  \n15807, 5507, 1949,  13169, 10832, 10092,  10832, 13169, 13148,  \n10134, 1310, 15617,  13860, 12434, 9277,  5760, 13862, 6647,  \n4539, 9860, 9861,  7657, 13867, 7658,  12432, 13869, 12405,  \n13869, 13840, 12405,  12449, 12446, 13871,  13871, 12446, 13181,  \n5148, 5149, 1929,  13183, 13874, 10106,  10096, 10106, 13874,  \n10096, 13874, 13168,  13134, 13876, 13161,  13161, 13879, 12432,  \n13879, 13869, 12432,  3457, 10269, 3868,  13879, 13161, 13886,  \n4612, 812, 21402,  13186, 12449, 13871,  13889, 3207, 3476,  \n10104, 13890, 13183,  13891, 13183, 13890,  13890, 10104, 10863,  \n13186, 13892, 12478,  13208, 12496, 13206,  13763, 1956, 3273,  \n18653, 17287, 11323,  13208, 13905, 12501,  10118, 11653, 12500,  \n13905, 12512, 12501,  13911, 13912, 4409,  13913, 12512, 13905,  \n11269, 9761, 6343,  13226, 12512, 13913,  12539, 12531, 13226,  \n20683, 15047, 12969,  10893, 13920, 11653,  12357, 13699, 13813,  \n7670, 13923, 20338,  21456, 11185, 12677,  10893, 12546, 13926,  \n13239, 10899, 12539,  6521, 13928, 13929,  13931, 11676, 12549,  \n11676, 13931, 12551,  14585, 12556, 13245,  10133, 10134, 3427,  \n8129, 8128, 17683,  12556, 13934, 12558,  11089, 11848, 9357,  \n13252, 13245, 11685,  13938, 13939, 13269,  8724, 13945, 2038,  \n17434, 7168, 7167,  4107, 2706, 17291,  5325, 14120, 12645,  \n13951, 9438, 5071,  3128, 13004, 3127,  13264, 14101, 4053,  \n12247, 6895, 13088,  11344, 13954, 11342,  10192, 13958, 13286,  \n13287, 10193, 9392,  13961, 3391, 5485,  10172, 13884, 13963,  \n13964, 13965, 8519,  9644, 13966, 10528,  13967, 11715, 11729,  \n7954, 13968, 14982,  13969, 13965, 13964,  4946, 10676, 10425,  \n7899, 13757, 8265,  320, 13423, 13971,  13298, 13305, 13306,  \n10975, 13298, 11729,  11722, 13980, 13295,  11722, 13288, 13980,  \n3223, 6994, 7087,  10934, 8736, 9135,  16461, 18745, 13983,  \n13984, 13985, 1323,  13986, 13100, 4122,  13305, 10974, 12610,  \n13988, 13989, 11005,  13295, 13980, 13991,  13993, 1779, 986,  \n13991, 13980, 13998,  17345, 13999, 14000,  17213, 14001, 6980,  \n13991, 12610, 13295,  14003, 12250, 12956,  814, 17299, 18066,  \n12630, 13991, 13998,  14004, 12630, 12624,  2449, 2450, 9461,  \n2441, 5772, 2961,  11749, 14010, 12624,  11409, 11952, 14011,  \n11749, 11763, 14010,  13231, 11626, 20086,  14020, 9019, 9018,  \n19576, 14021, 14022,  13316, 14023, 11762,  9447, 13336, 11763,  \n11762, 14023, 14031,  12657, 14033, 10272,  11762, 14031, 13354,  \n6540, 3131, 15470,  14040, 12996, 14041,  15142, 14043, 12905,  \n11823, 14039, 12657,  14045, 9446, 14046,  13354, 11009, 11762,  \n12022, 12023, 13939,  14053, 12665, 13354,  6427, 6428, 14054,  \n8493, 8842, 1289,  14055, 14056, 14954,  935, 14059, 4540,  \n11834, 11844, 14060,  11476, 4813, 3627,  14064, 14065, 14066,  \n11048, 12673, 13371,  13887, 14070, 14071,  11844, 12698, 14060,  \n9336, 14073, 7829,  13363, 12665, 14053,  2653, 14074, 14075,  \n14077, 14078, 6190,  13377, 13371, 14076,  13377, 11053, 13371,  \n2494, 14080, 2495,  12707, 13377, 14076,  11850, 13377, 12707,  \n10322, 13388, 12698,  14084, 14085, 14086,  10034, 14088, 14089,  \n2489, 14092, 2039,  14093, 15126, 2450,  13414, 12717, 13400,  \n14096, 10565, 10567,  13414, 13403, 11134,  6017, 8701, 6015,  \n12717, 12707, 13400,  14099, 10178, 4170,  11143, 14722, 11907,  \n6156, 8172, 14103,  14722, 11143, 13402,  13402, 11143, 13403,  \n11435, 6063, 14105,  15802, 11141, 14109,  15802, 8216, 11141,  \n9597, 11907, 13434,  7222, 5624, 2881,  14114, 11141, 12740,  \n13434, 14115, 11183,  4487, 14116, 7103,  14117, 1188, 1265,  \n12740, 13438, 14118,  12505, 5014, 14415,  15773, 7418, 14126,  \n3134, 1271, 1272,  14127, 14128, 14129,  15852, 7078, 7077,  \n2670, 20880, 14131,  7771, 2542, 8314,  12751, 14130, 12756,  \n12765, 10435, 12757,  18181, 10990, 6655,  9347, 10994, 1478,  \n14135, 12751, 12766,  14135, 12766, 13460,  13460, 12789, 14141,  \n14148, 13466, 12793,  6888, 14149, 9905,  10472, 11965, 13463,  \n14151, 13200, 9409,  14152, 14148, 12793,  11988, 14152, 12793,  \n9305, 7301, 4464,  14158, 14152, 11988,  10478, 14158, 11988,  \n6115, 6960, 14159,  9822, 12737, 9821,  9448, 7524, 7394,  \n10478, 13491, 14158,  10476, 13480, 12806,  14162, 11088, 14163,  \n14164, 11858, 11859,  7068, 7730, 14167,  14168, 14169, 14170,  \n1050, 12884, 12876,  10494, 14178, 8942,  8942, 14178, 8949,  \n11317, 14180, 11318,  8949, 14178, 13496,  8336, 12346, 9042,  \n14185, 7979, 14186,  1468, 1469, 14187,  6229, 14189, 1237,  \n12213, 14191, 11678,  14198, 12848, 4545,  14199, 14200, 14201,  \n12878, 12077, 13523,  13523, 13522, 14206,  9313, 5575, 1783,  \n14206, 14208, 13523,  14210, 14211, 5771,  13523, 14208, 13536,  \n4496, 14213, 4497,  14210, 14214, 14211,  18877, 14215, 18201,  \n13523, 13536, 12878,  5469, 12119, 10285,  10571, 11356, 14212,  \n11356, 13549, 14212,  1411, 3744, 14645,  14232, 7870, 12823,  \n12891, 14234, 13580,  12891, 13536, 14234,  14239, 14240, 14241,  \n14245, 14244, 12919,  14244, 13577, 12919,  12509, 11062, 13772,  \n14245, 12919, 13585,  12547, 14255, 4537,  7712, 20358, 645,  \n18275, 15969, 3895,  13589, 12963, 12148,  1569, 12090, 14256,  \n13585, 12939, 14258,  12915, 12899, 13580,  9894, 7378, 3495,  \n10178, 14263, 5085,  12945, 14258, 12939,  21038, 1623, 6867,  \n13011, 14266, 14267,  13824, 14268, 8692,  12972, 12963, 14259,  \n9265, 14269, 4692,  12159, 10361, 12160,  12790, 11102, 11104,  \n14264, 12915, 13580,  14274, 19574, 14275,  14276, 12168, 9120,  \n14276, 9120, 11389,  7805, 6026, 6025,  11389, 9882, 14288,  \n14289, 14290, 14291,  4956, 14293, 3368,  11998, 11767, 12668,  \n11404, 12961, 14296,  2338, 11772, 857,  16263, 14297, 14298,  \n1554, 1054, 11130,  14264, 13613, 12915,  2322, 4623, 13972,  \n7392, 5803, 5804,  12202, 12140, 13614,  14310, 12051, 10128,  \n12973, 12975, 14303,  1430, 14315, 14316,  14117, 1265, 6408,  \n4762, 14325, 5451,  20961, 3168, 7877,  14328, 14038, 4697,  \n4780, 9830, 2546,  8071, 12722, 20926,  12985, 6879, 7313,  \n14333, 8296, 2057,  14334, 14335, 8483,  14337, 7679, 14338,  \n2419, 2420, 6382,  14340, 19600, 2072,  3413, 5272, 8287,  \n14343, 7717, 7001,  7977, 14346, 6318,  4688, 14349, 14350,  \n10003, 7867, 6879,  11892, 14355, 3627,  3994, 1198, 14357,  \n12264, 10686, 11425,  14364, 7639, 17618,  4263, 14365, 5092,  \n1858, 1959, 13605,  3694, 14366, 14367,  2752, 14369, 2750,  \n13749, 12999, 13698,  12536, 12537, 1346,  4583, 14372, 4584,  \n9251, 14376, 9252,  14378, 1483, 4828,  14379, 10725, 5882,  \n13721, 14381, 13022,  14383, 14384, 20298,  13097, 14385, 4997,  \n12311, 14386, 9205,  7766, 8643, 4806,  13749, 13741, 12999,  \n13684, 12256, 13746,  4385, 17684, 11330,  13022, 14381, 14387,  \n13028, 13022, 13760,  4102, 14389, 14390,  12321, 10780, 14393,  \n14394, 8606, 14393,  11515, 13211, 11516,  14395, 14387, 14381,  \n3885, 10911, 7109,  7142, 2921, 8066,  13760, 13022, 14387,  \n10720, 965, 966,  7698, 10044, 6611,  866, 12090, 7346,  \n13204, 13725, 14405,  13760, 13051, 13028,  7654, 5554, 5555,  \n7941, 4974, 3027,  1677, 14407, 2754,  14408, 14395, 14403,  \n6655, 2997, 601,  14395, 13760, 14387,  701, 3421, 700,  \n7354, 9536, 9537,  361, 362, 6163,  10826, 8052, 14415,  \n12762, 14419, 14420,  2713, 3220, 7879,  13051, 13760, 14413,  \n14426, 13051, 14413,  14426, 13063, 13051,  12344, 10806, 13761,  \n14408, 14430, 14395,  14433, 14434, 14435,  13073, 13777, 12352,  \n5226, 18091, 1789,  13303, 13304, 9571,  14413, 14395, 14430,  \n899, 900, 14445,  13792, 14177, 13793,  5439, 13246, 17488,  \n14446, 2370, 2369,  13106, 13063, 14426,  13791, 14449, 13057,  \n14464, 13106, 15053,  14453, 8428, 8427,  8750, 8749, 14454,  \n14319, 14320, 9955,  8179, 3585, 7518,  14456, 14457, 14458,  \n5001, 5000, 7796,  6117, 14466, 6116,  1371, 945, 14467,  \n13832, 13140, 13815,  14472, 13104, 13808,  14475, 11902, 10410,  \n21109, 14340, 14477,  13350, 14090, 355,  13797, 12386, 14468,  \n14481, 2547, 9830,  14472, 13808, 13847,  13104, 14472, 13090,  \n14488, 13856, 13833,  12147, 14997, 13165,  14485, 13090, 14472,  \n1137, 14494, 14495,  1775, 1354, 1774,  11574, 14982, 7116,  \n8724, 14726, 13945,  13134, 13849, 13876,  14501, 13871, 13181,  \n4919, 4918, 14503,  13168, 13874, 14504,  11467, 9584, 10033,  \n13169, 10092, 13168,  7570, 9769, 11587,  9861, 18956, 4539,  \n13876, 14509, 13886,  11730, 5399, 10640,  7227, 14510, 7228,  \n6200, 14516, 3118,  3150, 17035, 3966,  14519, 13182, 11731,  \n16387, 14522, 12942,  13876, 13886, 13161,  5066, 19177, 14524,  \n11337, 1027, 14525,  17661, 14529, 7261,  13879, 14527, 13869,  \n9238, 9237, 3815,  9484, 14531, 11055,  13871, 14514, 13186,  \n13183, 14504, 13874,  14514, 14535, 13186,  13213, 14541, 14542,  \n5760, 9081, 14543,  2110, 18063, 14440,  13892, 13206, 12478,  \n5165, 14547, 14548,  10863, 14546, 13890,  11634, 14546, 10863,  \n5718, 7882, 4652,  14551, 13208, 13206,  14546, 11634, 12500,  \n6701, 5607, 14555,  3533, 1519, 14556,  14563, 14564, 14565,  \n13226, 14562, 12539,  6322, 7925, 3698,  13926, 13920, 10893,  \n2785, 12079, 14570,  10655, 8000, 12283,  2451, 10128, 1170,  \n12539, 13925, 13239,  12549, 10899, 13239,  15173, 12549, 13239,  \n7378, 5304, 7379,  14582, 14583, 14584,  12556, 14585, 13934,  \n14592, 602, 9194,  707, 2969, 9001,  10916, 10917, 14591,  \n10916, 13958, 10192,  14602, 14603, 15609,  12586, 14601, 13280,  \n14606, 2946, 9218,  12586, 12587, 14601,  14609, 12587, 11715,  \n14610, 11715, 13967,  14613, 7134, 14614,  14615, 11808, 7144,  \n13980, 13288, 14628,  9582, 1771, 1772,  12610, 13991, 13996,  \n12610, 13996, 13305,  13306, 13305, 13996,  14630, 14631, 6972,  \n13980, 14628, 13998,  6074, 6075, 7723,  13996, 13991, 14004,  \n21725, 10292, 14638,  14640, 13313, 14628,  13998, 13313, 12630,  \n14628, 13313, 13998,  12523, 736, 12797,  3252, 3251, 529,  \n1695, 14642, 14643,  14004, 13991, 12630,  12624, 14010, 14004,  \n3108, 4796, 19375,  9871, 1797, 12887,  7276, 6933, 13556,  \n11763, 14647, 14010,  1792, 1793, 14650,  14023, 13316, 14653,  \n9114, 12676, 14654,  16126, 8314, 2542,  12082, 19002, 11011,  \n14659, 3624, 14660,  14661, 14662, 7255,  14664, 14665, 14666,  \n8092, 14670, 8093,  14428, 14671, 14672,  14033, 13336, 10272,  \n13336, 9447, 10272,  12538, 1730, 18367,  14035, 629, 2694,  \n11912, 5242, 14677,  14678, 6247, 13955,  5066, 14524, 7828,  \n14680, 14681, 7831,  14685, 9638, 9639,  9982, 17797, 8383,  \n11823, 14051, 14686,  1528, 1527, 2285,  14687, 12395, 11015,  \n14689, 2229, 14676,  10225, 14690, 12896,  13895, 13894, 20177,  \n14691, 1574, 14692,  14060, 15263, 11834,  7958, 14699, 9042,  \n14703, 14704, 17977,  8697, 11039, 14705,  15269, 14060, 12698,  \n5133, 2018, 2017,  13371, 13363, 14076,  15269, 12698, 13388,  \n14707, 11682, 6708,  13363, 12707, 14076,  3511, 1965, 14710,  \n13400, 12707, 14711,  14715, 6892, 1068,  20054, 19249, 14717,  \n14718, 14719, 14720,  20244, 7271, 1813,  4740, 13259, 6036,  \n4218, 4219, 5962,  15075, 14726, 6418,  16703, 14727, 9027,  \n18015, 3436, 9568,  11907, 14729, 14730,  11141, 14114, 14109,  \n14730, 13434, 11907,  4197, 14734, 14309,  1991, 14739, 12147,  \n14740, 14741, 12001,  9669, 2403, 10157,  11927, 11183, 14115,  \n4672, 8363, 15867,  11928, 13445, 13438,  8811, 2668, 6939,  \n12741, 7909, 618,  14747, 14748, 17744,  14746, 10416, 11927,  \n7280, 6584, 18474,  14749, 14750, 17807,  12756, 14751, 13445,  \n9305, 4399, 7301,  14557, 6246, 4890,  14757, 14758, 14759,  \n14731, 1080, 14318,  14762, 5840, 12046,  10728, 1393, 14764,  \n10727, 13191, 14765,  10727, 10728, 14764,  14135, 14768, 12751,  \n12751, 14768, 14130,  8700, 6017, 14769,  14141, 14135, 13460,  \n1739, 9252, 12250,  14144, 14141, 12789,  14784, 28350, 9240,  \n14144, 12789, 13466,  13424, 14153, 4153,  12807, 13463, 14779,  \n14792, 7893, 14793,  14794, 12806, 13480,  1817, 1816, 10111,  \n14796, 4779, 1013,  3308, 12298, 12299,  14797, 3655, 5001,  \n12815, 10484, 12806,  14803, 10068, 14804,  14028, 9290, 14805,  \n14812, 1017, 1018,  18749, 1259, 2845,  14815, 8141, 22931,  \n11376, 11624, 14816,  17155, 995, 14821,  14822, 14823, 5305,  \n14827, 14828, 20594,  1681, 1680, 14830,  14831, 14832, 14028,  \n12259, 6097, 12258,  14845, 7729, 8026,  14835, 14834, 6582,  \n14166, 6067, 14846,  12879, 10571, 14212,  14848, 13526, 6279,  \n14852, 3096, 14853,  1512, 14855, 11304,  13536, 14208, 14856,  \n3255, 3876, 9368,  12119, 14860, 10285,  6932, 14867, 18569,  \n14868, 13549, 12123,  10157, 14869, 9669,  14870, 2359, 18260,  \n13536, 14856, 14234,  14875, 14876, 6945,  13589, 12155, 14882,  \n12155, 13577, 14882,  14883, 14884, 12164,  14885, 25069, 11796,  \n14795, 10905, 10906,  13938, 6467, 12022,  3303, 22065, 3302,  \n14069, 14892, 6689,  7814, 14893, 2510,  13585, 14254, 14245,  \n14900, 13580, 14234,  12963, 13589, 15419,  14576, 14903, 14904,  \n14259, 12963, 14905,  13585, 14258, 14254,  14258, 14907, 14254,  \n20934, 9813, 10209,  5674, 14909, 14910,  10604, 9759, 1202,  \n18795, 9419, 4238,  8892, 8891, 12699,  13580, 14900, 14917,  \n4838, 3395, 3396,  14917, 14264, 13580,  6859, 6054, 11916,  \n14921, 1958, 13816,  8892, 12699, 14922,  14923, 11637, 14924,  \n5808, 5809, 5560,  12945, 14925, 14258,  10703, 14717, 5940,  \n527, 4431, 968,  14927, 11277, 13994,  6768, 10052, 10051,  \n7968, 14931, 2941,  9882, 11404, 14288,  11404, 14296, 14288,  \n12972, 14259, 14932,  14928, 14925, 12945,  14264, 14917, 14935,  \n7320, 14938, 6453,  7800, 14945, 14946,  14928, 12973, 14947,  \n19012, 14948, 21326,  14950, 13613, 14264,  19051, 10977, 14956,  \n14947, 12973, 14303,  14264, 14935, 14950,  13000, 12972, 14932,  \n2350, 8987, 4844,  19327, 6600, 11110,  14961, 18758, 14962,  \n1153, 7108, 7843,  14963, 1978, 2365,  14966, 13737, 11181,  \n13000, 14932, 13698,  14968, 8588, 14969,  14970, 14020, 13416,  \n14971, 13614, 13613,  14972, 13505, 14973,  12202, 13614, 14967,  \n8742, 14251, 14979,  13614, 14971, 14967,  13675, 12202, 14967,  \n14967, 12992, 13675,  1275, 964, 14695,  12975, 13684, 14977,  \n6791, 1931, 10837,  18907, 10732, 10731,  14985, 8883, 14292,  \n14988, 4173, 14989,  10770, 3898, 2287,  14990, 13749, 13698,  \n14992, 23222, 2139,  14993, 13061, 16489,  14986, 12992, 14967,  \n14641, 5620, 6717,  14998, 11472, 14386,  7291, 15001, 15002,  \n15004, 12953, 3191,  11989, 15005, 4868,  6873, 6872, 15006,  \n10744, 10003, 13761,  14386, 11472, 9205,  3804, 1549, 3203,  \n14403, 15007, 15013,  15007, 14403, 14381,  13721, 15007, 14381,  \n3200, 15014, 3199,  15016, 14386, 12311,  9372, 450, 13064,  \n2412, 8052, 18086,  10148, 12451, 4455,  866, 15018, 4724,  \n13741, 15019, 15020,  13741, 15020, 13035,  7048, 15021, 331,  \n14408, 14403, 15013,  13328, 15023, 9621,  15020, 13746, 13035,  \n15024, 13746, 15020,  14223, 2616, 594,  15026, 15027, 522,  \n14395, 14381, 14403,  15033, 12281, 3033,  651, 15034, 652,  \n12708, 415, 12709,  3043, 12771, 3099,  15032, 14430, 14408,  \n13760, 14395, 14413,  924, 8044, 13824,  15032, 15037, 14430,  \n899, 14445, 11512,  3369, 10439, 10441,  15050, 15051, 8113,  \n14426, 14413, 15053,  2218, 16324, 21806,  14391, 1870, 14021,  \n3540, 3015, 8789,  14430, 15056, 15053,  14430, 15053, 14413,  \n13849, 15053, 15056,  13106, 14426, 15053,  21503, 7280, 11942,  \n15058, 2773, 13005,  7029, 7028, 2235,  5838, 5361, 830,  \n4855, 15064, 5929,  15065, 15066, 4136,  12632, 9724, 9223,  \n3136, 6128, 3135,  5228, 5229, 6378,  2324, 15068, 15069,  \n13832, 13815, 13083,  12850, 13629, 2341,  15072, 15073, 15074,  \n14464, 15053, 13849,  15076, 15077, 15078,  15080, 6855, 6656,  \n10227, 11254, 8648,  1538, 15085, 8727,  10583, 18366, 439,  \n14468, 12386, 13840,  13832, 14488, 13833,  13822, 13090, 14485,  \n10728, 6248, 15092,  13822, 14485, 15094,  15084, 13849, 15056,  \n1138, 14494, 1137,  13849, 15084, 13876,  2173, 358, 2172,  \n13325, 12958, 1784,  15101, 5090, 15102,  777, 6598, 17808,  \n13169, 13168, 15105,  15106, 2124, 13436,  13169, 15105, 15107,  \n13169, 14508, 13148,  13169, 15107, 14508,  15108, 11278, 9611,  \n2891, 15109, 13236,  15110, 13847, 14508,  13148, 14508, 13847,  \n14472, 13847, 14485,  1700, 15112, 15113,  15115, 905, 20496,  \n14514, 13871, 15118,  673, 15120, 15121,  15123, 14509, 15084,  \n15084, 14509, 13876,  10247, 3363, 3362,  8957, 2030, 7776,  \n15126, 19545, 589,  15100, 14504, 13183,  6312, 1196, 5372,  \n14884, 14883, 10850,  8402, 15063, 14137,  15128, 13886, 14509,  \n2540, 3584, 13242,  4538, 18934, 15132,  14527, 13879, 13886,  \n15125, 2251, 2253,  13431, 11779, 11778,  14535, 13892, 13186,  \n10672, 18224, 6527,  14527, 13886, 15128,  15140, 14527, 15128,  \n14335, 8048, 15143,  15141, 13206, 13892,  15141, 13892, 14535,  \n10780, 15148, 10781,  13206, 15144, 14551,  13206, 15141, 15144,  \n4838, 1254, 18663,  8316, 15151, 1999,  6218, 9002, 15152,  \n17864, 15157, 15158,  12500, 15154, 14546,  14551, 13905, 13208,  \n15160, 13905, 14551,  3036, 10230, 15161,  5315, 6059, 5316,  \n15162, 15154, 12500,  14438, 9132, 6230,  13913, 13905, 15160,  \n10556, 7572, 10557,  14562, 13913, 14560,  13913, 14562, 13226,  \n9292, 15170, 3371,  19865, 7151, 17019,  14562, 13925, 12539,  \n8056, 14250, 9836,  15173, 13239, 13925,  15176, 15177, 7708,  \n2581, 4219, 2580,  15179, 17304, 5866,  7484, 3650, 21204,  \n6943, 5963, 6942,  15187, 14585, 13245,  15187, 13245, 13252,  \n10213, 2377, 2797,  7024, 5381, 7023,  15190, 15191, 15192,  \n23630, 11465, 13519,  11190, 15195, 8133,  8941, 5348, 14349,  \n14294, 8997, 3838,  10245, 15198, 15199,  16556, 12991, 15201,  \n15202, 13280, 14601,  15204, 723, 15688,  6997, 6996, 15206,  \n14601, 12587, 15205,  15205, 12587, 14609,  14609, 11715, 14610,  \n6016, 15210, 15211,  13298, 15219, 11729,  11729, 15219, 13967,  \n14637, 13996, 14004,  13306, 13996, 14637,  7492, 14217, 5494,  \n14640, 13316, 13313,  5112, 6380, 5113,  14647, 14637, 14004,  \n15233, 15234, 15235,  14640, 14653, 13316,  17843, 11799, 15236,  \n2669, 1800, 16756,  3348, 20552, 15242,  14004, 14010, 14647,  \n2608, 679, 2609,  14032, 13152, 3593,  15250, 14033, 12657,  \n14039, 11823, 14686,  13354, 14031, 14679,  9922, 15262, 6222,  \n11384, 15264, 16389,  11834, 15263, 14051,  10696, 11455, 21250,  \n4550, 15266, 15231,  15263, 14060, 15269,  4374, 4155, 2033,  \n15271, 17232, 8552,  13388, 15272, 15269,  15275, 12707, 13363,  \n7666, 11100, 994,  2185, 4095, 15276,  15275, 14711, 12707,  \n956, 6438, 10419,  5147, 1029, 1028,  14716, 13414, 14711,  \n14711, 13414, 13400,  11907, 14722, 14729,  17360, 10745, 15281,  \n14722, 13402, 15282,  5176, 8229, 5177,  9820, 6759, 15284,  \n12763, 12573, 13923,  9722, 8994, 6201,  13438, 15298, 14118,  \n13438, 13445, 15298,  10425, 15299, 15300,  13487, 383, 15301,  \n6412, 15052, 5945,  7419, 8215, 15302,  14751, 15298, 13445,  \n5646, 15306, 5647,  15309, 4959, 16461,  15310, 12756, 14130,  \n15310, 14751, 12756,  11875, 3088, 10789,  14768, 15310, 14130,  \n4072, 11865, 4073,  9892, 21539, 1086,  14779, 12765, 15318,  \n14768, 14135, 14141,  14779, 13463, 12765,  14768, 14141, 14144,  \n3284, 15324, 12138,  14144, 13466, 14148,  7950, 10191, 1168,  \n14148, 14152, 15323,  15323, 14152, 14158,  15326, 15328, 12807,  \n5627, 635, 7503,  15849, 14158, 13491,  371, 372, 14448,  \n15336, 15331, 15332,  13006, 6198, 7838,  1886, 10339, 3271,  \n15331, 15336, 15337,  13480, 12807, 15328,  2997, 12318, 5279,  \n5073, 8970, 15343,  2980, 5695, 12959,  6362, 8525, 8389,  \n15304, 1293, 1776,  13111, 13112, 15345,  489, 6242, 3126,  \n12806, 15346, 12815,  1326, 1128, 16428,  12829, 15348, 10494,  \n15348, 14178, 10494,  12822, 12840, 15349,  12840, 13496, 15349,  \n2257, 13771, 15355,  10271, 11296, 10965,  14178, 15359, 13496,  \n13496, 15359, 15349,  5581, 5706, 14579,  10825, 15362, 15363,  \n18913, 5525, 10923,  15365, 1641, 1642,  4492, 2781, 2783,  \n3078, 22592, 10522,  5770, 4317, 17914,  10767, 15369, 4665,  \n8185, 8186, 12030,  15373, 15374, 15375,  11122, 15379, 13955,  \n6930, 6929, 3709,  20859, 10962, 15381,  14206, 13522, 15376,  \n15378, 12879, 14212,  15376, 14208, 14206,  1861, 11318, 1862,  \n15384, 4788, 8884,  3923, 15386, 2169,  16866, 14424, 14425,  \n12035, 15400, 16306,  294, 15389, 15390,  10285, 1431, 10286,  \n12343, 15392, 15393,  14619, 8836, 7635,  7667, 15407, 2472,  \n13577, 14244, 15408,  15410, 11101, 16413,  15412, 5258, 12575,  \n14245, 15414, 14244,  1658, 1659, 7287,  2011, 16756, 14231,  \n15428, 15421, 10762,  15424, 14245, 14254,  13883, 5568, 5570,  \n4373, 2605, 15426,  15419, 15420, 12963,  14905, 12963, 15420,  \n6175, 4764, 4961,  15430, 6125, 11504,  3551, 17809, 6441,  \n4191, 4192, 18336,  10609, 14285, 15438,  2105, 23300, 2239,  \n4186, 4185, 7530,  14917, 14900, 15435,  6449, 15440, 15441,  \n12026, 12025, 5567,  14259, 14905, 15990,  12973, 14928, 12945,  \n1212, 17130, 2887,  15447, 15448, 15449,  15989, 15450, 15451,  \n13686, 12072, 13687,  14932, 14259, 15990,  4128, 15371, 15372,  \n15458, 883, 14280,  14917, 15435, 15460,  12001, 10194, 15462,  \n13740, 13739, 23866,  15463, 3788, 3787,  13755, 1770, 674,  \n5185, 15465, 12389,  12403, 2429, 14739,  6912, 4526, 15470,  \n9961, 3764, 9960,  12985, 9179, 12944,  9807, 9808, 21410,  \n15478, 14935, 14917,  15479, 15480, 14022,  15481, 13412, 3710,  \n998, 8754, 2027,  15088, 15482, 15483,  3176, 8692, 3177,  \n1589, 6405, 2492,  15485, 13069, 3969,  15492, 508, 9807,  \n1498, 29025, 12631,  15497, 11461, 11472,  3226, 2519, 2521,  \n10644, 10654, 10645,  15498, 4022, 6806,  11662, 11210, 11211,  \n15499, 17252, 6265,  14303, 12975, 14977,  15500, 15501, 14607,  \n5979, 14469, 14470,  3045, 15504, 15169,  6060, 15505, 1493,  \n15506, 1542, 5332,  15510, 15511, 15512,  14971, 13613, 15502,  \n7952, 11181, 13738,  15516, 3289, 3290,  11425, 12992, 14986,  \n14692, 1574, 16631,  12264, 11425, 14986,  12692, 302, 15522,  \n10536, 13753, 13449,  15523, 7256, 12265,  15526, 15527, 15528,  \n12821, 15529, 12820,  15530, 15531, 13175,  4925, 15535, 15536,  \n13721, 12264, 14986,  2761, 1240, 6119,  3159, 4452, 389,  \n14990, 15538, 13749,  5530, 5529, 5531,  7284, 15543, 8422,  \n8516, 6861, 7147,  6897, 15388, 13655,  13746, 15545, 13684,  \n7851, 8826, 4847,  13749, 15019, 13741,  6726, 15549, 14754,  \n12106, 9641, 10278,  13746, 15551, 15545,  2929, 7409, 15554,  \n12311, 13058, 15016,  1689, 5308, 8599,  3293, 3752, 14129,  \n4935, 13289, 608,  8929, 13969, 9542,  15564, 15565, 13777,  \n12020, 15567, 15568,  12015, 6780, 8221,  15013, 15558, 15032,  \n15032, 14408, 15013,  7859, 15571, 1083,  9045, 5178, 9044,  \n12306, 5384, 12307,  13073, 15564, 13777,  15581, 15582, 15583,  \n14888, 15588, 14889,  15592, 14430, 15037,  12852, 8779, 8781,  \n13073, 12352, 13797,  15592, 15037, 15594,  1829, 9350, 1830,  \n9268, 9934, 2788,  15592, 15056, 14430,  13791, 15597, 14449,  \n13832, 15089, 14488,  15592, 15594, 15599,  15592, 15084, 15056,  \n12521, 17025, 3400,  13919, 13914, 20909,  15087, 15088, 806,  \n15601, 11698, 6586,  13822, 15094, 13791,  15094, 15597, 13791,  \n15599, 15084, 15592,  14468, 13840, 15096,  12131, 12130, 15609,  \n15110, 14485, 13847,  11286, 12504, 2592,  15611, 15612, 15613,  \n13181, 13856, 14501,  15618, 12838, 6164,  6163, 15619, 6164,  \n13168, 14504, 15620,  13168, 15620, 15105,  15622, 8667, 15623,  \n12716, 12727, 3841,  4347, 2275, 15626,  15627, 9407, 15628,  \n15629, 15094, 14485,  9210, 15631, 16308,  9274, 15632, 9273,  \n15633, 8462, 14411,  14501, 15118, 13871,  15634, 15118, 14501,  \n15072, 15074, 12480,  15100, 15620, 14504,  17864, 15158, 5132,  \n5454, 10987, 11388,  15110, 14508, 15624,  15641, 1238, 11070,  \n5622, 14461, 21349,  15599, 15123, 15084,  11796, 8917, 8918,  \n17067, 7380, 1913,  14018, 3399, 14017,  8940, 14549, 15648,  \n6840, 10966, 15652,  15655, 13007, 5976,  14535, 14514, 15118,  \n13183, 13891, 15100,  15123, 15128, 14509,  10230, 15661, 15662,  \n1087, 5980, 1961,  14535, 15664, 15141,  4273, 15670, 4207,  \n13891, 15671, 15100,  4947, 2241, 4948,  17393, 3003, 15674,  \n14551, 15144, 15675,  15678, 883, 12104,  7437, 15681, 9991,  \n15684, 5763, 14536,  15162, 12500, 13920,  12602, 7472, 4332,  \n15687, 5247, 6509,  12500, 11653, 13920,  15692, 11614, 15693,  \n15695, 7243, 2370,  14737, 10522, 14147,  4899, 4822, 3339,  \n4563, 10776, 2425,  19214, 9132, 14438,  3650, 8921, 21204,  \n15173, 13931, 12549,  15707, 13934, 14585,  15709, 15578, 16012,  \n5660, 8205, 3220,  12558, 14591, 12557,  14591, 10917, 12557,  \n15715, 15187, 13252,  14591, 15716, 10916,  13252, 15718, 15715,  \n14594, 12567, 13280,  13958, 10916, 15716,  13252, 12567, 15718,  \n12567, 14594, 15718,  12130, 15721, 15609,  15722, 7919, 15723,  \n5541, 13649, 15407,  15728, 15729, 15730,  7113, 4891, 1156,  \n6273, 6272, 1768,  1661, 8200, 17517,  6403, 6146, 15734,  \n15735, 10331, 15736,  15738, 5655, 15739,  8201, 15741, 15742,  \n10193, 13287, 13288,  15746, 13332, 1528,  15747, 5120, 15748,  \n14610, 13967, 15749,  16822, 14628, 15750,  13288, 13287, 15750,  \n14628, 13288, 15750,  1691, 840, 8179,  13967, 15219, 15749,  \n9357, 15754, 11089,  8475, 14069, 6689,  11668, 5854, 320,  \n14637, 15752, 13306,  10334, 15758, 6048,  15757, 16981, 694,  \n15760, 28400, 15761,  13316, 11746, 13313,  21249, 13805, 8286,  \n15764, 4582, 21649,  9414, 3979, 6211,  15767, 5521, 1243,  \n10742, 443, 10743,  15768, 15769, 15135,  11763, 15765, 14647,  \n15770, 15765, 11763,  15771, 8383, 15772,  15774, 13336, 14033,  \n11675, 8261, 15776,  12854, 12705, 15777,  15778, 4229, 11329,  \n10462, 11382, 8855,  2798, 5772, 2441,  12657, 14039, 15250,  \n7634, 18079, 8038,  15788, 8821, 15789,  14686, 14051, 15787,  \n15790, 3203, 1549,  14051, 15263, 15787,  16289, 15263, 15269,  \n15793, 14053, 13354,  15802, 15272, 13388,  15275, 13363, 14053,  \n15802, 15803, 15272,  1948, 15806, 15807,  8956, 8955, 15809,  \n15810, 7048, 14576,  8076, 4916, 5506,  15812, 15923, 2938,  \n14894, 15813, 12484,  13402, 13403, 14716,  13403, 13414, 14716,  \n14729, 15282, 15814,  14722, 15282, 14729,  1883, 11827, 10100,  \n15816, 10082, 10081,  22765, 15819, 12270,  16794, 14090, 2620,  \n12226, 28816, 26285,  15821, 11927, 14115,  15822, 14746, 11927,  \n15821, 15822, 11927,  5062, 15824, 2393,  15298, 14751, 15313,  \n12757, 10416, 14746,  15313, 14751, 15310,  4442, 15832, 20104,  \n15833, 12765, 12757,  15318, 12765, 15833,  15834, 15310, 14768,  \n15835, 5355, 10655,  15834, 14768, 14144,  14144, 15323, 15834,  \n14779, 15839, 15326,  15323, 14144, 14148,  14346, 7977, 8813,  \n5426, 11895, 15844,  12807, 14779, 15326,  12027, 15847, 13203,  \n15331, 15853, 15854,  15849, 15323, 14158,  9978, 18194, 636,  \n15842, 15850, 15332,  15855, 15856, 13182,  9895, 10199, 2731,  \n15843, 15842, 15332,  15851, 15843, 15332,  15851, 15332, 15331,  \n15859, 8121, 5942,  12273, 15860, 15861,  11769, 2397, 3700,  \n15863, 11471, 6768,  15337, 15865, 15331,  5926, 5464, 5927,  \n15865, 15853, 15331,  7915, 7916, 5942,  15868, 3917, 15136,  \n2420, 2419, 7231,  15850, 15336, 15332,  10889, 14639, 5028,  \n3408, 13897, 3164,  15876, 13480, 15328,  11140, 11139, 15870,  \n15336, 15850, 15869,  15070, 12333, 14985,  15875, 15865, 15337,  \n6508, 6785, 15879,  14794, 13480, 15880,  15880, 13480, 15876,  \n15881, 10427, 10428,  15883, 3579, 15884,  3646, 11270, 3647,  \n11549, 2046, 14126,  15885, 15336, 15869,  10048, 10481, 15733,  \n15888, 15337, 15336,  775, 3279, 4189,  540, 8882, 9746,  \n15875, 15337, 15888,  15336, 15885, 15891,  15891, 15888, 15336,  \n8000, 17473, 2974,  11087, 11088, 14162,  15892, 13491, 12822,  \n7029, 2235, 13732,  15893, 5285, 1410,  13778, 15894, 6832,  \n15895, 15896, 8610,  15348, 15898, 14178,  15359, 14178, 15898,  \n5481, 9012, 5482,  2170, 9089, 20691,  11766, 15901, 22109,  \n15904, 16427, 16430,  15905, 15902, 15903,  15904, 15905, 16427,  \n11042, 8875, 15908,  15905, 15904, 15909,  15912, 15909, 15904,  \n15902, 15905, 15909,  15913, 15902, 15909,  15912, 15904, 15914,  \n15909, 15912, 15915,  15916, 15917, 15466,  8296, 15918, 8295,  \n15913, 15915, 15919,  15913, 15909, 15915,  15920, 15913, 15919,  \n15921, 11686, 1635,  15915, 15912, 15919,  15920, 15919, 15925,  \n15927, 15912, 15914,  15919, 15912, 15927,  15919, 15927, 15924,  \n15919, 15924, 15925,  15928, 8520, 11766,  15159, 14108, 4997,  \n8996, 11242, 15610,  15929, 12801, 12118,  18913, 5899, 5525,  \n3217, 15931, 7824,  15932, 13489, 15933,  4129, 15935, 1316,  \n4649, 14737, 14476,  5945, 11742, 6412,  9876, 5490, 8311,  \n9231, 4165, 15940,  13736, 3477, 2691,  3286, 12427, 548,  \n15641, 6375, 7778,  16041, 15945, 15946,  3888, 4687, 15948,  \n8911, 2019, 8471,  14856, 14208, 15401,  5757, 10750, 6797,  \n14234, 14856, 15401,  12426, 6500, 15955,  11619, 5563, 7314,  \n15957, 10220, 5483,  12652, 13065, 6823,  20966, 6260, 11994,  \n1693, 15963, 18306,  15408, 14244, 15414,  15969, 15970, 15651,  \n15968, 15419, 15967,  9224, 15972, 3196,  13589, 14882, 15419,  \n14882, 15971, 15419,  2924, 15412, 2925,  7200, 7199, 2832,  \n15959, 14882, 13577,  15971, 14882, 15959,  13326, 14668, 14669,  \n12335, 10942, 5787,  13728, 16844, 20247,  15959, 13577, 15408,  \n15424, 15414, 14245,  29737, 15976, 15977,  10610, 15404, 12123,  \n15979, 15980, 15968,  15968, 15980, 15420,  15968, 15420, 15419,  \n15985, 10749, 15986,  14234, 15997, 14900,  14234, 15401, 15997,  \n3819, 4300, 5395,  13851, 8187, 13850,  10610, 10609, 15438,  \n12455, 9206, 6423,  5323, 745, 14019,  14905, 15979, 15990,  \n15991, 13046, 15992,  14900, 15997, 15435,  14905, 15420, 15980,  \n549, 15124, 550,  16001, 16002, 16003,  14258, 14925, 14907,  \n11118, 11119, 8912,  14905, 15980, 15979,  8974, 7469, 8975,  \n11351, 10124, 6843,  14276, 11389, 14288,  14929, 16017, 1087,  \n10609, 11414, 14339,  12168, 16552, 12944,  14285, 10609, 14339,  \n9832, 16024, 5137,  14932, 15990, 15472,  16021, 16020, 12379,  \n9909, 15221, 16027,  16025, 12961, 12218,  15460, 15478, 14917,  \n14935, 15478, 16586,  4348, 19726, 11265,  6440, 14084, 16034,  \n12849, 9905, 12850,  5792, 16037, 5791,  9238, 3815, 1624,  \n7139, 1072, 12885,  14781, 7725, 2896,  15472, 13698, 14932,  \n5483, 2480, 15957,  12033, 10262, 16043,  16044, 16045, 12508,  \n16586, 14950, 14935,  16046, 5250, 5249,  11130, 16050, 1554,  \n15525, 11411, 13627,  13215, 5625, 2710,  13698, 15472, 14990,  \n14303, 14977, 15513,  1752, 17110, 1911,  6867, 1623, 346,  \n10003, 6879, 12985,  15497, 11472, 14998,  15516, 3290, 16053,  \n9122, 6517, 8447,  16060, 12572, 1845,  16751, 12659, 11341,  \n16062, 530, 7385,  13613, 14950, 15502,  3681, 16068, 16069,  \n14977, 13684, 15533,  14977, 15533, 16052,  14971, 17636, 16071,  \n14971, 16071, 14967,  11097, 11073, 12081,  16075, 13721, 14986,  \n7957, 11706, 11705,  1569, 5527, 12090,  13721, 16075, 15007,  \n13777, 16065, 13045,  16076, 16077, 9307,  6576, 4504, 16078,  \n14990, 16061, 15538,  16079, 8889, 7482,  15545, 15533, 13684,  \n16082, 14986, 14967,  3787, 11780, 15463,  6104, 14260, 20008,  \n15007, 15552, 15013,  15007, 16075, 15552,  16084, 7212, 3446,  \n16085, 1131, 19150,  369, 16086, 21118,  12714, 7687, 16469,  \n941, 17799, 2360,  16089, 2878, 18873,  13045, 11509, 13777,  \n15553, 13779, 13761,  13058, 16090, 15016,  15019, 13749, 15538,  \n15024, 15551, 13746,  13455, 9117, 19586,  15552, 15558, 15013,  \n16098, 6316, 13590,  16100, 15020, 15019,  16103, 13322, 13327,  \n16104, 14093, 2450,  4780, 3111, 16054,  9651, 7925, 6321,  \n5748, 2583, 2582,  13380, 10144, 16109,  8381, 11819, 11505,  \n15558, 16110, 15037,  15558, 15037, 15032,  16111, 8858, 2633,  \n15932, 6353, 6352,  16113, 9970, 2281,  16114, 10028, 18355,  \n16116, 21724, 15222,  16118, 16119, 8149,  7206, 11747, 8102,  \n13832, 13083, 12356,  4225, 2269, 8674,  13440, 18571, 10857,  \n7689, 14604, 9344,  13073, 13797, 15564,  9156, 5188, 5189,  \n13832, 12356, 15586,  15594, 15037, 15590,  3525, 1873, 10190,  \n16131, 13832, 15586,  13784, 13222, 16136,  6633, 16137, 1607,  \n16131, 15089, 13832,  16144, 10803, 1214,  14359, 9515, 16145,  \n3272, 4210, 7454,  15089, 13856, 14488,  15607, 13856, 15089,  \n2748, 2749, 7911,  14501, 13856, 15607,  16150, 15597, 15094,  \n13869, 15096, 13840,  11769, 11768, 10755,  16160, 20326, 16161,  \n29756, 29754, 5171,  15107, 15105, 15620,  14508, 15107, 15624,  \n5851, 9470, 5852,  2976, 3974, 15572,  16165, 14331, 11007,  \n15629, 16150, 15094,  16698, 15123, 15599,  13283, 13663, 4815,  \n16167, 15096, 13869,  15118, 15634, 16169,  4815, 779, 762,  \n15171, 8212, 15841,  15118, 15664, 14535,  17668, 16178, 12519,  \n7870, 15487, 7871,  15128, 15123, 16179,  15664, 16182, 15141,  \n7895, 16184, 16185,  16186, 16187, 16188,  13409, 16189, 12417,  \n16182, 15144, 15141,  16192, 13077, 2662,  16195, 10869, 16196,  \n427, 9630, 13636,  13890, 14546, 13891,  15675, 15160, 14551,  \n15673, 14546, 15154,  15162, 16202, 15154,  14560, 15160, 17247,  \n1046, 12884, 1050,  6144, 8492, 7225,  13926, 15162, 13920,  \n22983, 16207, 16208,  14562, 16210, 13925,  12546, 12551, 16212,  \n13925, 16210, 15173,  15178, 16212, 12551,  14129, 3752, 4603,  \n15178, 13931, 16216,  16217, 3343, 3342,  16216, 13931, 16218,  \n15178, 12551, 13931,  13931, 15173, 16218,  4140, 4139, 16223,  \n9042, 1754, 7958,  16224, 16225, 9491,  16226, 15707, 14585,  \n8809, 1626, 8810,  1666, 16228, 8238,  16233, 16234, 14123,  \n18157, 15327, 755,  16236, 16237, 16238,  13473, 13474, 7430,  \n15580, 3365, 16242,  14854, 18831, 785,  18546, 9713, 14747,  \n637, 9119, 21534,  13286, 15731, 13287,  20346, 17338, 5735,  \n12117, 16248, 16249,  14601, 15205, 15202,  13287, 15731, 15750,  \n16250, 16251, 16252,  16255, 14609, 14610,  7730, 16256, 14167,  \n14610, 15749, 16255,  15749, 15219, 16259,  16822, 16260, 14628,  \n15219, 13298, 16262,  14628, 16260, 14640,  16267, 3790, 9039,  \n13306, 15752, 13298,  14647, 15765, 14637,  16271, 16270, 16269,  \n16269, 16270, 14653,  14653, 16270, 14023,  15770, 11763, 13336,  \n18099, 6206, 1694,  6258, 16273, 6502,  8484, 6557, 1553,  \n15770, 13336, 15774,  16275, 11805, 822,  6663, 14284, 16276,  \n14033, 15250, 15774,  14031, 14023, 15780,  12890, 3144, 19597,  \n13489, 16284, 6349,  14518, 14348, 9343,  16285, 15250, 14039,  \n14686, 16285, 14039,  14686, 15787, 16285,  10589, 2865, 14593,  \n16289, 15787, 15263,  844, 843, 3769,  15269, 15272, 16289, 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8466, 10504, 16346,  16348, 16349, 5651,  \n16350, 16351, 9975,  16341, 15842, 15843,  16341, 15843, 16344,  \n16344, 15843, 15851,  15854, 16344, 15851,  5116, 16352, 5117,  \n17468, 16355, 12814,  14105, 6063, 1732,  16359, 16360, 16361,  \n5135, 5134, 22911,  16340, 15323, 15849,  13798, 16365, 16366,  \n15842, 16356, 15850,  8756, 11855, 16370,  15851, 15331, 15854,  \n4302, 15646, 6761,  16371, 4279, 4628,  1673, 12946, 1674,  \n15869, 15850, 16356,  3404, 3405, 3484,  16368, 11938, 11939,  \n14481, 16375, 14317,  16363, 15853, 15865,  16363, 15865, 15328,  \n15326, 16363, 15328,  15849, 13491, 15342,  15328, 15865, 15875,  \n16380, 10387, 16381,  16382, 3758, 1263,  12580, 576, 9266,  \n4243, 16384, 20083,  12395, 14687, 15039,  16385, 16386, 5651,  \n15328, 15875, 15876,  10539, 10540, 8705,  15876, 15875, 15880,  \n3171, 3942, 2339,  4933, 16390, 14418,  11691, 11693, 11237,  \n7729, 14845, 16392,  14145, 5390, 12206,  16377, 15885, 15869,  \n16393, 16394, 13711,  16397, 15875, 15888,  15880, 15875, 16397,  \n16399, 15880, 16397,  16399, 14794, 15880,  16400, 12132, 10650,  \n6534, 5974, 7528,  16401, 1906, 17200,  16404, 15885, 16405,  \n16404, 15891, 15885,  15891, 16397, 15888,  15437, 2502, 13960,  \n15346, 12806, 14794,  12634, 8745, 16124,  16411, 12822, 15349,  \n15892, 12822, 16411,  16407, 15891, 16404,  12815, 15346, 12829,  \n4806, 2520, 2519,  16413, 6126, 16414,  3742, 16415, 17584,  \n22727, 14417, 11998,  16418, 16420, 16423,  7998, 6058, 6217,  \n16420, 16418, 16419,  16420, 16419, 16426,  16423, 16420, 16427,  \n16423, 16427, 15903,  16420, 16426, 16430,  16427, 16420, 16430,  \n16427, 15905, 15903,  1599, 5869, 16227,  8346, 16433, 20792,  \n16432, 15904, 16430,  4682, 10479, 3037,  16434, 16734, 7899,  \n16435, 16436, 16437,  16438, 3799, 3798,  15904, 16432, 15914,  \n16432, 16439, 15914,  5213, 12485, 5212,  6536, 16442, 1931,  \n16443, 15920, 15925,  9163, 8895, 9164,  3993, 3282, 16444,  \n16439, 16446, 15914,  15914, 16446, 15927,  15867, 11664, 1004,  \n16446, 16450, 15927,  15927, 16450, 15924,  15924, 16450, 16451,  \n15924, 16451, 15925,  1401, 6805, 16453,  16454, 16455, 1451,  \n11188, 11189, 6927,  17644, 9321, 16461,  10877, 15778, 13467,  \n3794, 16514, 3793,  1118, 11166, 16464,  16466, 19946, 5380,  \n14212, 16468, 15378,  2977, 13736, 11568,  16471, 16239, 16472,  \n298, 9770, 10517,  12276, 12801, 10734,  2840, 6498, 15418,  \n16479, 13138, 10314,  16480, 16055, 8249,  5709, 4096, 4097,  \n22945, 16484, 5616,  21779, 12234, 11929,  14868, 12123, 15404,  \n16369, 13783, 11225,  12295, 13121, 12308,  6927, 16490, 12135,  \n16491, 16492, 16493,  15967, 16495, 16491,  385, 16498, 21893,  \n16491, 16493, 16499,  16499, 16493, 16500,  16491, 16499, 15968,  \n15967, 16491, 15968,  16495, 15967, 16502,  16502, 15967, 15971,  \n16503, 15959, 15408,  16503, 15408, 16504,  3029, 16505, 3030,  \n15401, 16496, 15997,  1233, 1201, 4704,  4073, 16507, 2098,  \n13964, 10984, 10985,  4478, 13719, 2722,  15967, 15419, 15971,  \n11176, 6087, 6086,  16213, 5495, 16514,  15979, 16499, 16500,  \n15968, 16499, 15979,  9446, 14045, 8758,  14370, 14371, 2390,  \n747, 746, 19644,  14718, 16522, 14719,  5732, 9752, 16523,  \n8041, 636, 13194,  1020, 7184, 7297,  533, 16527, 15744,  \n5293, 15638, 16528,  3398, 8578, 3399,  10152, 16129, 16198,  \n10291, 10960, 14142,  7312, 16541, 6224,  16544, 14695, 6747,  \n16552, 12168, 14276,  12365, 14785, 8286,  14941, 5435, 5434,  \n15366, 12188, 10824,  15435, 16557, 15460,  10954, 10733, 9981,  \n8987, 2350, 2351,  16555, 15472, 15990,  4754, 11303, 13676,  \n10905, 16558, 14919,  14928, 14947, 16559,  16561, 16562, 9109,  \n16564, 12150, 12151,  9795, 10851, 9796,  8056, 21020, 8063,  \n16028, 12985, 12944,  16570, 12218, 11461,  13940, 2748, 16571,  \n14303, 15513, 14947,  15036, 1533, 7846,  15513, 16574, 14947,  \n11461, 15497, 16570,  13374, 13375, 16578,  16919, 14754, 16580,  \n12295, 7914, 13121,  16574, 16559, 14947,  15460, 16581, 15478,  \n9910, 2778, 16342,  16583, 2970, 2791,  7755, 13608, 1032,  \n21163, 11563, 7952,  17091, 14990, 15472,  9930, 7707, 5203,  \n13655, 15388, 4081,  14339, 11414, 13045,  13761, 10003, 16588,  \n14219, 16589, 14218,  16590, 8595, 8594,  11728, 9296, 1214,  \n8969, 16594, 16595,  16597, 15502, 14950,  9437, 8897, 12585,  \n9429, 4699, 9428,  17091, 16061, 14990,  15513, 14977, 16592,  \n16600, 4427, 16601,  16596, 14950, 16586,  4940, 978, 7817,  \n16067, 14998, 14386,  16605, 16061, 17091,  16052, 16591, 16592,  \n14977, 16052, 16592,  14636, 9415, 10297,  6695, 6694, 2585,  \n17636, 14971, 15502,  7140, 16196, 15505,  15565, 16065, 13777,  \n10180, 16611, 16612,  4852, 4853, 16614,  16052, 15533, 16616,  \n16591, 16052, 16616,  14209, 13425, 13529,  16618, 16619, 16620,  \n16621, 16622, 6897,  16623, 8681, 9900,  3070, 16624, 15580,  \n2735, 4201, 2734,  17451, 11822, 9181,  11020, 21015, 7267,  \n7541, 15917, 15916,  16627, 9487, 16628,  5686, 23537, 12203,  \n8059, 5425, 5427,  16082, 14967, 16071,  16632, 11299, 6492,  \n11188, 640, 16634,  7450, 7451, 16636,  16638, 16639, 1825,  \n7326, 15930, 10109,  16640, 8776, 9561,  16641, 4802, 20362,  \n1582, 1583, 2245,  16646, 13510, 16647,  16650, 3035, 9344,  \n2116, 12051, 14310,  16100, 15019, 15538,  10785, 5921, 7157,  \n7063, 16441, 13488,  16651, 13951, 5071,  15124, 11380, 16653,  \n16654, 5890, 16655,  16110, 15558, 15552,  2456, 14078, 8773,  \n16658, 16659, 16660,  8509, 29735, 16662,  16664, 16665, 16666,  \n6506, 6505, 8452,  16667, 3746, 3747,  16042, 4970, 14643,  \n4511, 14469, 6171,  4319, 473, 472,  8168, 16669, 16670,  \n16671, 15565, 15564,  16672, 15037, 16110,  6177, 25329, 19319,  \n6272, 8803, 19689,  16113, 2281, 13068,  7777, 4897, 12073,  \n13823, 14382, 319,  15845, 14557, 11863,  16681, 16682, 20516,  \n15570, 13058, 14449,  16683, 13773, 7671,  347, 16684, 16685,  \n16671, 15564, 13797,  16686, 16671, 13797,  16838, 8066, 15985,  \n16688, 16689, 16183,  7793, 11029, 7745,  2926, 5259, 15412,  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3843,  15144, 16182, 15675,  13891, 14546, 15673,  \n15673, 16749, 13891,  13891, 16749, 15671,  12438, 2687, 11424,  \n17247, 15160, 15675,  16202, 16201, 15154,  14560, 13913, 15160,  \n16202, 15162, 13926,  413, 16759, 16760,  13926, 17746, 16202,  \n14562, 14560, 16210,  11866, 8327, 3998,  3532, 16764, 5905,  \n9035, 1180, 1859,  16218, 15173, 16210,  16766, 3155, 13910,  \n5717, 3281, 3838,  13451, 16325, 16769,  16770, 16768, 16767,  \n7987, 5625, 323,  16771, 16772, 16773,  16772, 16771, 16768,  \n16768, 16771, 16767,  16767, 16771, 16774,  16767, 16774, 16775,  \n9726, 8240, 2385,  16771, 16773, 16778,  16774, 16771, 16778,  \n8823, 5200, 14818,  16779, 6137, 16780,  17286, 16773, 16776,  \n17286, 16778, 16773,  1652, 11303, 1650,  16778, 17286, 16784,  \n6964, 16788, 6963,  16778, 16784, 16787,  8533, 18938, 8532,  \n16787, 16774, 16778,  4687, 3888, 3887,  12792, 16786, 11320,  \n16789, 18033, 13587,  14591, 12558, 16790,  13934, 16790, 12558,  \n8823, 14818, 16791,  18938, 8533, 1739,  18149, 4921, 16793,  \n14591, 16795, 15716,  5457, 403, 402,  15731, 13958, 16800,  \n4964, 12745, 7230,  13958, 15731, 13286,  13280, 15202, 14594,  \n16805, 15731, 16806,  1764, 12839, 11596,  15731, 17323, 16806,  \n16800, 17323, 15731,  16808, 11353, 4804,  5789, 3293, 16813,  \n16814, 16815, 787,  16810, 15731, 16805,  15731, 16810, 15750,  \n15205, 16817, 15202,  6438, 9536, 16818,  10347, 9563, 5666,  \n16822, 15750, 16810,  16817, 15205, 16823,  14609, 16823, 15205,  \n6912, 11023, 4526,  15514, 16824, 11156,  18931, 4965, 4964,  \n14609, 16255, 16823,  16827, 16255, 15749,  16828, 7563, 6814,  \n15749, 16259, 16827,  8160, 4648, 8161,  16262, 16259, 15219,  \n11036, 16829, 10269,  14640, 16260, 16269,  12309, 16830, 3825,  \n11295, 16831, 12061,  15752, 16262, 13298,  4186, 7530, 1485,  \n14653, 14640, 16269,  14637, 16835, 15752,  16835, 16262, 15752,  \n6950, 8176, 11681,  14637, 15765, 16835,  16836, 15765, 15770,  \n19120, 16837, 9642,  13509, 6683, 13508,  14023, 16270, 16850,  \n14654, 9771, 7753,  11345, 16843, 16844,  14537, 14538, 5621,  \n10639, 11296, 10271,  14023, 16850, 15780,  16285, 16848, 15250,  \n1189, 11586, 15301,  11067, 16855, 16002,  16857, 14679, 14031,  \n16854, 16285, 15787,  20241, 4680, 4679,  11528, 14465, 10492,  \n17382, 15787, 16289,  16293, 13354, 14679,  16861, 16289, 15272,  \n7004, 7003, 16193,  9643, 16804, 9644,  15272, 15803, 16861,  \n16866, 16867, 23115,  5478, 5480, 16868,  15793, 16302, 15275,  \n7922, 9639, 16869,  8814, 15229, 8813,  16302, 16872, 15282,  \n10685, 10698, 13156,  5636, 16918, 20343,  4111, 13794, 16560,  \n16875, 14179, 9269,  16317, 14114, 12740,  2668, 8811, 1289,  \n6437, 2687, 12438,  10315, 16121, 420,  16326, 14118, 15313,  \n6692, 4409, 16195,  8298, 14225, 6929,  1085, 1811, 16889,  \n2452, 1170, 6901,  2918, 16892, 8546,  12517, 20953, 5856,  \n16334, 16326, 15313,  16334, 15313, 15310,  5626, 2618, 9596,  \n16893, 15833, 12757,  13939, 13391, 13269,  16896, 16897, 7424,  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3861,  1319, 14809, 9216,  16959, 16962, 16963,  \n16960, 16959, 16418,  16418, 16423, 16960,  16401, 1907, 1906,  \n16959, 16963, 16418,  16423, 16965, 16960,  16963, 16964, 16419,  \n16418, 16963, 16419,  11562, 13264, 16966,  16965, 16423, 16970,  \n16419, 16964, 16426,  3653, 3654, 11095,  936, 16975, 937,  \n16970, 16423, 15903,  16426, 16964, 16978,  16970, 15903, 15902,  \n2899, 16983, 2703,  10099, 16984, 2250,  4534, 4985, 16985,  \n16430, 16426, 16432,  4466, 7641, 7597,  16426, 16978, 16432,  \n5376, 16987, 5377,  16988, 16986, 15913,  14982, 15578, 15579,  \n16989, 13519, 13520,  16986, 15902, 15913,  5172, 16153, 16840,  \n16988, 15913, 15920,  15920, 16991, 16988,  13762, 9413, 3094,  \n16991, 15920, 16443,  16443, 16992, 16991,  2738, 5412, 16993,  \n16443, 16995, 16992,  8182, 4579, 16449,  16994, 16446, 16439,  \n16451, 16995, 15925,  15925, 16995, 16443,  3592, 5089, 1456,  \n16446, 16998, 16450,  16451, 17000, 16995,  14342, 2586, 23022,  \n14718, 14720, 2235,  16450, 17001, 16451,  17000, 16451, 17001,  \n15929, 10735, 12801,  17005, 764, 11981,  13197, 7442, 7441,  \n17009, 17010, 7977,  3461, 8336, 19491,  2133, 18535, 11024,  \n577, 6268, 12469,  16474, 14208, 15376,  16474, 15376, 17013,  \n14212, 17017, 16468,  14868, 17017, 14212,  14212, 13549, 14868,  \n7921, 17023, 11369,  13472, 6922, 6353,  14208, 16486, 15401,  \n6041, 4636, 4638,  15401, 16486, 16496,  17026, 14868, 15404,  \n9550, 8272, 18744,  17027, 16492, 16491,  16495, 17027, 16491,  \n16502, 17027, 16495,  10790, 2039, 14092,  15516, 17028, 8774,  \n8601, 3938, 810,  23711, 15210, 6016,  7241, 1398, 17032,  \n15971, 17029, 16502,  8651, 13795, 13839,  7228, 17036, 7226,  \n17029, 15971, 16503,  16503, 15971, 15959,  929, 17037, 18906,  \n17043, 15414, 15424,  8413, 4297, 17047,  15176, 12902, 9390,  \n17049, 15424, 14254,  16496, 17050, 15997,  3577, 17051, 7398,  \n15404, 10610, 17054,  17056, 17046, 17057,  4765, 17058, 5958,  \n15035, 1355, 13564,  17055, 15979, 16500,  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18432, 18428,  18588, 14797, 18912,  \n18432, 18910, 18434,  6694, 3219, 18601,  5899, 18913, 5898,  \n14049, 15356, 8424,  12322, 9135, 402,  6326, 15353, 4304,  \n18434, 18914, 17907,  11464, 9317, 9318,  18445, 18453, 18454,  \n8589, 6435, 5303,  17613, 6986, 18918,  18919, 18920, 10122,  \n5731, 14756, 14755,  5019, 2441, 2440,  17918, 17907, 19401,  \n2506, 11340, 2507,  17918, 19401, 18922,  17671, 3849, 3848,  \n6774, 5958, 2087,  18924, 16936, 18922,  17941, 14127, 18925,  \n12433, 8846, 8847,  18924, 17457, 16936,  5263, 3638, 18928,  \n4400, 15625, 4401,  9627, 6501, 10963,  18766, 18861, 8423,  \n18932, 18933, 14867,  5378, 21543, 18936,  1819, 11093, 11092,  \n5820, 5821, 17441,  17460, 18939, 16404,  16404, 18939, 17939,  \n17932, 16407, 17939,  1735, 1734, 18180,  15348, 17465, 16954,  \n18322, 11193, 18089,  16954, 19417, 18479,  18946, 18944, 18486,  \n18946, 18486, 18948,  17482, 18948, 18486,  17236, 7595, 4264,  \n18947, 17944, 18485,  17944, 18947, 17947,  18947, 18953, 17947,  \n17950, 17947, 18953,  810, 8408, 9287,  18152, 3817, 18955,  \n5274, 7447, 13828,  18957, 12128, 12329,  15977, 7126, 7125,  \n16280, 3753, 3791,  18495, 18497, 18959,  18492, 17950, 18953,  \n1739, 12250, 18938,  9643, 9644, 10528,  18962, 18491, 17497,  \n5342, 478, 16890,  18495, 17957, 18497,  9276, 8798, 6284,  \n16669, 3443, 488,  18964, 534, 533,  11061, 9917, 7294,  \n12754, 9608, 13147,  17497, 17506, 18962,  18496, 18968, 18505,  \n17957, 17510, 17960,  17508, 18967, 17506,  6953, 933, 6546,  \n17768, 17727, 18545,  11254, 3346, 1179,  18492, 18508, 17501,  \n1434, 14997, 12266,  4129, 1316, 12184,  17516, 18978, 18514,  \n21174, 9840, 1699,  17964, 18978, 17516,  16163, 12339, 2667,  \n17670, 11126, 13972,  18981, 18982, 18983,  16197, 14252, 19938,  \n17964, 17966, 18984,  4154, 13788, 1167,  11984, 16410, 18985,  \n17967, 17520, 19966,  18519, 17967, 19966,  14362, 1007, 13396,  \n18519, 18984, 17966,  5876, 5877, 11246,  18990, 8329, 18991,  \n18992, 7697, 14492,  10396, 7749, 14367,  17981, 17530, 18993,  \n15935, 4129, 4128,  5254, 8959, 4463,  5525, 5437, 10923,  \n18995, 17694, 18969,  13652, 9123, 1294,  17981, 18536, 17982,  \n17535, 17982, 18536,  12701, 17635, 18998,  10157, 2402, 5427,  \n18536, 18537, 17535,  19000, 17990, 19001,  19001, 17990, 17992,  \n15028, 11607, 19003,  19005, 10770, 17810,  17990, 19006, 17995,  \n19006, 17990, 19000,  17005, 19007, 6342,  17992, 19008, 19001,  \n17998, 19008, 17992,  11214, 2932, 7162,  13419, 8735, 10933,  \n17995, 19011, 17999,  19006, 19011, 17995,  19009, 17998, 17555,  \n18554, 16486, 18537,  19014, 18544, 17555,  17555, 17029, 16503,  \n19014, 16504, 21035,  3845, 14559, 9976,  17026, 15404, 18548,  \n17999, 19011, 18549,  8846, 12433, 667,  19016, 18549, 19011,  \n19017, 8709, 7215,  15424, 17048, 17043,  2195, 12548, 13142,  \n1621, 13689, 13690,  18761, 13369, 4747,  19020, 9309, 4226,  \n9863, 2864, 20217,  18981, 4826, 19022,  18560, 18549, 19016,  \n1363, 11999, 1362,  18059, 13233, 12785,  19024, 9300, 936,  \n19025, 19026, 7156,  18013, 18549, 18560,  14829, 19027, 16256,  \n3787, 18923, 11780,  19028, 17564, 17566,  19029, 9898, 16645,  \n11470, 7065, 9848,  9396, 15283, 10329,  3719, 7433, 8695,  \n2907, 22116, 2908,  19031, 16629, 11851,  13314, 18493, 19032,  \n7878, 340, 11352,  8793, 7131, 12867,  19036, 1270, 1859,  \n21013, 12867, 7131,  17582, 17569, 18568,  14649, 19037, 2436,  \n18046, 18561, 19038,  18567, 17097, 18047,  13778, 10954, 10953,  \n18563, 14285, 18050,  1989, 10754, 10753,  314, 19040, 313,  \n11117, 1588, 18423,  12269, 14972, 18459,  17596, 17595, 2357,  \n11543, 19041, 943,  19038, 19039, 18046,  5148, 22458, 7348,  \n19042, 19043, 3696,  12327, 10080, 6620,  13224, 13720, 11871,  \n3722, 5886, 17496,  19042, 19051, 19043,  17606, 17582, 18568,  \n3561, 18565, 8503,  18046, 19049, 17610,  9955, 9954, 14319,  \n14570, 585, 1507,  18568, 19056, 17606,  7599, 13340, 15725,  \n9819, 5215, 9673,  6459, 8622, 9997,  16067, 19058, 18051,  \n18064, 4861, 4087,  19062, 8482, 5687,  11444, 17188, 12506,  \n19063, 6908, 6909,  9280, 5404, 19064,  19061, 17605, 18062,  \n17887, 7631, 20337,  16067, 17629, 19067,  1622, 1290, 1291,  \n15508, 9308, 5104,  17130, 478, 2887,  10759, 2677, 11743,  \n4967, 12689, 4968,  19071, 18050, 18608,  19075, 19149, 10986,  \n18907, 10731, 4955,  10652, 4777, 10653,  18295, 13974, 12882,  \n2493, 463, 464,  742, 14558, 777,  6189, 11201, 2551,  \n20539, 15553, 17624,  15570, 16090, 13058,  19076, 18613, 18596,  \n9576, 10880, 17562,  3991, 17396, 16539,  11379, 17670, 4623,  \n8409, 19079, 17921,  13428, 12626, 17727,  17648, 18626, 18628,  \n19080, 18597, 18077,  18068, 19081, 17116,  3167, 16741, 3528,  \n19083, 15570, 19084,  19085, 19086, 19087,  5141, 18963, 5140,  \n17154, 18628, 19088,  4364, 3005, 5326,  15431, 13393, 19089,  \n17156, 18078, 19090,  2290, 16885, 2289,  3539, 16725, 6133,  \n15994, 15993, 16518,  9224, 14192, 19092,  19093, 17184, 15553,  \n15570, 17199, 19084,  1197, 1196, 15659,  19095, 13443, 15720,  \n16613, 19507, 15082,  10591, 15602, 10592,  17584, 21855, 6506,  \n21123, 19097, 12846,  17657, 18102, 19099,  19100, 17657, 19099,  \n9486, 9485, 11701,  14346, 8813, 19101,  18643, 18659, 18169,  \n18643, 18169, 18107,  18102, 18101, 18648,  6825, 4433, 9900,  \n18113, 19104, 18120,  19102, 18659, 18643,  12488, 14886, 14887,  \n10891, 14804, 19106,  19107, 17193, 19093,  18166, 18659, 19105,  \n1506, 11169, 12273,  6835, 6834, 9558,  18925, 4603, 12579,  \n9155, 18038, 6596,  19109, 19110, 8458,  4069, 19112, 10513,  \n9646, 16004, 16888,  17193, 16131, 15586,  18166, 19115, 18669,  \n12385, 19116, 6894,  16690, 18661, 17692,  6012, 6013, 13696,  \n6887, 6960, 6886,  8778, 10542, 18623,  11494, 19121, 13254,  \n3730, 5552, 5553,  8113, 8114, 13122,  18135, 19125, 18641,  \n15010, 18929, 17452,  18662, 17212, 17715,  18669, 18713, 18186,  \n11817, 11816, 19130,  8105, 388, 17817,  7422, 18503, 6589,  \n19131, 13634, 5836,  19135, 16696, 18676,  16142, 19136, 2558,  \n1804, 974, 975,  17451, 9181, 9180,  17012, 3532, 3533,  \n18687, 18228, 18218,  3741, 1454, 9873,  5807, 4311, 19512,  \n19135, 18183, 16696,  16868, 18476, 5478,  19141, 12982, 18436,  \n14706, 12616, 19143,  586, 2151, 2148,  19146, 18193, 17215,  \n19146, 17215, 16712,  16712, 18183, 19147,  17644, 19149, 17224,  \n10171, 10172, 9034,  18713, 19151, 18246,  18682, 18151, 18699,  \n9674, 15203, 12802,  18670, 19154, 19125,  18135, 18670, 19125,  \n18228, 18193, 19170,  19155, 19170, 18193,  16098, 19156, 16838,  \n17233, 18223, 18712,  18203, 17233, 18712,  2883, 22871, 2884,  \n16828, 12824, 7563,  1484, 12266, 7359,  6444, 14675, 19160,  \n18228, 19170, 17246,  18712, 17736, 19163,  17736, 18712, 18223,  \n8613, 19164, 9925,  18383, 15806, 1948,  19165, 16511, 19166,  \n19153, 19167, 18225,  14253, 16626, 19168,  19170, 17745, 17246,  \n19171, 13076, 16192,  17736, 18219, 19163,  18734, 19172, 19173,  \n18225, 19167, 18230,  21579, 703, 4900,  18254, 18239, 17253,  \n18230, 19167, 18732,  18732, 19167, 19176,  18198, 18270, 18670,  \n19154, 18670, 18270,  1244, 9429, 1143,  2511, 2510, 18121,  \n13688, 10217, 10407,  18208, 18740, 18699,  10605, 17440, 15108,  \n16930, 15868, 14536,  19176, 18291, 18732,  14560, 17745, 16206,  \n17745, 19178, 16206,  16788, 19185, 6963,  2934, 2935, 13732,  \n7113, 13716, 13718,  7815, 3283, 778,  19186, 8855, 8856,  \n15889, 18294, 8831,  15860, 12273, 11169,  19188, 18282, 16206,  \n7831, 888, 10420,  17768, 18545, 17769,  19190, 1390, 29333,  \n14901, 8121, 15859,  19191, 292, 9952,  19192, 5398, 5399,  \n18754, 17746, 17765,  4967, 4968, 16612,  17086, 19195, 17087,  \n28799, 4558, 19197,  15033, 3033, 29665,  17770, 18763, 16216,  \n16553, 12664, 4393,  16216, 18762, 18288,  19010, 18080, 18725,  \n10860, 8798, 14963,  14196, 21062, 13526,  18762, 17765, 18288,  \n9449, 15654, 15406,  18277, 19194, 18304,  4130, 15379, 2168,  \n19203, 18311, 18291,  19206, 3850, 12421,  1753, 1474, 16155,  \n18272, 18777, 18779,  5613, 8062, 7450,  17737, 3362, 19210,  \n701, 11084, 3421,  19213, 12465, 19214,  1800, 2669, 12369,  \n5900, 3625, 13149,  13767, 19215, 8891,  4283, 7410, 6787,  \n18304, 19217, 18300,  7514, 4478, 2722,  19203, 19225, 18311,  \n1331, 19226, 17333,  19227, 9149, 5744,  6562, 6561, 4545,  \n18300, 18805, 18793,  18802, 18311, 19225,  11821, 12419, 8743,  \n19224, 18285, 17780,  4265, 5340, 17921,  16968, 13131, 8231,  \n19655, 19230, 19231,  19232, 19656, 19231,  18315, 18313, 19234,  \n2586, 10819, 23022,  16569, 719, 19235,  19237, 3362, 4593,  \n17940, 8815, 17438,  1166, 1165, 9570,  9224, 3196, 14192,  \n868, 16543, 19141,  15242, 1178, 1179,  19234, 18313, 18810,  \n6562, 12848, 19239,  18803, 18806, 19240,  16869, 9639, 9327,  \n2688, 2689, 11301,  4575, 16018, 16019,  19234, 18810, 19243,  \n12142, 8913, 10161,  18810, 18799, 19246,  21253, 980, 19247,  \n2720, 2721, 4813,  19250, 2901, 7201,  4474, 16661, 4475,  \n18792, 19241, 18799,  18799, 19245, 19246,  11422, 14642, 15691,  \n12341, 12844, 19253,  19230, 19254, 19231,  6169, 19255, 10065,  \n18799, 19241, 19245,  5237, 3756, 22267,  19240, 18330, 18803,  \n11005, 13989, 2569,  3631, 1952, 4776,  18330, 19240, 18823,  \n18814, 17780, 18836,  5610, 10861, 10862,  17780, 18334, 18836,  \n19262, 9933, 18179,  19263, 18824, 18330,  9656, 16388, 16389,  \n15950, 12372, 11706,  13113, 2642, 1640,  19263, 18837, 18824,  \n18334, 18333, 18838,  19273, 18334, 18838,  18085, 13901, 12261,  \n18837, 19263, 19275,  19276, 18837, 19275,  19276, 18838, 18837,  \n19276, 19277, 18838,  18838, 19277, 19273,  5468, 12120, 12119,  \n2797, 2796, 3717,  19279, 19754, 19280,  10295, 1204, 6388,  \n19280, 19754, 19283,  14502, 16668, 2619,  5040, 5041, 17775,  \n19287, 5444, 11142,  4208, 1503, 1502,  4973, 19289, 17221,  \n19283, 19286, 19290,  4459, 15858, 15857,  19291, 19280, 19283,  \n9319, 4652, 7882,  19283, 19290, 19291,  12355, 16573, 18093,  \n13019, 16097, 8862,  6824, 6823, 13065,  1149, 2962, 8769,  \n9165, 16919, 16915,  788, 789, 9147,  16098, 3352, 6316,  \n19293, 19292, 19296,  2203, 19297, 16459,  14918, 1757, 2514,  \n4235, 19122, 5467,  19291, 19290, 19301,  19302, 19291, 19301,  \n19292, 19300, 19296,  19303, 19293, 19296,  19304, 18423, 15970,  \n19300, 19302, 19305,  12324, 9051, 558,  4064, 3751, 19306,  \n835, 19311, 17707,  8869, 15863, 18065,  19302, 19301, 19305,  \n19305, 19301, 20348,  14373, 633, 8689,  653, 10519, 19319,  \n19296, 19320, 19303,  13771, 9600, 18849,  19309, 19308, 19307,  \n17864, 5132, 8982,  19320, 19296, 19300,  19322, 9575, 17562,  \n19308, 19323, 19307,  19324, 11430, 19325,  19300, 19305, 19321,  \n13771, 4111, 9600,  19308, 19320, 19328,  19323, 19308, 19328,  \n19317, 19307, 19323,  19300, 19321, 19320,  19332, 10896, 10305,  \n19321, 19305, 19333,  19321, 19333, 19334,  19338, 3801, 18141,  \n19339, 19317, 19323,  19320, 19321, 19328,  19323, 19328, 19337,  \n19342, 2822, 2287,  19339, 19323, 19337,  19321, 19334, 19328,  \n19337, 19328, 19341,  21806, 14224, 2218,  19339, 19337, 19345,  \n852, 6273, 1768,  11036, 10269, 3457,  18842, 17784, 17788,  \n17788, 18843, 18842,  5273, 1117, 3430,  506, 505, 14287,  \n19347, 19317, 19348,  19341, 19328, 19334,  1841, 8250, 15489,  \n19317, 19339, 19348,  19350, 5462, 4703,  10828, 19351, 11111,  \n17793, 18843, 17788,  17284, 18850, 17795,  18854, 17805, 17795,  \n17795, 18850, 18854,  18852, 18855, 18847,  16825, 4168, 6542,  \n19353, 678, 12005,  6064, 6585, 16747,  4613, 3235, 799,  \n11909, 18681, 3581,  19358, 18368, 18860,  7926, 5019, 9615,  \n9528, 7469, 8974,  19359, 19360, 18860,  19359, 18372, 18376,  \n19359, 18860, 18372,  19358, 18860, 19360,  18376, 19361, 19359,  \n14382, 16264, 19363,  12948, 15303, 8647,  18380, 18865, 20963,  \n18381, 15718, 14594,  13654, 19364, 9079,  21729, 6949, 6570,  \n6616, 18336, 18335,  8960, 2408, 23629,  18839, 10999, 3882,  \n13787, 17187, 7649,  17851, 18874, 19366,  7891, 8712, 17430,  \n14171, 13228, 5457,  16801, 12492, 11044,  19366, 18391, 17851,  \n8436, 16229, 13475,  1784, 10184, 10183,  19370, 18878, 18392,  \n17366, 18391, 19369,  19370, 18392, 18880,  17366, 19369, 18882,  \n13825, 14268, 13824,  12458, 19371, 19372,  18880, 19373, 19370,  \n6264, 13878, 18571,  15252, 4665, 15369,  19373, 18880, 18884,  \n18884, 19376, 19373,  14759, 14758, 19458,  8403, 8729, 3232,  \n664, 2797, 3717,  3399, 10205, 15296,  18414, 19376, 18884,  \n20066, 18199, 13493,  7842, 18338, 19381,  696, 2921, 7142,  \n15756, 12538, 18367,  19891, 3659, 4840,  16293, 16857, 18412,  \n7879, 5643, 2713,  19383, 19384, 14505,  19385, 7361, 18727,  \n19386, 4152, 1762,  16872, 17394, 18892,  18414, 15803, 17399,  \n7557, 7361, 19385,  2324, 2325, 13353,  16872, 18892, 17882,  \n846, 17718, 4220,  19365, 7641, 13478,  11920, 19392, 18462,  \n16881, 19393, 6653,  18900, 19395, 18903,  19397, 18910, 19395,  \n15758, 19015, 9928,  18910, 18432, 19395,  17120, 13088, 8365,  \n19395, 18432, 18903,  5621, 6422, 18413,  18431, 17406, 19399,  \n11013, 10618, 4062,  3462, 19294, 11539,  19400, 19401, 17907,  \n882, 3526, 14786,  18458, 18464, 19403,  13443, 5298, 5297,  \n14129, 14128, 7742,  18266, 19409, 15757,  18325, 18590, 19342,  \n18924, 19410, 17457,  1841, 15489, 5272,  13636, 13982, 5523,  \n17922, 19411, 18464,  19415, 17457, 19410,  17457, 19415, 17929,  \n18479, 16411, 15359,  11714, 11713, 11363,  8014, 14896, 2833,  \n8235, 11916, 6054,  11700, 1268, 12590,  19415, 17460, 17929,  \n8201, 8200, 1661,  4198, 4784, 3523,  14359, 2765, 9206,  \n6180, 13804, 2065,  19420, 13218, 11199,  19421, 5097, 3163,  \n17465, 19417, 16954,  16092, 11491, 5593,  3870, 14522, 6150,  \n13683, 10738, 13682,  19424, 19425, 18944,  18946, 19424, 18944,  \n18485, 19425, 18947,  19425, 18485, 18944,  16358, 9008, 7605,  \n1507, 585, 587,  19430, 16763, 20629,  19431, 18495, 19432,  \n2614, 6735, 2615,  19433, 19434, 18495,  19431, 19433, 18495,  \n17733, 14853, 3096,  18495, 18959, 19432,  18953, 18947, 19428,  \n12193, 12022, 6467,  824, 4052, 12267,  19434, 19436, 18496,  \n11234, 16520, 16573,  10750, 1854, 19287,  18496, 18495, 19434,  \n19439, 13018, 13935,  4465, 4934, 19440,  6090, 11724, 17563,  \n6301, 9883, 19441,  15474, 7082, 18607,  11479, 552, 1396,  \n19437, 18492, 18953,  5994, 3071, 19443,  14404, 3104, 10827,  \n12373, 4438, 10155,  3860, 2114, 19444,  14409, 9876, 4984,  \n9672, 8006, 18096,  802, 14667, 16608,  10639, 10271, 10638,  \n11140, 9712, 11139,  19442, 18959, 18497,  18497, 19448, 19442,  \n18508, 18492, 19437,  2813, 14463, 10509,  15883, 18776, 981,  \n18962, 17506, 18967,  4875, 19278, 19449,  18968, 18967, 17508,  \n18505, 18968, 17508,  8945, 19450, 14906,  18507, 19448, 18497,  \n18507, 19452, 19448,  19454, 19452, 18514,  19452, 18507, 18514,  \n19454, 18514, 18978,  17509, 19455, 18515,  13111, 6634, 4918,  \n19454, 18978, 19457,  7422, 1729, 5737,  19457, 18978, 17964,  \n18984, 19457, 17964,  18515, 17965, 16994,  2230, 17872, 19694,  \n17706, 7049, 15810,  11330, 17684, 12941,  850, 14915, 9051,  \n18744, 24396, 9550,  19462, 18519, 19966,  18984, 18519, 19462,  \n14131, 7104, 14377,  317, 19464, 2836,  18522, 19467, 18523,  \n19469, 12398, 12397,  2850, 14018, 14017,  3167, 3528, 3422,  \n9948, 4449, 13629,  18993, 17530, 19470,  7733, 19474, 9764,  \n18533, 17017, 17026,  19475, 18537, 18536,  13202, 19075, 10986,  \n5128, 12010, 13193,  4250, 6452, 20648,  17424, 16469, 2733,  \n19011, 19006, 19480,  19481, 19480, 19000,  19006, 19000, 19480,  \n19008, 17998, 19009,  18537, 19482, 18554,  514, 513, 8472,  \n18544, 19009, 17555,  16503, 19014, 17555,  16503, 16504, 19014,  \n3956, 2548, 2547,  19484, 19485, 11223,  19011, 19480, 19016,  \n19016, 19480, 19486,  19488, 16504, 17043,  19489, 16694, 4479,  \n16956, 6363, 11852,  16187, 16186, 7577,  19490, 19016, 19486,  \n7399, 19491, 7400,  17551, 18554, 19492,  29727, 29506, 16193,  \n2815, 8096, 14089,  18560, 19016, 19490,  10151, 10152, 12388,  \n1415, 6526, 6357,  19028, 17049, 17564,  13640, 4905, 19497,  \n12585, 17933, 5853,  8472, 18309, 514,  13952, 5100, 15251,  \n17551, 19492, 17569,  1262, 919, 11565,  19490, 18561, 18560,  \n15125, 2253, 17494,  5970, 8606, 19504,  4182, 4183, 19506,  \n6971, 6959, 6046,  19490, 19038, 18561,  18568, 17569, 19508,  \n12253, 2588, 10550,  14276, 18573, 16552,  17169, 16501, 11627,  \n5495, 9008, 20177,  8107, 389, 388,  18708, 15390, 13094,  \n10136, 2014, 2015,  17093, 19513, 14296,  19514, 19513, 17093,  \n19515, 16371, 7794,  15438, 18563, 19044,  3522, 18008, 9279,  \n17601, 12293, 13132,  19519, 17093, 16570,  19514, 17093, 19519,  \n18044, 19519, 16570,  2315, 17194, 19520,  19049, 18046, 19039,  \n16028, 18577, 19521,  16028, 16552, 18577,  9197, 10794, 6876,  \n15455, 5811, 13033,  17232, 5904, 16135,  5911, 7237, 19525,  \n19060, 19049, 19526,  7109, 18809, 8577,  4499, 16628, 3672,  \n11878, 19110, 19109,  17604, 18051, 19058,  3613, 12046, 12047,  \n12320, 8606, 4887,  18057, 17610, 19049,  19061, 19529, 17103,  \n17605, 19061, 17103,  1451, 15734, 1450,  6689, 14892, 6690,  \n19058, 16067, 19067,  3245, 13544, 2832,  18591, 17606, 19056,  \n18563, 18050, 19071,  5820, 11193, 654,  20179, 15407, 7667,  \n6469, 19927, 19531,  19532, 19067, 15016,  18057, 19049, 19060,  \n1407, 17877, 12637,  17629, 15016, 19067,  19532, 15016, 16090,  \n17814, 15782, 17691,  16651, 19534, 13951,  17158, 14057, 19535,  \n7668, 16916, 17356,  18596, 18057, 19060,  18598, 19537, 18062,  \n17624, 16588, 18592,  10932, 7006, 16282,  18596, 19060, 19076,  \n16873, 19540, 19541,  2831, 11086, 17053,  13914, 13919, 9983,  \n10452, 2140, 3127,  19543, 18598, 18597,  16165, 6383, 19544,  \n19378, 19545, 14093,  18591, 19538, 19077,  12873, 18768, 7986,  \n18613, 18624, 17165,  17176, 18624, 18626,  19548, 7602, 16704,  \n3350, 12430, 13688,  15895, 15182, 16665,  8559, 19549, 2278,  \n18628, 18626, 19088,  18077, 17156, 19090,  4515, 4546, 16657,  \n7143, 7018, 2131,  1959, 1355, 13605,  19080, 18077, 19552,  \n19077, 19546, 18068,  18081, 17116, 19081,  19553, 18081, 19081,  \n5032, 15712, 16742,  17154, 19088, 18078,  18078, 19088, 19556,  \n2198, 2197, 4074,  17389, 17390, 19557,  19558, 19090, 18078,  \n19090, 19552, 18077,  10020, 4451, 7989,  18084, 18619, 19553,  \n9917, 10856, 18743,  18886, 5968, 15820,  13572, 19566, 13248,  \n8002, 19560, 21011,  7416, 11772, 2331,  18084, 19553, 18633,  \n14407, 19459, 5752,  18633, 19102, 18643,  19100, 19561, 17657,  \n1959, 13846, 1355,  7445, 19563, 5658,  19561, 18113, 17657,  \n5967, 1081, 19564,  13494, 19564, 1081,  17184, 19093, 17193,  \n18659, 19102, 19105,  3926, 19569, 3925,  19477, 19101, 19566,  \n11701, 13270, 7426,  19571, 18648, 18649,  18648, 19571, 18102,  \n19571, 19099, 18102,  17771, 3708, 2926,  6725, 6726, 14754,  \n15066, 4370, 4135,  3535, 3534, 8927,  6167, 10526, 9602,  \n6597, 15433, 1424,  19111, 17199, 16702,  15883, 981, 982,  \n19115, 18713, 18669,  18166, 19105, 19115,  2882, 11482, 8804,  \n19575, 17692, 18661,  18676, 16131, 17193,  16445, 12517, 5396,  \n3612, 13029, 3613,  12046, 5840, 3189,  19577, 18649, 18668,  \n5758, 5759, 1477,  16804, 15705, 19580,  19443, 19581, 2622,  \n17692, 19138, 17698,  19584, 19585, 11294,  7332, 7990, 2182,  \n17081, 12433, 7764,  4611, 8466, 16346,  15817, 19588, 16010,  \n19036, 1859, 7309,  17234, 17698, 18705,  8039, 8272, 9550,  \n19147, 18183, 19135,  1915, 2505, 15330,  18203, 19590, 17715,  \n6852, 6443, 20050,  19172, 18246, 19151,  15998, 7229, 16730,  \n18682, 19591, 18668,  19593, 18574, 10355,  12906, 17308, 3680,  \n18831, 20676, 18614,  18193, 19595, 19155,  19146, 19595, 18193,  \n19599, 17768, 2331,  16712, 19147, 19146,  16744, 19606, 17719,  \n18700, 17719, 19606,  18700, 19159, 19153,  17618, 7639, 17313,  \n6218, 12064, 6219,  16676, 19608, 5717,  14555, 3748, 3750,  \n19147, 19601, 19146,  19153, 19159, 19167,  8849, 11580, 8854,  \n7805, 8259, 6026,  2473, 975, 974,  17609, 3526, 3099,  \n18254, 19613, 18239,  9442, 810, 812,  19229, 19614, 5513,  \n18095, 16477, 19324,  17183, 14442, 4838,  16729, 19617, 7994,  \n18734, 19173, 18277,  18742, 19619, 13407,  12873, 17955, 10849,  \n8079, 17170, 22290,  18254, 19182, 19179,  18254, 18754, 19182,  \n18277, 19173, 19194,  19554, 4956, 5700,  18291, 19176, 19623,  \n15368, 8258, 19621,  16206, 19178, 19188,  1776, 12376, 15304,  \n15506, 5332, 18171,  4450, 6262, 7989,  17870, 13027, 5175,  \n904, 19626, 4439,  3283, 19627, 3083,  815, 7762, 16999,  \n18699, 18740, 19202,  9259, 14437, 2516,  3499, 626, 12406,  \n19630, 19198, 17770,  18282, 19630, 17770,  1723, 4869, 16366,  \n9967, 16482, 7327,  13836, 14358, 14058,  18304, 19194, 19628,  \n18740, 18750, 19202,  15617, 6807, 10134,  7338, 19632, 19633,  \n19198, 18763, 17770,  11158, 11157, 19634,  5567, 21637, 12026,  \n19198, 19637, 18763,  18762, 18763, 19637,  18304, 19628, 19217,  \n19640, 4685, 12752,  13149, 3625, 3626,  13591, 18215, 11390,  \n7814, 16571, 19643,  5190, 2681, 2683,  1288, 20097, 7057,  \n19202, 18750, 18272,  15147, 11725, 19645,  11831, 2196, 2198,  \n19202, 18272, 18779,  7341, 6290, 17968,  19651, 18285, 19224,  \n17752, 16031, 15121,  9183, 13544, 19654,  12096, 19402, 10860,  \n18300, 20155, 18805,  2238, 2237, 13921,  17702, 5749, 1151,  \n5531, 5529, 12968,  19657, 19658, 20158,  2331, 7008, 22781,  \n13138, 16479, 5638,  9924, 4499, 18710,  19232, 19657, 19656,  \n5686, 12203, 4326,  19660, 7642, 17261,  19661, 18777, 18315,  \n18802, 18317, 18311,  19231, 19656, 19655,  15278, 14522, 16387,  \n19655, 20170, 19662,  19658, 19657, 19232,  10667, 17068, 10668,  \n6017, 6016, 15211,  17166, 14489, 5594,  11271, 7611, 18753,  \n19666, 11167, 10937,  19655, 19662, 19230,  19661, 18315, 19234,  \n19393, 16484, 6653,  13085, 694, 10232,  19236, 18798, 18805,  \n19671, 19236, 18805,  1764, 19672, 1765,  12225, 19673, 1519,  \n1100, 4851, 10141,  17780, 18814, 19224,  2318, 2040, 6113,  \n19669, 19230, 19662,  2589, 823, 824,  7533, 1319, 7532,  \n19678, 1845, 15837,  1721, 1134, 10530,  11399, 16657, 10523,  \n19236, 19681, 18798,  3825, 16274, 10774,  19682, 14306, 7192,  \n5601, 8574, 6451,  19230, 19669, 19256,  15906, 10108, 2292,  \n19232, 19231, 19254,  19232, 19254, 19658,  19681, 19241, 18798,  \n18792, 18798, 19241,  11773, 11447, 14984,  19243, 18810, 19246,  \n17363, 631, 16470,  19687, 20693, 17245,  19256, 19669, 19674,  \n14791, 8494, 3036,  19243, 19246, 19693,  7569, 17330, 13337,  \n7254, 3478, 19696,  19168, 22895, 6946,  19697, 19241, 19691,  \n6654, 5420, 5421,  13759, 9616, 18130,  16047, 19698, 10908,  \n19254, 19230, 19256,  12565, 12566, 11063,  7099, 11187, 5112,  \n13487, 17985, 383,  4952, 5239, 5238,  11364, 2794, 18566,  \n19254, 19256, 19700,  8055, 18357, 9987,  8139, 2696, 2695,  \n10248, 9265, 4692,  16237, 15237, 19701,  19703, 19704, 9561,  \n19706, 19256, 19674,  19256, 19706, 19700,  14796, 9878, 12583,  \n2321, 4588, 4240,  19254, 19700, 19699,  16300, 3664, 3660,  \n7224, 12351, 1187,  5980, 1088, 6561,  17099, 1843, 18720,  \n16458, 8036, 8035,  15508, 18466, 9308,  7905, 19711, 6661,  \n18685, 5429, 16114,  1913, 7380, 19712,  19713, 19699, 19700,  \n8821, 4588, 9816,  18330, 18823, 19263,  14880, 15135, 19716,  \n19263, 19260, 19270,  8722, 16762, 22081,  19273, 18836, 18334,  \n19273, 19715, 18836,  5488, 5489, 4307,  16617, 10144, 13380,  \n6419, 10559, 6420,  3619, 15270, 2720,  1296, 11906, 8210,  \n18481, 10845, 10844,  19275, 19721, 19276,  7190, 10227, 8648,  \n21085, 19722, 4793,  19277, 19276, 19721,  19273, 19277, 19723,  \n4914, 12294, 5174,  14863, 23365, 7764,  16063, 19726, 12286,  \n6602, 14824, 3160,  3973, 6798, 15289,  19731, 19727, 19729,  \n8776, 16640, 12974,  19731, 19729, 19733,  19731, 19733, 19734,  \n5063, 3230, 5058,  13048, 6813, 17626,  19735, 19734, 19738,  \n19734, 19733, 19736,  19737, 19738, 19734,  19734, 19736, 19741,  \n19736, 19739, 19741,  16932, 19740, 29690,  19734, 19741, 19737,  \n10117, 19742, 16457,  21970, 1685, 9109,  12041, 6982, 12096,  \n19747, 19741, 19739,  9774, 896, 17871,  7627, 15870, 18159,  \n23824, 9445, 10116,  8969, 16595, 15343,  19741, 19747, 19749,  \n19737, 19741, 19750,  19751, 19737, 19750,  7821, 2689, 2688,  \n19747, 19752, 19749,  17390, 15109, 19748,  19743, 19737, 19751,  \n19750, 19741, 19749,  19754, 19750, 19749,  19754, 19749, 19756,  \n19751, 19750, 19754,  19279, 19753, 19751,  19757, 19279, 19285,  \n19279, 19751, 19754,  19757, 19753, 19279,  19279, 19280, 19285,  \n19286, 19754, 19756,  19754, 19286, 19283,  19761, 7082, 17356,  \n13732, 2235, 629,  4532, 13449, 13753,  19746, 7798, 13644,  \n18675, 19196, 10697,  19292, 19757, 19285,  19286, 19756, 19764,  \n9577, 9579, 19762,  10124, 13942, 759,  19285, 19280, 19759,  \n19292, 19285, 19759,  19010, 10540, 10539,  14404, 14497, 3104,  \n7108, 1152, 9749,  19286, 19768, 19769,  19280, 19291, 19759,  \n16007, 9943, 6848,  19292, 19759, 19302,  13151, 16308, 9959,  \n19763, 19292, 19293,  3331, 3814, 14121,  19290, 19286, 19769,  \n19770, 19763, 19293,  11249, 2715, 11158,  1352, 1353, 17844,  \n21776, 5410, 13204,  17107, 2847, 12946,  17822, 2763, 15415,  \n19778, 12723, 12678,  14580, 9701, 13649,  11691, 19780, 19781,  \n10577, 14499, 16292,  3469, 17300, 8497,  19300, 19292, 19302,  \n19308, 19770, 19293,  3329, 15982, 15983,  11866, 9543, 19785,  \n15994, 1378, 7889,  19765, 19793, 19766,  19787, 7652, 7651,  \n3986, 9856, 17598,  4156, 16026, 14957,  19788, 19489, 18242,  \n19759, 19291, 19302,  21665, 1876, 513,  5655, 418, 419,  \n19789, 1176, 13716,  13827, 7406, 18866,  9107, 11619, 6128,  \n19308, 19293, 19303,  19770, 19308, 19309,  19775, 19779, 19310,  \n19796, 19775, 19310,  19775, 19796, 19792,  20327, 19797, 19792,  \n19782, 19766, 19793,  12940, 21456, 12677,  1646, 2296, 968,  \n670, 14305, 14995,  19784, 19307, 19779,  19782, 19793, 19794,  \n12542, 12337, 1619,  19784, 19309, 19307,  13265, 6424, 10558,  \n19331, 19792, 19796,  19792, 19331, 19793,  19301, 19290, 19799,  \n17843, 2446, 19800,  19779, 19307, 19310,  19794, 19793, 19331,  \n19801, 19192, 18726,  19301, 19799, 20348,  7398, 17051, 17023,  \n5944, 12819, 15085,  10278, 1010, 1009,  19310, 19307, 19317,  \n17041, 3914, 19191,  12858, 953, 2904,  7425, 2803, 1511,  \n18529, 15656, 10276,  7998, 13888, 15546,  19308, 19303, 19320,  \n15813, 14894, 11182,  12653, 15341, 11287,  14095, 16469, 7686,  \n18686, 10545, 2184,  19331, 19330, 19794,  12508, 2351, 2984,  \n8914, 9473, 18603,  11241, 2702, 15446,  10690, 3126, 6242,  \n19796, 19310, 19347,  19331, 19796, 19347,  8775, 16809, 15362,  \n19808, 20348, 19811,  12403, 1991, 13165,  17291, 2706, 6081,  \n380, 11217, 5471,  19330, 19813, 19794,  18653, 17559, 16903,  \n8852, 19326, 24271,  19310, 19317, 19347,  2523, 5517, 12476,  \n15361, 9319, 11862,  5817, 6367, 8845,  19305, 19808, 19333,  \n19817, 12375, 4277,  14930, 1296, 11799,  19330, 19331, 19347,  \n19330, 19821, 19813,  6232, 6233, 12192,  19823, 18840, 18346,  \n6284, 6066, 4275,  19347, 19348, 19822,  19821, 19330, 19822,  \n19347, 19822, 19330,  14593, 2865, 2864,  11940, 12568, 9299,  \n19836, 19337, 19341,  19821, 19831, 20363,  15022, 18738, 19833,  \n19334, 19333, 19834,  13486, 2956, 21588,  19341, 19835, 19836,  \n19348, 19339, 19345,  19822, 19831, 19821,  5012, 19838, 10978,  \n17785, 19832, 18845,  19334, 19835, 19341,  19840, 19345, 19836,  \n4917, 2664, 2219,  15910, 3877, 3878,  23383, 8954, 3387,  \n19822, 19348, 19841,  5009, 7339, 9474,  1371, 18327, 945,  \n11690, 3476, 14949,  4551, 13294, 13293,  19334, 19834, 19835,  \n8548, 13114, 9662,  11697, 5783, 11696,  19345, 19337, 19836,  \n19348, 19345, 19844,  19831, 19822, 19841,  13658, 13657, 721,  \n19348, 19844, 19841,  17221, 18965, 15560,  10910, 11554, 11555,  \n986, 8586, 17094,  3596, 13911, 4409,  14460, 9351, 13285,  \n19631, 19849, 5991,  19851, 18847, 18855,  19852, 15449, 19853,  \n19854, 21768, 19855,  5102, 10852, 18398,  9741, 4485, 21182,  \n19861, 21768, 19862,  19861, 19862, 19863,  3868, 8285, 1128,  \n9070, 9071, 18097,  17728, 15495, 19869,  19860, 19856, 19863,  \n9197, 17845, 9198,  16226, 18368, 17305,  14804, 15044, 6002,  \n17062, 17108, 15186,  19134, 19313, 16006,  3270, 12872, 13810,  \n15112, 9806, 15113,  10870, 13418, 14615,  4062, 19873, 1036,  \n19361, 18376, 19872,  19359, 19361, 19360,  19360, 19361, 19874,  \n14534, 11881, 3478,  19871, 19872, 18862,  4041, 8684, 4042,  \n18376, 18862, 19872,  12105, 7385, 5921,  16246, 3410, 10695,  \n7043, 17837, 7047,  13821, 19596, 19597,  19877, 18380, 20963,  \n1133, 2618, 2619,  18813, 19878, 17338,  14177, 19879, 13793,  \n3066, 5453, 12748,  17849, 19880, 18871,  19881, 17849, 17853,  \n5625, 7987, 5626,  13052, 13053, 11417,  18385, 19881, 17853,  \n18385, 18878, 19881,  18878, 19883, 19881,  18391, 18879, 19369,  \n3189, 10492, 12046,  19370, 19883, 18878,  6437, 11994, 5985,  \n19369, 19885, 18882,  5557, 14782, 2897,  15978, 19205, 7351,  \n10542, 5257, 18623,  6203, 15215, 8147,  18882, 19887, 18883,  \n17873, 18883, 18885,  11511, 10682, 13852,  14502, 2619, 19890,  \n1715, 1714, 6490,  1836, 13471, 15730,  8557, 7201, 2901,  \n18406, 19894, 18412,  4205, 12969, 5670,  17394, 16293, 18891,  \n8867, 14456, 19897,  8577, 10237, 19901,  19898, 18414, 17399,  \n17882, 18892, 18895,  15814, 17882, 18895,  7102, 15357, 13855,  \n8713, 5861, 4664,  12517, 19053, 5649,  1170, 5355, 19902,  \n11419, 6003, 6004,  19903, 1731, 2032,  16385, 5651, 18773,  \n13133, 11566, 13132,  19906, 9939, 4595,  4080, 17272, 20915,  \n845, 5001, 15315,  9830, 16375, 14481,  19497, 4905, 5341,  \n19905, 19397, 19395,  17272, 4080, 13893,  18900, 19905, 19395,  \n19781, 2081, 19907,  1181, 1182, 19908,  12631, 11694, 3611,  \n19910, 14311, 11466,  18910, 19397, 19909,  12607, 12211, 993,  \n18434, 18910, 18914,  17406, 17414, 19399,  16652, 10089, 10090,  \n17023, 17051, 18042,  19400, 17907, 18914,  11811, 1544, 19914,  \n14612, 15823, 7751,  13783, 10356, 19915,  835, 17707, 836,  \n2804, 8537, 1511,  3787, 4616, 10326,  3210, 6779, 10466,  \n18922, 19407, 18924,  18419, 3251, 17137,  11791, 19917, 4871,  \n16455, 15734, 1451,  13951, 12651, 9439,  13101, 8584, 4368,  \n18924, 19918, 19410,  17410, 13653, 5947,  14639, 19343, 18446,  \n19410, 19918, 19920,  19412, 14462, 19789,  19922, 19410, 19920,  \n19410, 19922, 19415,  17191, 408, 10160,  17922, 16411, 18479,  \n19923, 1990, 5144,  19415, 19925, 17460,  5652, 18773, 5651,  \n17932, 17939, 19929,  6537, 19932, 16711,  16919, 9165, 6725,  \n19933, 19425, 19930,  5096, 5997, 19522,  19930, 19425, 19424,  \n18946, 18948, 19424,  1992, 13995, 22979,  19935, 628, 16281,  \n6011, 18839, 18157,  19425, 19933, 18947,  19933, 20459, 18947,  \n6310, 11040, 10317,  18086, 9388, 11002,  12724, 15710, 12044,  \n19936, 19431, 19432,  19937, 19936, 19432,  10994, 9347, 10398,  \n18947, 20459, 19428,  15177, 15176, 18819,  19941, 18948, 17482,  \n19937, 19432, 18959,  6011, 754, 19949,  5817, 6299, 20528,  \n17482, 18491, 19941,  19937, 18959, 19442,  14167, 13810, 11145,  \n19477, 14696, 19101,  19428, 19437, 18953,  17666, 18529, 16345,  \n3935, 8227, 3480,  9229, 19952, 10595,  10538, 4458, 4457,  \n19954, 16391, 8420,  19955, 17880, 16641,  21082, 12525, 19609,  \n14216, 5478, 18559,  7708, 7709, 12901,  20473, 18962, 18967,  \n13198, 19611, 4359,  5934, 13845, 5277,  19448, 19953, 19442,  \n13042, 13999, 4071,  3570, 5421, 11904,  5594, 6290, 17166,  \n2141, 11853, 19957,  19962, 17965, 18515,  19457, 18984, 19961,  \n17645, 5044, 5808,  11869, 19965, 14098,  12373, 10155, 895,  \n12295, 12308, 384,  19462, 19966, 19967,  6090, 5255, 19969,  \n19970, 20063, 5537,  18606, 18605, 19972,  4931, 1899, 1900,  \n12037, 8547, 5339,  304, 7673, 7672,  18533, 19977, 17017,  \n14018, 11503, 10205,  6327, 1078, 8779,  23058, 8334, 19978,  \n18601, 3866, 6694,  16395, 5885, 5894,  8112, 12223, 2377,  \n13423, 19981, 13971,  19982, 17718, 19983,  17694, 6207, 18969,  \n19008, 19984, 19001,  19985, 6091, 809,  18548, 19980, 17026,  \n4676, 12529, 4677,  19481, 19000, 19001,  19984, 19481, 19001,  \n19008, 19987, 19984,  19009, 19987, 19008,  6786, 4284, 4283,  \n15633, 1166, 2601,  19480, 19481, 19486,  19140, 1944, 1943,  \n19014, 19483, 18544,  12249, 2922, 7410,  16587, 2173, 10419,  \n4731, 4732, 18072,  19728, 8900, 9526,  14763, 16780, 863,  \n11381, 4117, 11379,  3003, 9091, 3506,  19149, 17644, 1543,  \n19028, 17566, 18567,  19998, 19999, 19028,  9156, 12304, 1340,  \n752, 753, 20001,  2508, 2509, 9804,  20002, 13775, 1107,  \n19508, 17569, 19492,  10859, 18159, 20784,  7448, 923, 4306,  \n7062, 20003, 18963,  18047, 19998, 18567,  8221, 5350, 12015,  \n19507, 9476, 13308,  16253, 1386, 1387,  7756, 6991, 6992,  \n10243, 18674, 10244,  16552, 18573, 18577,  20006, 380, 5471,  \n17575, 14296, 19513,  1269, 10070, 1082,  20011, 16117, 11481,  \n14215, 18202, 18201,  4276, 8957, 1825,  2465, 2466, 15593,  \n19049, 19039, 19526,  19040, 13301, 313,  19530, 19056, 18568,  \n19508, 19530, 18568,  19044, 18563, 19071,  19664, 1056, 1055,  \n16737, 16984, 10099,  14374, 20019, 20020,  13650, 15304, 12377,  \n19060, 19526, 20531,  20021, 17477, 16851,  18047, 17103, 19529,  \n18581, 16028, 19521,  4475, 20024, 15413,  20026, 12466, 16508,  \n17604, 19058, 20027,  5068, 5067, 20029,  8990, 13046, 15991,  \n20023, 19058, 19067,  4661, 20031, 4662,  20032, 18062, 19537,  \n20032, 19061, 18062,  6706, 20033, 5893,  18319, 5213, 19806,  \n9504, 10843, 20034,  18591, 19056, 20035,  4681, 6112, 6113,  \n2167, 15028, 19939,  2819, 17740, 17840,  8712, 20036, 1719,  \n18602, 2204, 19893,  18591, 20035, 19538,  19543, 19537, 18598,  \n18898, 5728, 20043,  20045, 19538, 20035,  16090, 15570, 19083,  \n18597, 19080, 19543,  11911, 20049, 9372,  8841, 15944, 12369,  \n19077, 19538, 19546,  18608, 20051, 19071,  15553, 20539, 20052,  \n2939, 11465, 4835,  4167, 459, 458,  18068, 19546, 20546,  \n19093, 15553, 20052,  19189, 21712, 12658,  21712, 3682, 12658,  \n4808, 12625, 17007,  19556, 19558, 18078,  20055, 9794, 15055,  \n11246, 13622, 5876,  19081, 18068, 20546,  16029, 13535, 20057,  \n772, 650, 606,  1665, 12659, 16751,  19088, 20061, 19556,  \n20062, 12098, 9723,  20064, 17989, 20065,  18081, 19553, 18619,  \n9500, 2784, 5448,  19102, 19553, 20067,  18633, 19553, 19102,  \n2664, 2665, 2219,  17045, 19745, 20070,  18608, 18641, 20051,  \n19084, 17199, 19111,  8398, 8780, 969,  19105, 20071, 19115,  \n9389, 10521, 9856,  19104, 18113, 19561,  5300, 15877, 5301,  \n7235, 6607, 1242,  14140, 2816, 20073,  970, 8398, 969,  \n19572, 9245, 11795,  554, 20074, 16594,  3683, 6778, 19017,  \n1323, 14295, 4061,  18648, 18668, 18649,  2486, 18474, 18890,  \n15426, 2605, 17160,  16702, 18662, 20076,  20826, 18582, 15665,  \n12104, 15458, 13796,  17781, 11107, 1702,  20080, 18676, 19107,  \n18676, 17193, 19107,  20077, 20076, 18662,  12749, 3065, 12748,  \n19219, 5046, 15488,  5607, 2835, 8666,  20084, 19571, 18649,  \n7243, 16706, 20087,  19575, 19138, 17692,  16766, 13910, 16878,  \n20084, 18649, 19577,  4686, 1889, 4687,  20089, 17715, 19590,  \n20089, 18662, 17715,  906, 905, 5630,  1769, 1770, 19952,  \n20080, 19135, 18676,  3303, 17883, 17884,  20091, 4061, 9686,  \n5213, 5212, 19806,  5358, 7446, 20093,  17231, 13047, 19742,  \n11498, 856, 18326,  8494, 14791, 2457,  17125, 17124, 3072,  \n20099, 19147, 19135,  11772, 20100, 2331,  19577, 19591, 20102,  \n19577, 18668, 19591,  20103, 14736, 14588,  19606, 16744, 20105,  \n19606, 20107, 18700,  18700, 20107, 19159,  16176, 4512, 359,  \n14239, 7559, 12111,  20110, 12932, 7055,  10879, 10878, 2171,  \n14836, 12425, 10073,  18712, 21116, 18203,  876, 17764, 15230,  \n4275, 4274, 20501,  3272, 18801, 4210,  10022, 15626, 2275,  \n4621, 839, 12220,  6641, 537, 12044,  4585, 3748, 8666,  \n16638, 12349, 12350,  19170, 19178, 17745,  3212, 3211, 8807,  \n4773, 9746, 6988,  19170, 20115, 19178,  20116, 3316, 20117,  \n18973, 13772, 8164,  18421, 17310, 20095,  18027, 1023, 1275,  \n13566, 13565, 20120,  15732, 16534, 11803,  19294, 7084, 7083,  \n7762, 5948, 16999,  18682, 18699, 20122,  20122, 19591, 18682,  \n18401, 3256, 16674,  2353, 8693, 12584,  19624, 19179, 19182,  \n20127, 9356, 7715,  19268, 11182, 16374,  4477, 7514, 7359,  \n398, 9462, 17717,  11113, 17481, 5139,  18754, 19624, 19182,  \n8575, 14625, 8576,  9451, 19087, 9452,  18282, 19188, 19630,  \n4860, 7628, 7386,  7467, 16160, 16161,  20133, 8880, 14396,  \n20134, 19624, 20135,  20135, 19624, 18754,  5769, 2037, 4840,  \n18699, 19202, 20122,  19203, 18291, 19623,  20136, 20137, 20138,  \n18754, 17765, 20135,  9227, 2207, 13163,  13133, 4914, 11590,  \n4602, 8625, 6780,  20143, 20144, 5986,  20145, 15191, 15190,  \n8806, 19939, 18032,  18762, 19637, 20148,  18762, 20148, 17765,  \n2186, 14707, 6708,  511, 14707, 15276,  4831, 8230, 13381,  \n18285, 19651, 18270,  20152, 20151, 19652,  5124, 14927, 1992,  \n19657, 20152, 19652,  19981, 1188, 13971,  17005, 6342, 20159,  \n20152, 19657, 20158,  18300, 19217, 20155,  18779, 20149, 19202,  \n825, 6078, 7534,  21678, 20164, 16575,  20151, 20160, 19652,  \n19657, 19652, 19656,  2484, 11718, 10246,  13729, 13728, 6920,  \n20160, 19655, 19656,  18779, 20174, 20149,  1582, 5484, 10688,  \n16537, 20175, 1448,  20170, 19655, 20160,  16220, 7841, 17213,  \n6866, 9890, 5980,  19658, 20167, 20158,  12723, 4318, 10500,  \n5642, 2088, 15356,  15725, 13340, 13994,  980, 6819, 6577,  \n8183, 17667, 14370,  15690, 13880, 5873,  4625, 1613, 1614,  \n18805, 20155, 19671,  11688, 19976, 15464,  9629, 20177, 13894,  \n18777, 19661, 18779,  12773, 8861, 20179,  20167, 19658, 19668,  \n17532, 17129, 12460,  5641, 8340, 5642,  13118, 13117, 7355,  \n19662, 20183, 19669,  17186, 20015, 1605,  16115, 19180, 15706,  \n20178, 18806, 18802,  10850, 14450, 20186,  2923, 6786, 2922,  \n13163, 13162, 7550,  2296, 2541, 968,  20188, 11531, 10129,  \n15602, 20193, 14672,  10820, 5081, 5082,  16191, 20194, 10677,  \n1918, 15628, 9407,  19674, 19669, 20212,  10142, 4851, 11443,  \n19676, 19234, 19243,  20187, 19234, 19676,  4825, 4827, 22220,  \n4648, 21695, 4647,  20200, 3557, 20085,  14798, 20676, 20201,  \n1369, 7452, 1370,  19236, 20198, 19681,  19668, 19658, 19699,  \n14028, 18629, 14831,  2895, 1803, 18829,  20214, 19674, 20212,  \n19658, 19254, 19699,  12459, 18227, 12654,  17237, 8374, 7658,  \n19245, 19241, 19697,  7674, 19986, 19377,  20216, 6004, 20217,  \n3653, 11095, 11097,  19241, 19681, 19691,  19697, 19246, 19245,  \n15527, 8136, 9572,  4165, 10093, 15940,  596, 17373, 7318,  \n19674, 20214, 19706,  20218, 19691, 19681,  2929, 15554, 20265,  \n18943, 10386, 16095,  1689, 11125, 5308,  19699, 19713, 19710,  \n2948, 20208, 10268,  19484, 7093, 14773,  18388, 16382, 9126,  \n19700, 19706, 19713,  11204, 11604, 8156,  19124, 13665, 877,  \n16290, 12389, 5280,  20225, 19246, 19697,  20211, 20210, 20226,  \n20227, 19983, 17718,  4624, 13726, 19344,  20228, 18836, 19715,  \n18664, 2983, 19096,  13723, 13965, 13969,  20229, 19710, 19713,  \n19263, 18823, 19260,  20230, 10769, 9613,  9040, 15540, 11133,  \n20226, 20210, 20233,  20233, 20210, 20235,  19075, 17224, 19149,  \n20210, 20232, 20235,  18911, 20242, 18354,  20244, 6146, 19037,  \n20246, 20226, 20233,  3732, 19718, 3733,  19273, 20245, 19715,  \n20233, 20235, 20248,  20246, 20243, 20226,  20249, 19263, 19270,  \n19275, 19263, 20249,  19720, 20245, 19273,  19275, 20249, 19721,  \n5753, 5752, 13398,  19273, 19723, 19720,  20233, 20248, 20246,  \n20251, 20246, 19725,  20667, 15175, 14392,  20252, 1998, 20253,  \n12564, 4092, 3404,  16653, 11380, 2322,  20254, 19277, 19721,  \n19277, 20254, 19723,  20257, 20251, 19725,  4870, 4869, 1722,  \n19724, 20246, 20248,  20246, 19724, 19725,  16654, 16655, 9767,  \n20248, 20258, 19724,  3642, 490, 6587,  20262, 8763, 8764,  \n6899, 19169, 21504,  20257, 19725, 20263,  20725, 20257, 20263,  \n12913, 20265, 14705,  20264, 19724, 20258,  19725, 19724, 20264,  \n475, 15442, 15443,  19725, 20264, 20263,  3889, 6692, 3077,  \n6098, 20119, 1756,  10415, 22033, 6302,  1444, 10159, 7054,  \n20263, 20264, 20266,  20264, 20268, 20266,  20268, 20271, 20272,  \n20270, 20266, 20268,  21343, 19200, 10000,  20270, 20268, 20273,  \n20274, 20736, 20270,  20266, 20270, 20736,  20273, 20268, 20275,  \n14185, 10930, 18572,  7853, 19988, 1944,  12721, 13474, 13473,  \n20273, 20275, 20277,  8904, 3314, 588,  20273, 20277, 20270,  \n20279, 20270, 20277,  19670, 14962, 18758,  9172, 14281, 16703,  \n11760, 1940, 23132,  20280, 20275, 20281,  20277, 20275, 20280,  \n20282, 20277, 20280,  20284, 20778, 20285,  20284, 20285, 20286,  \n17360, 4262, 10745,  20783, 20287, 20285,  10781, 5780, 5385,  \n425, 8880, 20133,  19727, 20289, 20288,  5358, 20093, 5359,  \n5879, 7377, 2398,  20292, 20289, 19727,  12459, 12091, 19205,  \n20294, 20295, 3881,  22634, 14708, 14480,  5910, 2166, 20515,  \n11989, 6392, 16733,  9106, 2007, 7412,  20296, 20293, 19727,  \n19730, 20288, 20290,  10179, 20001, 893,  20292, 19727, 20293,  \n19729, 19727, 20288,  10434, 570, 571,  11711, 14871, 12869,  \n19729, 20288, 19730,  20290, 20291, 19730,  19733, 19729, 19730,  \n19727, 19731, 20296,  18784, 18785, 10290,  1617, 7219, 4803,  \n13361, 18158, 1955,  2275, 14582, 10022,  8315, 14029, 9822,  \n19731, 19734, 20296,  19735, 20296, 19734,  6931, 14867, 6932,  \n25069, 13817, 18175,  8678, 20069, 8679,  20835, 19738, 20299,  \n8282, 15456, 15457,  4326, 12203, 2272,  4785, 7807, 9301,  \n10336, 9058, 18025,  19733, 19739, 19736,  20301, 20299, 19743,  \n20299, 19738, 19743,  19738, 19737, 19743,  4698, 11718, 2484,  \n20302, 20301, 19743,  3941, 7522, 3940,  11361, 997, 998,  \n9862, 20304, 14593,  5707, 11745, 2728,  19753, 20301, 20302,  \n16343, 13301, 20306,  20302, 19743, 19751,  19739, 20303, 20308,  \n20309, 19739, 20308,  20302, 19751, 19753,  17617, 15112, 1700,  \n11151, 18538, 6358,  19747, 19739, 20309,  16251, 19551, 16252,  \n19752, 19747, 20309,  1189, 4560, 11586,  19749, 19752, 20311,  \n11385, 6117, 7304,  15112, 11811, 11812,  4673, 17345, 14708,  \n11932, 20312, 11933,  19091, 1329, 20313,  3873, 11043, 8040,  \n11117, 18423, 18424,  20314, 19755, 19757,  19755, 19753, 19757,  \n19756, 19749, 20311,  6148, 3014, 6133,  19765, 21372, 20316,  \n20868, 21372, 20320,  7546, 2296, 1646,  21372, 19765, 20320,  \n15124, 5860, 5859,  12880, 11400, 11401,  4953, 9138, 2852,  \n4533, 16346, 5114,  20320, 19765, 19766,  19776, 20320, 19766,  \n18112, 3128, 19726,  3071, 9176, 19443,  19773, 19763, 19770,  \n20322, 19773, 19770,  19775, 20323, 19779,  20323, 19784, 19779,  \n5127, 5126, 18636,  18202, 12038, 18201,  21220, 1656, 18133,  \n20326, 16955, 19650,  19775, 19792, 19797,  19378, 14093, 19377,  \n19286, 19764, 19768,  20330, 20322, 19770,  20331, 20330, 19784,  \n12400, 9938, 19968,  2384, 7181, 11258,  6441, 1364, 6442,  \n19765, 20316, 20327,  18149, 20329, 4921,  19770, 19309, 20330,  \n13144, 15745, 18846,  10177, 12930, 10176,  7569, 7570, 18759,  \n16665, 13566, 16666,  16705, 20333, 16706,  19784, 20330, 19309,  \n19792, 19793, 20327,  20327, 19793, 19765,  8304, 18323, 8654,  \n2280, 2279, 19600,  16910, 18614, 18615,  10658, 10012, 10013,  \n731, 15258, 17539,  19776, 19766, 19782,  19799, 19290, 19769,  \n25634, 29090, 8629,  20337, 7272, 17887,  16669, 488, 16670,  \n19782, 20339, 19776,  4700, 8094, 1647,  12389, 12518, 5280,  \n9728, 9000, 10375,  1421, 1752, 1911,  20345, 13050, 2782,  \n19799, 20347, 20348,  1496, 4155, 6538,  20350, 11222, 3206,  \n20352, 19794, 19813,  14329, 14330, 19996,  19808, 19305, 20348,  \n4703, 4259, 4704,  8843, 2138, 2227,  8013, 20242, 15496,  \n4704, 4259, 5504,  4803, 12617, 1617,  7044, 7677, 20355,  \n20356, 6093, 10814,  3149, 3148, 17362,  7449, 7605, 5103,  \n13736, 10804, 3477,  5700, 4956, 8852,  18842, 18346, 17784,  \n19333, 19808, 20360,  11126, 16141, 13972,  19813, 19821, 20354,  \n20354, 20363, 20357,  9549, 5024, 5583,  13175, 9397, 15530,  \n8785, 20366, 14412,  19834, 19333, 20360,  20363, 20354, 19821,  \n5581, 17347, 16023,  20369, 2383, 6967,  7768, 18501, 8032,  \n14398, 7242, 2620,  5662, 13087, 19355,  19446, 13150, 13187,  \n21668, 5656, 10309,  19842, 18843, 17793,  19836, 19835, 19843,  \n18850, 17284, 20371,  6292, 4976, 4977,  5793, 11383, 10462,  \n9716, 6011, 20886,  20374, 19831, 19841,  20375, 19831, 20374,  \n13327, 7625, 12370,  2557, 15535, 1936,  19851, 19842, 18847,  \n19844, 19345, 19840,  11034, 7277, 11035,  19840, 19836, 20373,  \n6662, 18788, 19406,  17550, 9187, 18605,  7778, 13862, 5761,  \n19841, 19844, 20377,  15440, 6449, 13210,  15147, 19645, 20379,  \n20374, 19841, 20377,  20381, 20382, 19856,  19860, 18857, 19859,  \n7916, 1560, 15859,  8873, 17752, 3101,  2264, 9686, 13915,  \n14262, 487, 947,  20384, 18460, 1357,  4553, 10611, 4552,  \n20385, 5747, 14781,  4470, 10848, 9221,  17305, 18368, 19358,  \n4099, 823, 2589,  17732, 5507, 10756,  7185, 20386, 3691,  \n18377, 18854, 20387,  7130, 19391, 16677,  725, 726, 6719,  \n20389, 2739, 2740,  15267, 13382, 8354,  19872, 20391, 19361,  \n14186, 1311, 13694,  19361, 20391, 19874,  14164, 11859, 5214,  \n2820, 3615, 3830,  20394, 9283, 6479,  19871, 18862, 18381,  \n18865, 18377, 20963,  13814, 479, 481,  18874, 18380, 20396,  \n18380, 19877, 20396,  6178, 16104, 6179,  8667, 3199, 6339,  \n18874, 20396, 19366,  9918, 6846, 11405,  20401, 16133, 23307,  \n19880, 17849, 19881,  14642, 11422, 5295,  16012, 8484, 3565,  \n19675, 20403, 16681,  18391, 19366, 18879,  1203, 8289, 19350,  \n7824, 15931, 12334,  10510, 20888, 18180,  6588, 5982, 7423,  \n18882, 19885, 20405,  19883, 19370, 19373,  2287, 6801, 2286,  \n3632, 6501, 1962,  20405, 19887, 18882,  19373, 19376, 19883,  \n5879, 5595, 5880,  19376, 18414, 19883,  20977, 18885, 18883,  \n20409, 15488, 20410,  18406, 18885, 19894,  20411, 14872, 6153,  \n19894, 19895, 18412,  20412, 22571, 11210,  4971, 15197, 12730,  \n3414, 14351, 3415,  18412, 19895, 18891,  2721, 11474, 11892,  \n15423, 8403, 10197,  8149, 20414, 16118,  17394, 18891, 18892,  \n6261, 2112, 4633,  2128, 20415, 13246,  4823, 6058, 14630,  \n9829, 16256, 7730,  16957, 14336, 8575,  18996, 17808, 6836,  \n3375, 20041, 579,  19905, 16876, 18895,  2882, 17419, 2881,  \n825, 826, 6078,  18900, 16876, 19905,  14712, 15418, 6498,  \n13937, 15537, 20417,  5755, 17474, 2540,  19397, 19905, 19909,  \n20416, 17399, 14109,  4954, 6916, 17225,  6281, 10324, 8331,  \n20422, 18910, 19909,  7432, 15260, 14515,  18914, 18910, 20422,  \n5743, 20423, 19257,  14352, 9423, 14353,  9302, 12495, 12494,  \n17602, 14857, 11987,  10477, 4594, 18578,  18914, 20427, 19400,  \n19399, 18458, 19403,  5705, 4262, 1524,  16239, 20429, 4691,  \n19400, 20430, 19401,  20431, 20432, 20433,  20430, 18922, 19401,  \n4, 12154, 8658,  16658, 20435, 16968,  9476, 9478, 13308,  \n6552, 7123, 8456,  2363, 14650, 4710,  15938, 9330, 991,  \n17079, 9095, 7665,  2562, 15934, 7373,  20437, 20438, 16896,  \n2038, 3386, 15911,  5089, 3592, 8921,  13332, 12453, 19414,  \n17922, 18479, 20442,  19920, 20444, 19922,  6908, 6340, 6909,  \n17932, 19417, 17465,  1474, 1473, 14030,  20446, 19415, 19922,  \n19415, 20446, 20447,  19415, 20447, 19925,  9138, 9137, 10952,  \n19929, 19417, 17932,  20448, 20449, 19930,  19424, 20448, 19930,  \n6467, 6466, 11849,  19434, 19431, 20446,  20446, 19922, 19434,  \n20446, 19431, 19936,  20447, 19936, 20450,  20447, 20446, 19936,  \n19930, 20449, 19933,  11548, 20452, 20453,  19434, 19433, 19431,  \n7945, 4749, 8440,  11445, 8126, 18510,  14503, 20455, 20456,  \n5762, 12689, 12688,  19922, 20444, 19436,  19922, 19436, 19434,  \n6470, 6895, 2914,  20520, 5392, 20457,  739, 740, 1536,  \n20450, 19936, 19937,  20461, 20462, 20463,  18621, 10927, 10928,  \n7371, 18043, 17489,  16215, 8176, 6950,  19428, 20459, 20464,  \n14648, 20465, 970,  9166, 9614, 19707,  16590, 7809, 20466,  \n4220, 5000, 846,  19937, 19442, 20468,  5472, 20129, 19248,  \n19436, 20471, 18496,  18496, 20471, 18968,  2396, 10198, 4874,  \n19953, 20468, 19442,  5944, 15216, 5943,  11099, 3630, 6935,  \n12005, 1789, 18091,  18968, 20473, 18967,  6622, 21271, 18337,  \n19452, 19953, 19448,  20475, 19452, 19454,  20477, 12261, 9423,  \n11959, 9338, 20478,  10496, 11817, 19130,  20475, 19454, 19457,  \n19961, 18984, 19462,  11074, 13802, 13801,  19457, 19961, 20475,  \n7221, 18853, 13744,  19962, 18515, 19455,  19966, 17520, 17965,  \n6029, 7791, 7790,  10035, 7980, 12674,  13564, 12674, 13173,  \n3657, 10146, 9225,  4959, 17644, 16461,  5750, 2777, 18714,  \n17981, 18993, 20489,  15036, 7846, 14727,  6000, 13177, 6001,  \n18262, 18148, 7621,  19476, 18536, 17981,  20986, 8333, 10018,  \n17026, 20490, 18533,  19977, 18533, 20490,  6888, 20491, 2810,  \n14326, 10422, 6049,  20490, 17026, 19980,  16628, 4499, 7408,  \n10456, 5904, 15549,  20493, 11293, 20494,  11512, 20495, 899,  \n11880, 11537, 7693,  18544, 19483, 19009,  10886, 4166, 23711,  \n5105, 3915, 8501,  19481, 19984, 19486,  23705, 3072, 20497,  \n19009, 20498, 19987,  19483, 20498, 19009,  20499, 19483, 19014,  \n10137, 12208, 7749,  18703, 6770, 20994,  20500, 14257, 4495,  \n18537, 19989, 19482,  17241, 20501, 930,  17669, 10564, 12675,  \n13216, 8197, 11363,  9318, 12877, 16489,  13953, 16135, 4511,  \n19486, 20502, 19490,  9558, 7607, 6483,  8154, 20162, 16853,  \n19492, 18554, 19482,  19490, 20502, 19997,  20505, 20441, 20117,  \n931, 13281, 7663,  12025, 14681, 14680,  10702, 1354, 13846,  \n17049, 19028, 20507,  20508, 20509, 19492,  11375, 10415, 6302,  \n20508, 19492, 19482,  19039, 19490, 19997,  7602, 19466, 11275,  \n19490, 19039, 19038,  20000, 17054, 15438,  7107, 20513, 3373,  \n19028, 18567, 19998,  3147, 3149, 8683,  18202, 19364, 13654,  \n14916, 1438, 11474,  5311, 10628, 738,  16939, 2545, 18259,  \n19513, 20519, 17575,  15438, 19044, 20000,  10172, 13963, 9033,  \n9938, 19902, 5355,  18370, 14788, 14789,  5436, 2347, 20522,  \n20523, 18044, 17604,  17825, 8312, 15647,  9483, 18603, 9473,  \n14881, 9869, 2775,  1158, 8234, 20059,  20527, 4245, 11645,  \n1789, 17924, 4265,  20524, 19056, 19530,  18592, 17112, 18581,  \n19067, 19532, 20023,  18592, 18581, 20530,  17628, 2472, 2473,  \n7700, 14441, 18148,  19728, 8899, 8900,  2325, 3258, 10135,  \n19071, 20037, 19044,  13576, 1247, 13574,  20532, 9990, 17248,  \n18145, 7117, 18146,  760, 9656, 15264,  18727, 1344, 1671,  \n19056, 20535, 20536,  16102, 738, 18009,  14199, 14201, 15054,  \n19666, 10937, 10321,  18065, 8867, 8869,  9418, 3891, 10502,  \n9126, 9083, 9124,  19537, 19543, 20533,  12146, 18927, 4144,  \n5120, 11258, 5121,  20045, 20048, 19538,  11237, 11236, 19780,  \n9215, 514, 7881,  19546, 19538, 20048,  20545, 20061, 19088,  \n11890, 16620, 12727,  11298, 4014, 14231,  6421, 16115, 3564,  \n469, 16870, 470,  9260, 20549, 14676,  18658, 21692, 3688,  \n2601, 1166, 22994,  20550, 19081, 20546,  22776, 5836, 20551,  \n1889, 15948, 4687,  8730, 10200, 3232,  5550, 21519, 20552,  \n8816, 15887, 8817,  13128, 2780, 727,  6202, 15317, 15099,  \n9516, 9513, 249,  12977, 11830, 17289,  19104, 19570, 18120,  \n20071, 19105, 20557,  2900, 3886, 9534,  19102, 20557, 19105,  \n7571, 5159, 5158,  20051, 18641, 20548,  20558, 20559, 20556,  \n18661, 18120, 19570,  20056, 11152, 6237,  19093, 20559, 19107,  \n7544, 14067, 8718,  3951, 7831, 10316,  7998, 11733, 13888,  \n19111, 16702, 20076,  20077, 18662, 20089,  19115, 20564, 18713,  \n8800, 17342, 2290,  17280, 12056, 17396,  16287, 15062, 6958,  \n14494, 15119, 2650,  4530, 2543, 4531,  1291, 13873, 17831,  \n19125, 21112, 18641,  1518, 16802, 20036,  10799, 20384, 20570,  \n20080, 20568, 19135,  652, 6513, 16888,  16353, 4467, 13506,  \n12036, 20030, 4700,  20568, 20099, 19135,  16744, 17234, 20105,  \n17234, 18706, 20105,  7536, 7216, 731,  19601, 19595, 19146,  \n17879, 9235, 1314,  20099, 19601, 19147,  16539, 20576, 2674,  \n9021, 10768, 7138,  14465, 11528, 10229,  363, 364, 5275,  \n5429, 15509, 13962,  15941, 20578, 13767,  17254, 11929, 10463,  \n12814, 11227, 13924,  19623, 19167, 20582,  19167, 19159, 20582,  \n564, 6877, 11543,  19163, 18239, 19613,  15487, 17486, 18684,  \n19176, 19167, 19623,  5688, 3677, 5689,  13915, 4013, 2264,  \n18123, 7489, 4263,  19613, 18254, 19179,  19194, 19173, 20577,  \n6089, 6311, 8909,  19125, 19154, 20586,  10138, 13333, 15532,  \n19624, 19613, 19179,  7557, 7556, 13745,  15721, 14266, 15708,  \n22780, 14783, 19426,  19188, 19178, 20588,  1307, 10720, 966,  \n24631, 7244, 7310,  13588, 13645, 13151,  9805, 12907, 16718,  \n3947, 2661, 18342,  20593, 19188, 20590,  1956, 20594, 3273,  \n20417, 4286, 13727,  20596, 5064, 4720,  19630, 19188, 20593,  \n7312, 6224, 19033,  19630, 20593, 20132,  19447, 11468, 689,  \n20591, 19624, 20134,  1930, 1929, 5149,  9223, 794, 14983,  \n20122, 20598, 19591,  18270, 19651, 19154,  12595, 20599, 16851,  \n19630, 20132, 19198,  20600, 5806, 18562,  10409, 1683, 6548,  \n8983, 860, 18259,  20132, 20603, 19198,  19637, 19198, 20603,  \n13086, 13142, 12548,  7568, 742, 395,  1951, 13390, 14573,  \n20606, 8925, 6021,  16869, 9327, 20607,  2564, 9101, 6166,  \n17765, 20148, 20135,  20609, 5215, 17861,  20610, 3955, 4181,  \n2859, 13648, 4637,  11140, 12444, 9711,  1648, 13425, 20150,  \n17345, 14000, 14708,  15051, 18916, 15257,  8651, 23193, 2590,  \n20605, 20148, 19637,  20148, 20605, 20608,  20613, 20151, 20152,  \n3676, 9618, 3677,  20510, 8558, 11118,  15441, 15440, 1672,  \n20122, 20149, 20598,  20160, 20616, 20170,  14691, 5069, 12422,  \n20158, 20614, 20152,  17266, 17265, 8792,  20149, 20122, 19202,  \n20620, 20171, 20170,  20170, 20616, 20620,  20160, 19656, 19652,  \n6648, 11162, 5232,  20623, 632, 17522,  8102, 20624, 8103,  \n15459, 13707, 13706,  20627, 5882, 706,  19224, 20625, 19651,  \n16718, 3603, 9805,  16536, 19788, 3502,  16536, 8700, 19788,  \n8289, 12283, 19350,  9909, 2659, 2658,  19662, 20170, 20171,  \n20174, 18779, 20631,  14614, 9930, 5077,  20183, 19662, 20171,  \n9860, 15132, 16615,  4712, 14261, 8637,  20635, 5268, 2310,  \n8505, 8506, 3451,  20183, 20171, 20639,  20628, 19671, 20155,  \n9398, 16525, 7179,  8714, 2602, 20640,  4840, 19193, 19891,  \n17768, 13427, 13426,  7839, 5181, 7070,  1834, 7719, 12017,  \n20167, 19668, 21589,  18832, 6672, 5706,  1548, 10614, 20645,  \n20637, 20646, 20636,  13236, 15109, 23267,  19668, 20185, 21589,  \n3609, 4610, 18502,  20631, 18779, 19661,  20632, 20213, 20639,  \n10021, 12498, 624,  20137, 4884, 20138,  13322, 17346, 13323,  \n20632, 20636, 20213,  3141, 8401, 1147,  9064, 19698, 6236,  \n13075, 4872, 14020,  20187, 19661, 19234,  8797, 3420, 4588,  \n19224, 20654, 20625,  20213, 20636, 20646,  20185, 20678, 20656,  \n20659, 8335, 21969,  20185, 19668, 20678,  19671, 20660, 19236,  \n10822, 4939, 10823,  19803, 15165, 14865,  19204, 3577, 20661,  \n20662, 18016, 9765,  3393, 4283, 4284,  13957, 10738, 10739,  \n14644, 7084, 19294,  19224, 18814, 20654,  20213, 20646, 20210,  \n20667, 3893, 16488,  5073, 20668, 8970,  20660, 20198, 19236,  \n12932, 20110, 4850,  20655, 20213, 20666,  17306, 15591, 20669,  \n20183, 20212, 19669,  17240, 1913, 4086,  9955, 14320, 1728,  \n1070, 2507, 12028,  20671, 15065, 20672,  20673, 13887, 6829,  \n3500, 6486, 12215,  16826, 4268, 4770,  8626, 8187, 4760,  \n19699, 20678, 19668,  12448, 6894, 12983,  11739, 6867, 348,  \n18459, 14972, 14973,  2586, 4263, 10819,  20210, 20211, 20213,  \n14772, 20675, 11723,  5384, 12196, 15347,  18119, 3412, 4152,  \n7455, 8546, 16892,  14492, 14491, 15255,  11295, 5875, 12232,  \n9195, 16038, 12482,  9327, 20679, 2623,  5308, 20680, 8599,  \n20213, 20211, 20666,  4381, 12633, 13831,  8255, 8254, 7664,  \n21194, 19681, 20198,  6304, 10651, 22556,  14207, 9682, 13408,  \n13436, 18142, 13437,  9554, 10986, 1542,  20210, 20646, 20685,  \n20624, 20687, 20688,  10852, 3870, 6150,  14227, 19055, 20256,  \n18836, 20228, 18814,  13627, 11411, 5577,  5016, 10579, 3335,  \n19681, 20220, 20690,  19693, 19246, 20225,  20666, 20211, 20226,  \n20243, 20666, 20226,  20666, 20243, 20681,  20691, 13863, 11564,  \n4674, 7710, 7711,  10880, 11821, 8743,  20702, 19693, 20225,  \n20693, 12721, 13473,  20232, 20210, 20695,  20214, 20697, 19706,  \n20704, 19699, 19710,  20218, 19681, 20690,  19691, 20218, 19697,  \n20700, 20701, 20702,  5129, 480, 9591,  20703, 19710, 20229,  \n20704, 19710, 20703,  6956, 8899, 14944,  20225, 19697, 20700,  \n3898, 19342, 2287,  4094, 1130, 1129,  10013, 10012, 1286,  \n20708, 20232, 20695,  13209, 11085, 8811,  19087, 19824, 7340,  \n21200, 20243, 20251,  5194, 6434, 20709,  20235, 20232, 20710,  \n20243, 20246, 20251,  11096, 17634, 11073,  20232, 20708, 20710,  \n17672, 19017, 7215,  17865, 15157, 17864,  17122, 16697, 17250,  \n10879, 15778, 10877,  3431, 20713, 3432,  10933, 20717, 13419,  \n20710, 20250, 20235,  10616, 1928, 8107,  20715, 20251, 20257,  \n18717, 4390, 5048,  20249, 20716, 19721,  20710, 20718, 20250,  \n13894, 11656, 20719,  20254, 19721, 20720,  13310, 15229, 5264,  \n20250, 20718, 20721,  20250, 20248, 20235,  20722, 20723, 20257,  \n13470, 12502, 9248,  20230, 7138, 10768,  20258, 20248, 20250,  \n15889, 15890, 18294,  6131, 16204, 15186,  20258, 20250, 20721,  \n9546, 12416, 12732,  20725, 20722, 20257,  11771, 12085, 15432,  \n1411, 14645, 12471,  20730, 20725, 20731,  5150, 16631, 20732,  \n13343, 10782, 14584,  20733, 20258, 20721,  20734, 16759, 13794,  \n20294, 10591, 20520,  20725, 20263, 20266,  17894, 2822, 19342,  \n9225, 7367, 4679,  20735, 2501, 20365,  20271, 20264, 20258,  \n20258, 20733, 20271,  981, 11620, 11621,  6318, 14346, 14696,  \n20736, 20725, 20266,  20268, 20264, 20271,  20271, 20733, 20272,  \n13863, 16114, 13444,  20268, 20272, 20275,  20275, 20272, 20737,  \n6235, 6234, 1722,  20739, 20274, 20270,  11335, 14668, 13326,  \n20275, 20737, 20281,  20739, 20270, 20279,  1342, 2557, 1936,  \n3861, 3860, 14336,  20740, 20739, 20741,  20279, 20277, 20282,  \n20741, 20739, 20742,  20739, 20279, 20742,  20279, 20282, 20742,  \n15662, 7083, 7085,  3667, 3652, 19464,  2656, 7879, 4421,  \n2202, 17542, 20063,  20280, 20745, 20282,  20742, 20282, 20746,  \n20741, 20746, 20747,  20280, 20744, 20745,  20746, 20282, 20745,  \n18658, 3688, 13930,  8396, 2871, 16512,  3320, 13899, 1589,  \n20745, 20744, 20750,  17498, 14943, 11575,  20746, 20745, 20751,  \n13108, 8590, 17308,  16613, 13027, 17870,  20751, 20745, 20750,  \n20754, 20749, 20746,  9855, 5682, 5324,  2232, 5062, 15200,  \n20754, 20746, 20751,  19378, 19377, 19986,  10288, 20756, 10289,  \n18009, 738, 11184,  4591, 4592, 16554,  19786, 14226, 15394,  \n20749, 20754, 20757,  20758, 9136, 9785,  3913, 10740, 4344,  \n11696, 11980, 11979,  25581, 9553, 20759,  520, 19168, 6946,  \n20760, 15751, 6093,  3934, 14175, 13842,  17078, 11399, 11840,  \n2949, 20041, 13256,  20754, 20751, 20761,  13156, 2649, 19268,  \n1542, 19149, 1543,  18656, 18292, 8893,  20754, 20762, 20757,  \n2799, 19419, 12402,  7144, 9270, 14615,  17375, 1958, 14921,  \n21273, 20765, 20764,  14540, 3668, 2063,  4027, 17958, 12933,  \n20768, 20765, 20766,  12900, 5983, 14832,  20770, 21273, 20763,  \n21273, 20770, 20765,  929, 18906, 17241,  17693, 19112, 20772,  \n20766, 20773, 20769,  20773, 20765, 20770,  20766, 20765, 20773,  \n8119, 18350, 8120,  20770, 20763, 20774,  20770, 20774, 20777,  \n20778, 20773, 20770,  17272, 1989, 10753,  20781, 4039, 29562,  \n20335, 7735, 10957,  20770, 20777, 20778,  20780, 20773, 20778,  \n7935, 14944, 6260,  20240, 2648, 16549,  20284, 20780, 20778,  \n20777, 20783, 20778,  11246, 5877, 5670,  14707, 1281, 11682,  \n20285, 20778, 20783,  20777, 20785, 20783,  11817, 11403, 20379,  \n20785, 20777, 20782,  14772, 390, 17822,  10057, 5414, 20476,  \n20284, 20286, 20786,  4872, 13075, 15947,  20791, 20284, 20786,  \n20791, 20786, 20789,  2566, 7735, 289,  18383, 20792, 20793,  \n16017, 14929, 24915,  3952, 3951, 9783,  15163, 5299, 15583,  \n6853, 6852, 20050,  20786, 20292, 20789,  15537, 12504, 17271,  \n13384, 10808, 20798,  788, 9148, 20801,  4509, 7866, 16236,  \n20787, 20788, 20802,  9768, 11028, 13277,  9163, 3443, 8895,  \n20783, 20806, 20287,  20786, 20286, 20289,  20286, 20285, 20808,  \n507, 7947, 19819,  20285, 20287, 20808,  20289, 20286, 20808,  \n20292, 20786, 20289,  20808, 20287, 20809,  4240, 5860, 2321,  \n8590, 9157, 20811,  1587, 17764, 876,  6972, 20771, 6973,  \n20808, 20288, 20289,  18826, 8106, 1056,  6425, 6424, 13265,  \n10469, 16883, 10354,  20815, 13212, 10499,  20288, 20808, 20290,  \n18345, 7004, 16193,  12310, 8490, 9839,  15638, 10766, 17974,  \n11966, 2870, 9475,  13937, 12504, 15537,  20807, 20817, 20814,  \n13586, 19181, 15534,  20291, 20809, 20818,  20808, 20291, 20290,  \n20808, 20809, 20291,  15319, 3390, 15320,  20292, 20293, 20820,  \n21321, 20821, 20817,  20824, 20814, 20817,  20807, 20814, 20822,  \n19498, 17931, 13831,  20820, 20293, 20296,  20827, 20820, 20296,  \n11790, 8218, 8217,  20817, 20828, 20829,  20814, 20824, 20822,  \n20827, 20296, 19735,  13861, 16350, 9975,  5549, 20831, 17478,  \n20828, 20821, 20832,  20817, 20821, 20828,  16098, 13590, 10875,  \n20824, 20817, 20829,  20291, 21699, 20833,  20827, 19735, 20835,  \n20833, 19730, 20291,  20828, 20836, 20829,  20837, 5970, 19504,  \n875, 20838, 9111,  738, 4329, 4331,  19738, 20835, 19735,  \n1244, 1245, 2099,  2114, 6021, 15040,  622, 5564, 19916,  \n15240, 16465, 6009,  19627, 18902, 3083,  14516, 1295, 3118,  \n329, 15006, 330,  19123, 5466, 19122,  20833, 20840, 19730,  \n9187, 18989, 18605,  20836, 20846, 20829,  17100, 14790, 9095,  \n20848, 20841, 20299,  19733, 19730, 20840,  20848, 20299, 20301,  \n20836, 20845, 20846,  19739, 19733, 20840,  20679, 16904, 16544,  \n20845, 20836, 20850,  17837, 29630, 7047,  16381, 10387, 3179,  \n10471, 10661, 11753,  20856, 20846, 20845,  2948, 10268, 2946,  \n20303, 19739, 20840,  6046, 12482, 12483,  7128, 8324, 11173,  \n16908, 15402, 5052,  20301, 19753, 19755,  10315, 20860, 16121,  \n16018, 4575, 4574,  8451, 11726, 11728,  20845, 20850, 20856,  \n1499, 12371, 1752,  12957, 18877, 15102,  21550, 3965, 16233,  \n6785, 526, 525,  19949, 754, 6392,  17577, 14456, 8867,  \n13661, 2706, 11803,  20866, 3459, 3237,  19633, 19632, 2957,  \n3190, 8713, 10501,  9614, 5596, 2493,  4393, 2089, 2090,  \n20850, 20865, 20856,  6719, 18685, 13863,  3285, 18287, 15456,  \n20865, 20870, 20856,  19498, 12633, 10637,  19677, 4734, 1100,  \n20875, 20314, 19757,  20862, 20868, 20878,  15008, 17081, 1783,  \n20311, 19752, 20309,  21372, 20868, 20869,  4642, 4896, 4643,  \n19196, 20234, 9524,  17867, 4676, 4678,  19221, 3802, 3803,  \n20865, 20319, 20870,  20308, 20882, 20883,  13333, 4373, 19078,  \n21372, 20885, 20316,  12171, 4831, 4832,  19757, 19292, 20875,  \n19763, 19773, 20875,  18467, 5053, 4564,  20311, 20309, 20883,  \n3113, 20890, 21180,  1949, 5507, 17732,  1986, 7238, 12193,  \n20878, 20868, 20320,  20889, 20891, 20319,  3538, 6223, 7268,  \n19763, 20875, 19292,  10308, 19043, 10102,  15300, 15299, 2282,  \n19775, 19797, 20892,  20316, 20885, 21386,  20318, 20889, 20319,  \n7964, 7965, 3925,  19775, 20892, 20323,  18557, 15368, 6659,  \n20878, 20893, 20319,  12328, 9201, 13378,  20331, 19784, 20323,  \n8213, 4519, 4520,  20878, 20320, 19776,  20451, 18982, 20894,  \n15523, 8478, 9082,  20311, 20883, 20896,  655, 3685, 5503,  \n19756, 20311, 19764,  29181, 7626, 15223,  8959, 18587, 8960,  \n5949, 14518, 9343,  21386, 20327, 20316,  20878, 19776, 20893,  \n20898, 20889, 20318,  7126, 15782, 17814,  19764, 20311, 20896,  \n21386, 19797, 20327,  20319, 20893, 20318,  10748, 2993, 1351,  \n20332, 20903, 12044,  20898, 20899, 20889,  20318, 20905, 20898,  \n2980, 2981, 5810,  19764, 20896, 19768,  20339, 20893, 19776,  \n20318, 20893, 20906,  20905, 20318, 20906,  19768, 20896, 20907,  \n20906, 20893, 20339,  20905, 20906, 21401,  12794, 5765, 20911,  \n20906, 20339, 20910,  9874, 2599, 9875,  4873, 4872, 15947,  \n21401, 20906, 20910,  19769, 19768, 20347,  16993, 1489, 19026,  \n15555, 19714, 13179,  14096, 13017, 8368,  21401, 20910, 20914,  \n19799, 19769, 20347,  19782, 20352, 20339,  6422, 20917, 10638,  \n19782, 19794, 20352,  20910, 20339, 20914,  13007, 18374, 16440,  \n10964, 19869, 20918,  17540, 15790, 1550,  20348, 20347, 20349,  \n3691, 20919, 4980,  10964, 20918, 29591,  20339, 20352, 20928,  \n20914, 20339, 20928,  3973, 12626, 3972,  13204, 21594, 16467,  \n20349, 20353, 19811,  10500, 20926, 12722,  20348, 20349, 19811,  \n20352, 19813, 20354,  9776, 5841, 7498,  20354, 20357, 20352,  \n20357, 20928, 20352,  3125, 20930, 7121,  15369, 20332, 19830,  \n18840, 19832, 17785,  1302, 362, 361,  20661, 4684, 15958,  \n15266, 16950, 15231,  20932, 5534, 6208,  20933, 17671, 7504,  \n9844, 9845, 20935,  20936, 20357, 20363,  16932, 29690, 20503,  \n17009, 7976, 9640,  11164, 10621, 16898,  17095, 1412, 20724,  \n17162, 20938, 15550,  18744, 15350, 3774,  12986, 12133, 20985,  \n17284, 18845, 20371,  20363, 20939, 20936,  19834, 20360, 20944,  \n19835, 19834, 20944,  19831, 20375, 20363,  834, 12325, 835,  \n19842, 17793, 18847,  5501, 5500, 3325,  439, 9349, 21468,  \n7068, 14167, 11145,  20943, 18850, 20371,  19851, 19862, 19842,  \n19860, 19851, 18857,  20942, 19843, 19835,  19836, 19843, 20373,  \n12255, 996, 995,  4471, 2919, 14016,  7459, 10016, 20947,  \n20377, 19844, 19840,  20377, 20948, 20374,  6356, 20025, 16601,  \n17801, 941, 8546,  9611, 9610, 8792,  17305, 20383, 20951,  \n6532, 1557, 12684,  2212, 20955, 2213,  9885, 13369, 16550,  \n7157, 2723, 4378,  2066, 4493, 7393,  20957, 20383, 17305,  \n19199, 644, 16483,  6451, 1282, 709,  2804, 1614, 11029,  \n12138, 19352, 18543,  4459, 4460, 15858,  6449, 6448, 13211,  \n18377, 20387, 20963,  412, 400, 977,  1670, 20385, 18853,  \n5829, 22955, 18547,  20960, 19872, 19871,  20960, 20391, 19872,  \n20561, 20961, 1442,  19874, 20393, 19360,  20958, 19358, 19360,  \n10775, 8926, 4353,  4209, 4208, 7131,  20517, 16273, 10404,  \n9651, 10552, 7926,  20396, 19877, 20963,  20966, 12438, 7935,  \n8982, 5132, 5131,  11911, 14032, 20440,  20397, 19880, 20967,  \n18871, 19880, 20397,  10115, 20968, 741,  19366, 20396, 20969,  \n8315, 16483, 644,  4207, 15670, 20970,  20110, 11443, 4851,  \n10224, 12541, 20108,  11549, 10510, 18180,  19586, 9117, 12594,  \n5689, 11798, 5688,  19885, 20972, 20405,  9323, 6501, 3632,  \n9801, 14789, 14788,  7243, 5655, 419,  18883, 20976, 20977,  \n18883, 19887, 20976,  6222, 3836, 6244,  4058, 17014, 9378,  \n16050, 5236, 4895,  6874, 16512, 3676,  1632, 10353, 10352,  \n18891, 20981, 18892,  6417, 11396, 18901,  18892, 20981, 20982,  \n3572, 5949, 9635,  18895, 20984, 19905,  1618, 13519, 16989,  \n19873, 10618, 20983,  10294, 7204, 10242,  20984, 19909, 19905,  \n9364, 12017, 7548,  11044, 7704, 14104,  19914, 1544, 14693,  \n10035, 6378, 8406,  14109, 16317, 20416,  16317, 18431, 20416,  \n8636, 3451, 4242,  10018, 13396, 20986,  18914, 20987, 20988,  \n20989, 9106, 9710,  20988, 20427, 18914,  12154, 14512, 12396,  \n5951, 12808, 20597,  19399, 17414, 18458,  18701, 20406, 13558,  \n2416, 4054, 14102,  20427, 20430, 19400,  4052, 4098, 1373,  \n18922, 20430, 19407,  8473, 899, 20495,  17391, 1971, 18896,  \n1039, 12768, 3907,  22288, 17494, 2253,  2881, 11482, 2882,  \n746, 5404, 1962,  16951, 10796, 1191,  13825, 16845, 14268,  \n19918, 20993, 19920,  13469, 13470, 18408,  19411, 17922, 20442,  \n2238, 20995, 9299,  2895, 7515, 15189,  22061, 15797, 13570,  \n6899, 7164, 7166,  19988, 5797, 6567,  20996, 20449, 20448,  \n20997, 20998, 19925,  20997, 19925, 20447,  19925, 20998, 17460,  \n17460, 20998, 18939,  19929, 17939, 21000,  18939, 21000, 17939,  \n20449, 20996, 21001,  21002, 19424, 18948,  19120, 9642, 9647,  \n20450, 21003, 20447,  12865, 21004, 7576,  21003, 20997, 20447,  \n20449, 21006, 19933,  21001, 21006, 20449,  14953, 3868, 10269,  \n21008, 18097, 9326,  11350, 15017, 11349,  21006, 20459, 19933,  \n5129, 12563, 480,  20460, 20450, 19937,  20460, 21003, 20450,  \n21006, 20464, 20459,  21009, 20460, 19937,  2015, 17679, 13353,  \n21010, 9958, 3801,  3871, 13844, 10209,  19941, 18491, 18962,  \n21012, 21009, 20468,  19937, 20468, 21009,  11109, 9947, 6446,  \n11015, 11016, 4991,  13076, 3036, 13077,  20470, 20494, 20469,  \n21820, 18962, 20473,  3951, 14680, 7831,  6783, 905, 15115,  \n21014, 18968, 20471,  5115, 5117, 6066,  14155, 10988, 1139,  \n14881, 2775, 2774,  21014, 20473, 18968,  19953, 21012, 20468,  \n6169, 6553, 19255,  19161, 8324, 8314,  15820, 14077, 20068,  \n19953, 19452, 21019,  19452, 20475, 21019,  9587, 433, 13888,  \n20475, 21023, 21019,  4367, 15060, 15293,  6960, 4488, 13709,  \n6236, 14345, 19679,  7196, 2139, 7197,  21024, 19505, 4823,  \n21022, 21023, 19961,  12850, 2341, 12849,  19961, 21023, 20475,  \n13601, 13602, 3049,  9110, 15436, 2016,  18795, 4237, 14302,  \n21025, 19966, 17965,  21026, 1877, 18498,  21027, 19462, 19967,  \n3713, 20389, 2740,  504, 18517, 502,  11832, 10667, 10668,  \n4887, 18170, 12320,  15248, 960, 20204,  13881, 20355, 7679,  \n2534, 2533, 10866,  18325, 15464, 19976,  1728, 7422, 21031,  \n10005, 14470, 15031,  2501, 13960, 2502,  19476, 17981, 20489,  \n16242, 3070, 15580,  19475, 18536, 19476,  6008, 9151, 2092,  \n15753, 1584, 1585,  5605, 11786, 19938,  15253, 18745, 3222,  \n19989, 18537, 19475,  19989, 19475, 21034,  10190, 13827, 18866,  \n12758, 3192, 2767,  17613, 583, 6986,  6986, 583, 6987,  \n9470, 14247, 5173,  19488, 21035, 16504,  8352, 20053, 9435,  \n4829, 4830, 7137,  19486, 19984, 21037,  20508, 19482, 19989,  \n19486, 21037, 20502,  21038, 21039, 9238,  21040, 17048, 21041,  \n5258, 5259, 12575,  7612, 7437, 15151,  9283, 7517, 7516,  \n17048, 17049, 20507,  14521, 14638, 19964,  2582, 6372, 12842,  \n12937, 7311, 641,  17054, 20000, 18548,  15630, 11923, 21264,  \n20512, 19039, 19997,  21045, 20507, 19999,  3021, 12185, 3022,  \n18657, 18177, 359,  14906, 3520, 8945,  16883, 3727, 21047,  \n9342, 14619, 3280,  1931, 8178, 6536,  18636, 21048, 21503,  \n3088, 6575, 9563,  21497, 19039, 20512,  20509, 20508, 21049,  \n20509, 19508, 19492,  11484, 14721, 4405,  1958, 12186, 4241,  \n20509, 21049, 19508,  18548, 20000, 21050,  21497, 19526, 19039,  \n20096, 20097, 6294,  12124, 12704, 8419,  17575, 20519, 18573,  \n1564, 6450, 4580,  19530, 19508, 21053,  18577, 18573, 20012,  \n2701, 3167, 3422,  1191, 15375, 16951,  7212, 7214, 8253,  \n3277, 17682, 17697,  19114, 10997, 14241,  21054, 3044, 19660,  \n13723, 13969, 8929,  18044, 20523, 19519,  13810, 12872, 11145,  \n21051, 20531, 19526,  11835, 2056, 4810,  9042, 14569, 8336,  \n4931, 21055, 21056,  20523, 17604, 20027,  19058, 21057, 20027,  \n21051, 21059, 20531,  16561, 1685, 9070,  20565, 15320, 3390,  \n19605, 2519, 10518,  20023, 21060, 19058,  10988, 12851, 973,  \n3184, 19354, 18396,  19532, 21061, 20023,  14906, 19450, 21062,  \n14931, 2940, 2941,  3523, 6082, 3524,  21059, 21063, 20531,  \n371, 5421, 5420,  3677, 9990, 5689,  20535, 20524, 21064,  \n8244, 21065, 18323,  9019, 7221, 13744,  21063, 21067, 20531,  \n20535, 21064, 21516,  7942, 13086, 2241,  19056, 20524, 20535,  \n19498, 10637, 17930,  20531, 21067, 19060,  20533, 21068, 20032,  \n14607, 6190, 2837,  7060, 13339, 9932,  21067, 19076, 19060,  \n7290, 7291, 17114,  16157, 21071, 7320,  20533, 20536, 21068,  \n20035, 19056, 20536,  15804, 4250, 20648,  3928, 19864, 19865,  \n13609, 17717, 13709,  20032, 19537, 20533,  20536, 20535, 21068,  \n20051, 20037, 19071,  18592, 20534, 17624,  13138, 5638, 19536,  \n1436, 11594, 1392,  7803, 9067, 6522,  17773, 12670, 4024,  \n21077, 20035, 20536,  21077, 20045, 20035,  6224, 16014, 12827,  \n13979, 21079, 18921,  18624, 18613, 20541,  18626, 21083, 19550,  \n21075, 20533, 19543,  21075, 20536, 20533,  11008, 6919, 10694,  \n12653, 18692, 13243,  20388, 6705, 5155,  14439, 437, 436,  \n11505, 11819, 12994,  4750, 17374, 4751,  17835, 8346, 21086,  \n19543, 19080, 21087,  6926, 15562, 2869,  12681, 19215, 12019,  \n16807, 8419, 10073,  10876, 13590, 3830,  14841, 21088, 21089,  \n6687, 6688, 18575,  4709, 14879, 11359,  21087, 19080, 19552,  \n13289, 18086, 10826,  6203, 9593, 15215,  19556, 21097, 19558,  \n21097, 19556, 20061,  5098, 4025, 6315,  21097, 21091, 19558,  \n21091, 19090, 19558,  12920, 20379, 12921,  19553, 20550, 20067,  \n19553, 19081, 20550,  20067, 20557, 19102,  19093, 20555, 20556,  \n16370, 8757, 8756,  13337, 1511, 8537,  12324, 9414, 12859,  \n17313, 7639, 21283,  19100, 19099, 21100,  21101, 6559, 21102,  \n19104, 19561, 21103,  19093, 20556, 20559,  17961, 18175, 14673,  \n13014, 888, 4048,  19115, 20071, 20564,  8628, 10487, 13099,  \n15155, 18940, 8232,  5163, 5162, 7164,  16288, 5210, 24631,  \n9880, 15133, 21106,  20080, 19107, 20559,  5127, 3359, 19717,  \n18713, 20564, 19151,  1671, 1219, 1221,  18641, 21112, 20548,  \n21113, 20559, 20558,  17359, 5196, 17956,  16540, 6844, 21107,  \n5260, 5354, 4093,  9008, 16358, 20177,  7528, 15944, 21893,  \n20564, 19173, 19172,  21110, 21108, 19590,  21111, 19173, 20572,  \n17698, 19138, 18705,  15222, 1807, 1809,  8363, 8910, 8909,  \n16953, 12166, 12385,  21114, 9823, 12693,  3317, 3318, 6373,  \n429, 4528, 10427,  19590, 18203, 21116,  21117, 19577, 20102,  \n12215, 2507, 11340,  20099, 21119, 19601,  5618, 7353, 18930,  \n20429, 16471, 563,  22924, 13428, 392,  12035, 4611, 15400,  \n19606, 21120, 20107,  19159, 20107, 21120,  7412, 15456, 9106,  \n20115, 19155, 19595,  10259, 9081, 18679,  19601, 21119, 21121,  \n19595, 19601, 21121,  10724, 17064, 2488,  18712, 19163, 20580,  \n17556, 15249, 21123,  21120, 20582, 19159,  19155, 20115, 19170,  \n10526, 9603, 9602,  9533, 3304, 3305,  7674, 19377, 16104,  \n19595, 21121, 20115,  6021, 4656, 15040,  12096, 10860, 5956,  \n19163, 18219, 18239,  19163, 21124, 20580,  21124, 19163, 21128,  \n10807, 12734, 7199,  10531, 7981, 10521,  19623, 20582, 21125,  \n12399, 2263, 11076,  19194, 20577, 20587,  21130, 6053, 6052,  \n20590, 19188, 20588,  19624, 21128, 19613,  9978, 13253, 20197,  \n17580, 16669, 8168,  16033, 18003, 3832,  16599, 18872, 2348,  \n20591, 21128, 19624,  15043, 16497, 2854,  20134, 21135, 20591,  \n3109, 4796, 3108,  14749, 19970, 5537,  20584, 16019, 17219,  \n3987, 8147, 19171,  4689, 578, 10648,  8308, 15639, 20874,  \n20598, 21134, 19591,  18220, 5767, 2902,  21140, 20132, 20593,  \n6398, 6604, 950,  1742, 8060, 9044,  21135, 20134, 20602,  \n17823, 18550, 14036,  21136, 20602, 20616,  21136, 21135, 20602,  \n7392, 5804, 15225,  21137, 6054, 6859,  19154, 19651, 20586,  \n21140, 21141, 20132,  8052, 10826, 18086,  21142, 10868, 10783,  \n14559, 3845, 15439,  10712, 5856, 20953,  20135, 20608, 20134,  \n5267, 10710, 10709,  2282, 8580, 2231,  20602, 20134, 20604,  \n20160, 20151, 20616,  14340, 15630, 14477,  6290, 6289, 17968,  \n5766, 16142, 16143,  15696, 21143, 510,  5506, 377, 21828,  \n21162, 20586, 19651,  16929, 15112, 17617,  20603, 20132, 21141,  \n20603, 20605, 19637,  20608, 20135, 20148,  17712, 23115, 16867,  \n20134, 20608, 20604,  11592, 21146, 11591,  20602, 20620, 20616,  \n20602, 20604, 20620,  17931, 1037, 6748,  21136, 20616, 20151,  \n9959, 16308, 15631,  13781, 1393, 1395,  21147, 13192, 21148,  \n18666, 17916, 21149,  21144, 20152, 20614,  12129, 10079, 12128,  \n1088, 13342, 6561,  9033, 8878, 1025,  20603, 21141, 20605,  \n4300, 19682, 6880,  20837, 21156, 21157,  20605, 21155, 20604,  \n4937, 9697, 7089,  19217, 19628, 20155,  18474, 11942, 7280,  \n10358, 8734, 10359,  21152, 20605, 21141,  21173, 21152, 21141,  \n20608, 20605, 20604,  18121, 16372, 8523,  18811, 17896, 11539,  \n3561, 18564, 18565,  20621, 20614, 20158,  1875, 21665, 869,  \n21155, 20605, 21152,  21156, 20418, 21157,  1156, 4892, 7113,  \n428, 3074, 425,  17118, 7229, 13062,  12056, 12055, 4908,  \n20621, 20158, 20167,  3880, 18650, 21166,  20155, 21164, 20628,  \n21167, 16585, 5865,  4432, 10453, 18063,  3194, 20683, 12969,  \n21155, 21165, 20632,  20632, 20620, 21155,  20620, 20632, 20171,  \n9968, 18673, 9969,  18925, 12579, 16975,  9621, 16610, 19762,  \n5882, 20627, 5883,  21165, 21172, 20636,  21165, 21173, 21172,  \n5650, 1777, 4978,  5576, 3755, 13261,  21165, 20636, 20632,  \n21175, 21176, 15167,  3025, 14188, 14787,  7915, 6717, 3543,  \n7683, 7682, 12009,  750, 5097, 5099,  9849, 13565, 13566,  \n20639, 20171, 20632,  21172, 21179, 20637,  21172, 20637, 20636,  \n15978, 21180, 20952,  15294, 11532, 14401,  16478, 12754, 5351,  \n10103, 15335, 454,  5137, 9833, 9832,  15840, 11856, 8756,  \n2446, 17843, 20086,  20187, 20631, 19661,  11854, 6823, 6825,  \n6250, 19675, 5192,  4438, 18969, 14550,  20639, 20655, 20183,  \n4409, 20300, 10869,  20655, 20639, 20213,  20187, 19676, 21189,  \n8937, 1487, 844,  7010, 15931, 19633,  15046, 10277, 18741,  \n14942, 10233, 17442,  20646, 20637, 20685,  20183, 20655, 20212,  \n20681, 20212, 20655,  384, 8170, 12295,  16358, 7605, 15507,  \n1536, 3088, 9563,  20666, 20681, 20655,  2687, 1858, 11424,  \n11952, 5064, 15010,  15753, 1585, 7906,  17484, 5589, 11408,  \n19199, 16266, 644,  20854, 12369, 7529,  1053, 22437, 12020,  \n21192, 6175, 4963,  20678, 20682, 20656,  18812, 2048, 1496,  \n15195, 20259, 8133,  16997, 1828, 6751,  22267, 3756, 10808,  \n21195, 20420, 668,  21196, 19243, 19693,  21196, 19676, 19243,  \n21197, 20654, 18814,  20210, 20685, 20695,  17301, 17302, 3904,  \n20212, 20681, 20689,  20214, 20212, 20689,  6497, 6465, 6498,  \n18500, 9690, 8030,  20689, 20681, 21200,  2856, 12239, 2857,  \n20678, 19699, 20682,  19681, 21194, 20220,  15622, 22070, 8667,  \n15635, 15636, 11839,  5196, 423, 2244,  20685, 21198, 20695,  \n3591, 13493, 21204,  12837, 9431, 13731,  21196, 19693, 20702,  \n20695, 21198, 20708,  21205, 21206, 20689,  21206, 20214, 20689,  \n21206, 20697, 20214,  20704, 20682, 19699,  6252, 3513, 6251,  \n9268, 15429, 9934,  2691, 10669, 13736,  11502, 14018, 2850,  \n19706, 20697, 19713,  20855, 3842, 4841,  20702, 20225, 20700,  \n21200, 20681, 20243,  13766, 21213, 15417,  14402, 1552, 9137,  \n9654, 6711, 9793,  4116, 4118, 9521,  11951, 5634, 11348,  \n20700, 19697, 20218,  13575, 13574, 12348,  18130, 16875, 13759,  \n21212, 21200, 20251,  20697, 20229, 19713,  1675, 5199, 1676,  \n20218, 20690, 20706,  20700, 20218, 20706,  20717, 20079, 13419,  \n14671, 11086, 15602,  5927, 12584, 8693,  21355, 3772, 12175,  \n4861, 18064, 14246,  20182, 22043, 17722,  6630, 4893, 4894,  \n6062, 7080, 5111,  10794, 15163, 14235,  21219, 20249, 19270,  \n8147, 13076, 19171,  14176, 17844, 14037,  20251, 20715, 21218,  \n16145, 7868, 4009,  9390, 2482, 2483,  767, 18539, 17098,  \n14552, 9219, 16891,  21222, 21223, 19720,  21222, 21224, 21223,  \n19720, 19723, 21222,  20715, 20257, 20723,  9809, 8542, 11138,  \n3796, 19422, 6974,  1346, 16278, 1345,  20254, 21222, 19723,  \n6169, 10065, 8212,  19721, 20716, 21227,  19721, 21227, 20720,  \n4553, 21026, 9451,  20730, 20723, 20722,  13254, 5930, 5932,  \n21229, 8857, 7332,  15400, 16346, 4533,  20730, 20722, 20725,  \n12177, 7918, 12178,  3303, 17884, 22065,  21231, 20721, 20718,  \n5980, 6561, 6562,  4336, 20164, 21101,  2031, 3665, 5344,  \n20733, 20721, 21234,  20731, 20725, 20736,  7621, 18653, 16903,  \n21235, 18645, 3370,  20733, 21234, 20737,  7888, 21236, 2137,  \n20736, 20274, 20738,  20272, 20733, 20737,  8412, 5607, 15168,  \n21237, 2504, 16485,  21238, 1992, 5118,  21239, 14820, 5532,  \n20738, 20274, 20739,  21242, 20738, 20739,  15106, 13436, 5917,  \n19127, 16394, 16146,  11157, 18795, 2024,  10757, 5335, 10758,  \n20281, 20737, 21240,  4084, 7748, 15314,  12614, 13241, 21499,  \n4382, 4381, 21245,  15163, 15583, 15582,  16798, 1049, 5058,  \n21243, 20740, 20741,  9044, 12514, 12288,  15867, 1004, 4598,  \n21246, 21243, 20741,  5114, 16346, 20060,  8530, 18378, 21249,  \n20744, 20280, 20281,  20744, 20281, 21248,  20742, 20746, 20741,  \n21246, 20741, 20747,  3123, 9008, 16213,  22277, 14760, 16943,  \n21251, 21252, 7092,  20747, 20746, 20749,  2734, 4201, 4200,  \n6069, 10860, 14963,  20757, 20747, 20749,  13093, 21258, 11841,  \n10764, 12008, 8902,  16730, 7229, 16729,  4260, 14209, 13529,  \n13302, 8250, 1841,  21262, 21263, 20744,  20744, 21263, 20750,  \n11349, 11612, 11350,  11462, 13002, 21264,  20757, 21266, 21639,  \n15792, 14584, 10782,  21259, 21261, 21267,  21268, 21259, 21267,  \n4199, 3849, 17671,  21259, 21268, 21269,  21647, 21269, 21268,  \n19673, 9398, 12491,  21266, 20757, 20762,  21267, 21261, 21270,  \n20751, 21272, 20761,  11630, 5579, 11975,  21267, 21273, 21268,  \n21268, 21274, 21647,  9939, 12002, 9940,  20764, 21268, 21273,  \n21274, 21268, 20764,  319, 21278, 13299,  20761, 21275, 20762,  \n20762, 21275, 21279,  20754, 20761, 20762,  1294, 9123, 16745,  \n15093, 15646, 8663,  21277, 20762, 21279,  8162, 11572, 5763,  \n21275, 20761, 21281,  20768, 21274, 20765,  20763, 21273, 21282,  \n21283, 6846, 15514,  5493, 8010, 8022,  20764, 20765, 21274,  \n6851, 302, 12692,  10715, 16589, 18194,  20766, 21284, 20768,  \n6247, 3843, 2523,  16297, 4819, 4820,  11398, 21285, 758,  \n9786, 21286, 23699,  8920, 15425, 8919,  21279, 21275, 21288,  \n21281, 21290, 21287,  21275, 21281, 21287,  2439, 19423, 19422,  \n19995, 19996, 20395,  9544, 8901, 9545,  21284, 20766, 20769,  \n21284, 20769, 21291,  9439, 17082, 9438,  17082, 9566, 9438,  \n21288, 21275, 21287,  10319, 21289, 10318,  5437, 15448, 21293,  \n21282, 20776, 20763,  15572, 3974, 15573,  6647, 18679, 9081,  \n17600, 17329, 14785,  20773, 20780, 20769,  21298, 12980, 12979,  \n21294, 21288, 21295,  14624, 17908, 21299,  21300, 13204, 16467,  \n20774, 20763, 20776,  5543, 5542, 14745,  20378, 5649, 1074,  \n20776, 21301, 20774,  21304, 20769, 20780,  21287, 21302, 21303,  \n21288, 21287, 21303,  21295, 21288, 21303,  870, 15366, 871,  \n20774, 21301, 20782,  11294, 20056, 16005,  20777, 20774, 20782,  \n20780, 20284, 20791,  21309, 21295, 21303,  8996, 8995, 11242,  \n20788, 21303, 21302,  21305, 21309, 21310,  18782, 16431, 12669,  \n21303, 20788, 20787,  21309, 21303, 20787,  4081, 13893, 4080,  \n7364, 3901, 16164,  21310, 21309, 20787,  961, 21311, 18715,  \n3427, 20692, 4320,  9111, 20838, 1966,  1325, 10449, 11873,  \n12282, 3866, 12281,  19879, 21312, 13793,  1682, 15360, 6549,  \n16692, 12282, 12281,  20788, 21302, 21313,  10632, 13114, 19979,  \n11105, 10408, 3334,  17354, 3854, 4777,  21313, 21302, 21315,  \n4099, 2589, 2575,  20609, 21292, 5215,  20802, 21310, 20787,  \n13858, 16180, 2394,  10934, 10933, 8735,  3923, 3922, 15386,  \n20783, 20785, 20794,  20806, 20783, 20794,  20338, 19678, 20677,  \n8917, 20799, 21319,  19196, 9524, 20847,  8418, 14308, 8419,  \n21315, 21321, 21313,  1545, 1546, 7743,  20807, 20788, 20805,  \n12522, 14567, 17665,  5373, 5372, 1197,  16213, 16214, 3124,  \n21313, 20805, 20788,  21321, 21315, 21333,  19367, 16068, 304,  \n21322, 20802, 20807,  20807, 20802, 20788,  20806, 20809, 20287,  \n20805, 21313, 21321,  7215, 7052, 14170,  20816, 20292, 20820,  \n17177, 16159, 13223,  20807, 20805, 20817,  19327, 372, 6600,  \n9281, 9283, 10677,  20821, 21333, 21334,  21321, 20817, 20805,  \n20807, 20822, 21322,  20821, 21321, 21333,  3012, 21336, 3011,  \n21339, 20820, 20827,  11885, 3134, 3133,  20822, 21698, 21322,  \n6953, 4328, 16922,  21334, 21340, 20821,  14181, 782, 12205,  \n7881, 18309, 10498,  20835, 21342, 21339,  9659, 13307, 780,  \n21341, 21698, 20822,  2754, 10360, 9851,  1997, 20252, 6764,  \n20835, 20299, 20841,  20832, 20821, 21340,  21699, 20291, 20818,  \n20835, 20841, 21342,  7946, 16777, 7945,  15271, 5904, 17232,  \n7402, 16777, 7946,  6358, 8986, 11151,  21343, 10000, 20888,  \n9432, 6019, 2851,  14438, 6230, 6229,  21699, 21345, 20833,  \n20836, 20828, 20832,  2352, 6865, 5009,  13360, 18954, 9398,  \n21341, 20822, 20824,  12018, 16146, 16393,  9241, 21316, 7277,  \n20824, 20829, 21344,  21341, 20824, 21344,  21348, 21341, 21344,  \n13726, 1192, 10796,  20846, 21344, 20829,  20833, 21345, 21350,  \n2951, 5830, 2952,  16621, 6897, 13655,  15409, 9928, 7191,  \n21353, 20850, 21352,  20836, 20832, 20850,  18339, 17801, 8763,  \n12596, 12597, 18438,  20840, 20833, 21350,  12924, 10233, 14942,  \n7207, 7206, 10391,  10862, 10631, 326,  20846, 21356, 21357,  \n21344, 21357, 21348,  8992, 15415, 21815,  20840, 21350, 20861,  \n1658, 21359, 21360,  21353, 20857, 20850,  21344, 20846, 21357,  \n21361, 11284, 9675,  20864, 20301, 19755,  1180, 8568, 13424,  \n13845, 366, 365,  21364, 11750, 14161,  18488, 16239, 10550,  \n20864, 20848, 20301,  6543, 4434, 21365,  21362, 20862, 21353,  \n21356, 20846, 20856,  12464, 4298, 19692,  16561, 9070, 8936,  \n21368, 21353, 20862,  15944, 7528, 7529,  20861, 20303, 20840,  \n2441, 5019, 3909,  20862, 21362, 21367,  21369, 18460, 10746,  \n2114, 3860, 2113,  21353, 21368, 20857,  3059, 7821, 2688,  \n607, 7591, 13603,  5263, 3639, 3638,  21367, 20869, 20862,  \n14538, 10328, 5621,  21370, 13188, 13743,  2614, 16181, 8647,  \n19695, 16779, 12228,  20864, 19755, 20314,  15697, 10045, 5107,  \n20869, 21367, 21372,  20850, 20857, 20865,  20863, 21356, 20856,  \n20868, 20862, 20869,  1267, 4127, 12761,  8154, 4000, 20162,  \n20864, 20314, 21374,  14342, 8019, 18240,  20857, 21368, 20865,  \n21374, 20314, 20875,  4779, 4778, 18258,  20878, 21368, 20862,  \n2458, 12953, 11125,  7735, 2566, 5346,  20878, 20865, 21368,  \n20878, 20319, 20865,  4782, 11784, 11213,  20856, 21377, 20863,  \n10021, 10020, 7988,  19773, 21374, 20875,  3479, 4759, 11232,  \n4607, 6178, 816,  14029, 2001, 2000,  21377, 20856, 20870,  \n13974, 6399, 16678,  21723, 20885, 21372,  2671, 4550, 15231,  \n20309, 20308, 20883,  5490, 9876, 5491,  4181, 10948, 5484,  \n10366, 9592, 15271,  19515, 7794, 11935,  15992, 13394, 3995,  \n20891, 21389, 20870,  21377, 20870, 21389,  20323, 20892, 21380,  \n20891, 20870, 20319,  17015, 8233, 12580,  12452, 7872, 8269,  \n20308, 21716, 20882,  18253, 1082, 15571,  15838, 3326, 8396,  \n20003, 5140, 18963,  11955, 4410, 13410,  17913, 1288, 12889,  \n20892, 19797, 21386,  21380, 20892, 21386,  14257, 12474, 15601,  \n20330, 20331, 21383,  5968, 8093, 14077,  11707, 7500, 2313,  \n14588, 17945, 18150,  20891, 20899, 21389,  20883, 20882, 21396,  \n11610, 905, 906,  17954, 4230, 13748,  20891, 20889, 20899,  \n11787, 19141, 10316,  20883, 21396, 20896,  3387, 4430, 21397,  \n11407, 4545, 6561,  13973, 13972, 16141,  21398, 4072, 6286,  \n1329, 7663, 16782,  12380, 4028, 12654,  1070, 15575, 2966,  \n20347, 19768, 20913,  19768, 20907, 20913,  17194, 13196, 19520,  \n8726, 5563, 6237,  16447, 4085, 10861,  18701, 10918, 20406,  \n19139, 15680, 11074,  21405, 20347, 20913,  20347, 21405, 21406,  \n12666, 2842, 8721,  21401, 20914, 21403,  2846, 12265, 1673,  \n9852, 6555, 8885,  20349, 20347, 21406,  5567, 3952, 6709,  \n19250, 19048, 2901,  20920, 20914, 20928,  21403, 20914, 20920,  \n432, 10237, 18809,  14281, 21407, 3601,  11615, 4633, 4871,  \n11282, 11283, 21408,  20920, 21409, 21403,  6276, 9826, 12924,  \n18840, 21412, 19832,  21413, 21412, 19823,  21411, 19823, 18346,  \n18842, 21414, 18346,  6383, 6384, 17195,  18842, 18843, 21415,  \n9211, 4044, 5357,  21417, 20371, 18845,  19808, 19811, 20360,  \n20920, 20357, 20936,  20920, 20928, 20357,  19811, 20353, 21420,  \n5080, 8305, 21421,  21424, 9461, 6155,  16267, 19804, 13584,  \n842, 10757, 10758,  3035, 1977, 1827,  21422, 20920, 20936,  \n5786, 1133, 13373,  13494, 9614, 9166,  9920, 9921, 13518,  \n12982, 3904, 18436,  22983, 9256, 16152,  20939, 20363, 20375,  \n21426, 21422, 20936,  18854, 18850, 20943,  4171, 8701, 16536,  \n14614, 13095, 9930,  19835, 20944, 21428,  20936, 21429, 21426,  \n3516, 26391, 4164,  20375, 21430, 21431,  19861, 19856, 20382,  \n5489, 17175, 8017,  3044, 21054, 922,  19859, 18857, 16790,  \n20954, 20373, 19843,  20954, 19843, 20942,  20374, 20948, 21430,  \n18156, 19456, 9955,  10259, 18681, 17239,  20374, 21430, 20375,  \n16821, 21118, 1724,  19856, 19860, 19857,  17307, 19857, 19859,  \n20990, 18665, 18664,  12030, 14813, 8185,  21432, 20382, 20381,  \n21763, 20951, 20383,  1635, 7798, 17463,  17633, 5066, 5065,  \n20380, 20377, 19840,  19205, 12091, 7351,  4926, 21714, 3766,  \n21434, 21763, 21435,  21435, 21763, 20383,  21435, 20383, 20957,  \n14096, 1149, 13017,  20957, 17305, 19358,  13404, 11897, 11240,  \n21436, 21437, 20377,  1831, 1832, 6927,  21437, 20948, 20377,  \n13652, 21668, 10309,  20958, 20957, 19358,  3876, 3875, 10821,  \n14785, 12365, 11550,  3840, 19449, 20184,  2461, 2460, 1440,  \n19840, 20373, 20380,  20377, 20380, 21436,  6083, 9666, 6084,  \n548, 12427, 18930,  20393, 20958, 19360,  21438, 20373, 20954,  \n1830, 13630, 1829,  21439, 19874, 20391,  21439, 20393, 19874,  \n15163, 10794, 9199,  18381, 21441, 19871,  8814, 7977, 17010,  \n5634, 11951, 8715,  4132, 4131, 17633,  5622, 8239, 14461,  \n21443, 19881, 19883,  7869, 1999, 10996,  20969, 18879, 19366,  \n21349, 6445, 4252,  15587, 15588, 14888,  19369, 18879, 19885,  \n17669, 12675, 977,  19506, 4183, 21444,  18905, 10890, 18906,  \n20405, 20972, 21445,  2303, 10503, 8741,  20405, 21446, 19887,  \n21447, 19883, 18414,  12156, 17824, 10827,  20976, 19887, 21446,  \n5754, 1584, 6430,  12886, 17377, 9637,  20977, 21450, 19894,  \n21444, 4183, 13708,  18885, 20977, 19894,  19895, 19894, 21450,  \n21447, 18414, 19898,  459, 3550, 7015,  18891, 19895, 20981,  \n15745, 13144, 5030,  7488, 5489, 8017,  13519, 12604, 14311,  \n3737, 15987, 3738,  18895, 18892, 20982,  1963, 12014, 8969,  \n8196, 14565, 5913,  10584, 10586, 11864,  20416, 19898, 17399,  \n21235, 9884, 20592,  7540, 18834, 11663,  13534, 21073, 13552,  \n2498, 10379, 13668,  21453, 22377, 20984,  8548, 9662, 18240,  \n13203, 8522, 12027,  19265, 8569, 21381,  10182, 6579, 16120,  \n21423, 10418, 18960,  12514, 9044, 5178,  20422, 20987, 18914,  \n20321, 24833, 10125,  20988, 21801, 20427,  21459, 20430, 20427,  \n12525, 9278, 10681,  2645, 16219, 2500,  20430, 21459, 19407,  \n18464, 19411, 19403,  15268, 20684, 6174,  16294, 17593, 535,  \n19407, 21461, 18924,  18924, 21461, 19918,  20993, 19918, 21461,  \n5336, 12318, 2997,  1290, 3666, 1291,  18829, 1802, 14372,  \n9107, 6128, 813,  20444, 19920, 20993,  6899, 6900, 7164,  \n19417, 21467, 21465,  18479, 19417, 21465,  21001, 21469, 21006,  \n21006, 21469, 20464,  21470, 18948, 19941,  16460, 3746, 15656,  \n21471, 21003, 20460,  1908, 12276, 9144,  5357, 7319, 5356,  \n13229, 21474, 5457,  14674, 14673, 11054,  19228, 11580, 21629,  \n21816, 19428, 20464,  20471, 21821, 21014,  12217, 16261, 14250,  \n18918, 21477, 21478,  17157, 802, 801,  19535, 17157, 17158,  \n2560, 10259, 7808,  19428, 21816, 21479,  21479, 19437, 19428,  \n21481, 21012, 19953,  18508, 21482, 17509,  21482, 18508, 19437,  \n21481, 19953, 21019,  15286, 18547, 16335,  7642, 3264, 12783,  \n460, 24877, 461,  7758, 6060, 12228,  922, 8263, 3975,  \n16005, 20056, 3800,  13182, 1576, 11731,  21486, 2792, 22425,  \n1350, 14182, 8840,  9495, 5474, 5473,  15656, 18529, 16460,  \n19962, 21487, 17965,  5564, 621, 13532,  10133, 1309, 1310,  \n1177, 1176, 14462,  12417, 10934, 9135,  4441, 4442, 10280,  \n19462, 21027, 19961,  19967, 19966, 21025,  19085, 19087, 9451,  \n9513, 9516, 7896,  4456, 12452, 8269,  6730, 11455, 6372,  \n399, 10126, 400,  19470, 21030, 20488,  21490, 21491, 13291,  \n18993, 19470, 20488,  18786, 18413, 4739,  21032, 18993, 20488,  \n20489, 18993, 21032,  19475, 19476, 21033,  13379, 13615, 1890,  \n16514, 3794, 690,  7358, 7359, 7514,  6446, 16073, 6447,  \n18530, 13023, 15632,  21037, 19984, 19987,  21037, 19987, 21496,  \n20508, 19989, 21034,  21037, 21496, 20502,  2456, 8773, 318,  \n19980, 18548, 21036,  7298, 16611, 10028,  21043, 20512, 19997,  \n19997, 20502, 21043,  7222, 16668, 14960,  1823, 8320, 4953,  \n20748, 18352, 10117,  2690, 2691, 3477,  7436, 21499, 13327,  \n7634, 8038, 21504,  3605, 7693, 11537,  9522, 6110, 10775,  \n16239, 16471, 20429,  21497, 21505, 19526,  19423, 11931, 15233,  \n5614, 13153, 5615,  21505, 21051, 19526,  18047, 19529, 21507,  \n19998, 18047, 21507,  3517, 15350, 8145,  4890, 6246, 3809,  \n15475, 15476, 14663,  2690, 4622, 9405,  21509, 19513, 19514,  \n15081, 16977, 14087,  21509, 19514, 19519,  21510, 19519, 20523,  \n20523, 20027, 21511,  3247, 21215, 11556,  1703, 6508, 15879,  \n5582, 2837, 6190,  7944, 11692, 11691,  10093, 5909, 15940,  \n14230, 6149, 9479,  4657, 8925, 8924,  21512, 21059, 21051,  \n18935, 20547, 4859,  19521, 18577, 20012,  19311, 15149, 20537,  \n3762, 3763, 18293,  21060, 20023, 21061,  13006, 13734, 12728,  \n11146, 11148, 2069,  21515, 19529, 19061,  21053, 21517, 21064,  \n19530, 21053, 20524,  21518, 18150, 21044,  5550, 1615, 21519,  \n1147, 3140, 3141,  16139, 18736, 11700,  5945, 4628, 4629,  \n14740, 17122, 17250,  639, 638, 16286,  20524, 21053, 21064,  \n6800, 7416, 18465,  20032, 21516, 19061,  20032, 21068, 21516,  \n9721, 13102, 9419,  18581, 19521, 20530,  388, 17816, 17817,  \n20535, 21516, 21068,  16090, 21066, 19532,  5484, 1582, 2245,  \n21440, 15672, 2589,  5864, 5865, 16585,  21860, 21525, 19076,  \n21067, 21860, 19076,  15900, 4712, 4713,  2488, 2489, 10724,  \n20037, 20051, 21527,  18613, 21525, 21528,  16313, 17083, 12667,  \n3951, 10316, 18724,  18613, 21528, 20541,  20541, 21083, 18624,  \n21083, 18626, 18624,  10235, 19607, 10236,  16860, 17953, 2839,  \n20545, 18626, 19550,  21077, 20536, 21075,  6728, 3703, 3702,  \n20045, 21077, 21530,  19088, 18626, 20545,  21531, 20040, 9099,  \n21087, 21075, 19543,  21530, 20048, 20045,  21533, 19552, 19090,  \n11315, 16349, 3236,  4087, 15086, 11228,  21530, 21077, 21075,  \n20546, 19546, 20048,  6142, 7316, 17601,  19121, 11427, 5930,  \n20052, 20555, 19093,  18739, 5604, 524,  4972, 15560, 9706,  \n8164, 7560, 18973,  13927, 12968, 5529,  9893, 1653, 21539,  \n20067, 20550, 20557,  18965, 21540, 15560,  5577, 9112, 5578,  \n14297, 16018, 12436,  14579, 5706, 6672,  8633, 3994, 2526,  \n21541, 17760, 21542,  12650, 15002, 1756,  21543, 7818, 6616,  \n19099, 20084, 21100,  12638, 8277, 13164,  16760, 8362, 8361,  \n8831, 5306, 15889,  9069, 10984, 2727,  19099, 19571, 20084,  \n12037, 5339, 5338,  21544, 21113, 20558,  8005, 21099, 3711,  \n19172, 19151, 20564,  20077, 20089, 21108,  14995, 14305, 14304,  \n21113, 20080, 20559,  19173, 20564, 20572,  13253, 15247, 20197,  \n13137, 18731, 13138,  21113, 20568, 20080,  21113, 21548, 20568,  \n16085, 10755, 21549,  249, 247, 271,  7264, 6884, 5654,  \n19173, 21111, 20577,  21112, 19125, 21129,  7354, 9537, 956,  \n13228, 21550, 16233,  21116, 18712, 21551,  20581, 21116, 21551,  \n1738, 19010, 10539,  20105, 21120, 19606,  11809, 11584, 7144,  \n21119, 21554, 21121,  2633, 392, 16072,  6610, 17354, 20276,  \n17674, 4791, 16235,  21556, 20115, 21554,  21554, 20115, 21121,  \n19163, 19613, 21128,  7835, 13177, 14752,  11738, 7512, 1829,  \n8961, 11872, 13109,  10587, 17306, 19973,  19125, 20586, 21129,  \n4708, 4709, 6226,  8735, 21550, 14171,  20115, 20588, 19178,  \n5972, 23437, 9489,  9305, 4464, 477,  4356, 21558, 2658,  \n2439, 19422, 3796,  20131, 19623, 21125,  19628, 19194, 20587,  \n14406, 5519, 12753,  460, 5519, 9458,  20591, 21562, 21128,  \n6206, 18099, 16679,  21557, 21128, 21562,  8516, 10689, 6861,  \n5026, 12710, 5027,  10389, 313, 1124,  7784, 7811, 3070,  \n21117, 20102, 21134,  20102, 19591, 21134,  15461, 9703, 17533,  \n20591, 21135, 21562,  1282, 8574, 13673,  4534, 17342, 4535,  \n20613, 21904, 21136,  18399, 8214, 21565,  4029, 6793, 7351,  \n21135, 21136, 21562,  2260, 11386, 14766,  20151, 20613, 21136,  \n19748, 15109, 2893,  22893, 10270, 13122,  19203, 19623, 20131,  \n3241, 5119, 17262,  5961, 22736, 4555,  20152, 21144, 20613,  \n7860, 4718, 7279,  18108, 13734, 16701,  21568, 16005, 18470,  \n17647, 9980, 13619,  16497, 9031, 12550,  18642, 12779, 15345,  \n18177, 18657, 8187,  21141, 21140, 21570,  20538, 21571, 15576,  \n12193, 7238, 11457,  21173, 21141, 21570,  15381, 379, 20859,  \n9825, 2969, 707,  1046, 20109, 21545,  21164, 20155, 21573,  \n14257, 2491, 4495,  5422, 11041, 12755,  17843, 21225, 11799,  \n7366, 4000, 13454,  12566, 18442, 16641,  4494, 4495, 2491,  \n21173, 21165, 21152,  19950, 2444, 21577,  4892, 1156, 1157,  \n20604, 21155, 20620,  6529, 6528, 19582,  10125, 14572, 19572,  \n21152, 21165, 21155,  13681, 17264, 21578,  12263, 9997, 10381,  \n19695, 4692, 14269,  9618, 3676, 17741,  4295, 4296, 20161,  \n20149, 20174, 21170,  20149, 21170, 20598,  10012, 8801, 1286,  \n21172, 21173, 22222,  21589, 21583, 20621,  11466, 2939, 2938,  \n11370, 8181, 16416,  22222, 21179, 21172,  20621, 20167, 21589,  \n13078, 12603, 13079,  19671, 20628, 21183,  20631, 21585, 20174,  \n20625, 21586, 19651,  22924, 16475, 13428,  21587, 13059, 21588,  \n4200, 17797, 9956,  21588, 13059, 6193,  21919, 21590, 21179,  \n2076, 2078, 21591,  18806, 20178, 20650,  18011, 2841, 12382,  \n3458, 5536, 10729,  5862, 5848, 5847,  19803, 13012, 15165,  \n10244, 6988, 19746,  506, 21593, 505,  19671, 21183, 20660,  \n19240, 18806, 20665,  20685, 20637, 21179,  21596, 18252, 1420,  \n20130, 4619, 2142,  20626, 18709, 12748,  15857, 17669, 5458,  \n4206, 6554, 1917,  11003, 11002, 9724,  2284, 16254, 2285,  \n4936, 4937, 21209,  21198, 20685, 21590,  11018, 3670, 3669,  \n14375, 17035, 10474,  18022, 3780, 11377,  18875, 15327, 2177,  \n15398, 7855, 3095,  12753, 461, 24877,  14567, 12521, 3400,  \n19148, 3020, 18256,  13219, 5537, 7507,  13224, 4568, 13720,  \n2582, 11673, 7183,  10432, 5307, 8830,  534, 20479, 6421,  \n18823, 19240, 21600,  16957, 5778, 3861,  14284, 5109, 16276,  \n11707, 9041, 11995,  4072, 21398, 15079,  21200, 21212, 20689,  \n891, 16357, 11564,  5295, 16752, 21601,  11587, 18759, 7570,  \n19258, 15335, 9379,  10980, 3361, 21602,  18823, 21603, 19260,  \n20370, 3629, 10204,  7773, 7772, 17865,  21205, 20689, 21212,  \n5188, 1340, 1339,  1234, 831, 5361,  18671, 6975, 15235,  \n11745, 19336, 9068,  8632, 17593, 21592,  13015, 3948, 9269,  \n8616, 10256, 17661,  4010, 16339, 7856,  4094, 15329, 3268,  \n9497, 9496, 7573,  20224, 19414, 5679,  21606, 21604, 20703,  \n21604, 20704, 20703,  15809, 9727, 17589,  21607, 20702, 20701,  \n18243, 2378, 1886,  19270, 19260, 21603,  14251, 12805, 8860,  \n13534, 16235, 1666,  21608, 20229, 20697,  21608, 20703, 20229,  \n5810, 5811, 15455,  9240, 13538, 4753,  20700, 20706, 20701,  \n21212, 20251, 21205,  20300, 4521, 6595,  21603, 21219, 19270,  \n21223, 20245, 19720,  18611, 14277, 5296,  6611, 6418, 5713,  \n13990, 6046, 6959,  20723, 21218, 20715,  19646, 11149, 5190,  \n19761, 20949, 21612,  22078, 19787, 7651,  14111, 8764, 8763,  \n10300, 5477, 3276,  14534, 9899, 19518,  5207, 9839, 2827,  \n6639, 14869, 16971,  8219, 20915, 20916,  8409, 17921, 5340,  \n20101, 11318, 1861,  20731, 21616, 20730,  20718, 21615, 21231,  \n9559, 3742, 20767,  7597, 7641, 9148,  5768, 14911, 22248,  \n21616, 20731, 21617,  4222, 12248, 6012,  21234, 20721, 21231,  \n13315, 5586, 5585,  20731, 20736, 21617,  9560, 21619, 14191,  \n9182, 4103, 9024,  20949, 19761, 16916,  20736, 20738, 21617,  \n8554, 8151, 8711,  19435, 581, 583,  7627, 9511, 15837,  \n3867, 18390, 7726,  20737, 21234, 21621,  21617, 20738, 21242,  \n21622, 21973, 21979,  8751, 12399, 17726,  7618, 743, 9455,  \n21242, 20739, 20740,  10573, 20317, 12243,  21202, 5873, 15518,  \n15625, 12435, 2874,  16693, 15111, 18339,  10339, 16292, 3271,  \n3152, 2139, 7196,  21625, 21622, 21979,  12565, 17595, 18442,  \n21630, 21622, 21625,  9810, 9811, 11238,  10156, 21311, 960,  \n6504, 14570, 12079,  21627, 2291, 14697,  20281, 21240, 21628,  \n2042, 2043, 11311,  21623, 21622, 21626,  15900, 12983, 4712,  \n13452, 21631, 16892,  2428, 826, 444,  21626, 21622, 21630,  \n9530, 4799, 8264,  2485, 21632, 18637,  10156, 2108, 21311,  \n21633, 21626, 21630,  6928, 13646, 1818,  21248, 20281, 21628,  \n21636, 16667, 15468,  21634, 21633, 21259,  11999, 389, 4624,  \n3174, 11606, 3173,  21630, 21260, 21633,  14482, 21637, 9547,  \n21638, 21987, 21634,  7866, 2273, 21494,  21246, 20747, 21639,  \n21630, 21635, 21260,  20307, 21640, 21641,  16977, 20304, 13389,  \n5561, 18307, 1360,  21262, 21248, 21628,  20494, 21524, 13717,  \n4980, 10262, 3691,  21639, 20747, 20757,  20667, 14392, 3893,  \n21634, 21259, 21638,  21259, 21633, 21261,  21261, 21633, 21260,  \n1162, 15391, 20688,  21259, 21269, 21638,  21646, 21638, 21647,  \n10838, 16004, 9646,  4151, 3275, 1366,  10311, 938, 21160,  \n5814, 15764, 21649,  21260, 21635, 21265,  21261, 21260, 21270,  \n4946, 10643, 5269,  3270, 13809, 3269,  10759, 11214, 2677,  \n10000, 4224, 11159,  18933, 623, 18570,  21265, 21635, 21653,  \n21639, 21266, 21650,  12903, 18957, 11620,  7704, 13672, 4861,  \n11728, 13074, 9296,  9466, 6158, 6160,  8969, 12014, 16594,  \n21709, 15210, 20830,  21270, 21260, 21265,  9073, 12338, 10557,  \n5555, 9404, 9403,  4117, 4116, 1786,  21272, 20751, 20750,  \n21272, 20750, 21263,  11495, 16688, 5241,  6801, 2822, 2665,  \n21657, 21270, 21265,  814, 815, 18375,  21655, 21650, 21266,  \n21656, 21657, 21265,  21654, 20768, 21658,  21654, 21647, 20768,  \n2077, 18255, 1014,  18020, 356, 18021,  21266, 20762, 21277,  \n17890, 16715, 21659,  3007, 21660, 3008,  21270, 21657, 21267,  \n20768, 21647, 21274,  21272, 21662, 20761,  6139, 4037, 16126,  \n21267, 21657, 21282,  13821, 18211, 18757,  4253, 12774, 5259,  \n21266, 21277, 21655,  12108, 12506, 12107,  21664, 21282, 21657,  \n21273, 21267, 21282,  21281, 20761, 21662,  13844, 13843, 8151,  \n6543, 12379, 10295,  2201, 5808, 12877,  21158, 7175, 7216,  \n5468, 9929, 12120,  8122, 1604, 20015,  7389, 5996, 5995,  \n957, 959, 9781,  21669, 21655, 21277,  8686, 1341, 8433,  \n17905, 17245, 12133,  4525, 16626, 14253,  17379, 3122, 20482,  \n21277, 21279, 21294,  13426, 13428, 17727,  7838, 16701, 13734,  \n21671, 11981, 23667,  21662, 21290, 21281,  21296, 21277, 21294,  \n21669, 21277, 21296,  20776, 21282, 21664,  1273, 18164, 6844,  \n21288, 21294, 21279,  21294, 21295, 21296,  20776, 21664, 21670,  \n14380, 9304, 5372,  21301, 20776, 21670,  581, 2718, 9609,  \n9906, 16510, 2876,  7448, 922, 923,  21676, 21290, 21674,  \n12690, 16277, 21575,  10370, 17448, 22702,  1379, 9600, 4110,  \n4155, 1496, 2048,  21670, 21673, 21301,  6920, 20247, 16751,  \n11568, 6773, 15866,  21680, 17920, 7231,  20798, 14017, 19130,  \n21295, 21305, 21296,  21290, 21676, 21287,  6847, 13756, 12759,  \n3223, 13506, 6995,  21572, 18144, 288,  11516, 6448, 5914,  \n14018, 10205, 3399,  21302, 21287, 21676,  21679, 21304, 20780,  \n11308, 12738, 21489,  19384, 666, 16531,  21679, 20780, 20791,  \n12447, 19381, 13908,  9125, 5249, 6397,  2715, 20203, 17776,  \n8888, 11896, 10164,  19798, 10562, 21681,  21305, 21295, 21309,  \n14668, 11335, 6099,  20785, 20782, 21682,  16480, 8249, 10268,  \n21105, 11512, 11217,  14694, 8358, 13194,  4284, 17238, 3393,  \n9247, 4147, 17445,  24236, 2641, 4533,  21684, 20791, 20789,  \n6901, 12400, 13213,  10823, 8835, 8834,  18371, 10163, 12188,  \n20186, 14094, 15808,  21685, 21305, 21310,  21682, 21686, 20785,  \n1033, 3530, 9949,  21685, 21310, 21688,  14738, 3291, 20956,  \n10674, 8142, 14217,  527, 18634, 4431,  13264, 3888, 16966,  \n9443, 13155, 17833,  12246, 11689, 13705,  20802, 21688, 21310,  \n20785, 21686, 20794,  20789, 20292, 20816,  4018, 20053, 8352,  \n12573, 2574, 12444,  10413, 3201, 10414,  10729, 13567, 20652,  \n899, 17279, 900,  20806, 20794, 21323,  4580, 6450, 6403,  \n5509, 2034, 20153,  6597, 6305, 15433,  20802, 21322, 21688,  \n617, 20256, 16901,  16763, 19430, 18869,  8133, 17281, 17616,  \n12703, 8218, 21695,  21697, 20806, 21323,  20806, 21697, 20809,  \n21337, 20816, 20820,  13382, 13383, 18245,  21337, 20820, 21339,  \n14034, 12124, 12125,  20818, 20809, 21697,  6355, 4797, 20188,  \n4113, 18136, 15288,  13922, 7760, 14859,  21691, 21322, 21698,  \n19419, 2799, 15274,  4955, 20790, 7038,  21699, 21697, 21700,  \n20818, 21697, 21699,  20827, 20835, 21339,  21341, 21702, 21698,  \n8582, 9075, 14070,  15452, 6122, 3634,  11297, 499, 4652,  \n20796, 8628, 13099,  15574, 14599, 21082,  1301, 12524, 1471,  \n4840, 3659, 3658,  2336, 11321, 7950,  12206, 5390, 16711,  \n21352, 20832, 21701,  3340, 4099, 15461,  5247, 15687, 15856,  \n4242, 19288, 5328,  5466, 5467, 19122,  7437, 7612, 1447,  \n2721, 3627, 4813,  3209, 3210, 5192,  11305, 1266, 20884,  \n3053, 16032, 10808,  5531, 10935, 10121,  20850, 20832, 21352,  \n21341, 21348, 21703,  21704, 21705, 20848,  21352, 21363, 21353,  \n301, 2733, 2900,  10481, 3886, 2900,  13551, 13080, 11525,  \n29709, 7495, 17573,  22080, 1915, 4327,  16290, 5280, 17684,  \n5929, 2655, 8188,  21704, 20848, 20864,  19602, 752, 20001,  \n21353, 21363, 21362,  3928, 2377, 8473,  22065, 7027, 11775,  \n9219, 21681, 10562,  14187, 1270, 14774,  10113, 21709, 10114,  \n7888, 11284, 21361,  8152, 14589, 9764,  3047, 13622, 288,  \n10918, 18701, 12412,  682, 7722, 681,  16760, 20734, 8362,  \n12529, 4676, 16928,  17281, 3219, 6695,  7281, 6584, 7280,  \n21371, 20864, 21374,  16758, 12703, 8946,  8389, 18100, 7987,  \n21713, 21357, 21356,  15563, 3766, 21714,  718, 17066, 719,  \n7580, 2462, 12062,  21356, 20863, 21713,  21357, 21713, 21707,  \n17142, 15848, 23480,  20303, 20861, 21716,  17778, 21717, 9979,  \n3282, 16355, 16444,  5402, 5403, 9895,  21719, 11100, 7666,  \n21707, 21713, 21720,  19574, 16928, 17867,  21718, 21723, 21372,  \n18928, 17404, 17403,  15004, 5308, 11125,  21716, 20308, 20303,  \n1445, 2969, 9825,  14695, 12277, 6209,  21713, 21377, 21727,  \n20863, 21377, 21713,  18963, 8211, 7061,  21383, 19773, 20322,  \n21374, 19773, 21383,  3339, 3341, 4899,  17046, 14491, 14492,  \n6785, 6508, 1924,  1009, 19477, 18788,  8757, 9363, 21726,  \n21720, 21713, 21733,  15148, 14393, 10780,  21723, 21380, 21386,  \n5751, 1717, 17560,  7712, 15999, 12431,  21713, 21727, 21733,  \n20331, 21380, 21722,  13646, 9902, 4675,  21723, 21386, 20885,  \n2738, 16993, 19921,  19641, 16685, 19025,  21383, 20322, 20330,  \n20323, 21380, 20331,  19569, 7964, 3925,  21727, 21377, 21389,  \n21730, 17591, 19786,  20882, 21716, 22076,  18622, 10875, 11945,  \n13501, 1937, 17448,  20044, 13041, 11067,  21733, 21727, 21732,  \n13265, 15644, 17262,  21727, 21389, 21732,  5416, 5415, 11456,  \n2371, 21737, 2372,  21736, 21396, 20882,  14898, 4046, 8420,  \n21738, 21733, 21732,  20651, 9453, 16815,  21389, 20899, 21399,  \n4435, 11375, 4436,  11491, 11490, 8834,  20896, 21396, 21740,  \n19248, 20129, 13599,  20899, 20898, 21399,  2952, 5714, 2950,  \n21742, 20898, 20905,  13012, 5208, 15165,  21742, 21399, 20898,  \n21401, 22087, 20905,  10658, 828, 827,  12641, 1407, 12637,  \n798, 812, 799,  21401, 21403, 21743,  20353, 20349, 21406,  \n1148, 1149, 8769,  10294, 8045, 8044,  2565, 4738, 18646,  \n12481, 1682, 1684,  21412, 21746, 19832,  14543, 2756, 8795,  \n21412, 18840, 19823,  21411, 18346, 21414,  3971, 13629, 9905,  \n10536, 8828, 10535,  18842, 21415, 21414,  10749, 9169, 15986,  \n21748, 21409, 20920,  21417, 18845, 19832,  15940, 8046, 4091,  \n18843, 21419, 21415,  19446, 12510, 21750,  13855, 775, 7785,  \n19031, 11851, 21751,  2586, 18240, 9662,  21420, 20353, 21752,  \n19054, 19053, 18942,  15238, 8030, 21753,  19832, 21746, 21417,  \n21748, 20920, 21422,  6884, 3013, 4401,  19811, 21420, 20360,  \n10109, 11915, 8235,  21420, 21752, 21755,  9493, 10653, 7252,  \n20360, 21420, 21755,  21757, 21748, 21422,  21422, 21426, 21757,  \n11864, 16087, 21758,  21756, 20944, 20360,  11962, 11963, 6505,  \n18854, 20943, 21759,  9415, 14639, 18447,  13303, 21762, 16008,  \n20936, 20939, 21429,  13515, 19473, 2169,  21763, 19856, 20951,  \n13185, 20358, 17362,  19888, 16447, 5610,  18255, 12086, 1014,  \n5784, 11697, 4255,  20942, 19835, 21428,  20939, 20375, 21431,  \n21429, 20939, 21431,  21429, 22105, 21767,  7239, 13521, 15960,  \n19861, 20382, 21768,  9626, 770, 11439,  29154, 17099, 18720,  \n21428, 20944, 21765,  8761, 20908, 6811,  14096, 11440, 1149,  \n11745, 5707, 19336,  21769, 4550, 4549,  10318, 11248, 8894,  \n20387, 18854, 21759,  9445, 9800, 10116,  18546, 10155, 9713,  \n8021, 11482, 2881,  21771, 20942, 21428,  3701, 2179, 5999,  \n21430, 20948, 21437,  16328, 20887, 2144,  22105, 21429, 21431,  \n21773, 20960, 21772,  21434, 21773, 21772,  21774, 21773, 21434,  \n3828, 3827, 10324,  12479, 11997, 8468,  20373, 21438, 20380,  \n3205, 8487, 15759,  7798, 1635, 15701,  10710, 20717, 10711,  \n20960, 21773, 20391,  8432, 8686, 8433,  6020, 4981, 14891,  \n19189, 12658, 21020,  21193, 13263, 17919,  16013, 17244, 1907,  \n3458, 10729, 18994,  21781, 20960, 19871,  19871, 21441, 21781,  \n4199, 3429, 10946,  20958, 20393, 21782,  21784, 20954, 21778,  \n9557, 15935, 20423,  20380, 21438, 21780,  11116, 852, 5561,  \n22430, 8109, 9062,  18441, 18440, 21785,  20396, 20963, 21786,  \n18381, 18871, 20397,  10583, 439, 21468,  7851, 939, 8826,  \n21789, 7882, 5717,  20969, 19885, 18879,  8399, 4082, 8400,  \n6085, 6219, 22187,  21446, 20405, 21791,  14754, 17722, 16580,  \n614, 5203, 6985,  21792, 20976, 21446,  20976, 21793, 20977,  \n20976, 21792, 21793,  4304, 15353, 17293,  20977, 21793, 21795,  \n18937, 7346, 5527,  7615, 19598, 7614,  4046, 14898, 21796,  \n7525, 5776, 13546,  3823, 16750, 7296,  7033, 17597, 7034,  \n2983, 18771, 20549,  13534, 12818, 21073,  20811, 3680, 8590,  \n19895, 21450, 21797,  19895, 21797, 20981,  2782, 13050, 17868,  \n21798, 21799, 3076,  18889, 6805, 1401,  15115, 20496, 9906,  \n9833, 1459, 2741,  19818, 8796, 6283,  9769, 11029, 9768,  \n20500, 4495, 11855,  20984, 18895, 20982,  2967, 3508, 2968,  \n21453, 20984, 20982,  21546, 7812, 7813,  16980, 20368, 16979,  \n12735, 1876, 12543,  22377, 19909, 20984,  20595, 7991, 14321,  \n22377, 21455, 19909,  6292, 4977, 15136,  20422, 19909, 21455,  \n21338, 20796, 13099,  885, 8544, 12238,  21801, 20988, 20987,  \n20649, 5538, 5539,  21801, 21802, 20427,  19403, 18431, 19399,  \n6266, 18994, 6267,  21804, 19407, 21459,  12706, 11686, 8984,  \n12165, 15540, 16900,  4329, 20175, 16537,  17748, 3162, 11807,  \n20203, 15727, 554,  21809, 19436, 20444,  7088, 18920, 7094,  \n19443, 11982, 19581,  9176, 11982, 19443,  1214, 9295, 12966,  \n2505, 12606, 2965,  3461, 1475, 8336,  20442, 18479, 21807,  \n519, 19168, 520,  21464, 21810, 20996,  20996, 21810, 21001,  \n21464, 20996, 21808,  21808, 20996, 20448,  20448, 19424, 21002,  \n20444, 20993, 21809,  16629, 21814, 11851,  21471, 20997, 21003,  \n20464, 21469, 21816,  21817, 10940, 12277,  21821, 20471, 21809,  \n19436, 21809, 20471,  8827, 16865, 10616,  12753, 10267, 3093,  \n21822, 20460, 21009,  21822, 21471, 20460,  21820, 19941, 18962,  \n3080, 7524, 8088,  21823, 21820, 20473,  21823, 20473, 21821,  \n21821, 20473, 21014,  21822, 21009, 21012,  6660, 6661, 19711,  \n21822, 21012, 21481,  655, 654, 2942,  6008, 2092, 2809,  \n17509, 21482, 21825,  11017, 545, 15046,  2449, 5518, 15475,  \n19455, 17509, 21825,  6876, 7341, 17968,  5247, 15856, 588,  \n21487, 21025, 17965,  14704, 7089, 20971,  6522, 10488, 13917,  \n10746, 18460, 20384,  19967, 21025, 21827,  15609, 15721, 14602,  \n21828, 19221, 8076,  21571, 9952, 15576,  19646, 2683, 11300,  \n1078, 21829, 1079,  20484, 19977, 20490,  21790, 14744, 18714,  \n15399, 9522, 10752,  3963, 6124, 14379,  6370, 9030, 18025,  \n13098, 2470, 2471,  19475, 21033, 21034,  9492, 15628, 1918,  \n22157, 21034, 21033,  21831, 19980, 21036,  19014, 21035, 20499,  \n11348, 4039, 5572,  21496, 19987, 20498,  21496, 20498, 21833,  \n13137, 11960, 11959,  19483, 21833, 20498,  21833, 19483, 20499,  \n15270, 21834, 21835,  21836, 20502, 21496,  5759, 12127, 20058,  \n8785, 8784, 12094,  19488, 17043, 21040,  11789, 17764, 14944,  \n20502, 21836, 21043,  21040, 17043, 17048,  20079, 18438, 428,  \n15542, 19344, 15541,  19994, 17048, 20507,  21843, 8970, 19762,  \n21837, 20512, 21043,  21497, 20512, 21837,  21840, 21846, 20508,  \n9157, 5189, 16068,  4473, 15046, 18741,  20507, 19028, 19999,  \n15747, 15748, 9457,  21750, 7910, 10980,  21211, 1742, 12288,  \n19371, 20050, 21478,  21036, 18548, 21050,  23936, 13567, 10729,  \n21846, 21049, 20508,  7693, 3605, 3607,  5290, 6954, 2591,  \n12911, 2769, 2770,  21844, 20364, 7445,  21845, 7398, 7921,  \n13842, 12272, 13841,  21053, 19508, 21049,  8259, 8661, 6026,  \n20096, 6294, 11547,  21505, 21847, 21051,  21053, 21049, 21848,  \n17331, 9910, 16027,  20519, 19513, 21509,  15398, 12448, 21849,  \n21850, 21509, 19519,  21850, 19519, 21510,  11807, 4885, 4884,  \n21511, 21510, 20523,  18723, 19208, 10256,  21051, 21853, 21512,  \n21847, 21853, 21051,  21492, 8339, 20090,  21582, 4075, 19123,  \n8381, 11505, 14667,  21852, 20027, 21057,  21057, 19058, 21060,  \n20658, 718, 22745,  14320, 13421, 1728,  16650, 1978, 3035,  \n15867, 8363, 19353,  2316, 21098, 1141,  13304, 14013, 20643,  \n20017, 6227, 6226,  9727, 21854, 17589,  11347, 15703, 4990,  \n21515, 19061, 21516,  21517, 21515, 21516,  21517, 21516, 21064,  \n11611, 9254, 11350,  13846, 1354, 1355,  16985, 17343, 4534,  \n17262, 15644, 7344,  4384, 13553, 13997,  19875, 18550, 15526,  \n19614, 9689, 5512,  20000, 19044, 21523,  19044, 20037, 21523,  \n5703, 18778, 11179,  21855, 6505, 6506,  21857, 21063, 21059,  \n11334, 6518, 6519,  653, 2704, 21858,  21857, 21859, 21063,  \n21067, 21063, 21859,  21074, 21066, 16090,  21859, 21860, 21067,  \n13568, 10177, 20652,  18592, 20530, 21861,  21074, 16090, 19083,  \n18998, 12935, 16174,  21523, 20037, 21527,  18613, 19076, 21525,  \n2729, 12377, 19494,  20975, 18389, 21864,  20539, 17624, 20534,  \n6583, 20779, 15174,  21083, 20541, 21528,  8095, 19143, 19924,  \n4651, 11168, 11297,  21866, 2743, 6951,  21245, 4381, 19389,  \n1588, 3319, 3320,  21867, 12005, 18091,  20545, 19550, 21529,  \n11150, 9300, 6024,  9003, 13563, 20402,  13511, 3297, 5434,  \n20539, 21868, 20052,  13678, 13679, 18343,  21530, 21075, 21087,  \n5676, 4076, 11944,  21870, 19084, 19111,  20061, 21871, 21097,  \n2957, 7010, 19633,  17619, 9691, 1544,  21533, 21087, 19552,  \n14564, 6270, 14294,  8625, 10004, 16743,  20548, 21527, 20051,  \n7587, 21538, 21537,  20052, 21536, 20555,  19111, 21873, 21870,  \n14072, 11707, 2313,  21872, 21091, 21097,  6629, 18575, 8975,  \n11090, 10061, 22655,  6695, 2585, 14532,  20546, 20048, 21535,  \n21874, 21535, 20048,  20546, 21535, 20550,  3053, 13384, 3054,  \n20550, 21535, 21878,  20557, 20550, 21878,  3004, 3643, 17096,  \n410, 15799, 15798,  21102, 4336, 21101,  21879, 20557, 21878,  \n20556, 20555, 20558,  20506, 15680, 5202,  20692, 2207, 14851,  \n19100, 21881, 19561,  12797, 736, 6932,  5380, 5381, 7024,  \n19607, 18704, 6950,  20077, 19111, 20076,  21879, 20564, 20071,  \n20557, 21879, 20071,  21645, 16250, 21883,  19570, 21884, 18661,  \n21884, 19575, 18661,  1738, 7171, 19010,  15368, 11598, 8258,  \n13408, 9682, 18472,  5146, 1960, 2118,  7967, 11354, 3121,  \n6796, 2374, 6797,  2904, 4630, 12858,  5018, 7315, 20583,  \n7395, 7394, 2579,  3383, 7611, 14322,  12481, 8089, 1682,  \n21108, 20089, 19590,  21888, 20084, 19577,  8233, 576, 12580,  \n21890, 19590, 21116,  21891, 21112, 21129,  21548, 20099, 20568,  \n17113, 10400, 18122,  21890, 21116, 20581,  19585, 19584, 16553,  \n9654, 21018, 21895,  13561, 9003, 15338,  2910, 15509, 2909,  \n18712, 20580, 21551,  843, 10758, 18531,  8514, 3095, 13992,  \n20813, 19504, 8606,  19577, 21117, 21897,  16566, 7213, 10525,  \n19748, 14424, 17390,  12527, 16540, 21107,  12485, 21898, 17884,  \n20588, 20115, 21556,  12226, 14321, 4864,  6089, 8909, 8910,  \n10873, 21863, 1731,  6367, 1806, 7782,  21124, 21128, 21899,  \n3240, 5119, 3241,  13610, 21900, 13611,  21125, 20582, 21901,  \n6042, 6041, 4638,  12222, 18528, 9050,  21128, 21557, 21899,  \n21125, 21903, 20131,  12212, 4706, 12211,  21557, 21562, 21904,  \n18735, 2919, 20345,  10870, 18244, 18539,  8603, 12746, 8604,  \n11583, 13505, 14972,  10419, 19322, 17562,  14704, 14432, 17977,  \n20590, 21902, 20593,  15922, 13462, 13461,  21562, 21136, 21904,  \n21904, 20613, 21905,  16151, 14660, 16152,  20593, 21902, 21140,  \n6812, 8762, 6811,  21144, 21905, 20613,  21902, 21907, 21908,  \n21140, 21902, 21908,  21910, 21570, 21908,  7932, 7931, 13034,  \n21144, 20614, 22215,  19628, 20587, 20155,  11041, 21911, 7468,  \n21912, 19466, 4696,  21140, 21908, 21570,  12301, 9569, 9570,  \n11633, 12880, 11401,  21151, 7513, 2996,  17800, 1207, 8389,  \n7601, 4666, 14197,  21913, 20614, 20621,  21913, 20621, 21583,  \n12590, 18253, 8445,  15209, 2973, 9562,  21570, 21910, 21173,  \n21134, 20598, 21915,  21915, 20598, 21170,  7935, 7937, 6956,  \n21910, 22222, 21173,  13349, 5313, 13348,  15795, 3924, 5078,  \n10643, 15300, 4063,  17341, 2290, 17342,  16812, 9582, 16811,  \n8130, 16507, 13812,  21162, 19651, 21917,  1754, 19065, 7958,  \n17084, 17472, 17471,  19996, 15815, 20395,  12591, 9898, 9556,  \n21179, 22222, 21920,  19651, 21586, 21917,  9596, 18511, 5626,  \n21183, 20628, 21921,  20462, 3218, 20463,  21920, 21919, 21179,  \n4664, 5861, 11460,  14150, 9739, 6860,  21922, 20174, 21585,  \n1683, 10409, 1684,  1926, 1927, 17400,  6804, 854, 4299,  \n16217, 21923, 5449,  15320, 20565, 6771,  4524, 4525, 14253,  \n17333, 18025, 9058,  12626, 6305, 3972,  7400, 9912, 2825,  \n7932, 20205, 13042,  14442, 17183, 16516,  20187, 21595, 20631,  \n2856, 11602, 7561,  21179, 21590, 20685,  20660, 22233, 20198,  \n21929, 9072, 10007,  20187, 21189, 21595,  3785, 5379, 16722,  \n21198, 21590, 21597,  11577, 2390, 20043,  9274, 17777, 5230,  \n20117, 7466, 20116,  12180, 11355, 13082,  15051, 8114, 8113,  \n19911, 542, 17020,  19240, 20665, 21600,  11032, 11494, 11033,  \n14036, 19875, 16245,  20656, 20682, 21932,  18814, 20228, 21197,  \n21933, 21932, 20682,  19676, 21196, 21934,  21603, 18823, 21600,  \n5578, 13627, 5577,  4205, 9173, 4902,  7058, 21936, 6159,  \n20220, 21937, 20690,  2716, 20797, 24391,  4215, 16361, 16360,  \n21939, 20682, 20704,  999, 1000, 11220,  15549, 6726, 21941,  \n21939, 20704, 21604,  21933, 20682, 21939,  20634, 5549, 17478,  \n16257, 14833, 15130,  2579, 3417, 3416,  20228, 19715, 21942,  \n19715, 20245, 21942,  21943, 21206, 21205,  7948, 2168, 2660,  \n20697, 21206, 21605,  20697, 21605, 21608,  21608, 21606, 20703,  \n20706, 20690, 21609,  21943, 21605, 21206,  15549, 5904, 15271,  \n18327, 12419, 12420,  21607, 20701, 22241,  3325, 11098, 8396,  \n23979, 3843, 14678,  5253, 16410, 21480,  660, 661, 5520,  \n20245, 21223, 21942,  21205, 20251, 21218,  21224, 21942, 21223,  \n4700, 2127, 12036,  21611, 20710, 20708,  10663, 19910, 13461,  \n5520, 2120, 411,  5457, 16143, 403,  21614, 20716, 20249,  \n16355, 7626, 11227,  20710, 21611, 21615,  10001, 12262, 3047,  \n6238, 13451, 3231,  11115, 11116, 1995,  1979, 7162, 2932,  \n5302, 18475, 5303,  21227, 20716, 21614,  21828, 8076, 5506,  \n1667, 14065, 20611,  20720, 21951, 20254,  20254, 21952, 21222,  \n20254, 21951, 21952,  20710, 21615, 20718,  10156, 6707, 7154,  \n1955, 1904, 6980,  2860, 14675, 2692,  19777, 17245, 17905,  \n21231, 21615, 21954,  14639, 10889, 19343,  21618, 21234, 21231,  \n21618, 21954, 21956,  21957, 21958, 21959,  21618, 21231, 21954,  \n11448, 1136, 19564,  3188, 16946, 8174,  3552, 6729, 6863,  \n3623, 3624, 7552,  10395, 7567, 7566,  4753, 13538, 21961,  \n21963, 22261, 21623,  3432, 21029, 17216,  21714, 4926, 3648,  \n19161, 16126, 19206,  16290, 2442, 7949,  19378, 15974, 19945,  \n21966, 568, 17209,  8609, 19819, 8610,  21623, 22261, 21967,  \n6942, 2581, 3166,  21234, 21618, 21621,  21965, 21617, 21242,  \n9985, 8013, 7678,  21970, 5964, 18074,  5725, 21651, 10767,  \n16907, 9557, 16908,  16919, 16580, 11914,  2016, 383, 2017,  \n19970, 17807, 9695,  21974, 13337, 8537,  21623, 21967, 21622,  \n2147, 4959, 15309,  21963, 21976, 21977,  19024, 936, 12816,  \n18320, 12485, 5213,  24236, 8650, 8649,  21979, 21973, 21971,  \n17955, 13748, 10490,  21967, 21973, 21622,  21240, 20737, 21621,  \n20740, 21243, 21242,  21243, 21978, 21242,  1394, 8318, 11628,  \n5553, 16230, 18162,  8995, 8994, 9722,  21963, 21623, 21976,  \n5170, 1525, 11773,  21971, 21972, 21979,  6170, 10651, 13309,  \n15723, 11369, 9280,  1105, 4544, 1466,  13525, 13984, 20615,  \n21625, 21979, 21985,  21979, 21984, 21985,  21976, 21623, 21626,  \n450, 7909, 12741,  14725, 5200, 10025,  21986, 21240, 21621,  \n12216, 10109, 14866,  9481, 22044, 9479,  4549, 4550, 2671,  \n7410, 2922, 6787,  21976, 21634, 21983,  13476, 17921, 19079,  \n2678, 15614, 17459,  21976, 21626, 21634,  380, 20006, 379,  \n21989, 1691, 4030,  21983, 21634, 21987,  13502, 15057, 17825,  \n20694, 8234, 12032,  21634, 21626, 21633,  14516, 21991, 16149,  \n5260, 3444, 13663,  21990, 21243, 21246,  21635, 21625, 21985,  \n5111, 16739, 16940,  12327, 6620, 7020,  8429, 21993, 16112,  \n17099, 19539, 2476,  21630, 21625, 21635,  21987, 21638, 21994,  \n4660, 4659, 14473,  5662, 19355, 5661,  5108, 21995, 5985,  \n16704, 6724, 21996,  21635, 21985, 21997,  4446, 3635, 16015,  \n19814, 15190, 19815,  2190, 21534, 8600,  5588, 1940, 14617,  \n21990, 21246, 22003,  2885, 2529, 9649,  5913, 4652, 499,  \n22003, 21246, 21639,  21262, 21628, 22000,  7662, 932, 7663,  \n8235, 6055, 15312,  558, 9414, 12324,  21638, 21269, 21647,  \n20744, 21248, 21262,  1669, 17131, 10219,  22003, 21639, 21650,  \n22002, 21646, 21647,  21654, 22002, 21647,  20193, 21166, 18650,  \n5043, 6356, 6357,  4936, 21209, 13184,  22006, 22002, 21654,  \n20109, 21929, 16225,  17642, 12569, 13096,  21262, 22000, 22005,  \n14646, 5525, 2744,  21656, 21265, 21653,  22006, 21654, 21658,  \n957, 4735, 958,  17589, 9738, 17588,  10611, 4553, 9453,  \n22006, 21658, 22009,  14038, 14328, 14176,  17439, 2302, 1335,  \n11947, 8824, 9369,  1858, 13605, 15035,  19645, 11817, 20379,  \n6094, 17646, 24915,  21263, 22012, 21662,  14084, 14417, 22013,  \n13727, 7650, 20417,  21657, 21656, 22014,  18252, 21596, 9773,  \n21272, 21263, 21662,  8404, 13323, 9778,  20768, 21284, 21658,  \n18678, 6544, 2647,  22014, 21664, 21657,  21284, 22009, 21658,  \n22009, 21284, 22015,  8556, 1526, 19413,  18472, 9682, 9433,  \n17839, 20973, 17910,  21655, 21669, 22010,  13976, 11260, 7705,  \n20492, 8728, 13987,  14434, 22018, 14435,  18896, 1971, 22019,  \n10098, 10110, 6194,  6711, 6710, 9793,  11003, 9724, 12632,  \n15805, 15456, 7412,  22015, 21284, 21291,  18653, 14441, 17287,  \n9471, 7310, 8332,  22010, 21669, 22020,  21670, 21664, 22014,  \n21674, 21290, 21662,  21674, 21662, 22012,  14705, 11039, 20351,  \n7807, 4785, 1416,  21669, 21296, 22020,  22012, 22021, 21674,  \n9752, 18233, 21451,  21291, 20769, 21304,  22023, 21291, 21679,  \n2243, 3714, 10042,  24060, 17989, 20064,  22025, 19992, 12841,  \n21670, 22026, 21673,  10903, 11828, 20669,  7538, 8856, 6488,  \n19931, 17162, 15550,  8935, 17656, 8818,  21291, 21304, 21679,  \n13071, 18182, 13072,  2615, 18640, 17229,  5731, 14755, 18232,  \n9291, 2957, 19632,  777, 17808, 18996,  9169, 10750, 19287,  \n16889, 6702, 19559,  21296, 21305, 22027,  5936, 15769, 688,  \n11845, 2353, 9510,  1914, 13116, 4214,  931, 932, 8344,  \n21676, 21674, 22021,  21673, 22028, 21301,  20726, 22611, 1581,  \n21676, 22021, 22029,  14589, 7733, 9764,  9325, 6675, 9931,  \n16189, 7940, 7913,  14693, 8357, 14694,  7379, 9284, 21636,  \n22030, 22027, 21305,  21676, 21315, 21302,  9729, 14577, 21052,  \n20782, 21301, 22028,  12957, 19364, 14215,  21315, 21676, 22029,  \n21682, 20782, 22028,  5604, 20686, 5605,  22029, 22032, 21315,  \n14198, 12931, 13567,  15434, 12167, 22034,  9030, 8593, 16093,  \n6352, 17249, 15932,  9316, 8801, 10012,  20956, 9076, 20340,  \n21684, 22039, 22037,  21684, 20789, 20816,  21315, 22032, 21333,  \n21685, 21688, 21689,  22039, 21684, 20816,  21689, 21688, 21691,  \n4114, 11284, 4857,  10045, 15697, 12798,  19503, 5909, 10093,  \n9511, 7627, 18159,  21688, 21322, 21691,  20794, 21686, 21323,  \n11611, 11911, 9372,  14800, 2770, 8043,  13674, 22044, 9481,  \n1135, 11349, 15017,  21334, 21333, 22042,  12839, 1764, 21559,  \n11550, 11551, 17600,  2650, 15119, 2651,  10099, 10098, 16648,  \n1350, 8840, 5087,  21691, 21698, 21689,  2663, 10999, 6011,  \n2268, 23138, 22391,  22045, 21689, 21698,  4343, 18429, 11368,  \n21339, 22049, 21337,  14169, 7211, 20341,  21698, 21702, 22045,  \n21876, 17750, 7760,  15550, 11595, 16265,  2094, 4150, 4151,  \n21334, 22047, 21340,  21697, 21323, 22048,  22045, 21702, 22050,  \n21697, 22048, 21700,  7243, 15695, 5655,  21340, 22047, 21701,  \n8487, 3205, 16656,  22053, 8510, 8509,  1491, 12299, 3290,  \n22054, 8510, 22053,  3832, 17969, 4653,  21340, 21701, 20832,  \n5643, 1219, 1671,  21702, 22055, 22050,  21699, 21700, 22056,  \n21342, 20841, 20848,  11347, 4990, 4991,  9918, 11405, 7295,  \n21699, 22056, 21345,  15142, 12905, 19356,  21352, 21701, 21363,  \n21702, 21341, 21703,  22055, 21702, 21703,  3212, 17602, 22059,  \n10503, 9009, 18778,  13483, 696, 20195,  10801, 18224, 13788,  \n7690, 9650, 3280,  2068, 2067, 16350,  9195, 2940, 16038,  \n1406, 8152, 8151,  17757, 20575, 9519,  21704, 22060, 21705,  \n1631, 15951, 11212,  17205, 430, 1192,  7950, 4528, 2336,  \n7420, 12991, 22066,  21363, 21367, 21362,  22063, 21367, 21363,  \n3795, 12039, 19685,  8737, 8458, 7539,  21371, 21704, 20864,  \n2092, 21168, 1693,  14077, 8093, 8772,  6709, 21637, 5567,  \n16483, 9821, 379,  21348, 21357, 21706,  21703, 21348, 21706,  \n21350, 21345, 21708,  22060, 21371, 21710,  21706, 21357, 21707,  \n2298, 6983, 2297,  19447, 13715, 10601,  499, 1506, 1038,  \n21372, 21367, 21711,  21706, 21707, 22068,  21710, 21371, 21374,  \n4248, 9851, 9982,  21710, 21374, 22069,  2994, 12618, 2995,  \n21350, 21708, 21715,  10696, 21250, 572,  20861, 21350, 21715,  \n4765, 5958, 6774,  15209, 9562, 17361,  16708, 2629, 17375,  \n10591, 19790, 5392,  13644, 18674, 10243,  2765, 14825, 9206,  \n5230, 5231, 15600,  4154, 1167, 5819,  21722, 21380, 21723,  \n22071, 21722, 21723,  12038, 12037, 2737,  13215, 8065, 323,  \n12456, 19686, 11252,  760, 761, 19650,  21716, 20861, 21715,  \n22072, 22073, 21722,  2522, 18342, 17197,  16220, 16874, 7840,  \n12316, 15152, 22074,  16660, 7405, 21382,  18671, 15235, 7470,  \n20331, 22075, 21383,  800, 16608, 6125,  22076, 21716, 21715,  \n14248, 1611, 1612,  21720, 21733, 21734,  5918, 9681, 7270,  \n20882, 22076, 21736,  22079, 21734, 21733,  2818, 2819, 6477,  \n14475, 10410, 10409,  3039, 18264, 14575,  16892, 21631, 12371,  \n7512, 9622, 3705,  21733, 21738, 22079,  6562, 4545, 12848,  \n15635, 3248, 15636,  4730, 11714, 8653,  21457, 15901, 2993,  \n9691, 14693, 1544,  21153, 4737, 14265,  20896, 21740, 22085,  \n15077, 19267, 19266,  21732, 21389, 21399,  5369, 16945, 8273,  \n11043, 11042, 15908,  22086, 21738, 21732,  22059, 14263, 15116,  \n22086, 21732, 21399,  17744, 4281, 18546,  8357, 8358, 14694,  \n6727, 3703, 6728,  20896, 22085, 20907,  17676, 10969, 10968,  \n11350, 11612, 11611,  21399, 21742, 22086,  5710, 16522, 14718,  \n22088, 22086, 21742,  20905, 22087, 21742,  22087, 22089, 21742,  \n6519, 5152, 4354,  5438, 5437, 13503,  20913, 20907, 21405,  \n23711, 11302, 15210,  20221, 20466, 16064,  19964, 14142, 14500,  \n598, 6520, 7742,  22087, 21401, 21743,  6463, 6462, 25443,  \n21406, 21405, 22091,  21403, 22093, 21743,  21403, 21409, 22093,  \n13408, 18472, 13407,  21411, 21413, 19823,  7541, 7542, 15917,  \n10596, 7568, 21256,  19342, 18590, 17894,  6191, 2246, 14983,  \n22094, 20912, 2937,  9531, 15598, 4799,  21752, 20353, 22580,  \n12208, 19648, 17973,  21409, 21748, 22093,  20345, 2782, 2781,  \n10165, 10166, 10809,  8858, 7990, 8857,  17335, 7554, 1828,  \n18843, 19842, 21419,  19862, 21419, 19842,  19137, 5376, 17369,  \n521, 18235, 16699,  20943, 20371, 20945,  9643, 14841, 16804,  \n2718, 19435, 17615,  19851, 19860, 19863,  21756, 20360, 21755,  \n17169, 6417, 18901,  5198, 18336, 5573,  15291, 18490, 4733,  \n14192, 3196, 3198,  18045, 21753, 8030,  1312, 5640, 17443,  \n16718, 15863, 17571,  13633, 14193, 14192,  21918, 3175, 9630,  \n18857, 19851, 18855,  11516, 12960, 12917,  21174, 1699, 18830,  \n21774, 21434, 21435,  880, 1820, 20139,  14513, 17979, 8671,  \n21782, 20957, 20958,  13883, 20028, 15329,  8197, 367, 2314,  \n21767, 21426, 21429,  17143, 7052, 7215,  11254, 1179, 1178,  \n20381, 21763, 21772,  21772, 21763, 21434,  20960, 21781, 21772,  \n17387, 22930, 1185,  6596, 13068, 18418,  3117, 15243, 15244,  \n9149, 9685, 6253,  6898, 14541, 820,  8378, 1612, 1611,  \n4254, 4255, 5608,  11272, 2964, 5364,  10731, 20790, 4955,  \n21773, 21774, 21439,  7821, 7820, 2689,  10184, 14541, 6898,  \n8814, 15228, 15229,  22103, 21428, 21765,  15651, 9264, 9139,  \n2773, 824, 12267,  21430, 22105, 21431,  16264, 809, 17668,  \n14654, 12676, 9771,  22108, 17310, 17311,  21508, 17223, 12834,  \n21773, 21439, 20391,  21439, 21782, 20393,  17289, 10280, 17288,  \n8720, 17823, 8719,  21436, 20380, 21780,  10653, 18760, 7252,  \n22104, 21437, 21436,  14166, 14846, 8618,  14159, 6960, 13709,  \n15699, 13600, 3626,  20153, 16874, 5509,  22111, 17310, 22108,  \n21438, 20954, 21784,  18601, 12281, 3866,  8733, 16533, 12072,  \n6540, 15470, 4526,  21441, 18381, 20397,  8569, 15666, 6614,  \n15415, 20675, 14772,  17701, 12180, 7754,  14055, 10112, 14056,  \n20967, 22112, 20397,  22113, 20397, 22112,  10625, 2658, 10624,  \n10250, 12314, 10249,  9743, 9742, 6193,  19880, 19881, 20967,  \n20396, 22114, 20969,  21443, 20967, 19881,  8559, 14519, 19549,  \n7144, 17282, 9270,  17723, 1031, 13608,  2294, 22115, 14390,  \n8259, 442, 6327,  21443, 19883, 20974,  6134, 18275, 6067,  \n21445, 22118, 20405,  8795, 1238, 14543,  7641, 19365, 10526,  \n14740, 12001, 17122,  21446, 21791, 22119,  21792, 21446, 22120,  \n19883, 21447, 20974,  11364, 18566, 10037,  9853, 13515, 1045,  \n16109, 10144, 10145,  21148, 4839, 1386,  6081, 11137, 17291,  \n20977, 21795, 21450,  5827, 922, 21054,  6372, 2679, 2680,  \n22610, 20982, 21797,  21797, 20982, 20981,  7698, 23236, 10044,  \n20982, 22610, 22123,  20982, 22123, 21453,  19898, 20416, 21800,  \n5931, 18207, 3727,  3037, 10479, 5470,  14165, 21398, 20172,  \n9174, 1003, 503,  10817, 1471, 3917,  20422, 22125, 20987,  \n11913, 18698, 3232,  20987, 22126, 21801,  13868, 9839, 17980,  \n22128, 18431, 19403,  20192, 10369, 9572,  22129, 6360, 10353,  \n22130, 22131, 20427,  20427, 22131, 21459,  9416, 1118, 16464,  \n9128, 11462, 21935,  18983, 18982, 6225,  9691, 9692, 19889,  \n19407, 21804, 22134,  19429, 20876, 1630,  21560, 3875, 12986,  \n22135, 21461, 22134,  21461, 19407, 22134,  20993, 21461, 22135,  \n22136, 19403, 19411,  21805, 19411, 20442,  7063, 6377, 6376,  \n7168, 13921, 5387,  21807, 18479, 21465,  21001, 21810, 22139,  \n14833, 20663, 1393,  12741, 6188, 10548,  19417, 19929, 21467,  \n21001, 22139, 21469,  22141, 20998, 20997,  22141, 22142, 20998,  \n21000, 18939, 20998,  22141, 21471, 22143,  22141, 20997, 21471,  \n19496, 5011, 5010,  19828, 6779, 11609,  21470, 19941, 21820,  \n21385, 22144, 3406,  11630, 2725, 12957,  21820, 21823, 22145,  \n10179, 4968, 19602,  22392, 22146, 21821,  22147, 29157, 21458,  \n13697, 6909, 16154,  14819, 19383, 15181,  21821, 22146, 21823,  \n21471, 21822, 22143,  22143, 21822, 22148,  6877, 15196, 18069,  \n22148, 21822, 21481,  2735, 1770, 13755,  21482, 19437, 21479,  \n15797, 19801, 18726,  14015, 4491, 16394,  14970, 13416, 20826,  \n4596, 11902, 4905,  21484, 19455, 21825,  12225, 2327, 19673,  \n22149, 22150, 21587,  19962, 19455, 21484,  3121, 17281, 6695,  \n20594, 14828, 17292,  21384, 21385, 3406,  15023, 15295, 4659,  \n21022, 19961, 21027,  6067, 9097, 14846,  2266, 2267, 5805,  \n5051, 5050, 18076,  21027, 19967, 21827,  5100, 13092, 16336,  \n17017, 22151, 16468,  22152, 6693, 12812,  7282, 4868, 19249,  \n15316, 525, 12209,  4019, 6850, 21692,  14618, 2947, 5344,  \n22154, 20484, 20490,  20983, 13139, 12048,  3374, 1783, 19942,  \n21033, 19476, 22156,  20490, 19980, 21831,  3246, 14388, 8173,  \n19314, 640, 11188,  21496, 21833, 21836,  6095, 2707, 2709,  \n13094, 13093, 17022,  21043, 21836, 22158,  21034, 21840, 20508,  \n7006, 9337, 7005,  10932, 9337, 7006,  22158, 21837, 21043,  \n17251, 22159, 22160,  17687, 2184, 9086,  4686, 3547, 1889,  \n8446, 6419, 21875,  18114, 4773, 13492,  3327, 1457, 5138,  \n21837, 21505, 21497,  5991, 19849, 3906,  13019, 14064, 16097,  \n18616, 10613, 5065,  2861, 17151, 22162,  18267, 10185, 15001,  \n17611, 16054, 23676,  20244, 15734, 6146,  19998, 22163, 19999,  \n612, 4121, 12224,  22163, 19998, 21507,  21049, 21846, 22165,  \n20027, 21852, 21511,  19908, 18466, 21735,  19529, 21515, 21507,  \n12990, 14799, 14798,  10701, 9479, 4082,  14618, 13677, 2947,  \n11603, 17047, 6878,  17375, 2629, 1958,  1014, 4779, 13803,  \n22168, 21515, 21517,  21848, 21517, 21053,  9589, 17921, 13476,  \n2910, 19589, 11757,  22166, 20519, 21509,  17778, 9273, 7997,  \n15294, 11533, 11532,  6954, 1472, 2591,  18573, 20519, 20012,  \n22169, 21061, 19532,  22171, 22169, 19532,  21857, 21059, 21512,  \n20530, 19521, 20012,  4344, 5968, 18886,  22171, 19532, 21066,  \n3992, 10432, 8830,  5932, 18881, 8665,  20000, 21523, 22172,  \n8089, 774, 8090,  21066, 21074, 22173,  21859, 21857, 22174,  \n3055, 13267, 8532,  21050, 20000, 22172,  16813, 12331, 6073,  \n5936, 20222, 5926,  21859, 22175, 21860,  13176, 21404, 10847,  \n1129, 18001, 8579,  5662, 4122, 11744,  22177, 22178, 16118,  \n22070, 17158, 801,  15380, 515, 7911,  20539, 20534, 21868,  \n22181, 12795, 8755,  21083, 21528, 22179,  17038, 10260, 16314,  \n22182, 21083, 22179,  21083, 22182, 19550,  22182, 22183, 19550,  \n5804, 22184, 5831,  11658, 3816, 1324,  21529, 19550, 22183,  \n22186, 21529, 22183,  5760, 14543, 5761,  21870, 19083, 19084,  \n9423, 14352, 3433,  14812, 1018, 6411,  5279, 12318, 21454,  \n21868, 21536, 20052,  21868, 21869, 21536,  22180, 21869, 21868,  \n16873, 19541, 22187,  4993, 20342, 4994,  21940, 6446, 18796,  \n12065, 2438, 867,  9054, 8182, 2141,  21692, 6850, 12644,  \n22190, 21873, 19111,  8855, 11382, 8672,  21097, 22191, 21872,  \n8397, 642, 14770,  19090, 21091, 21533,  20555, 21536, 22192,  \n16311, 9820, 10590,  21872, 22193, 21091,  22193, 21533, 21091,  \n10162, 8913, 11922,  22190, 19111, 22196,  20555, 22192, 20558,  \n20077, 22196, 19111,  19561, 22198, 21103,  18488, 5214, 16472,  \n22199, 22200, 20558,  22192, 22199, 20558,  18308, 11576, 5095,  \n22198, 19561, 21881,  6419, 8446, 10560,  19570, 19104, 21103,  \n21884, 19570, 21103,  16535, 1206, 12615,  21108, 22196, 20077,  \n9657, 4472, 4372,  8659, 6219, 9406,  20558, 22200, 21544,  \n22203, 20572, 20564,  21879, 22203, 20564,  16039, 3636, 10777,  \n14901, 1560, 11877,  15546, 3983, 14630,  4071, 8682, 16623,  \n11459, 11041, 5422,  12804, 1570, 1569,  582, 4962, 6987,  \n5004, 17665, 5005,  4455, 4456, 1195,  20548, 21112, 21891,  \n5316, 6059, 17948,  16765, 13254, 5932,  16777, 15899, 7945,  \n22204, 15028, 2167,  15951, 22205, 11212,  22206, 21544, 22202,  \n8902, 1466, 10764,  21113, 22206, 21548,  1708, 9926, 13806,  \n15044, 3026, 3025,  6703, 16598, 3171,  21896, 20577, 21111,  \n22207, 18706, 18705,  18706, 17234, 18705,  20099, 22208, 21119,  \n22208, 20099, 21548,  11276, 11275, 19460,  12309, 1037, 11690,  \n20587, 20577, 21896,  16107, 10023, 5891,  2674, 7045, 7046,  \n19577, 21897, 21888,  22209, 21554, 21119,  22208, 22209, 21119,  \n21551, 20580, 22210,  1741, 9785, 9136,  15520, 3903, 12109,  \n3616, 8550, 7827,  21901, 20582, 22902,  3407, 11354, 7967,  \n20582, 21120, 22902,  19888, 5610, 15411,  4242, 1562, 1563,  \n22209, 21556, 21554,  18569, 7080, 7081,  20580, 21124, 22210,  \n14330, 10924, 15815,  20588, 21556, 22213,  21556, 22209, 22213,  \n20588, 22213, 20590,  5472, 14445, 15510,  10995, 16680, 14566,  \n20590, 22213, 21902,  21905, 21899, 21557,  20006, 5471, 5472,  \n18772, 17226, 13481,  5979, 6969, 14469,  21557, 21904, 21905,  \n15934, 21052, 7374,  22214, 18745, 15253,  21902, 22213, 21907,  \n21905, 21144, 22215,  22216, 21129, 20586,  20423, 15935, 4128,  \n9589, 5225, 5226,  21910, 21908, 22217,  2060, 12030, 8731,  \n21573, 20155, 20587,  21838, 6764, 14026,  3922, 753, 16983,  \n20159, 6342, 11957,  22216, 20586, 21162,  17538, 15258, 15596,  \n808, 9634, 15321,  13475, 16229, 12803,  19143, 10566, 19924,  \n5674, 5676, 17893,  3516, 17518, 13315,  21944, 7842, 8684,  \n22222, 21910, 22217,  14025, 14024, 15003,  21162, 21917, 21161,  \n6101, 14332, 19544,  4856, 9700, 12382,  2900, 16469, 10481,  \n2115, 15261, 3926,  768, 16716, 9802,  5680, 22226, 21241,  \n5087, 15265, 5935,  12142, 15299, 10425,  20628, 21164, 21921,  \n1028, 1029, 15273,  9383, 8868, 2143,  3485, 3484, 6545,  \n14461, 8239, 9726,  11542, 11541, 18576,  17961, 14673, 14674,  \n21346, 18919, 18237,  16928, 19574, 14274,  5042, 22229, 20017,  \n14996, 2031, 5344,  21921, 21924, 21183,  16607, 11677, 3997,  \n2377, 9305, 477,  1824, 16638, 1825,  21589, 20185, 21926,  \n6263, 19024, 7857,  17113, 18122, 10549,  20660, 21183, 21924,  \n21590, 21919, 21925,  9071, 1453, 9326,  20625, 20654, 21931,  \n20660, 21924, 22233,  20631, 21595, 21927,  16049, 12032, 20609,  \n21590, 21925, 21597,  7752, 8354, 18245,  17434, 7167, 10306,  \n20185, 20656, 21928,  20656, 21932, 21928,  22233, 21194, 20198,  \n21934, 21189, 19676,  13056, 3087, 13055,  11436, 20252, 11437,  \n10145, 10144, 609,  10962, 9287, 12401,  18096, 11735, 9819,  \n21938, 21198, 21597,  695, 694, 13085,  21937, 20220, 22238,  \n3126, 10690, 20843,  16177, 16170, 10097,  7708, 12901, 12902,  \n16120, 15117, 17724,  21815, 12475, 9087,  21197, 20228, 21942,  \n12820, 3479, 6833,  20708, 21198, 21938,  19160, 13671, 6983,  \n13846, 2393, 10702,  1975, 8671, 2191,  16208, 10959, 9256,  \n1244, 1143, 5230,  9402, 3755, 5576,  12767, 10824, 9353,  \n3175, 5867, 1017,  17621, 12470, 9064,  20496, 16974, 9906,  \n21943, 22243, 21605,  17733, 17735, 17658,  22243, 21608, 21605,  \n19688, 10221, 9890,  4630, 16678, 12858,  11849, 14895, 7025,  \n8534, 16463, 15508,  21218, 21943, 21205,  22244, 21943, 21218,  \n6371, 5915, 12715,  21609, 22245, 20701,  11992, 13593, 11990,  \n20708, 21938, 21611,  5643, 2656, 1219,  22244, 21218, 20723,  \n20706, 21609, 20701,  22246, 12021, 9678,  21480, 16410, 11984,  \n20723, 21949, 22244,  8789, 13582, 13581,  4573, 6045, 7386,  \n729, 5089, 3650,  10661, 21665, 13435,  22247, 21477, 18918,  \n22248, 18424, 19304,  16568, 22249, 12055,  8224, 16140, 15480,  \n12246, 7651, 7653,  22250, 20549, 9260,  22251, 21224, 21222,  \n3714, 10519, 21858,  21952, 22251, 21222,  20723, 20730, 21949,  \n21614, 22252, 21227,  10019, 8828, 13396,  21949, 20730, 21616,  \n22255, 20872, 7619,  17225, 10919, 10920,  14282, 5737, 5738,  \n9098, 21531, 9099,  19900, 17651, 11520,  21958, 22256, 21959,  \n22256, 21958, 22259,  3748, 14955, 13454,  12228, 10989, 19695,  \n22503, 22502, 21967,  12611, 1363, 12612,  4003, 4002, 21244,  \n7753, 693, 6514,  21617, 21955, 21616,  12656, 16532, 6518,  \n22259, 21971, 22502,  7344, 16537, 6910,  9790, 14913, 2949,  \n21959, 22262, 21957,  21967, 21971, 21973,  11684, 9387, 8900,  \n21955, 21617, 21965,  13423, 10786, 19981,  5553, 4031, 16230,  \n22502, 21971, 21967,  22264, 3880, 21166,  7855, 15398, 12181,  \n10138, 1043, 12206,  22259, 21958, 21957,  22259, 21957, 21971,  \n17454, 700, 9056,  22262, 21972, 21957,  21964, 22261, 21963,  \n9357, 9358, 18841,  21972, 22262, 22265,  21957, 21972, 21971,  \n4483, 11939, 11938,  16916, 14079, 22996,  8639, 22267, 16406,  \n20753, 8008, 12158,  10767, 21651, 6968,  21984, 21972, 22265,  \n10799, 12876, 20384,  9365, 9984, 13919,  15644, 13265, 10558,  \n4126, 11857, 9968,  21242, 21978, 21965,  21914, 4548, 11946,  \n21972, 21984, 21979,  19034, 8884, 8101,  18830, 1699, 1207,  \n8014, 560, 14896,  4457, 4458, 435,  1574, 20732, 16631,  \n6777, 9443, 17833,  14635, 19971, 8572,  20537, 7027, 12486,  \n21983, 21977, 21976,  13421, 7521, 5738,  3917, 1471, 3918,  \n20110, 7056, 11443,  18909, 19815, 7368,  22268, 21983, 21987,  \n22271, 21978, 21243,  9136, 21379, 11933,  12111, 10119, 14240,  \n5122, 2544, 18589,  22273, 21985, 21984,  8994, 14260, 6201,  \n11014, 557, 10039,  1511, 2803, 2804,  22273, 21988, 21985,  \n14864, 23365, 14863,  22271, 21243, 21990,  21994, 22268, 21987,  \n9412, 9411, 20126,  21990, 22275, 22271,  19388, 19387, 3112,  \n3855, 9422, 3856,  22275, 21990, 22003,  18899, 3607, 3606,  \n11222, 15212, 3206,  11993, 16575, 8416,  13271, 11774, 17041,  \n21997, 21985, 21988,  12576, 13135, 13136,  21788, 3425, 22224,  \n8988, 3837, 3838,  9083, 16382, 9084,  16583, 2791, 2541,  \n21240, 22279, 21628,  1554, 4895, 13054,  13541, 3338, 4590,  \n21571, 13271, 17041,  21988, 22280, 21997,  2787, 10236, 346,  \n21653, 21635, 21997,  21628, 22279, 22000,  20379, 11403, 12921,  \n22006, 22283, 22281,  22284, 6631, 6464,  22281, 22002, 22006,  \n21929, 10007, 16225,  21997, 22008, 21653,  5180, 5182, 3467,  \n21188, 3847, 15277,  4980, 4982, 16043,  21656, 21653, 22008,  \n21655, 22286, 21650,  20205, 7505, 6300,  12173, 21806, 16324,  \n21262, 22005, 21263,  21656, 22008, 22287,  5163, 11314, 5162,  \n13679, 22289, 18343,  7906, 2508, 5318,  21233, 21232, 7994,  \n10692, 11847, 10693,  22012, 21263, 22005,  18399, 18417, 12892,  \n7151, 19865, 19864,  19964, 14500, 2283,  22292, 22014, 21656,  \n394, 19940, 16548,  22294, 22295, 18451,  18069, 11702, 9594,  \n4544, 4808, 5512,  10405, 6257, 12395,  22298, 10604, 19771,  \n16763, 19142, 20629,  9467, 5357, 4043,  6222, 15262, 3836,  \n11023, 6912, 996,  9876, 1405, 5491,  16127, 12599, 20412,  \n3215, 3216, 13344,  22027, 22020, 21296,  22026, 22300, 22301,  \n748, 14479, 8436,  664, 3717, 15399,  22020, 22027, 22303,  \n22026, 22028, 21673,  18204, 4327, 11272,  2763, 10253, 15794,  \n14528, 5805, 20029,  22027, 22030, 22303,  20791, 21684, 21679,  \n22291, 21960, 9696,  14916, 354, 1438,  17499, 9824, 17500,  \n8537, 2804, 7793,  22037, 21679, 21684,  22030, 21305, 21685,  \n12842, 19837, 12843,  11825, 21214, 5051,  14963, 8798, 9276,  \n14247, 9470, 5851,  8593, 9030, 6370,  21685, 22040, 22030,  \n3121, 3120, 16722,  2221, 12021, 7327,  22306, 1807, 15804,  \n22042, 22032, 22307,  12110, 7441, 18116,  21333, 22032, 22042,  \n12820, 15529, 2678,  22040, 21685, 21689,  1333, 16516, 22321,  \n5257, 10542, 18781,  12910, 12869, 5160,  6471, 20201, 20676,  \n8028, 21887, 8029,  700, 17454, 22278,  22310, 22039, 20816,  \n15811, 7350, 4519,  21337, 22310, 20816,  22314, 22040, 21689,  \n22311, 21686, 22041,  18137, 12378, 18611,  4234, 12786, 21044,  \n21323, 21686, 22311,  20201, 6471, 21813,  21689, 22045, 22314,  \n21323, 22311, 22048,  22310, 21337, 22049,  22310, 22049, 22315,  \n22042, 22316, 22047,  5836, 13634, 5837,  7006, 8738, 16282,  \n21334, 22042, 22047,  15784, 22317, 7552,  12744, 15222, 1809,  \n20091, 9686, 4831,  9131, 11039, 9115,  3912, 3627, 14355,  \n19048, 22053, 19047,  11952, 17485, 4923,  9599, 2497, 22318,  \n22319, 22314, 22045,  6740, 8122, 20015,  21339, 21342, 22049,  \n22049, 21705, 22315,  3002, 5798, 5799,  22319, 22045, 22050,  \n12869, 19958, 5160,  21342, 21705, 22049,  7769, 5005, 17665,  \n7605, 15524, 18138,  22047, 22051, 21701,  17209, 14311, 21966,  \n22321, 11581, 18517,  15374, 15627, 16951,  15290, 2209, 15291,  \n22051, 22057, 21363,  4814, 11476, 15347,  11822, 10880, 9576,  \n20848, 21705, 21342,  21701, 22051, 21363,  22323, 22050, 22055,  \n2138, 7525, 8266,  15489, 22324, 16051,  14965, 19368, 8989,  \n9144, 12276, 9143,  8166, 6882, 11748,  16659, 16658, 14182,  \n4101, 9958, 9000,  14273, 5038, 22218,  8948, 2846, 6028,  \n22326, 21705, 22060,  11836, 3423, 1627,  8762, 439, 18366,  \n12700, 10523, 5654,  18764, 22306, 15804,  22063, 21363, 22057,  \n19564, 13494, 11448,  12647, 909, 17331,  22055, 21703, 21706,  \n1663, 1662, 7812,  16726, 22328, 567,  22329, 16238, 19701,  \n22327, 22055, 21706,  10959, 16208, 11160,  2502, 15437, 13751,  \n3847, 12271, 15277,  20013, 9704, 12126,  20361, 12068, 16020,  \n14282, 11643, 5565,  16782, 7663, 13349,  1327, 7784, 20408,  \n22060, 21704, 21371,  18832, 3090, 6672,  5853, 9087, 7360,  \n21367, 22063, 21711,  21706, 22068, 22327,  14644, 2047, 18737,  \n15413, 13275, 7334,  6279, 13526, 21062,  9520, 2603, 8714,  \n22331, 22332, 22333,  21723, 21718, 22071,  21372, 21711, 21718,  \n22137, 15236, 15218,  22068, 21707, 21720,  14773, 7093, 22336,  \n6614, 7339, 5009,  22069, 21374, 22334,  20088, 11377, 12871,  \n22072, 21722, 22071,  22337, 22338, 19884,  550, 15124, 19983,  \n19791, 12114, 12113,  2216, 6268, 18835,  21374, 21383, 22334,  \n22075, 22334, 21383,  22075, 20331, 22073,  22073, 20331, 21722,  \n5761, 13862, 5760,  21720, 22335, 22068,  2355, 18934, 16354,  \n3913, 18521, 748,  8033, 2436, 2437,  21574, 6203, 3166,  \n22335, 21720, 21734,  22335, 21734, 22341,  9568, 3436, 3435,  \n9932, 2319, 2318,  1328, 3366, 18945,  7428, 8429, 11663,  \n5667, 12861, 5668,  642, 9550, 24396,  21396, 21736, 22342,  \n16133, 18040, 16840,  22079, 21738, 22345,  16346, 10504, 20060,  \n4102, 22115, 3609,  15963, 2985, 18306,  14179, 2868, 22343,  \n21740, 21396, 22342,  21741, 22346, 13513,  903, 904, 4439,  \n18242, 16099, 3502,  887, 15604, 16428,  22347, 21738, 22086,  \n20907, 22085, 22348,  16903, 13261, 3755,  22088, 21742, 22089,  \n22348, 21405, 20907,  16610, 21521, 1772,  8601, 6165, 3938,  \n15220, 22349, 15221,  18886, 18521, 3913,  8242, 6373, 3318,  \n15182, 15183, 3558,  22090, 21405, 22348,  8885, 10674, 8101,  \n3238, 2911, 22098,  21405, 22090, 22091,  12261, 10457, 9423,  \n22350, 22087, 21743,  12582, 1867, 13423,  3854, 6609, 7181,  \n13941, 16044, 2984,  3723, 19533, 15268,  8717, 15291, 8716,  \n19249, 16146, 12018,  4969, 4609, 293,  10463, 8915, 17254,  \n15151, 8316, 7612,  21406, 22091, 22580,  2037, 19193, 4840,  \n21406, 22580, 20353,  15398, 3095, 12448,  17656, 17974, 8818,  \n3508, 8384, 19201,  10482, 7872, 16328,  1571, 4601, 12828,  \n22354, 22093, 21748,  13174, 7207, 15848,  22355, 12641, 12636,  \n1778, 1777, 19846,  7100, 23661, 21250,  20935, 3253, 11937,  \n12714, 9948, 9947,  7582, 16809, 15697,  21417, 20945, 20371,  \n15391, 11485, 20879,  14333, 16577, 8296,  16383, 10204, 12994,  \n22356, 21752, 22580,  3539, 3540, 21649,  7048, 9320, 15021,  \n2128, 6171, 6969,  5797, 4843, 6567,  12094, 12093, 16199,  \n22356, 21755, 21752,  14807, 17660, 8132,  16877, 11239, 18757,  \n3969, 15704, 13816,  3270, 3246, 8173,  21641, 17467, 22357,  \n22097, 21756, 21755,  12674, 12923, 13173,  20943, 22358, 21759,  \n13189, 2380, 10286,  1219, 2656, 1220,  1760, 18347, 6539,  \n2267, 7788, 5805,  21765, 20944, 21756,  22360, 21426, 21767,  \n22360, 21757, 21426,  6108, 11857, 18067,  21498, 14583, 2274,  \n5448, 9555, 15506,  21774, 21435, 20957,  11603, 8413, 17047,  \n4781, 19610, 17699,  18399, 13620, 18417,  20387, 21759, 22361,  \n13687, 12072, 13386,  12570, 19876, 18136,  16092, 11557, 3975,  \n21781, 20381, 21772,  20381, 21781, 21441,  21439, 21774, 21782,  \n21774, 20957, 21782,  543, 9745, 9874,  16728, 3905, 1916,  \n19404, 1640, 2642,  22302, 10752, 10751,  21508, 4505, 17223,  \n20954, 20942, 21778,  19974, 4157, 7736,  8883, 14985, 22362,  \n1267, 3746, 19297,  21437, 22104, 22824,  14067, 14068, 21940,  \n20942, 21771, 21778,  21436, 21780, 22104,  14780, 22363, 1111,  \n21430, 21437, 22110,  22105, 21430, 22110,  20963, 20387, 21786,  \n18356, 11025, 21286,  10578, 22925, 22364,  21438, 21784, 21780,  \n12441, 14776, 12442,  14343, 20189, 1687,  8292, 19033, 12827,  \n16332, 16518, 15993,  6029, 14776, 12441,  11220, 4649, 14202,  \n9905, 13629, 12850,  20855, 3438, 22366,  18677, 20894, 22367,  \n22368, 22112, 20967,  8080, 8079, 22370,  5866, 6874, 15179,  \n19885, 22371, 20972,  8713, 19758, 20321,  21791, 20405, 22118,  \n1424, 10881, 1314,  21446, 22119, 22120,  6936, 6633, 1607,  \n22120, 22374, 21792,  16838, 15985, 3352,  21795, 21793, 22375,  \n15246, 16070, 15245,  22121, 21450, 21795,  22121, 21797, 21450,  \n18012, 9024, 4103,  16004, 22376, 16888,  22610, 21797, 22121,  \n4620, 16311, 10590,  21447, 19898, 21800,  16777, 12262, 15899,  \n3031, 12281, 18601,  3031, 3033, 12281,  17901, 7965, 14095,  \n21455, 22377, 22378,  20422, 21455, 22378,  1635, 17463, 1636,  \n22379, 21584, 20462,  7841, 16515, 14112,  17036, 10907, 9065,  \n3044, 3045, 3264,  1400, 1399, 8912,  2873, 15625, 2874,  \n17676, 3556, 6433,  19726, 3128, 12286,  9816, 13769, 8821,  \n21802, 22130, 20427,  5035, 4567, 4566,  5479, 12049, 2117,  \n16889, 19559, 10060,  21804, 21459, 22131,  2924, 5258, 15412,  \n16392, 16375, 9829,  12671, 15442, 12914,  21804, 22381, 22134,  \n21808, 22383, 21464,  1740, 3512, 3642,  18196, 19491, 7399,  \n22383, 21810, 21464,  5277, 1874, 5934,  13143, 7680, 14154,  \n20448, 21002, 21808,  20993, 22135, 21809,  21809, 22135, 22138,  \n13154, 13155, 17276,  13300, 4125, 20075,  22385, 5033, 9721,  \n14587, 9762, 16740,  3537, 22388, 2657,  20130, 4489, 4619,  \n4173, 4172, 14989,  7418, 15773, 14846,  3574, 3575, 5910,  \n22142, 21000, 20998,  22389, 9168, 16935,  21002, 18948, 21470,  \n22145, 21470, 21820,  21809, 22138, 22392,  12393, 7713, 7647,  \n14518, 14517, 14348,  9295, 16119, 12965,  22145, 22146, 22392,  \n18036, 17514, 16510,  21821, 21809, 22392,  15729, 12649, 15730,  \n16454, 16449, 16455,  22145, 21823, 22146,  19568, 9625, 18017,  \n22143, 22148, 22393,  3349, 10058, 13654,  21479, 21816, 22855,  \n15567, 9916, 9915,  19046, 13659, 19848,  3847, 1579, 12271,  \n21481, 21019, 22394,  2396, 14544, 10198,  21019, 21023, 22394,  \n21023, 21022, 22395,  21487, 19962, 22396,  20694, 18834, 3647,  \n5315, 5316, 20165,  14773, 19485, 19484,  3015, 3014, 8695,  \n5715, 8937, 17115,  17845, 6876, 17968,  18605, 14737, 12397,  \n22399, 5590, 17484,  11897, 1692, 11755,  13780, 7517, 15227,  \n8374, 18846, 7808,  2214, 19393, 16881,  22156, 19476, 20489,  \n12984, 14061, 11454,  20490, 21831, 22154,  22400, 21833, 20499,  \n21836, 21833, 22400,  22639, 21840, 21034,  22400, 22158, 21836,  \n21041, 17048, 19994,  4448, 1680, 1681,  11111, 19560, 10828,  \n14618, 1940, 13677,  22158, 22403, 21837,  12460, 17971, 9420,  \n18894, 19993, 1089,  3764, 9961, 3765,  16434, 7901, 10308,  \n10811, 15667, 19265,  2716, 9721, 22404,  15361, 1590, 9319,  \n22403, 21847, 21505,  6416, 21230, 10139,  20443, 22406, 13026,  \n21045, 19999, 22163,  21848, 21049, 22165,  20315, 3524, 21476,  \n577, 7041, 18835,  2670, 14131, 15153,  3354, 4125, 12462,  \n20362, 7219, 7218,  7118, 10103, 7119,  8136, 14478, 9572,  \n22410, 22166, 21509,  22410, 21509, 21850,  15477, 5833, 9593,  \n4656, 6021, 8925,  7268, 16933, 7204,  22411, 21057, 21060,  \n22411, 21060, 22407,  22407, 21060, 21061,  22169, 22407, 21061,  \n21848, 22168, 21517,  2729, 7026, 7025,  1072, 9713, 21331,  \n9960, 9787, 9961,  6231, 11416, 20879,  17489, 2079, 21220,  \n16797, 2247, 17608,  11659, 22413, 1773,  11152, 5812, 8726,  \n8830, 21770, 3992,  8172, 5036, 8171,  4693, 22894, 18774,  \n22414, 21859, 22174,  4466, 4465, 13478,  6671, 5952, 6816,  \n13442, 7592, 10664,  7349, 10921, 10812,  2346, 5436, 2701,  \n22175, 21525, 21860,  16466, 7024, 7272,  22175, 22176, 21525,  \n22415, 16849, 20707,  20534, 18592, 21861,  20611, 21826, 14040,  \n21525, 22416, 21528,  21525, 22176, 22416,  13592, 13054, 9708,  \n14511, 17012, 3243,  11727, 17469, 17782,  9127, 13002, 11462,  \n21528, 22416, 22179,  7587, 20026, 7585,  22182, 22179, 22183,  \n4438, 4437, 10155,  15845, 1047, 14557,  21074, 19083, 21870,  \n18943, 19803, 20180,  21529, 22420, 20545,  5401, 5400, 17791,  \n4690, 3067, 778,  15985, 15986, 18484,  15578, 13053, 15579,  \n13157, 13158, 20253,  21869, 22421, 21536,  22423, 21536, 22421,  \n14507, 15635, 22682,  20545, 22424, 20061,  10979, 10980, 7910,  \n3311, 4841, 3842,  22192, 22664, 22199,  22192, 22423, 22664,  \n22423, 22192, 21536,  11079, 4334, 17650,  21874, 21530, 21087,  \n20048, 21530, 21874,  10979, 23051, 17161,  13877, 19718, 14568,  \n18691, 15191, 3216,  21874, 22428, 22195,  22195, 21535, 21874,  \n22195, 21878, 21535,  5715, 17115, 2226,  12568, 20419, 12095,  \n8655, 12809, 10549,  21879, 22195, 22429,  21878, 22195, 21879,  \n9152, 2041, 12989,  9097, 6067, 3895,  22202, 22200, 22199,  \n16694, 19489, 12743,  21881, 19100, 21100,  22430, 18718, 4817,  \n21891, 21527, 20548,  10521, 7981, 9856,  21544, 22200, 22202,  \n5762, 3217, 15070,  22201, 19138, 19575,  21891, 22431, 21527,  \n1041, 991, 993,  19506, 3911, 4182,  2302, 8232, 11487,  \n13065, 12652, 22432,  3945, 12489, 3944,  1230, 16593, 6019,  \n15071, 1381, 15532,  20084, 21888, 22434,  22206, 21113, 21544,  \n21110, 19590, 21890,  7520, 13526, 4176,  14089, 8096, 7335,  \n15167, 2533, 2966,  15897, 12980, 5501,  4398, 17949, 12238,  \n18705, 19138, 22436,  8567, 9043, 18394,  18213, 11083, 13265,  \n11836, 12811, 19354,  1996, 1995, 2320,  22438, 22439, 22208,  \n22206, 22438, 22208,  22206, 22208, 21548,  9423, 10457, 14353,  \n22431, 21891, 22441,  22438, 22442, 22439,  22439, 22209, 22208,  \n8826, 17386, 4847,  22440, 21551, 22210,  21551, 22440, 20581,  \n1810, 1811, 8805,  15184, 22443, 22270,  3547, 12374, 1889,  \n22442, 22209, 22439,  21124, 22444, 22210,  16473, 13828, 12721,  \n11588, 7271, 5987,  21892, 15603, 3970,  730, 14761, 1706,  \n22904, 21573, 20587,  19897, 19923, 8868,  16576, 18516, 14830,  \n22446, 22447, 19582,  4574, 17504, 5511,  21899, 22444, 21124,  \n22448, 21905, 22215,  5040, 8238, 18729,  4668, 13360, 20528,  \n21903, 21125, 21901,  7312, 19033, 12306,  22442, 21907, 22213,  \n22442, 22213, 22209,  22448, 22444, 21899,  22448, 21899, 21905,  \n5950, 5361, 5838,  21129, 22216, 21891,  16987, 19137, 13052,  \n5670, 12969, 15047,  9446, 18478, 14046,  1753, 1754, 1474,  \n936, 16819, 16975,  22215, 20614, 21913,  1046, 21545, 13602,  \n2120, 2119, 2778,  11083, 6425, 13265,  21117, 21134, 21915,  \n22450, 21913, 21583,  22221, 22450, 21583,  22678, 21164, 21573,  \n10765, 10766, 17117,  20014, 1488, 19828,  1268, 1269, 12590,  \n21920, 22222, 22452,  22453, 22352, 5651,  7669, 22454, 7668,  \n5585, 5586, 29709,  22456, 21915, 21170,  19225, 19203, 22457,  \n13482, 22727, 15174,  3916, 12390, 13256,  21919, 21920, 22227,  \n22458, 11952, 15010,  17250, 18214, 14740,  11816, 20798, 19130,  \n22460, 21925, 22227,  10301, 315, 17147,  21925, 21919, 22227,  \n8588, 13255, 14616,  21585, 20631, 21927,  22687, 21586, 21931,  \n20665, 18806, 20650,  4336, 19886, 13207,  21826, 20611, 14065,  \n15897, 5501, 3325,  21926, 20185, 21928,  21239, 5532, 14103,  \n19976, 11689, 17783,  21927, 21595, 22461,  21194, 22233, 22462,  \n15093, 15982, 6761,  18448, 6388, 6387,  21932, 21933, 22235,  \n21931, 20654, 21197,  21194, 22462, 22237,  7886, 16314, 13588,  \n2144, 12988, 10482,  5096, 19522, 5667,  22234, 21189, 21934,  \n22466, 7809, 7811,  4011, 4012, 19904,  22467, 21934, 21196,  \n2932, 10759, 2933,  22468, 22235, 21933,  15097, 11335, 11336,  \n22464, 21197, 21947,  3759, 16390, 3760,  22238, 21194, 22237,  \n22239, 22467, 21196,  3115, 22472, 22473,  20220, 21194, 22238,  \n20702, 22239, 21196,  17607, 21666, 18353,  10401, 18122, 10400,  \n21939, 22470, 21933,  22474, 10418, 22475,  20964, 19631, 2954,  \n20825, 1504, 16222,  21197, 21942, 21947,  14625, 4655, 22100,  \n8935, 8936, 17656,  8671, 2488, 14513,  22476, 22239, 20702,  \n10549, 11640, 8655,  4419, 4790, 11813,  6482, 3002, 3001,  \n21609, 20690, 21937,  9590, 13230, 9591,  21608, 22243, 21606,  \n8691, 8690, 10081,  765, 17098, 18539,  7417, 856, 857,  \n22480, 22481, 22482,  7627, 11140, 15870,  11892, 6455, 14355,  \n21943, 22244, 22243,  3504, 3468, 16244,  21947, 21942, 21224,  \n21947, 21224, 21948,  21475, 19722, 9767,  14473, 4091, 15589,  \n3552, 6862, 5966,  21938, 22477, 21611,  21609, 22485, 22245,  \n17211, 12261, 20477,  5396, 12517, 4960,  11734, 3955, 20610,  \n19788, 22488, 19489,  22489, 19112, 4095,  9321, 20755, 17398,  \n8465, 14987, 10344,  4052, 1373, 16598,  22481, 22484, 22482,  \n2417, 8616, 7261,  15474, 22490, 17355,  6920, 500, 4285,  \n20022, 9372, 20049,  17824, 22491, 14404,  14704, 3376, 14432,  \n22493, 4535, 19603,  12784, 3264, 3265,  8559, 2278, 15701,  \n2936, 18599, 18738,  21948, 21224, 22251,  22484, 22487, 22497,  \n21949, 22498, 22492,  21948, 22251, 22499,  22500, 22484, 22497,  \n12941, 5957, 15344,  21615, 21611, 22494,  21949, 21616, 22498,  \n16142, 10654, 7069,  21227, 22252, 20720,  21952, 22499, 22251,  \n22257, 22500, 22258,  4026, 6612, 3115,  2262, 8025, 8024,  \n22252, 21951, 20720,  20640, 2602, 20227,  21951, 22501, 21952,  \n21952, 22501, 22499,  18064, 4087, 11228,  22257, 22258, 22256,  \n19438, 6061, 17721,  17003, 1544, 10958,  22256, 22258, 21959,  \n18029, 14412, 20366,  15363, 7581, 15026,  22505, 22504, 22503,  \n8819, 4694, 18774,  22259, 22257, 22256,  14309, 13530, 17008,  \n22505, 22503, 22261,  9190, 11741, 4942,  15371, 4128, 4129,  \n22503, 21967, 22261,  15034, 651, 17344,  21964, 22505, 22261,  \n8663, 15645, 9788,  11028, 2953, 11360,  3608, 3113, 21180,  \n949, 4273, 4207,  21963, 22505, 21964,  21955, 21965, 22512,  \n22262, 22507, 22508,  22505, 21963, 21977,  22471, 22509, 12898,  \n22511, 21977, 21983,  16138, 17789, 14910,  22269, 21621, 21956,  \n17052, 17053, 20592,  21621, 21618, 21956,  11828, 19973, 17306,  \n6630, 4894, 29546,  14347, 4339, 4340,  12309, 3825, 13830,  \n18325, 19342, 3898,  15753, 10502, 3891,  22512, 21965, 21978,  \n18019, 13618, 14561,  22511, 21983, 22268,  13056, 13055, 21458,  \n2029, 2030, 8957,  12099, 6004, 20216,  3771, 479, 9734,  \n17106, 6641, 15710,  14750, 5770, 5771,  5443, 10083, 15877,  \n21621, 22269, 21986,  12105, 5921, 10785,  16824, 18276, 11156,  \n1547, 7290, 17270,  10680, 684, 9865,  8401, 14137, 1147,  \n5415, 16032, 3053,  18849, 9600, 22318,  6534, 16498, 385,  \n9594, 1649, 19041,  4401, 7779, 6883,  1007, 2845, 13396,  \n19983, 20227, 550,  2224, 14613, 5077,  18074, 9145, 2021,  \n5932, 5931, 18881,  13044, 19899, 22517,  21994, 21638, 21646,  \n4073, 6287, 4072,  21491, 21490, 5042,  22516, 21240, 21986,  \n22280, 21988, 22515,  1577, 4104, 17874,  6883, 7779, 2567,  \n22279, 21240, 22516,  20466, 8595, 16590,  20995, 11940, 9299,  \n21646, 22002, 21994,  13061, 19416, 2354,  16668, 7222, 2619,  \n5195, 12710, 22520,  22275, 22003, 22282,  22280, 22008, 21997,  \n17603, 1697, 1655,  22281, 21994, 22002,  14890, 14284, 6890,  \n11470, 4395, 21762,  4879, 9902, 8184,  22003, 22286, 22522,  \n15828, 16354, 17147,  21650, 22286, 22003,  13365, 12997, 13511,  \n16258, 12875, 7415,  22008, 22521, 22287,  7113, 7114, 13716,  \n7179, 14556, 12491,  21655, 22010, 22286,  18873, 22406, 20443,  \n13260, 22524, 1645,  16288, 16508, 5210,  10538, 9971, 18511,  \n9316, 9315, 22526,  6706, 6953, 16922,  13882, 16841, 13006,  \n9575, 9181, 9576,  1316, 15935, 1317,  10347, 5666, 3793,  \n20810, 19050, 16219,  17190, 11925, 10464,  4912, 8611, 22099,  \n21291, 22023, 22015,  22529, 22015, 22023,  20176, 10466, 3733,  \n21785, 18440, 27385,  614, 3400, 17025,  603, 13970, 604,  \n22297, 22010, 22020,  22297, 22020, 22530,  21787, 11972, 7389,  \n7795, 16532, 16531,  20884, 2642, 21454,  3038, 3039, 11534,  \n13120, 12390, 3915,  10630, 10677, 20394,  20537, 15149, 7027,  \n22020, 22303, 22533,  22021, 22532, 22759,  4304, 17293, 17203,  \n3761, 1422, 7719,  22023, 21679, 22037,  22028, 22026, 22534,  \n5655, 15738, 418,  13754, 676, 20900,  6354, 12821, 18538,  \n2339, 19581, 20100,  22537, 22032, 22029,  22535, 22303, 22030,  \n22032, 22537, 22307,  22535, 22030, 22040,  22028, 22534, 22538,  \n21582, 19122, 6790,  22028, 22538, 21682,  3466, 3467, 5020,  \n22310, 22539, 22039,  22041, 21682, 22538,  22985, 22040, 22308,  \n3454, 15921, 18297,  21686, 21682, 22041,  9098, 18258, 17863,  \n4199, 9530, 8264,  10953, 10954, 9981,  6568, 6567, 4214,  \n4813, 4814, 5844,  6449, 15484, 6448,  22040, 22314, 22308,  \n12003, 17194, 21841,  17011, 19616, 21028,  1031, 17723, 4163,  \n22042, 22307, 22316,  5785, 7947, 18269,  12450, 8094, 4700,  \n3307, 2857, 12298,  22308, 22314, 22541,  19622, 3810, 4376,  \n22316, 22051, 22047,  22048, 22311, 22320,  9799, 22542, 7933,  \n2813, 18468, 14462,  22541, 22314, 22319,  2413, 11806, 12489,  \n5280, 5281, 17684,  18222, 12959, 15394,  13555, 7275, 13556,  \n21705, 22326, 22315,  8019, 14342, 8020,  15245, 5273, 3430,  \n6384, 11007, 2266,  22319, 22050, 22546,  10423, 19220, 20409,  \n3577, 6544, 22140,  4924, 4923, 17485,  13595, 13596, 19820,  \n6345, 19471, 8594,  22048, 22545, 21700,  2457, 14160, 14598,  \n10822, 21749, 21945,  19134, 22189, 17787,  10488, 5852, 2645,  \n3126, 20843, 732,  6769, 2555, 16761,  22546, 22050, 22323,  \n5223, 12161, 2423,  6672, 1922, 21918,  7023, 9553, 22549,  \n16083, 7630, 12249,  22552, 22063, 22057,  15239, 8892, 15240,  \n2623, 16544, 5657,  19426, 8962, 11661,  22555, 22063, 22552,  \n22055, 22327, 22323,  11992, 15531, 13985,  21711, 22063, 22555,  \n17456, 14418, 5688,  22056, 22550, 21345,  6170, 22556, 10651,  \n3522, 15668, 11138,  22550, 21708, 21345,  20500, 12474, 14257,  \n2209, 22557, 13369,  1924, 5481, 7143,  22559, 21710, 22069,  \n22332, 22323, 22327,  22560, 11090, 11089,  8495, 7582, 15697,  \n13458, 4162, 19430,  22561, 22559, 22069,  5521, 15767, 20810,  \n1800, 1799, 16756,  22558, 22562, 21708,  22563, 22069, 22334,  \n4209, 7131, 15954,  8080, 16547, 17170,  22327, 22068, 22332,  \n22332, 22068, 22333,  20629, 13458, 19430,  729, 19511, 5089,  \n22075, 22563, 22334,  22071, 22566, 22072,  22071, 22564, 22566,  \n21718, 22564, 22071,  19760, 22312, 2255,  9245, 11218, 8425,  \n6447, 18796, 6446,  4294, 8635, 21416,  21715, 21708, 22562,  \n22068, 22335, 22333,  21715, 22562, 22783,  576, 15760, 575,  \n7530, 1305, 5617,  529, 13072, 3252,  10025, 2232, 15200,  \n496, 5363, 9393,  21715, 22783, 22567,  5278, 17088, 577,  \n22567, 22076, 21715,  10262, 12033, 13123,  9760, 6136, 16862,  \n10573, 10574, 20317,  13084, 19252, 18379,  7463, 15363, 15026,  \n1725, 11713, 1726,  7273, 17887, 7272,  3411, 5732, 16523,  \n17272, 370, 20915,  9899, 22415, 9714,  22341, 21734, 22568,  \n7409, 1917, 17302,  16623, 13864, 6105,  4560, 17963, 6928,  \n22076, 22569, 21736,  14110, 22570, 13750,  22079, 22568, 21734,  \n5610, 3449, 1058,  13100, 18251, 22572,  6966, 22573, 17930,  \n22569, 22342, 21736,  22574, 22342, 22569,  15641, 11070, 21696,  \n16831, 11295, 4284,  14973, 13505, 20163,  7939, 16725, 3114,  \n19576, 19767, 13338,  10025, 5200, 2232,  7443, 11495, 10629,  \n1326, 11700, 18736,  20781, 5572, 4039,  11503, 16752, 10205,  \n21738, 22347, 22345,  22348, 22085, 21740,  17377, 19686, 12456,  \n22086, 22088, 22347,  16123, 1107, 1540,  4036, 11557, 3850,  \n18632, 19184, 8614,  16907, 16908, 5052,  17916, 3208, 21149,  \n16665, 15182, 13566,  15004, 18212, 5308,  22089, 22087, 22350,  \n2179, 2180, 12715,  21414, 22351, 21411,  6695, 3056, 3120,  \n4924, 1028, 20597,  9830, 1879, 1880,  22581, 21417, 21746,  \n16416, 10445, 18851,  21743, 22093, 22350,  7029, 17192, 7028,  \n10335, 20540, 15882,  22584, 22093, 22354,  22581, 20945, 21417,  \n15252, 22272, 21449,  19557, 17390, 14424,  17046, 7697, 17057,  \n19854, 21419, 19862,  8288, 9874, 22585,  19007, 15792, 10782,  \n20044, 16009, 13041,  12327, 12329, 10080,  3613, 16747, 6005,  \n16795, 16790, 18857,  7138, 20230, 7139,  22580, 22586, 22356,  \n6210, 22437, 6747,  21748, 21757, 22354,  22354, 21757, 22584,  \n21768, 22587, 22588,  16392, 7730, 7729,  650, 649, 22862,  \n11837, 21452, 21335,  2172, 358, 359,  14736, 17945, 14588,  \n15660, 10764, 11296,  17307, 19859, 16790,  21755, 22356, 22097,  \n2177, 15327, 18157,  1616, 12443, 9569,  919, 918, 1080,  \n21472, 3347, 15417,  10126, 5458, 976,  3131, 6540, 15429,  \n8253, 5212, 5023,  21759, 22358, 22361,  9814, 9063, 18868,  \n19860, 19859, 19857,  7667, 2472, 17628,  1368, 9288, 12486,  \n21765, 21756, 22097,  18761, 7200, 12600,  9622, 13266, 7632,  \n22589, 22590, 22097,  22097, 22590, 21765,  17920, 12353, 21690,  \n21432, 21768, 20382,  1641, 15365, 18471,  15102, 2059, 25537,  \n13743, 2381, 21370,  4236, 4235, 12040,  29434, 16821, 1724,  \n7054, 16215, 20937,  13324, 21452, 2469,  22105, 22593, 21767,  \n10600, 18367, 2032,  20387, 22361, 21786,  21771, 21428, 22594,  \n4751, 11644, 18347,  15067, 16820, 20916,  15721, 19145, 22595,  \n8335, 20659, 7746,  8481, 2770, 15952,  18256, 22596, 22597,  \n19950, 9853, 2444,  3322, 3321, 18625,  14839, 11747, 7206,  \n21784, 21778, 22365,  7987, 18100, 5626,  22599, 22600, 18752,  \n781, 14314, 14332,  21441, 20397, 22113,  22598, 21780, 21784,  \n7663, 1329, 7662,  21786, 22602, 20396,  18371, 12188, 11599,  \n413, 16205, 16759,  8529, 4511, 15574,  20967, 21443, 22603,  \n12562, 12563, 11344,  19885, 20969, 22371,  5148, 1929, 14011,  \n6846, 18770, 11405,  22372, 21791, 22118,  20974, 21447, 21443,  \n22119, 21791, 22373,  21443, 21447, 22604,  22374, 22605, 21792,  \n22607, 21792, 22605,  22607, 21793, 21792,  13790, 880, 20139,  \n3613, 6005, 14762,  21793, 22607, 22375,  5819, 9437, 13103,  \n14110, 22608, 19659,  4262, 6613, 10745,  13937, 13637, 4474,  \n22121, 21795, 22375,  1835, 15468, 1217,  3123, 15524, 9008,  \n8239, 8240, 9726,  9000, 21769, 4549,  9507, 3200, 6126,  \n6905, 4441, 9707,  13121, 16633, 9717,  20923, 15080, 24007,  \n20422, 22378, 22125,  17755, 22611, 14577,  20987, 22125, 22126,  \n21800, 20416, 18431,  9167, 9166, 12280,  20554, 6817, 22466,  \n17066, 18280, 19235,  11017, 2693, 4481,  22612, 11932, 17395,  \n21801, 22126, 21802,  3475, 5201, 518,  16856, 15507, 7449,  \n6172, 15862, 2352,  13497, 15732, 2706,  8473, 2377, 477,  \n21026, 1878, 1877,  13358, 2435, 13422,  10812, 14365, 9663,  \n22131, 22130, 22613,  22131, 22613, 21804,  2924, 17728, 5258,  \n22613, 22381, 21804,  22613, 22845, 22614,  22614, 22381, 22613,  \n2179, 7465, 22615,  13546, 7901, 7900,  3048, 3049, 21906,  \n22381, 22135, 22134,  7899, 8265, 7900,  22381, 22614, 22382,  \n21805, 22136, 19411,  3010, 15059, 11974,  22614, 22846, 22382,  \n22381, 22382, 22135,  22618, 21810, 22616,  22616, 21810, 22383,  \n7211, 2131, 16546,  19539, 4986, 8279,  8152, 15676, 14589,  \n12139, 13307, 16056,  16914, 12317, 9165,  10944, 22620, 10158,  \n21002, 21470, 22621,  22138, 22135, 22382,  8305, 6542, 8306,  \n15071, 7153, 7152,  22138, 22382, 22623,  22624, 11201, 6189,  \n21467, 22387, 21465,  17264, 13680, 1695,  7228, 10907, 17036,  \n21469, 22139, 22390,  5310, 17601, 7316,  2005, 3427, 4320,  \n19929, 21000, 22387,  22145, 22850, 22622,  22622, 21470, 22145,  \n22138, 22623, 22392,  22625, 22141, 22626,  22626, 22141, 22143,  \n22390, 21816, 21469,  2565, 18646, 2566,  22392, 22623, 22145,  \n8086, 10598, 6095,  22626, 22143, 22393,  7031, 733, 7030,  \n13946, 28554, 13346,  21481, 22856, 22148,  21481, 22394, 22856,  \n13977, 14099, 22628,  16231, 9394, 8817,  3196, 11717, 3197,  \n29091, 8339, 8338,  19962, 21484, 22629,  22395, 22394, 21023,  \n22395, 21022, 22630,  21025, 21487, 22396,  21022, 21027, 22630,  \n12728, 13735, 20492,  16662, 29736, 17290,  20849, 14106, 19068,  \n21827, 21025, 22631,  4515, 8982, 4546,  6629, 8975, 21326,  \n8848, 9029, 1501,  1404, 18979, 1405,  7610, 20714, 14075,  \n8253, 1567, 19806,  5288, 5289, 11802,  17560, 8937, 5715,  \n6608, 21659, 1793,  1904, 19619, 2035,  22620, 9676, 10158,  \n15868, 15136, 4977,  9687, 8604, 18079,  20488, 22633, 21032,  \n21159, 2673, 13026,  18872, 16599, 14992,  7575, 3939, 6231,  \n17007, 4807, 4808,  21033, 22156, 22157,  22637, 20499, 21035,  \n5690, 13230, 5691,  22637, 22401, 20499,  22400, 20499, 22401,  \n22639, 21034, 22157,  22400, 22638, 22158,  15682, 7646, 4397,  \n6874, 15838, 16512,  22638, 22403, 22158,  1707, 8613, 9927,  \n12007, 18493, 13314,  15522, 6982, 5847,  21840, 22405, 21846,  \n22403, 21505, 21837,  16039, 17132, 3637,  5544, 13915, 4061,  \n20815, 13159, 13217,  3835, 1672, 15440,  22403, 22641, 21847,  \n22165, 21846, 22405,  4883, 13375, 4881,  9134, 16112, 21993,  \n6273, 16613, 17870,  11761, 10260, 10261,  5499, 8369, 8368,  \n6348, 3654, 3653,  22642, 21511, 21852,  17833, 5159, 6777,  \n22411, 21852, 21057,  17321, 600, 17322,  21995, 9730, 5985,  \n22643, 22163, 21507,  22644, 22163, 22643,  22168, 22643, 21507,  \n22168, 22645, 22643,  21515, 22168, 21507,  22646, 22168, 21848,  \n21848, 22165, 22646,  21036, 21050, 22647,  21850, 21510, 22648,  \n14960, 1441, 5624,  22645, 22168, 22646,  14575, 14540, 3903,  \n6571, 6949, 2029,  22410, 22649, 22166,  22648, 22410, 21850,  \n4951, 10626, 2555,  14670, 8092, 8772,  22650, 22166, 22649,  \n9075, 7739, 14071,  22651, 21512, 21853,  7011, 4444, 2386,  \n20012, 20519, 22412,  20519, 22166, 22412,  1929, 11452, 14011,  \n22173, 22171, 21066,  22654, 21861, 20530,  21502, 17438, 959,  \n22174, 22656, 22414,  22657, 22175, 22414,  17440, 18274, 22658,  \n11223, 7093, 19484,  2953, 11028, 11030,  22175, 21859, 22414,  \n13964, 8519, 11160,  6087, 18718, 17548,  16320, 15767, 1243,  \n3119, 2877, 2876,  22416, 22659, 22179,  10111, 13439, 10857,  \n22179, 22659, 22183,  3807, 2052, 13050,  22659, 22186, 22183,  \n22180, 21868, 22661,  20534, 22661, 21868,  12199, 9760, 16863,  \n22882, 22662, 22180,  13848, 15779, 19677,  6922, 13472, 8263,  \n8715, 3566, 5635,  21870, 22878, 21074,  4710, 10090, 13517,  \n11176, 18718, 6087,  21869, 22662, 22421,  6050, 13475, 15203,  \n9286, 17597, 7033,  21869, 22180, 22662,  20926, 1794, 8190,  \n18055, 1497, 1498,  10334, 10339, 19015,  12705, 12704, 12124,  \n16330, 1837, 20887,  22420, 22424, 20545,  22185, 21523, 21527,  \n22664, 22665, 22892,  1911, 1420, 1421,  21871, 20061, 22424,  \n9071, 9326, 18097,  16200, 10541, 3440,  4257, 5462, 740,  \n3735, 8222, 7954,  21527, 22427, 22185,  5853, 7360, 340,  \n8325, 16909, 15157,  22664, 22666, 22199,  12893, 6852, 6854,  \n6055, 8235, 6054,  22191, 21871, 22667,  1121, 13357, 19465,  \n4226, 20553, 4227,  21087, 21533, 22668,  22428, 21087, 22668,  \n22199, 22666, 22669,  16400, 10650, 13662,  22431, 22427, 21527,  \n5452, 11943, 5016,  9642, 21072, 16567,  22428, 21874, 21087,  \n11889, 1892, 15355,  3706, 8790, 9101,  5359, 20093, 11020,  \n8859, 13956, 13957,  22202, 22199, 22669,  15836, 16231, 19678,  \n23309, 21103, 22198,  23309, 21884, 21103,  19575, 21884, 22201,  \n1761, 2175, 6397,  13906, 3587, 12629,  14684, 19919, 6299,  \n20940, 3319, 3022,  5965, 13778, 18407,  12625, 20980, 17007,  \n5919, 17902, 14750,  11222, 15188, 15212,  10643, 10425, 15300,  \n19138, 22201, 22436,  1077, 16175, 2839,  14974, 3043, 17935,  \n7630, 17888, 16538,  21100, 20084, 22434,  16257, 15130, 2292,  \n22673, 21110, 21890,  10743, 14375, 10760,  14273, 12194, 5038,  \n14143, 2096, 12832,  18705, 22436, 22207,  22438, 22206, 22672,  \n21890, 20581, 22675,  4823, 6839, 6838,  13951, 9439, 9438,  \n20581, 22440, 22675,  18706, 21120, 20105,  17683, 8128, 17682,  \n22444, 22440, 22210,  3592, 11497, 12621,  22674, 22904, 20587,  \n14153, 4313, 13143,  13508, 22379, 17326,  14723, 12229, 18897,  \n22490, 11221, 17355,  11274, 1827, 4324,  4629, 4279, 2886,  \n6286, 4072, 6287,  21944, 8684, 8507,  14723, 6251, 12229,  \n17912, 5605, 14920,  4694, 17117, 854,  18309, 7881, 514,  \n22441, 21891, 22216,  22677, 22448, 22215,  12543, 20834, 12735,  \n22450, 22215, 21913,  9353, 4349, 13413,  22452, 21907, 22442,  \n21908, 21907, 22217,  13146, 1250, 9304,  973, 972, 1139,  \n1186, 1185, 18552,  19938, 6745, 14920,  21915, 22679, 21117,  \n20131, 21903, 22223,  19203, 20131, 22223,  13165, 1113, 2271,  \n15457, 15456, 18287,  22450, 22221, 22910,  21161, 22216, 21162,  \n3266, 6376, 6377,  22222, 22217, 22452,  19074, 19703, 19983,  \n22681, 21920, 22452,  3074, 14139, 1134,  5769, 3658, 7665,  \n21921, 21164, 22683,  22684, 21915, 22456,  22457, 19203, 22223,  \n18156, 19002, 19456,  17821, 13367, 19685,  19438, 18851, 10446,  \n5191, 721, 1389,  21170, 21922, 22456,  20241, 20853, 12372,  \n610, 16247, 850,  21170, 20174, 21922,  20178, 18802, 22457,  \n21208, 22167, 16301,  20986, 8503, 8333,  13118, 22096, 9363,  \n10480, 19573, 7152,  2826, 10169, 11114,  11825, 5051, 782,  \n22685, 21589, 21926,  20441, 29599, 22688,  10712, 20953, 20638,  \n16694, 16693, 8641,  21346, 20795, 14612,  22689, 22690, 21926,  \n21921, 22691, 21924,  21586, 22687, 21917,  14319, 9954, 10083,  \n21924, 22691, 22692,  20625, 21931, 21586,  8367, 16934, 3288,  \n22233, 21924, 22692,  22687, 21931, 22694,  1246, 5329, 3769,  \n2809, 18789, 14312,  7801, 15481, 3710,  14282, 14283, 5737,  \n9156, 8237, 12304,  22233, 22692, 22695,  11627, 16501, 2446,  \n22983, 16208, 9256,  6032, 18054, 9478,  512, 14755, 14756,  \n13368, 15462, 10194,  13762, 294, 18708,  22463, 20650, 22916,  \n22463, 20665, 20650,  23750, 6865, 2352,  618, 6187, 6188,  \n11195, 11196, 2637,  15549, 15271, 20182,  21189, 22234, 21595,  \n884, 22696, 20881,  22465, 21597, 21925,  21925, 22460, 22465,  \n5971, 23437, 5972,  22234, 22461, 21595,  3444, 4093, 7815,  \n18569, 18570, 1716,  21928, 21932, 22235,  17369, 18126, 19137,  \n22463, 21600, 20665,  22694, 21931, 22698,  21931, 21197, 22464,  \n2671, 18141, 3801,  22699, 22426, 22236,  18958, 14802, 8433,  \n5477, 3810, 3276,  7684, 12008, 7685,  16116, 12744, 792,  \n15908, 5193, 15247,  21947, 22700, 22464,  21938, 21597, 22465,  \n13170, 5105, 8513,  14433, 18635, 1154,  3492, 15117, 8910,  \n22471, 16594, 20074,  22468, 21933, 22470,  11686, 15701, 1635,  \n6093, 14341, 10814,  18370, 11852, 18369,  16607, 22704, 11677,  \n9720, 4083, 20013,  10078, 9096, 431,  2712, 10299, 16937,  \n1517, 6608, 1792,  16257, 20663, 14833,  5929, 15064, 2655,  \n16642, 18182, 14275,  8780, 1079, 11081,  2698, 2700, 8023,  \n20842, 1670, 7036,  7010, 11428, 7009,  21606, 22478, 21604,  \n14506, 4770, 4772,  20410, 10424, 20409,  21604, 22478, 21939,  \n22478, 22705, 21939,  12758, 20456, 20455,  21254, 15988, 8965,  \n22243, 22478, 21606,  21607, 22241, 22476,  22476, 20702, 21607,  \n22700, 21947, 22483,  22484, 22481, 22703,  9997, 12263, 6459,  \n16119, 15665, 8149,  22707, 22478, 22243,  3980, 10858, 11979,  \n21947, 21948, 22483,  22482, 22706, 22932,  5690, 8345, 13230,  \n13293, 15061, 6088,  22243, 22244, 22707,  22485, 21609, 21937,  \n20844, 11783, 10512,  22484, 22703, 22708,  14581, 6910, 1449,  \n22706, 22482, 22257,  22477, 22494, 21611,  1105, 19963, 5518,  \n15251, 22709, 15776,  6044, 14880, 11845,  20249, 21219, 21614,  \n22484, 22708, 22487,  10636, 13872, 13873,  22244, 21949, 22492,  \n21491, 9145, 15580,  22947, 20701, 22245,  21948, 22712, 22483,  \n22708, 22483, 22712,  21017, 22713, 22714,  22482, 22484, 22500,  \n22257, 22482, 22500,  16781, 18666, 9194,  22715, 20793, 20792,  \n22708, 22712, 22487,  17422, 19820, 10791,  14801, 16563, 22719,  \n18243, 13766, 1969,  19050, 2500, 16219,  22583, 3944, 22721,  \n12664, 11918, 21312,  22716, 22706, 22259,  16189, 13409, 10874,  \n22503, 22504, 22718,  3511, 14710, 16781,  8087, 6523, 11527,  \n22712, 21948, 22499,  17565, 19388, 3956,  11730, 10640, 10231,  \n14412, 18029, 7549,  22259, 22706, 22257,  9570, 19798, 12301,  \n13259, 1645, 1935,  22718, 22504, 22723,  3830, 3615, 5921,  \n7535, 3582, 1970,  3939, 1091, 11797,  22499, 22501, 22948,  \n22487, 22712, 22720,  22487, 22720, 22497,  22497, 22720, 22258,  \n22500, 22497, 22258,  22503, 22716, 22502,  18471, 14605, 11870,  \n15059, 9708, 21190,  21951, 22252, 22725,  22726, 21951, 22725,  \n22726, 22501, 21951,  6476, 13488, 6597,  1901, 1902, 15942,  \n6484, 6479, 7516,  8714, 2603, 2602,  6752, 15949, 8744,  \n17450, 17452, 18929,  22258, 22720, 22507,  21959, 22258, 22507,  \n6073, 5698, 5187,  8288, 5890, 1939,  15070, 14292, 5762,  \n3393, 17238, 4839,  22729, 21616, 21955,  21954, 21615, 22506,  \n19690, 879, 878,  22507, 22720, 22949,  2755, 10024, 3225,  \n3296, 3988, 19171,  17538, 15596, 5831,  20649, 5539, 14942,  \n2742, 15737, 9759,  7268, 6223, 9244,  13863, 20691, 9089,  \n22949, 22731, 22507,  22262, 21959, 22507,  18297, 17226, 20180,  \n14305, 12406, 626,  16874, 20153, 4614,  22505, 21977, 22510,  \n22510, 21977, 22511,  6289, 6940, 17968,  22508, 22507, 22731,  \n22262, 22508, 22265,  13074, 11728, 11727,  1281, 3466, 21760,  \n13969, 13964, 9542,  7933, 7934, 21687,  9728, 13046, 8990,  \n5539, 5538, 18647,  22268, 22513, 22511,  8647, 7942, 659,  \n18615, 18614, 14798,  20877, 3006, 10514,  15137, 8908, 4974,  \n13765, 21237, 11533,  15975, 18109, 16299,  21984, 22265, 22961,  \n14247, 5851, 15910,  16582, 11259, 13367,  22736, 9965, 4556,  \n4819, 16297, 16298,  19578, 8425, 8840,  4640, 4639, 24021,  \n4640, 24021, 22738,  20140, 9574, 13641,  2457, 10238, 18811,  \n8731, 18555, 13013,  12848, 7539, 21203,  22739, 22513, 22268,  \n22512, 21978, 22271,  14287, 14457, 10302,  18813, 22740, 19878,  \n2271, 4326, 2272,  22516, 21986, 22742,  22739, 22268, 21994,  \n4663, 3862, 9387,  21988, 22273, 22515,  16033, 1120, 16674,  \n2875, 2880, 2379,  22747, 22271, 22275,  2973, 17202, 15640,  \n22282, 22747, 22275,  17271, 7370, 1059,  12240, 8541, 3471,  \n16332, 1995, 13339,  4903, 16648, 4904,  21292, 9673, 5215,  \n22968, 21994, 22281,  4567, 3555, 4568,  1433, 9408, 21613,  \n22515, 22743, 22744,  9009, 10503, 1190,  22744, 22280, 22515,  \n15702, 22155, 2674,  8843, 13757, 11666,  22746, 22279, 22516,  \n16733, 15327, 18875,  3312, 22748, 3313,  22008, 22280, 22521,  \n2368, 18410, 2501,  22009, 22283, 22006,  22280, 22744, 22521,  \n22749, 22283, 22751,  22751, 22283, 22009,  2384, 11258, 19876,  \n8502, 6347, 6349,  4586, 22753, 4585,  14972, 12269, 19158,  \n3786, 11150, 6024,  1686, 21970, 6480,  22755, 486, 16945,  \n22286, 22297, 22527,  22005, 22000, 22754,  22756, 22522, 22527,  \n1539, 4982, 2854,  4245, 7905, 7906,  16437, 17632, 23073,  \n17359, 7847, 16331,  22292, 21656, 22287,  2221, 7327, 7328,  \n22286, 22010, 22297,  17363, 16470, 6458,  3963, 3965, 21550,  \n22009, 22015, 22528,  15894, 10953, 1512,  22653, 13311, 13900,  \n11735, 4454, 4453,  7740, 15827, 15826,  4328, 13579, 13578,  \n10319, 10318, 10561,  19596, 19807, 3342,  12916, 17418, 6245,  \n15212, 6903, 3206,  16159, 3842, 21493,  22015, 22529, 22528,  \n7647, 7713, 17949,  6884, 4401, 6883,  22287, 22757, 22292,  \n1768, 19689, 18070,  22757, 22014, 22292,  22721, 5653, 10585,  \n22014, 22757, 22300,  14912, 14911, 12522,  12804, 6464, 3497,  \n22012, 22005, 22532,  21670, 22014, 22300,  2484, 12036, 2127,  \n22026, 21670, 22300,  668, 11197, 5322,  5885, 2344, 2320,  \n22020, 22533, 22530,  5058, 1049, 1907,  6946, 18235, 520,  \n8066, 10749, 15985,  18970, 2383, 20369,  22021, 22012, 22532,  \n22533, 22762, 22530,  15595, 18065, 22763,  22023, 22037, 22529,  \n22534, 22026, 22301,  22766, 22529, 22037,  8454, 17675, 4795,  \n22029, 22021, 22537,  8050, 21257, 18684,  22534, 22301, 22764,  \n16865, 8827, 7694,  17477, 16852, 16851,  22303, 22535, 22533,  \n22764, 22536, 22534,  375, 377, 5506,  19208, 12927, 10256,  \n22538, 22534, 22536,  5940, 19127, 10703,  12087, 19258, 9379,  \n22040, 22985, 22535,  22037, 22039, 22539,  22766, 22539, 22767,  \n22037, 22539, 22766,  12864, 10160, 6595,  22041, 22538, 22768,  \n6956, 4915, 8900,  6998, 5446, 6996,  22308, 22541, 22985,  \n22311, 22041, 22769,  22770, 16604, 17175,  3552, 4375, 6727,  \n6549, 6978, 6548,  18014, 21975, 19996,  22320, 22311, 22772,  \n12635, 16124, 6020,  14250, 19261, 9837,  1158, 11270, 1227,  \n22316, 22987, 22322,  6475, 10900, 19667,  22316, 22322, 22057,  \n3059, 5677, 3060,  22545, 22048, 22320,  8175, 8174, 12940,  \n1974, 5650, 4978,  19186, 7538, 15544,  22552, 22057, 22322,  \n22056, 21700, 22545,  3037, 2600, 15826,  22546, 22553, 22774,  \n22545, 22550, 22056,  22546, 22323, 22553,  2051, 21862, 22242,  \n4596, 4597, 11902,  12272, 8987, 2351,  1105, 1466, 12772,  \n2419, 14902, 3704,  3722, 1390, 5886,  2006, 5247, 11326,  \n1119, 8081, 4509,  6882, 6881, 11748,  21710, 22559, 22777,  \n4914, 4913, 11590,  22553, 22323, 22332,  22553, 22332, 22774,  \n7253, 7254, 19696,  21708, 22550, 22558,  22555, 21718, 21711,  \n19709, 6155, 20980,  9366, 4107, 17291,  18769, 18889, 3102,  \n18019, 17689, 13619,  12825, 5767, 18221,  17769, 18465, 22781,  \n15817, 18014, 15003,  19903, 1730, 1731,  22563, 22075, 22073,  \n17292, 11137, 17842,  22332, 22331, 22778,  9502, 9501, 18717,  \n5414, 5413, 20476,  13241, 5293, 22255,  22333, 22335, 22784,  \n22786, 22784, 22335,  11039, 8697, 22787,  7462, 10825, 15363,  \n22335, 22341, 22786,  11489, 20670, 9646,  22788, 22786, 22568,  \n2357, 11063, 12853,  22786, 22341, 22568,  22076, 22567, 22569,  \n12128, 18957, 12129,  19221, 10171, 16825,  22079, 22345, 22568,  \n5645, 11327, 15351,  6863, 10733, 10954,  19672, 1764, 12459,  \n3239, 10183, 2382,  13859, 9628, 19148,  12061, 7357, 11295,  \n22348, 21740, 22792,  12377, 15304, 12376,  22796, 22797, 22795,  \n13456, 9077, 6914,  3767, 10812, 9663,  22795, 22799, 22796,  \n4914, 13133, 12294,  7533, 16101, 1319,  21452, 13324, 21335,  \n12580, 9266, 9267,  16055, 11863, 4890,  22799, 22800, 22796,  \n597, 22520, 13498,  22803, 22090, 22348,  22347, 22088, 22802,  \n21624, 18087, 13811,  22796, 22800, 22804,  22088, 22089, 22805,  \n20203, 11249, 15726,  22799, 22806, 22807,  22800, 22799, 22807,  \n8001, 12728, 13987,  10954, 13778, 5965,  22803, 22808, 22090,  \n3191, 12953, 12954,  11238, 7283, 7860,  22808, 22091, 22090,  \n22809, 22800, 22807,  11930, 4994, 20342,  21412, 21413, 22578,  \n22578, 22810, 21412,  22811, 22578, 21413,  22351, 21413, 21411,  \n22811, 21413, 22351,  12284, 10977, 12285,  21746, 22812, 22581,  \n22812, 21746, 21412,  22812, 21412, 22810,  22351, 21414, 22582,  \n15757, 11768, 16981,  9942, 9944, 6558,  22805, 22089, 22350,  \n8944, 12423, 4185,  14734, 7066, 4789,  22582, 21414, 21415,  \n2142, 10255, 20130,  20644, 3726, 3725,  827, 6043, 17309,  \n22814, 22581, 22812,  19468, 7203, 12163,  22753, 7461, 14657,  \n22580, 22091, 22815,  3560, 10143, 12620,  13843, 5102, 3567,  \n22093, 22816, 22350,  22814, 22817, 20945,  3920, 17978, 18106,  \n22581, 22814, 20945,  2780, 17354, 4777,  22818, 1538, 8727,  \n11741, 13459, 16602,  22576, 11420, 22577,  12012, 19516, 12011,  \n22816, 22093, 22584,  1330, 17133, 17243,  1194, 22819, 1195,  \n21199, 16392, 14845,  4061, 14295, 5544,  19861, 19863, 19856,  \n10839, 20670, 17397,  20945, 22358, 20943,  19857, 17307, 17305,  \n12050, 18585, 22820,  19210, 3362, 19237,  5613, 15874, 5612,  \n5940, 6202, 19127,  13196, 15608, 19335,  8591, 4090, 12925,  \n6574, 6573, 11301,  819, 7749, 10396,  20951, 19856, 19857,  \n2505, 2964, 15330,  21757, 22821, 22584,  11723, 8897, 17563,  \n6777, 2206, 8597,  6163, 362, 15619,  2211, 1823, 13763,  \n4035, 22822, 4034,  11580, 8850, 8971,  14598, 14160, 15662,  \n16682, 16681, 22823,  508, 3098, 3584,  6209, 8165, 11748,  \n7200, 2832, 12600,  6822, 6821, 17200,  8123, 11037, 5419,  \n7128, 11173, 20617,  17941, 12711, 12888,  22360, 21767, 22593,  \n22594, 21428, 22103,  20767, 3742, 17584,  8053, 21982, 14623,  \n22824, 21780, 22598,  11066, 20544, 14368,  17621, 16406, 11810,  \n21778, 22826, 22365,  4263, 2586, 14365,  22593, 22105, 22825,  \n22593, 22825, 22827,  15458, 12104, 883,  4675, 3660, 3664,  \n8628, 14429, 10487,  22824, 22104, 21780,  22825, 22105, 22110,  \n9139, 2670, 7022,  12749, 9488, 14005,  8121, 6435, 5942,  \n19118, 18658, 13930,  22601, 22110, 22824,  8758, 3147, 8683,  \n9830, 4780, 1879,  22114, 20396, 22602,  16388, 9656, 8111,  \n22368, 20967, 22603,  22371, 20969, 22114,  5790, 19912, 607,  \n16717, 2663, 9716,  22603, 21443, 22604,  15778, 10077, 13467,  \n21445, 22371, 22829,  22371, 21445, 20972,  11355, 12180, 17701,  \n18565, 18564, 11497,  29732, 6321, 15194,  22373, 21791, 22372,  \n1477, 5759, 19152,  17539, 14761, 731,  22120, 22119, 22374,  \n22119, 22830, 22374,  20420, 8111, 793,  3174, 11605, 11606,  \n1346, 1345, 3788,  976, 400, 10126,  22831, 22607, 22605,  \n10081, 1782, 15816,  365, 9091, 15243,  22607, 22832, 22375,  \n22607, 22831, 22832,  15296, 15825, 15717,  19396, 4602, 17210,  \n18289, 14553, 555,  16511, 19165, 2035,  22609, 21447, 21800,  \n3109, 8018, 2317,  22123, 22610, 22835,  22377, 21453, 22123,  \n19445, 6423, 1664,  13401, 12081, 11886,  6716, 21299, 17908,  \n22836, 11451, 22837,  1727, 14195, 9307,  1433, 1919, 1918,  \n6348, 9757, 12527,  12578, 14725, 1318,  22380, 22838, 21800,  \n2347, 5436, 2346,  9549, 21693, 13129,  354, 19117, 4705,  \n22380, 21800, 18431,  18396, 19354, 12811,  18431, 22128, 22380,  \n22840, 21802, 22126,  6572, 22133, 21565,  8498, 15655, 8497,  \n3623, 13814, 12361,  9822, 20428, 12737,  18530, 12392, 9202,  \n3005, 4364, 3006,  21802, 22840, 22130,  22840, 22842, 22130,  \n22130, 22842, 22613,  2501, 18410, 13960,  22842, 22843, 22844,  \n22613, 22842, 22845,  5202, 7427, 20506,  18158, 13361, 18807,  \n12275, 6660, 10385,  18627, 23622, 13547,  22844, 22843, 22846,  \n22845, 22844, 22846,  10557, 16542, 3545,  18323, 8304, 21307,  \n22136, 22128, 19403,  22845, 22846, 22614,  21058, 10363, 16080,  \n21808, 22617, 22383,  8015, 9544, 5431,  8358, 8040, 13194,  \n22846, 23064, 22382,  16663, 2408, 17257,  16542, 12338, 19385,  \n14807, 19934, 17660,  4228, 3673, 19020,  23357, 5086, 19582,  \n22382, 23064, 23067,  5353, 2271, 1113,  22017, 7120, 20515,  \n22849, 21805, 20442,  20442, 21807, 22849,  3621, 12730, 15197,  \n22139, 21810, 22618,  22139, 22618, 23065,  21808, 22621, 22617,  \n21808, 21002, 22621,  3092, 13789, 3167,  22622, 22621, 21470,  \n5317, 2945, 9086,  23067, 22850, 22382,  22851, 22850, 23067,  \n22850, 22851, 22622,  22382, 22850, 22623,  2226, 7014, 7015,  \n21467, 19929, 22387,  22387, 22386, 21465,  22139, 22853, 22390,  \n6873, 21253, 11594,  8366, 17120, 8365,  9334, 16238, 22329,  \n22142, 22141, 22625,  6674, 21253, 6873,  22145, 22623, 22850,  \n2315, 13405, 18827,  22583, 19868, 17537,  22148, 22856, 22393,  \n7114, 7113, 4892,  22184, 5803, 11131,  19368, 22857, 22858,  \n18906, 17037, 18905,  7974, 16066, 18736,  15758, 1947, 6048,  \n15339, 11554, 1225,  21798, 20852, 21799,  22396, 19962, 22629,  \n2905, 2906, 18767,  1452, 6130, 7324,  21827, 22859, 21027,  \n22631, 22859, 21827,  18998, 16174, 12701,  9818, 15320, 9817,  \n5437, 15449, 15448,  10760, 14375, 10474,  12320, 5739, 22861,  \n4476, 16909, 8325,  3362, 3363, 387,  9461, 15126, 6154,  \n14470, 4511, 15031,  1283, 17170, 16547,  12582, 11198, 1867,  \n11008, 9896, 19647,  4543, 18766, 20261,  22638, 22400, 22401,  \n8323, 7770, 7771,  18521, 14479, 748,  22867, 22868, 22638,  \n2856, 4368, 11602,  11353, 3278, 21440,  6558, 21678, 11993,  \n22638, 22868, 22403,  22868, 22641, 22403,  22405, 21840, 22870,  \n12708, 12709, 10657,  22165, 22405, 22870,  1287, 10013, 1286,  \n8196, 5913, 3906,  3091, 7322, 17596,  17756, 1679, 17755,  \n7512, 7633, 13266,  21096, 18815, 18816,  12182, 5984, 7431,  \n16735, 20136, 4715,  14267, 14266, 22595,  12752, 4054, 2416,  \n21853, 22641, 22873,  21847, 22641, 21853,  3236, 16349, 9603,  \n10679, 3258, 2325,  9762, 15481, 14813,  15086, 20106, 18887,  \n22648, 22649, 22410,  22874, 22599, 17319,  11793, 9626, 11439,  \n9776, 9775, 5841,  22875, 22169, 22171,  12488, 14168, 3807,  \n4277, 6571, 2029,  22660, 22647, 21050,  22650, 22412, 22166,  \n1104, 9442, 798,  20121, 19946, 9048,  22173, 22877, 22171,  \n1899, 19493, 4123,  13320, 341, 10239,  20530, 20012, 22412,  \n5925, 7586, 17386,  14266, 13011, 15708,  22173, 21074, 22878,  \n22879, 5197, 4745,  7181, 4569, 7182,  22880, 22657, 22414,  \n22175, 22657, 22176,  6269, 5455, 10506,  7808, 10259, 17239,  \n18694, 12703, 15962,  9258, 18348, 14436,  18348, 15385, 14436,  \n22416, 22884, 22659,  15194, 7336, 5256,  22416, 22886, 22884,  \n22659, 22884, 22186,  12074, 22887, 10309,  17699, 19610, 5960,  \n22180, 22661, 22882,  20534, 21861, 22661,  3813, 8538, 3289,  \n10657, 21490, 13291,  22660, 22172, 21523,  22889, 2222, 7328,  \n8438, 10714, 5063,  4315, 4317, 5770,  22420, 21529, 22186,  \n16949, 8565, 19692,  15884, 5275, 15883,  20465, 22890, 13167,  \n22888, 22665, 22423,  22421, 22888, 22423,  16803, 13417, 6191,  \n22888, 22421, 22662,  9559, 20474, 8488,  19324, 9193, 7356,  \n1435, 4444, 330,  22665, 22664, 22423,  14224, 16087, 11864,  \n14804, 10068, 15044,  1653, 6663, 16276,  18352, 21687, 2697,  \n22420, 22891, 22424,  22892, 22666, 22664,  2563, 3734, 17181,  \n13696, 6201, 14260,  18134, 2364, 10622,  18724, 10316, 957,  \n22191, 21097, 21871,  21872, 22191, 22193,  9216, 7532, 1319,  \n22670, 22427, 22431,  3535, 16231, 15836,  5827, 923, 922,  \n18461, 19340, 14317,  11454, 947, 14655,  3818, 1460, 10655,  \n22195, 22428, 23129,  22429, 22195, 23129,  22669, 22435, 22206,  \n18468, 17651, 19900,  22429, 23129, 22203,  21111, 20572, 22203,  \n301, 18870, 2733,  22897, 21881, 21100,  9993, 20325, 20324,  \n16318, 1027, 11338,  21884, 22896, 22201,  17419, 2882, 1133,  \n12439, 1306, 9889,  22196, 21108, 21110,  21879, 22429, 22203,  \n2784, 9500, 12079,  2323, 2835, 5607,  22898, 22670, 22431,  \n20587, 21896, 22674,  1492, 17500, 1491,  6636, 8369, 14976,  \n325, 324, 3624,  4686, 7173, 3547,  13524, 19474, 8192,  \n22444, 22900, 22440,  22675, 22440, 22900,  17910, 11121, 20038,  \n22901, 22212, 22207,  10830, 9786, 23699,  22212, 18706, 22207,  \n18706, 22212, 21120,  22343, 10513, 10512,  22902, 21120, 22212,  \n22672, 22442, 22438,  15847, 22903, 13203,  11289, 22490, 13710,  \n22905, 21901, 22902,  23135, 22444, 22448,  23135, 22448, 22677,  \n9421, 11346, 19510,  17155, 14821, 7981,  22450, 22677, 22215,  \n22904, 22678, 21573,  1976, 8710, 701,  2776, 5750, 8840,  \n21903, 21901, 22907,  529, 3251, 530,  12074, 13537, 22887,  \n6061, 18976, 7007,  5118, 1992, 7740,  21897, 21117, 22679,  \n8255, 15877, 5300,  22452, 22442, 23319,  22677, 22450, 22909,  \n22217, 21907, 22452,  16127, 6360, 12599,  15449, 5437, 5525,  \n3190, 10501, 3189,  17439, 10527, 2302,  22296, 13225, 13224,  \n12441, 16554, 7791,  7992, 4864, 14321,  5590, 5589, 17484,  \n17130, 19805, 12244,  2701, 21358, 2346,  7795, 16531, 29105,  \n22221, 21583, 21589,  7633, 11024, 11146,  7654, 9403, 838,  \n8726, 4920, 14608,  22686, 21161, 21917,  22221, 21589, 22685,  \n1550, 1549, 18329,  705, 704, 3940,  18145, 18146, 19911,  \n7936, 15035, 7937,  4970, 12730, 12729,  18802, 19225, 22457,  \n22227, 22681, 22912,  17517, 1662, 1661,  21917, 22687, 22686,  \n6471, 13787, 7649,  21920, 22681, 22227,  7994, 7993, 2387,  \n9660, 13033, 13214,  22914, 17529, 21936,  16987, 5376, 19137,  \n18360, 2033, 4155,  8458, 21203, 7539,  9017, 3408, 11288,  \n20178, 22457, 22916,  20178, 22916, 20650,  22917, 22915, 22687,  \n20527, 294, 15569,  8018, 3109, 3108,  12323, 14094, 13180,  \n11889, 11888, 9005,  20236, 17219, 15158,  22917, 22687, 22694,  \n2037, 5769, 18194,  11227, 22919, 8467,  18165, 2101, 2100,  \n22693, 21585, 21927,  22693, 21922, 21585,  22920, 22917, 22694,  \n15900, 15831, 21849,  22920, 22922, 22917,  14879, 4709, 4708,  \n22923, 10881, 22924,  22689, 21926, 21928,  15900, 11912, 15831,  \n9610, 12086, 18255,  17131, 14931, 10219,  13798, 20627, 16365,  \n22462, 22233, 22695,  1713, 3023, 2635,  18587, 7848, 17257,  \n22694, 22698, 22920,  7217, 21256, 18797,  7384, 1332, 6891,  \n18163, 15519, 10972,  22922, 22920, 22698,  21928, 22235, 22697,  \n10810, 20584, 20236,  18499, 4576, 4577,  11377, 20088, 18022,  \n14981, 22663, 21395,  440, 1341, 9349,  5913, 499, 1038,  \n3501, 10300, 17047,  8071, 20926, 6112,  22698, 22701, 22922,  \n21931, 22464, 22698,  10947, 3156, 13961,  22929, 22922, 22701,  \n13802, 6698, 13801,  22698, 22464, 22700,  22929, 22701, 22481,  \n22237, 22462, 23162,  22703, 22698, 22700,  22701, 22698, 22703,  \n1404, 10520, 5741,  22929, 22481, 22480,  7277, 21316, 22931,  \n7689, 9023, 3924,  4640, 14330, 14329,  21603, 21600, 22469,  \n22701, 22703, 22481,  22482, 22932, 22480,  12354, 3312, 11613,  \n22238, 22237, 22933,  14431, 19004, 20118,  12031, 9762, 14813,  \n22700, 22708, 22703,  3471, 8541, 1815,  8173, 14819, 8662,  \n14438, 6229, 15975,  22137, 20086, 17843,  21938, 22465, 22477,  \n692, 15874, 16200,  22700, 22483, 22708,  772, 13695, 648,  \n13851, 13850, 10784,  22470, 21939, 22705,  22469, 21219, 21603,  \n17252, 15499, 20518,  14961, 8834, 21739,  22938, 21385, 22939,  \n3652, 7270, 19904,  8495, 17174, 15027,  19647, 8416, 16575,  \n1274, 1275, 14695,  23163, 22941, 22718,  22707, 22244, 22492,  \n11754, 20173, 21104,  22941, 22706, 22716,  22503, 22941, 22716,  \n17291, 11137, 17292,  9077, 3065, 6914,  15746, 12453, 13332,  \n22494, 22477, 22940,  5173, 1337, 18858,  21937, 22944, 22485,  \n10764, 15660, 12008,  22941, 22503, 22718,  22330, 11936, 574,  \n20940, 11825, 782,  19404, 2642, 20884,  20701, 22947, 22710,  \n22241, 20701, 22710,  22946, 21614, 21219,  16722, 3120, 3785,  \n2835, 4586, 8666,  22498, 22943, 22492,  2281, 9970, 2468,  \n11061, 5724, 10767,  22716, 22259, 22502,  15643, 9262, 16518,  \n8478, 7714, 9082,  15358, 682, 681,  18366, 11820, 8761,  \n21614, 22946, 22252,  19298, 3326, 5866,  11785, 9498, 4137,  \n5194, 17676, 6433,  2845, 1259, 9217,  22499, 22948, 22712,  \n17558, 17559, 11323,  18607, 7082, 22095,  3981, 11980, 16952,  \n7389, 5995, 2992,  22725, 22252, 22946,  9631, 2157, 5090,  \n4593, 2118, 19237,  9526, 5576, 19728,  22712, 22949, 22720,  \n15005, 19249, 4868,  22951, 22726, 22725,  1559, 13101, 17500,  \n22501, 22726, 22948,  22712, 22948, 22949,  10016, 11378, 4680,  \n10026, 9525, 10352,  22498, 21616, 22729,  3475, 13916, 5201,  \n13319, 13318, 1566,  17808, 6834, 6836,  6660, 12275, 6661,  \n22717, 22718, 22723,  18370, 20432, 14788,  22949, 22948, 22952,  \n22723, 22504, 22730,  5657, 6747, 22437,  21615, 22494, 22506,  \n16135, 10456, 15574,  22504, 22505, 22730,  7124, 19047, 7125,  \n9561, 24188, 16640,  11827, 11012, 10100,  22730, 22505, 22510,  \n19372, 21478, 21477,  21721, 19958, 10441,  3572, 21182, 5949,  \n22730, 22511, 22732,  9518, 17757, 9519,  9801, 22954, 21532,  \n11424, 1858, 7936,  10860, 19402, 8798,  22956, 21954, 22506,  \n6405, 6334, 4743,  13936, 3240, 16839,  21956, 21954, 22956,  \n1939, 10277, 8288,  10972, 19503, 4422,  22508, 22731, 22957,  \n22732, 22511, 22513,  20117, 3316, 4164,  1836, 12649, 1185,  \n11303, 11302, 13676,  18786, 10913, 3805,  6531, 22959, 22385,  \n13923, 12573, 16060,  22508, 22961, 22265,  4330, 16537, 15644,  \n9268, 9608, 16478,  17461, 22962, 26005,  15962, 16630, 18695,  \n22960, 22512, 22271,  22965, 16194, 4108,  21104, 9677, 11754,  \n4082, 9479, 17378,  22963, 22513, 22739,  4167, 12332, 4168,  \n21984, 22961, 22741,  8004, 2626, 18139,  22273, 21984, 22741,  \n2877, 20195, 15115,  20542, 3122, 13312,  13094, 17022, 9413,  \n12151, 16862, 6136,  22967, 22963, 22739,  12121, 17202, 2973,  \n17771, 2926, 2925,  10433, 11867, 5326,  8853, 5857, 14313,  \n22739, 21994, 22968,  19114, 12834, 10997,  2981, 10207, 17663,  \n19459, 15185, 13398,  11201, 11920, 18462,  347, 18631, 16684,  \n18660, 17295, 3388,  22271, 22747, 22969,  19459, 13398, 5752,  \n5536, 3458, 16431,  10668, 15776, 11832,  11675, 15776, 10668,  \n1322, 12880, 5137,  2339, 2338, 3172,  12142, 10425, 8913,  \n7447, 20454, 4606,  10140, 17380, 10141,  3746, 16667, 21636,  \n18733, 23287, 18073,  6626, 16205, 413,  22281, 22749, 22971,  \n21370, 2381, 13189,  22283, 22749, 22281,  801, 800, 22070,  \n2889, 3346, 11254,  3082, 21364, 14161,  22522, 22282, 22003,  \n6856, 6855, 15080,  13262, 7544, 5586,  17803, 14612, 17273,  \n14584, 14583, 13343,  22000, 22279, 22746,  3751, 4063, 4513,  \n22523, 22521, 22744,  22000, 22746, 22754,  14446, 15695, 2370,  \n2620, 7567, 14398,  12338, 9073, 7556,  3633, 13174, 15848,  \n22522, 22286, 22527,  2522, 12475, 13733,  15775, 20399, 3487,  \n22287, 22521, 22523,  5187, 5698, 19593,  21158, 15582, 11792,  \n22532, 22005, 22754,  15357, 16976, 15358,  3496, 11116, 11115,  \n19079, 8638, 8637,  8763, 17801, 8546,  22532, 22754, 22974,  \n22287, 22976, 22757,  22758, 22528, 22529,  954, 19419, 2903,  \n16703, 9027, 12538,  22972, 22527, 22297,  18672, 22977, 11371,  \n12654, 18227, 12380,  22287, 22973, 22976,  19795, 21640, 20307,  \n10302, 6079, 3602,  7727, 8382, 18348,  22758, 22529, 22761,  \n1518, 6228, 13016,  4561, 3687, 10444,  22760, 10896, 19332,  \n22300, 22757, 22978,  8652, 11994, 10918,  22761, 22529, 22766,  \n9956, 6893, 3692,  22301, 22300, 22978,  19326, 1005, 16900,  \n18919, 2094, 7930,  20261, 8423, 20260,  14312, 18789, 11618,  \n22978, 22764, 22301,  5445, 22760, 6996,  22537, 22021, 22759,  \n22533, 22535, 22762,  6451, 6896, 17739,  2906, 16367, 18767,  \n2188, 12819, 436,  15009, 18815, 4416,  4222, 4221, 16083,  \n1815, 22274, 22980,  22762, 22535, 22985,  1574, 2663, 16717,  \n22307, 22537, 22982,  12361, 16207, 22983,  17665, 5004, 12639,  \n15380, 2749, 5485,  10944, 19807, 19596,  8835, 14742, 3851,  \n22536, 22984, 22538,  19645, 7703, 11817,  16410, 2516, 18985,  \n4993, 7467, 16161,  22041, 22768, 22769,  11661, 22780, 19426,  \n10290, 21900, 18784,  317, 2836, 2837,  9725, 1679, 1678,  \n22988, 22986, 22315,  16275, 7259, 13661,  9845, 15377, 17135,  \n10132, 2833, 15490,  3645, 8273, 16945,  22771, 22541, 22319,  \n22057, 22051, 22316,  22326, 22992, 22990,  22740, 18813, 22389,  \n1875, 6481, 12543,  17333, 9737, 15249,  22546, 22993, 22319,  \n22546, 22995, 22993,  9034, 4167, 4168,  5628, 14715, 1068,  \n14143, 19175, 1917,  15049, 5745, 2647,  22545, 22320, 22772,  \n2110, 4431, 4432,  11993, 8416, 3648,  1294, 7078, 13652,  \n14213, 22981, 22997,  6363, 22228, 11852,  2600, 21238, 5118,  \n20547, 6436, 7858,  14304, 625, 1273,  13709, 7240, 7241,  \n22998, 22558, 22545,  22550, 22545, 22558,  2970, 8076, 13060,  \n8602, 6427, 1127,  1486, 4186, 1485,  9194, 3511, 16781,  \n22777, 22060, 21710,  13424, 4153, 7309,  8543, 7540, 11663,  \n22332, 22778, 22774,  22563, 22561, 22069,  22073, 22072, 22566,  \n22555, 22564, 21718,  22774, 22778, 23000,  22779, 22563, 23002,  \n7639, 14364, 2494,  23003, 22073, 22566,  4745, 5197, 14081,  \n15874, 5613, 16200,  1979, 18001, 7162,  10822, 21215, 21749,  \n17806, 18152, 21247,  22331, 22784, 22778,  6815, 16828, 6814,  \n22331, 22333, 22784,  2901, 19048, 7124,  5560, 6357, 6526,  \n23006, 22567, 22783,  11386, 16479, 10314,  23009, 22786, 22788,  \n22569, 22567, 23008,  2114, 9175, 6021,  12225, 15982, 3517,  \n2341, 15654, 9450,  3187, 3188, 7640,  19667, 16120, 17724,  \n789, 20641, 17279,  9233, 20458, 13943,  1754, 9042, 12346,  \n22798, 23015, 22797,  22798, 23016, 23015,  22574, 23012, 22792,  \n22794, 22345, 22347,  586, 16070, 587,  8504, 7474, 8861,  \n23018, 22795, 23014,  23013, 22795, 22797,  22798, 22797, 22796,  \n17710, 18416, 18417,  14859, 14945, 5386,  13794, 15385, 16560,  \n22795, 23013, 23014,  22794, 22347, 23017,  23018, 22799, 22795,  \n16901, 16313, 617,  6662, 1009, 18788,  3971, 14149, 22267,  \n6542, 8305, 5080,  18504, 10350, 11783,  23017, 22347, 22802,  \n22799, 23018, 22806,  11259, 10812, 13367,  23019, 22348, 22792,  \n13157, 20087, 13158,  3944, 10586, 5653,  23020, 22796, 22804,  \n23020, 22798, 22796,  22798, 23020, 23021,  22348, 23019, 22803,  \n20321, 10125, 3661,  4061, 20091, 8411,  16195, 4409, 10869,  \n23022, 22624, 2682,  15519, 15518, 10972,  10256, 8615, 18723,  \n8206, 15341, 19554,  15473, 8223, 11223,  16522, 5710, 5709,  \n22088, 22805, 22802,  8615, 10256, 8616,  17170, 8079, 8080,  \n22804, 23023, 23020,  11523, 23026, 11934,  1668, 18211, 1667,  \n23024, 22812, 22810,  6390, 16695, 16737,  23024, 22810, 22578,  \n23027, 22811, 22351,  405, 15557, 1538,  23233, 22807, 22806,  \n22800, 22809, 22804,  22804, 22814, 23023,  18645, 4644, 4565,  \n23023, 22812, 23024,  23027, 22351, 22582,  3084, 2654, 4556,  \n22802, 22805, 23028,  12407, 3721, 17496,  1695, 14643, 12729,  \n16292, 10333, 17368,  14531, 9472, 12648,  5232, 8215, 6648,  \n15247, 13253, 11043,  21395, 10130, 12434,  8837, 14431, 3859,  \n17203, 12777, 9993,  23023, 22814, 22812,  4134, 4133, 12646,  \n22582, 21415, 23027,  20819, 16452, 13233,  23028, 22805, 23029,  \n15161, 10230, 6312,  14249, 19169, 5631,  22814, 22804, 22809,  \n13935, 6545, 3484,  13109, 11615, 22906,  22815, 22091, 22808,  \n4038, 20304, 16977,  22809, 23031, 22814,  2546, 3111, 4780,  \n22814, 23031, 22817,  14028, 18489, 9290,  5363, 5364, 9393,  \n3396, 13198, 10317,  22805, 23033, 23029,  7708, 12902, 15176,  \n23031, 23034, 22817,  21415, 19854, 23032,  19854, 21415, 21419,  \n18216, 1538, 22818,  22350, 22816, 23033,  22805, 22350, 23033,  \n23034, 20945, 22817,  1711, 2033, 18360,  5459, 9684, 693,  \n16979, 17818, 16980,  23034, 22358, 20945,  6064, 2486, 18890,  \n5408, 4742, 14688,  4811, 4184, 4707,  570, 23036, 3338,  \n13219, 10659, 5919,  13446, 13560, 15098,  23037, 22358, 23034,  \n20381, 19856, 21763,  22361, 22358, 23037,  12320, 20461, 12321,  \n4684, 20661, 4683,  19851, 19863, 19862,  23038, 22097, 22356,  \n10271, 10965, 6246,  17318, 16795, 18857,  23577, 22097, 23038,  \n20410, 23039, 3498,  22360, 22821, 21757,  4859, 4860, 18935,  \n19854, 19862, 21768,  11164, 16898, 15795,  20381, 21441, 22113,  \n22113, 21432, 20381,  20795, 21346, 18237,  2218, 3064, 16324,  \n23578, 22360, 22593,  12706, 15701, 11686,  2644, 15188, 11222,  \n15751, 1087, 1961,  22103, 21765, 22590,  23042, 22113, 22112,  \n22594, 22103, 23043,  22594, 22826, 21771,  21778, 21771, 22826,  \n22110, 21437, 22824,  12897, 15343, 12898,  2257, 1892, 1893,  \n11611, 13064, 9254,  22602, 21786, 23044,  19581, 3942, 2622,  \n19201, 8784, 12339,  22598, 21784, 23045,  1810, 6702, 1811,  \n22825, 22110, 23047,  9254, 13064, 9253,  5338, 15871, 11392,  \n2908, 22116, 4674,  22601, 23047, 22110,  6193, 2421, 18190,  \n5014, 10145, 6810,  22371, 22114, 23050,  10544, 2635, 3161,  \n3048, 1919, 1433,  21445, 22829, 22118,  9788, 15645, 12492,  \n23052, 22603, 22604,  23053, 22830, 22373,  12634, 12635, 9737,  \n13986, 8407, 8408,  7407, 2219, 17640,  22830, 23054, 22374,  \n22374, 23054, 22605,  22605, 23054, 23055,  15368, 13870, 14520,  \n22831, 22605, 23056,  21447, 22609, 22604,  22609, 23052, 22604,  \n21717, 17778, 7997,  3880, 20193, 15602,  22610, 22121, 23057,  \n22121, 22375, 22832,  14543, 9081, 10259,  2284, 10291, 16254,  \n22121, 22832, 23057,  1020, 15809, 17588,  10987, 8434, 8536,  \n12379, 15454, 10295,  22610, 23057, 22835,  13851, 18177, 8187,  \n13944, 4868, 7282,  22123, 22835, 22377,  12709, 5042, 21490,  \n22378, 22377, 22835,  22609, 22838, 23059,  22838, 22609, 21800,  \n11318, 3643, 3644,  7969, 7705, 11260,  17904, 3449, 5611,  \n17897, 5136, 9694,  11127, 17568, 13216,  12993, 19584, 16005,  \n4694, 1327, 4693,  15495, 14652, 12774,  22839, 22840, 22126,  \n18058, 7087, 20472,  2079, 5742, 8943,  19638, 12680, 23026,  \n22402, 10203, 29754,  23060, 22842, 22840,  22843, 23061, 23062,  \n22842, 23061, 22843,  2869, 10202, 4874,  22845, 22842, 22844,  \n16254, 16398, 15746,  19018, 20367, 5443,  22847, 22846, 22843,  \n22404, 18795, 11157,  19474, 7732, 7731,  7649, 10329, 15283,  \n4911, 12249, 4415,  13209, 6939, 9929,  23063, 22616, 22383,  \n8041, 13194, 8040,  1882, 6962, 14657,  17248, 884, 20881,  \n15090, 14452, 12373,  23064, 22846, 22847,  13353, 10136, 2015,  \n23067, 23064, 23066,  22622, 23066, 22621,  23067, 23066, 22622,  \n23067, 22622, 22851,  17342, 8800, 5746,  4656, 4655, 14625,  \n18813, 9168, 22389,  23069, 22386, 22387,  22626, 22393, 23072,  \n16320, 1243, 1242,  11242, 22959, 6531,  17248, 12764, 17249,  \n21026, 4552, 1878,  3960, 18262, 3323,  6708, 13909, 2186,  \n7754, 20404, 15827,  11192, 2155, 9665,  20800, 23074, 22903,  \n11217, 17014, 21105,  9225, 11378, 3657,  22447, 22446, 23075,  \n22630, 21027, 22859,  21025, 23076, 22631,  23268, 23077, 23078,  \n16211, 20305, 18324,  13575, 12053, 13576,  3752, 5789, 3751,  \n14931, 17131, 17895,  15775, 17179, 20399,  23079, 23078, 23081,  \n5435, 14941, 19512,  23082, 23077, 23080,  23078, 23077, 23082,  \n21156, 10780, 18018,  19512, 23083, 5435,  14225, 21806, 6929,  \n450, 7656, 13258,  7747, 16882, 7253,  23078, 23082, 23084,  \n23081, 23078, 23084,  23085, 23079, 23081,  23271, 23082, 23080,  \n17682, 8128, 17697,  10685, 19268, 17815,  7493, 9084, 16382,  \n3922, 16357, 753,  17668, 12519, 12520,  10638, 10271, 15846,  \n23081, 23084, 23086,  905, 11610, 20496,  23081, 23086, 23087,  \n23085, 23081, 23087,  6754, 15534, 19181,  14605, 19494, 11870,  \n23084, 23082, 23088,  14281, 19251, 16757,  23085, 23087, 23089,  \n4360, 4361, 14510,  23090, 23084, 23088,  23086, 23084, 23090,  \n19814, 9142, 9141,  5533, 5534, 20932,  23086, 23090, 23091,  \n23087, 23086, 23091,  23087, 23091, 23092,  23089, 23087, 23092,  \n23089, 23092, 23093,  23093, 23096, 23089,  29171, 6409, 7161,  \n8484, 16012, 6557,  23090, 23088, 23091,  1353, 3559, 8801,  \n14956, 10977, 20376,  4470, 9221, 16530,  18387, 15791, 10912,  \n23094, 23091, 23088,  10151, 13317, 7038,  16355, 2759, 8597,  \n23092, 23091, 23095,  23093, 23092, 23095,  23095, 23096, 23093,  \n23097, 23091, 23094,  23097, 23095, 23091,  23095, 23098, 23096,  \n23098, 23095, 23097,  12601, 6723, 6724,  11936, 573, 574,  \n15136, 3919, 20223,  6531, 22385, 24391,  14111, 8546, 7455,  \n10318, 8894, 10561,  20488, 21030, 22633,  6425, 5553, 18162,  \n2910, 2909, 3846,  23102, 20489, 21032,  19687, 16473, 20693,  \n5121, 6609, 6610,  10330, 8118, 19955,  9814, 2747, 3382,  \n1894, 10408, 11105,  22655, 10061, 18310,  22636, 22156, 23104,  \n22636, 22157, 22156,  21035, 21495, 22637,  1248, 3491, 3492,  \n17984, 783, 3202,  21035, 19488, 21495,  5576, 13261, 9322,  \n22401, 23105, 22638,  7848, 19567, 13691,  22866, 22154, 21831,  \n22867, 22638, 23105,  19858, 8465, 22417,  19994, 20507, 23106,  \n1606, 15981, 1607,  16645, 11720, 832,  6876, 6875, 17915,  \n8062, 7451, 7450,  15798, 9815, 18308,  22870, 21840, 22639,  \n21560, 12986, 10443,  14951, 6893, 15364,  5728, 18898, 8766,  \n985, 6204, 12574,  10561, 10562, 19798,  561, 7498, 14344,  \n20126, 13670, 19487,  21831, 21036, 22647,  23109, 22411, 22407,  \n2517, 15385, 16759,  14892, 7087, 6690,  2241, 13086, 12548,  \n11293, 13716, 7114,  5491, 1405, 3493,  3568, 17277, 2990,  \n22646, 22165, 22870,  13961, 21408, 11283,  9366, 14523, 4107,  \n5383, 2801, 12196,  11541, 8858, 11650,  19027, 16425, 3269,  \n22651, 21853, 22873,  14175, 12914, 14048,  15352, 9747, 12468,  \n5006, 14289, 19956,  9466, 6778, 4170,  2723, 7157, 6619,  \n22877, 22875, 22171,  16607, 3997, 16606,  17126, 6159, 21936,  \n12189, 7835, 8027,  4951, 16378, 5239,  335, 16489, 12877,  \n21512, 22651, 23294,  22650, 23111, 22412,  18927, 18926, 19478,  \n21857, 21512, 23294,  21050, 22172, 22660,  1878, 15039, 1877,  \n21857, 23113, 22174,  20530, 22412, 22654,  22174, 23113, 23114,  \n15655, 2313, 18189,  3903, 15520, 16789,  6206, 16679, 22024,  \n22174, 23114, 22656,  1406, 13843, 3567,  5318, 2508, 9804,  \n886, 885, 10403,  3599, 13071, 1042,  18898, 6673, 15541,  \n6098, 6097, 1402,  22880, 22414, 22656,  7572, 9261, 11765,  \n22880, 22883, 22657,  22657, 22883, 22886,  22657, 22886, 22176,  \n22176, 22886, 22416,  3029, 12532, 23115,  21477, 10699, 10700,  \n22884, 23117, 22186,  22884, 23116, 23117,  22660, 21523, 22185,  \n9780, 9779, 19495,  4090, 14979, 22514,  2392, 9475, 2870,  \n14664, 14420, 14419,  21870, 23297, 22878,  22186, 23117, 22420,  \n16912, 11098, 5500,  15751, 20760, 14929,  13821, 19597, 3144,  \n23119, 22888, 22662,  22276, 3236, 9603,  1991, 12147, 13165,  \n23120, 23119, 22662,  21870, 21873, 23297,  22891, 22420, 23117,  \n13690, 23792, 1290,  22185, 23121, 22660,  15879, 6785, 11873,  \n3451, 8506, 12671,  22667, 22424, 23123,  22669, 22666, 23633,  \n11511, 13852, 11510,  20413, 16246, 7598,  9551, 17160, 2605,  \n19299, 8257, 17876,  6125, 16608, 11504,  23124, 22190, 22196,  \n15145, 16409, 21485,  293, 12325, 2851,  8946, 8945, 16758,  \n23127, 22196, 21110,  20168, 6415, 15745,  21209, 14703, 645,  \n4057, 4058, 9378,  20325, 9993, 12777,  22202, 22669, 22206,  \n12412, 21539, 1653,  22668, 23128, 23129,  23129, 22428, 22668,  \n716, 11390, 11396,  22896, 21884, 23309,  22201, 22896, 23130,  \n12955, 8551, 8552,  23130, 22896, 23131,  4667, 14960, 3663,  \n23129, 21111, 22203,  5067, 5068, 9470,  23130, 22436, 22201,  \n12774, 14652, 23133,  10597, 2793, 3684,  4426, 1415, 2986,  \n13982, 13981, 5317,  22673, 21890, 22675,  11333, 3302, 22369,  \n22901, 22207, 22436,  21166, 20193, 22264,  16912, 8617, 11098,  \n5777, 2113, 3860,  811, 810, 9287,  22900, 22673, 22675,  \n22441, 22898, 22431,  1766, 1767, 3292,  10174, 1581, 9725,  \n6635, 4704, 5504,  5188, 9156, 1340,  11551, 3945, 17599,  \n23135, 22900, 22444,  11105, 1735, 5007,  492, 9493, 29449,  \n23137, 22902, 22901,  12301, 23138, 2268,  23316, 23135, 22677,  \n21901, 22905, 22907,  21280, 9666, 6083,  15991, 4550, 21769,  \n15262, 591, 3836,  9238, 1624, 1623,  18683, 23140, 18684,  \n9875, 1945, 16415,  22907, 23141, 21903,  7240, 9462, 1397,  \n11054, 3820, 3822,  23141, 22223, 21903,  7272, 20337, 7631,  \n15575, 21175, 2966,  12269, 14228, 22745,  549, 2604, 11381,  \n21915, 22684, 22679,  23142, 22679, 22684,  10405, 4552, 10404,  \n23143, 22216, 21161,  11812, 19914, 13195,  12119, 12120, 10367,  \n22681, 22452, 23144,  23145, 22910, 22221,  23141, 22913, 22223,  \n18727, 7361, 15614,  22686, 23143, 21161,  23145, 22221, 22685,  \n21921, 22683, 22691,  5605, 19938, 14920,  9636, 4541, 10434,  \n22223, 22913, 22457,  19139, 6153, 15305,  542, 19911, 18146,  \n22915, 22686, 22687,  23148, 9249, 13594,  22226, 19463, 21241,  \n1497, 5246, 29206,  17529, 17144, 21936,  21926, 22690, 22685,  \n22456, 21922, 23150,  22913, 22916, 22457,  17384, 11339, 13180,  \n14962, 11556, 13479,  15081, 14087, 15504,  2204, 14739, 2429,  \n17707, 19311, 20537,  23152, 22915, 23151,  23151, 22915, 22917,  \n18623, 15051, 15050,  16730, 14286, 15998,  14145, 7247, 5390,  \n22318, 2497, 20399,  22918, 22689, 22697,  7211, 16546, 11843,  \n21096, 21962, 18815,  16993, 5412, 5414,  22917, 22922, 23151,  \n595, 21473, 594,  10760, 10474, 13902,  5805, 18518, 4088,  \n12909, 5263, 22950,  23156, 23151, 22922,  343, 345, 21361,  \n3221, 15253, 3222,  22463, 22916, 22927,  21928, 22697, 22689,  \n1161, 6283, 1159,  22462, 22695, 23162,  1981, 9098, 11650,  \n23156, 22922, 22929,  2971, 5420, 6654,  9330, 17507, 3180,  \n22460, 23154, 22465,  23158, 22697, 22235,  9057, 1159, 6283,  \n22928, 22461, 22234,  23159, 22929, 22480,  6639, 16971, 6638,  \n7145, 7683, 14507,  20653, 23807, 390,  8875, 3590, 13701,  \n15650, 407, 14903,  23160, 22465, 23154,  21600, 22927, 23161,  \n446, 15583, 5299,  19795, 5633, 21640,  10881, 1424, 15433,  \n2688, 11301, 6573,  15139, 1223, 16412,  23159, 22480, 22932,  \n17441, 4258, 10346,  23140, 8050, 18684,  23163, 23159, 22932,  \n17972, 14366, 3694,  3257, 2156, 11657,  18294, 20359, 8831,  \n22469, 21600, 23161,  5371, 7461, 7985,  1109, 3160, 1110,  \n15062, 22765, 10981,  18455, 6923, 8687,  299, 10517, 23164,  \n22477, 22465, 23165,  10968, 8293, 16190,  6210, 11748, 6881,  \n23166, 22238, 22933,  14767, 9139, 7022,  23168, 23169, 22469,  \n6903, 22194, 3476,  22707, 22705, 22478,  8159, 21062, 19450,  \n664, 15399, 665,  1789, 1791, 17924,  22706, 22941, 22932,  \n22940, 22477, 23165,  13667, 2576, 15672,  23166, 22933, 22936,  \n21937, 22238, 23166,  18770, 2494, 18769,  12825, 12826, 14878,  \n7461, 1882, 14657,  23338, 23163, 22718,  5660, 3220, 16296,  \n7943, 16283, 11692,  16609, 21999, 8543,  6381, 1086, 1345,  \n21219, 22469, 23169,  1750, 8619, 15339,  9235, 20334, 18584,  \n4833, 9986, 13257,  19116, 12385, 9589,  22476, 22241, 23171,  \n19567, 18587, 5253,  17655, 17370, 20871,  3374, 9343, 1783,  \n7379, 22409, 3495,  11833, 22709, 7088,  20934, 10209, 13844,  \n3846, 19589, 2910,  21518, 14588, 18150,  21219, 23169, 22946,  \n4462, 16026, 9257,  14962, 8834, 14961,  10318, 13626, 11247,  \n14579, 6672, 427,  13393, 7721, 5494,  17909, 22447, 23075,  \n14706, 3697, 9615,  2838, 13700, 1077,  14446, 21186, 16282,  \n17329, 23172, 17330,  19890, 8525, 16956,  22947, 22245, 22485,  \n2674, 22155, 16539,  22253, 16692, 12281,  537, 536, 12043,  \n483, 482, 1726,  22725, 22946, 23173,  11614, 22526, 9315,  \n14154, 7680, 14614,  22725, 23173, 22951,  20474, 13660, 17747,  \n22729, 23175, 22498,  21280, 6551, 9666,  22948, 22726, 22951,  \n23176, 22948, 22951,  19702, 22419, 20658,  15299, 12142, 3465,  \n22948, 23176, 22952,  16688, 1215, 16689,  15174, 16194, 13482,  \n15080, 6656, 18816,  9173, 9152, 17449,  773, 12481, 12480,  \n14248, 8981, 6580,  11434, 18926, 12413,  1284, 20923, 19812,  \n22730, 22510, 22511,  2395, 2396, 10202,  9779, 19496, 19495,  \n19210, 19237, 11921,  21955, 22512, 22729,  22731, 22949, 22952,  \n19846, 7474, 8504,  15381, 16266, 19199,  22729, 22512, 23179,  \n10100, 11012, 10110,  20831, 21298, 12979,  7212, 10525, 7213,  \n17392, 913, 19409,  9285, 2800, 6103,  12006, 1198, 11245,  \n22963, 22732, 22513,  11533, 21237, 16485,  23179, 22512, 22960,  \n22957, 22731, 23180,  22961, 22508, 22957,  5895, 5451, 5452,  \n12293, 16249, 12696,  15006, 13357, 14134,  22269, 22956, 22964,  \n3077, 6692, 16195,  23181, 22961, 22957,  20108, 15619, 21672,  \n22741, 22961, 23181,  5208, 18082, 14865,  6827, 818, 3932,  \n13671, 2860, 5056,  12797, 776, 2802,  1530, 462, 18951,  \n4152, 14270, 1762,  4468, 12615, 11896,  22271, 22969, 22960,  \n11530, 1055, 15453,  22739, 22968, 22967,  22269, 22964, 21986,  \n21052, 15934, 9729,  15606, 5049, 21319,  3756, 2849, 10808,  \n23181, 23359, 22741,  15808, 23182, 14884,  22969, 22747, 22970,  \n22515, 22273, 22741,  22515, 22741, 22743,  14040, 18997, 20611,  \n5120, 5121, 15748,  11779, 15463, 11780,  22968, 22281, 22971,  \n18449, 21538, 5925,  21169, 3244, 15382,  686, 687, 23112,  \n22744, 22743, 23184,  10308, 7901, 8017,  21168, 2092, 9151,  \n22747, 22282, 22522,  8144, 14049, 4595,  23185, 22746, 22516,  \n4185, 12423, 13356,  18785, 18784, 12605,  3872, 3931, 14940,  \n4659, 4660, 21521,  17385, 22036, 22750,  10124, 13443, 9345,  \n6915, 9435, 6993,  3487, 20399, 2497,  17634, 18753, 1272,  \n9085, 5673, 4865,  5024, 7212, 8253,  22974, 22754, 24006,  \n12517, 5856, 4960,  12085, 13513, 15432,  22973, 22287, 22523,  \n8159, 19450, 8945,  11285, 4367, 2216,  15059, 21190, 5235,  \n12349, 4854, 10990,  4503, 22820, 1174,  17541, 22052, 15525,  \n22297, 22530, 22972,  11833, 11832, 15776,  6943, 3016, 10298,  \n8167, 6764, 21838,  9396, 21092, 5603,  23188, 22972, 22530,  \n22759, 22532, 22974,  16811, 21387, 21388,  22976, 22978, 22757,  \n10938, 14937, 2090,  15402, 10623, 5053,  1138, 1137, 6871,  \n15523, 19375, 4796,  10786, 17368, 10333,  16292, 17368, 10577,  \n8570, 5790, 13603,  21503, 11942, 18637,  16897, 10641, 2803,  \n23191, 22764, 22978,  22064, 5363, 496,  11720, 11719, 18904,  \n13525, 20615, 1869,  8884, 9852, 8885,  6735, 19719, 12039,  \n11032, 11427, 19121,  2485, 6064, 2561,  22766, 22767, 23192,  \n10094, 3149, 2304,  621, 13531, 13532,  22316, 22307, 23197,  \n18079, 18080, 19010,  20911, 18856, 997,  3169, 515, 2459,  \n22767, 22539, 22310,  22768, 22538, 22984,  3307, 12298, 3308,  \n1387, 10248, 16253,  10503, 2303, 1190,  23199, 22985, 22771,  \n10859, 12656, 11334,  7230, 2410, 4484,  22316, 23197, 22987,  \n11033, 12670, 11032,  9715, 831, 3685,  22985, 22541, 22771,  \n22310, 22315, 22986,  879, 6306, 11339,  18037, 3064, 12365,  \n9105, 9094, 11670,  21648, 21007, 9346,  13364, 9731, 983,  \n22311, 22769, 22991,  14644, 19635, 7062,  22315, 22326, 22990,  \n14250, 16261, 10287,  22988, 22315, 22990,  16395, 21226, 2345,  \n1964, 19120, 9647,  22772, 22311, 22991,  11350, 5021, 15017,  \n10555, 15617, 10542,  20726, 3317, 22611,  11457, 13392, 12023,  \n22993, 22771, 22319,  23203, 6697, 2028,  17716, 2212, 12186,  \n15386, 2867, 13515,  2774, 23205, 19542,  8948, 6028, 2892,  \n18583, 13588, 13151,  15184, 5445, 21953,  22322, 23206, 22552,  \n23204, 22992, 22326,  18482, 1778, 21094,  756, 9048, 19946,  \n12782, 12781, 19145,  23204, 22060, 22777,  12601, 11275, 10723,  \n9833, 2741, 5912,  4066, 13450, 16134,  2449, 9461, 21424,  \n16086, 21668, 13651,  7650, 13937, 20417,  22545, 22772, 22998,  \n23204, 22777, 23209,  19868, 12868, 17536,  5872, 12341, 3586,  \n22546, 22774, 23208,  2668, 2010, 6939,  22555, 22552, 22999,  \n1170, 10655, 5355,  9134, 6407, 4453,  1609, 5138, 1610,  \n8477, 15257, 18916,  21416, 9962, 12410,  10831, 18356, 9786,  \n19257, 4128, 15372,  22563, 22779, 22561,  12408, 23210, 20635,  \n2170, 837, 9089,  3705, 3710, 1829,  22219, 6422, 5621,  \n14199, 15054, 14923,  12361, 14660, 3623,  23211, 23003, 22566,  \n22558, 23212, 22562,  6853, 12458, 6854,  23002, 22563, 22073,  \n23004, 23000, 22778,  3080, 9658, 12595,  15270, 21835, 11473,  \n23004, 22778, 23215,  12736, 17014, 22046,  22778, 23217, 23215,  \n22778, 22784, 23217,  14839, 14203, 17429,  10499, 13159, 20815,  \n22784, 23009, 23217,  13719, 4478, 13756,  22784, 22786, 23009,  \n4902, 7019, 4901,  2676, 12947, 10573,  5425, 8059, 8058,  \n3140, 805, 3141,  22788, 22568, 23010,  4308, 6844, 18164,  \n14650, 11770, 10090,  23012, 22574, 22569,  23010, 22568, 22345,  \n22345, 22791, 23010,  23010, 22791, 23219,  22797, 23221, 23013,  \n23013, 23221, 23220,  23015, 23221, 22797,  22791, 22345, 22794,  \n9684, 6514, 693,  9863, 6003, 17662,  23013, 23220, 23014,  \n23222, 1456, 7197,  1324, 10719, 10718,  15289, 18465, 18545,  \n22342, 22574, 22792,  22792, 21740, 22342,  10180, 16612, 10179,  \n23014, 23224, 23018,  11502, 14345, 11503,  22798, 23021, 23016,  \n21568, 14744, 12993,  2281, 13067, 13068,  20253, 13158, 20252,  \n20095, 17310, 10188,  10742, 23200, 6047,  15467, 9564, 19447,  \n23224, 23225, 23018,  11366, 394, 393,  17936, 19991, 11161,  \n6074, 7723, 19527,  313, 19512, 1124,  12909, 20900, 676,  \n23021, 23020, 23226,  18916, 5256, 8477,  23225, 23227, 23018,  \n3255, 12883, 14300,  23226, 23020, 23024,  23226, 23024, 23228,  \n8411, 20091, 23229,  18140, 19899, 13044,  22802, 23028, 23017,  \n17925, 2093, 4151,  23227, 22806, 23018,  23023, 23024, 23020,  \n20935, 6006, 9844,  23024, 22578, 23228,  22811, 23228, 22578,  \n5375, 15975, 16299,  23027, 23230, 22811,  2993, 15901, 1351,  \n23227, 23232, 22806,  23233, 22806, 23232,  6912, 18639, 996,  \n16635, 22067, 16634,  21415, 23032, 23027,  7952, 7951, 21163,  \n17146, 19335, 15608,  15942, 15941, 18292,  669, 11110, 8270,  \n17722, 11045, 16580,  22807, 23030, 22809,  22809, 23030, 23031,  \n9728, 8990, 9000,  15168, 5781, 8412,  22807, 23233, 23030,  \n11557, 4036, 17738,  19855, 23032, 19854,  16921, 2672, 10594,  \n23234, 23034, 23031,  23234, 23031, 23030,  11117, 3319, 1588,  \n18477, 6194, 8431,  22586, 22580, 22815,  22587, 21768, 21432,  \n16858, 23235, 5815,  22544, 12350, 6752,  6481, 12337, 12542,  \n10694, 4285, 3521,  15923, 15812, 4576,  23037, 23034, 23234,  \n17305, 20951, 19857,  22356, 22586, 23237,  16864, 1518, 20036,  \n22781, 18465, 7416,  12932, 4850, 3574,  4942, 9736, 9735,  \n21376, 14412, 13162,  15539, 12388, 14188,  7835, 7836, 8027,  \n13817, 12776, 421,  20241, 663, 4680,  22589, 22097, 23577,  \n22360, 23578, 23040,  8027, 7836, 8026,  22361, 23041, 23044,  \n21786, 22361, 23044,  16157, 7320, 12971,  2406, 10987, 8535,  \n19443, 18869, 5994,  21360, 1659, 1658,  3745, 8058, 4876,  \n15895, 16665, 15896,  23043, 22103, 22590,  23042, 23238, 22113,  \n12733, 19791, 19790,  23239, 23043, 22590,  13885, 876, 15230,  \n15509, 726, 2909,  9642, 16567, 1963,  11481, 6603, 3385,  \n1568, 18319, 19806,  19635, 19294, 3462,  2276, 19351, 3490,  \n7130, 11695, 19391,  5540, 14580, 5541,  3618, 11046, 14821,  \n5231, 1142, 1144,  9672, 9673, 11739,  21784, 22365, 23045,  \n16421, 16422, 1021,  22825, 23047, 23240,  23807, 2763, 390,  \n8797, 4588, 2321,  22112, 22368, 23049,  22114, 22602, 23752,  \n9911, 19502, 14277,  17496, 3499, 12406,  12105, 1042, 16062,  \n23241, 22603, 23052,  21191, 6740, 8524,  9465, 11791, 11219,  \n9300, 12024, 16819,  2201, 9318, 2200,  6073, 5187, 6071,  \n15819, 16287, 12270,  10963, 15391, 10966,  756, 7631, 9048,  \n22830, 22119, 22373,  598, 597, 22293,  7783, 20554, 22466,  \n17971, 22153, 23243,  23055, 23056, 22605,  17078, 17413, 1145,  \n1318, 5281, 12578,  4172, 4174, 849,  23244, 23052, 22609,  \n7065, 7767, 9848,  22832, 22831, 23245,  23057, 22832, 23245,  \n4492, 13711, 20803,  18721, 17823, 8135,  23059, 23244, 22609,  \n22835, 23057, 23246,  5863, 8481, 1660,  22378, 22835, 23247,  \n13222, 17177, 13223,  16134, 13450, 12108,  17802, 19971, 4888,  \n14953, 2959, 14954,  10888, 19264, 18828,  22378, 23247, 22125,  \n23248, 22125, 23247,  20837, 14394, 23249,  22126, 22125, 23248,  \n23250, 22839, 23248,  9813, 7333, 7849,  22839, 22126, 23248,  \n4231, 9004, 2950,  5032, 4602, 19396,  14190, 22652, 12733,  \n19156, 10875, 16232,  23250, 23424, 23060,  6605, 15495, 12774,  \n22839, 23250, 22840,  23060, 22840, 23250,  22380, 22128, 23252,  \n23253, 23061, 23060,  23060, 23061, 22842,  5682, 9855, 14908,  \n6372, 19837, 12842,  6547, 1987, 1986,  20491, 9449, 13542,  \n19118, 13930, 14046,  22128, 22136, 23252,  3916, 670, 671,  \n19353, 6311, 678,  23254, 22843, 23062,  1485, 11165, 1486,  \n5601, 5603, 8574,  23254, 22847, 22843,  23063, 23255, 22616,  \n22847, 23254, 23257,  9130, 9812, 15605,  16674, 3256, 3257,  \n15294, 13765, 11533,  23256, 22383, 22617,  22847, 23257, 23064,  \n667, 5574, 594,  8434, 9234, 12222,  5638, 6462, 19536,  \n8699, 1130, 11534,  22617, 22621, 23258,  23257, 22621, 23066,  \n23257, 23258, 22621,  23064, 23257, 23066,  21805, 22849, 22136,  \n8176, 20476, 5413,  6390, 1870, 16695,  23065, 22853, 22139,  \n23065, 23259, 22853,  10885, 8926, 3534,  22386, 23767, 21807,  \n21807, 21465, 22386,  708, 709, 1282,  23602, 22390, 22853,  \n4634, 10266, 9724,  21000, 22142, 23068,  20189, 23112, 20844,  \n9475, 2686, 9730,  23260, 22626, 23072,  22393, 23261, 23072,  \n17515, 12688, 12689,  6287, 4073, 2098,  21029, 18344, 19052,  \n23261, 22393, 22856,  8975, 19012, 21326,  23261, 22856, 23263,  \n6835, 4272, 949,  2981, 14539, 9989,  22856, 22394, 22395,  \n5874, 11362, 14443,  23265, 22395, 22630,  8506, 8380, 15443,  \n23264, 22629, 21484,  20154, 17579, 1599,  23265, 22630, 23266,  \n22859, 23266, 22630,  5660, 12581, 4995,  316, 10301, 10776,  \n21314, 9640, 13527,  22078, 627, 18154,  2034, 16220, 6980,  \n18707, 18786, 4739,  5855, 2487, 12484,  2701, 5436, 3167,  \n23080, 23077, 23270,  8105, 8107, 388,  23269, 23268, 23079,  \n8192, 9720, 9719,  294, 15390, 18708,  23271, 23080, 23270,  \n23268, 23078, 23079,  7951, 22871, 21163,  10317, 13198, 6310,  \n23269, 23079, 23273,  3846, 24254, 13867,  4108, 18422, 22965,  \n14561, 10353, 1631,  13221, 19892, 17908,  10672, 7715, 7716,  \n14982, 15579, 7116,  4699, 17948, 9428,  6471, 18831, 14854,  \n23079, 23085, 23273,  23085, 23442, 23273,  6281, 6280, 546,  \n23082, 23271, 23274,  23089, 23275, 23085,  18704, 10235, 13321,  \n9667, 10753, 19269,  23082, 23274, 23088,  4588, 8821, 4589,  \n10099, 1883, 10100,  23274, 23276, 23088,  18467, 1317, 16907,  \n12206, 16711, 19932,  23089, 23096, 23277,  20743, 16997, 6751,  \n6116, 7304, 6117,  23279, 23277, 23096,  23094, 23088, 23276,  \n5900, 6411, 3625,  16396, 14006, 14007,  3378, 4944, 5285,  \n5480, 2117, 16868,  23098, 23280, 23096,  23096, 23280, 23279,  \n3513, 13653, 490,  23094, 23281, 23097,  23281, 23098, 23097,  \n18605, 7203, 10418,  12545, 12544, 4696,  9518, 8951, 22013,  \n21076, 18983, 6225,  15416, 13868, 14743,  23102, 22156, 20489,  \n16884, 16726, 567,  17202, 4828, 6583,  11960, 19536, 6462,  \n20911, 11548, 18856,  14724, 11966, 14620,  22637, 22864, 22401,  \n23455, 21495, 19488,  14099, 4170, 21712,  9614, 20216, 19707,  \n22867, 23105, 23286,  7473, 8330, 1847,  21247, 18152, 9847,  \n14804, 6002, 19106,  3767, 10632, 3795,  1336, 4781, 16402,  \n23286, 22868, 22867,  23286, 23289, 22868,  956, 9537, 6438,  \n23106, 20507, 21045,  12390, 9790, 13256,  4000, 7366, 4457,  \n23289, 22641, 22868,  22866, 21831, 23466,  17602, 3212, 8807,  \n22641, 23289, 23290,  14391, 7403, 1870,  13427, 17768, 19599,  \n12866, 7576, 7577,  19848, 11392, 19046,  21045, 22163, 22644,  \n20231, 6693, 17702,  22642, 21852, 22411,  5015, 10499, 13212,  \n10854, 460, 3852,  23290, 22873, 22641,  16697, 18901, 11396,  \n23293, 22645, 22646,  22646, 23108, 23293,  7458, 10009, 10251,  \n22646, 22870, 23108,  15114, 13600, 20573,  21510, 21511, 22642,  \n22648, 21510, 22642,  12184, 5193, 20709,  23465, 22875, 22877,  \n7224, 5977, 8415,  8213, 3442, 4519,  922, 3975, 17738,  \n20661, 7398, 4683,  15153, 18420, 1595,  14912, 12522, 12639,  \n14292, 15070, 14985,  18070, 11026, 11025,  23295, 22173, 22878,  \n23294, 23113, 21857,  21416, 16125, 9962,  1550, 15790, 1549,  \n4454, 10747, 23296,  16120, 19667, 10182,  4356, 22899, 21558,  \n18940, 15156, 12054,  3406, 22144, 3407,  3028, 12532, 3029,  \n22787, 14363, 9115,  22883, 23116, 22886,  4070, 18233, 14755,  \n1937, 13501, 1938,  22886, 23116, 22884,  14642, 5295, 21601,  \n23299, 22665, 22888,  12435, 4574, 5511,  23299, 22888, 23119,  \n23301, 23299, 23119,  11874, 4274, 21564,  9591, 480, 3771,  \n1594, 11164, 11163,  22882, 22885, 22662,  23120, 22662, 22885,  \n14100, 16029, 10521,  18155, 16424, 4345,  13214, 8065, 13215,  \n3879, 4163, 11534,  9345, 491, 3531,  22665, 23304, 22892,  \n23305, 23297, 21873,  13953, 4511, 6171,  23262, 16957, 23243,  \n23306, 22891, 23117,  22891, 23306, 23122,  22892, 23304, 22666,  \n23307, 8491, 7186,  20696, 21252, 21251,  1163, 17429, 17428,  \n8280, 18931, 1815,  22891, 23122, 23123,  22891, 23123, 22424,  \n22667, 21871, 22424,  1015, 13855, 7785,  22191, 22667, 23125,  \n6618, 9872, 4487,  6336, 10345, 10415,  6179, 16104, 2450,  \n22191, 23125, 22193,  15769, 10971, 4632,  2857, 12239, 12298,  \n17581, 11665, 5225,  16013, 11391, 6623,  21533, 22193, 23126,  \n21533, 23126, 22668,  12057, 17479, 14852,  8733, 12297, 18276,  \n4459, 15857, 17378,  13699, 18552, 13700,  22198, 21881, 23309,  \n16938, 10775, 4353,  410, 15798, 18602,  22206, 22435, 22672,  \n15734, 1813, 1450,  14414, 1642, 2902,  19123, 4075, 5675,  \n12875, 16258, 20128,  23129, 23128, 21111,  21187, 7444, 11750,  \n7501, 15198, 18363,  2208, 2207, 11065,  8197, 8198, 11363,  \n23311, 21896, 23128,  21111, 23128, 21896,  22897, 21100, 22434,  \n13978, 13294, 4551,  15023, 13328, 15295,  22674, 21896, 23311,  \n8649, 1638, 2641,  9829, 1880, 14829,  15465, 4043, 14818,  \n12672, 8781, 13167,  22904, 22674, 23314,  23312, 22673, 22900,  \n10647, 19586, 7308,  2893, 2892, 3168,  4460, 10564, 15858,  \n9378, 16969, 22344,  23313, 23312, 22900,  22434, 21888, 21897,  \n7105, 9687, 5631,  23313, 23135, 23316,  23313, 22900, 23135,  \n1656, 8944, 4185,  6312, 10230, 17408,  23317, 15014, 18404,  \n22902, 22212, 22901,  10136, 4004, 2014,  11679, 9411, 16015,  \n29105, 16531, 666,  21485, 20008, 16924,  22905, 22902, 23137,  \n10368, 9078, 13456,  12134, 1831, 6927,  14706, 3401, 3402,  \n22905, 23137, 23318,  22905, 23318, 23320,  23316, 22677, 22909,  \n22679, 23321, 21897,  17743, 22019, 1971,  16412, 3334, 15139,  \n8699, 16789, 13587,  22905, 23320, 22907,  18786, 18707, 10913,  \n22910, 22909, 22450,  23143, 23650, 22441,  2841, 12384, 12382,  \n995, 17155, 4184,  6928, 17963, 8184,  11441, 14262, 947,  \n7142, 8066, 16838,  5433, 11782, 8016,  23143, 22441, 22216,  \n22683, 21164, 22678,  7294, 9918, 7295,  6434, 15371, 20709,  \n1148, 19574, 13017,  22686, 23324, 23143,  7261, 12287, 19640,  \n18251, 9622, 7632,  7356, 18095, 19324,  3121, 17616, 17281,  \n10090, 5765, 16652,  2484, 2127, 16926,  5505, 5080, 11565,  \n16047, 16885, 16048,  15661, 10230, 23326,  5102, 13843, 3871,  \n4397, 7646, 7647,  1603, 15937, 1602,  22721, 3944, 5653,  \n5600, 5537, 20063,  13877, 14824, 19718,  6592, 13880, 15689,  \n23205, 8930, 19542,  16396, 2159, 14006,  8157, 15409, 19795,  \n9367, 2088, 6452,  2813, 8825, 18468,  23327, 22686, 22915,  \n16756, 2011, 2010,  23328, 22913, 23141,  2123, 2122, 11829,  \n11254, 10227, 2889,  9452, 787, 16815,  17431, 18980, 1026,  \n22227, 22912, 23329,  806, 808, 15087,  15234, 15233, 11931,  \n22913, 23328, 22916,  13170, 8513, 23330,  8936, 21008, 17370,  \n23153, 22460, 22227,  8814, 17010, 15228,  23153, 22227, 23329,  \n632, 8958, 4440,  1559, 17500, 5693,  17059, 1442, 7877,  \n22916, 23328, 22921,  12438, 20966, 6437,  13872, 10636, 15459,  \n11664, 18091, 11665,  13416, 9018, 5556,  23331, 23332, 22921,  \n22460, 23153, 23154,  23154, 23153, 23155,  23333, 21927, 22461,  \n1846, 11459, 5422,  23493, 22929, 23159,  9849, 13566, 10485,  \n16487, 17931, 17930,  11443, 7056, 6830,  23335, 22927, 22921,  \n8183, 1362, 4624,  7131, 8793, 15954,  1159, 4411, 1160,  \n21600, 22463, 22927,  12569, 23336, 13096,  15479, 4843, 5797,  \n12498, 10773, 1853,  6264, 4316, 13878,  23337, 22237, 23162,  \n22928, 22234, 21934,  16121, 14673, 13817,  6100, 6490, 1374,  \n23163, 23338, 23159,  674, 676, 13754,  13901, 9865, 10457,  \n13029, 6064, 16747,  5058, 3230, 16798,  16939, 3084, 2545,  \n22932, 22941, 23163,  6276, 20540, 12045,  21934, 22467, 23340,  \n23168, 22469, 23161,  11468, 9230, 689,  22465, 23160, 23165,  \n16133, 20401, 18040,  7244, 24631, 5211,  18053, 3641, 18728,  \n12309, 6748, 1037,  22239, 22935, 22467,  2818, 15665, 20991,  \n2842, 14486, 13039,  9043, 8567, 8568,  14223, 10664, 9236,  \n22718, 22717, 23338,  22717, 23342, 23338,  8260, 14957, 7378,  \n22935, 22239, 22476,  16510, 17513, 2876,  11487, 3724, 12457,  \n22707, 23344, 22705,  5858, 5857, 8853,  17528, 2644, 17868,  \n22036, 7960, 22750,  2810, 20491, 13542,  22940, 23165, 23345,  \n14177, 12664, 19879,  4319, 17105, 4318,  10947, 3157, 3156,  \n2908, 4674, 7711,  20465, 15583, 446,  11257, 11539, 19294,  \n12639, 5004, 11117,  15224, 17739, 6896,  22944, 21937, 23166,  \n23171, 22241, 22710,  5985, 2687, 6437,  16413, 11101, 21719,  \n2280, 19600, 23347,  23348, 18652, 9454,  22717, 22723, 23174,  \n22485, 23349, 23350,  2572, 5321, 4158,  3533, 17433, 17012,  \n23349, 22485, 22944,  6754, 19181, 17379,  23173, 22946, 23169,  \n16372, 23148, 13597,  22494, 22940, 23345,  22947, 23351, 22710,  \n15658, 7085, 18599,  20062, 5136, 7675,  22723, 22730, 23177,  \n22494, 23345, 22506,  23174, 22723, 23177,  20367, 21811, 10084,  \n21185, 16403, 7608,  22731, 22952, 23176,  18733, 9659, 23287,  \n17426, 15483, 15087,  23177, 22730, 22732,  12451, 4456, 4455,  \n22731, 23176, 23354,  22732, 23355, 23177,  8257, 2914, 17876,  \n14278, 17847, 18586,  1686, 9071, 9070,  23356, 23355, 22732,  \n3883, 8307, 19272,  22729, 23179, 23352,  9827, 11030, 1614,  \n12410, 9962, 13813,  11095, 3654, 11096,  8595, 21154, 8594,  \n4838, 11581, 17183,  14741, 4896, 12001,  4230, 19068, 10704,  \n22732, 22963, 23356,  18378, 8531, 18759,  14830, 12169, 16576,  \n2311, 18027, 5665,  12686, 12929, 14806,  14830, 1680, 12169,  \n14239, 14241, 10458,  17065, 1507, 14896,  23180, 23358, 22957,  \n18234, 16811, 21388,  14223, 9236, 14850,  22269, 21956, 22956,  \n23359, 22957, 23358,  3171, 16598, 1373,  18532, 4747, 9634,  \n21502, 21501, 17940,  874, 10887, 875,  23181, 22957, 23359,  \n7348, 22458, 17452,  19364, 18202, 14215,  7348, 2771, 5148,  \n23364, 22967, 22968,  20096, 12589, 2991,  20657, 2433, 10046,  \n11882, 20543, 1480,  3967, 1750, 18351,  21986, 22964, 22742,  \n23203, 2028, 8754,  22743, 22741, 23359,  13640, 19458, 13641,  \n16323, 9529, 8974,  2921, 696, 13483,  23183, 22969, 22970,  \n12881, 15832, 7221,  1813, 15734, 20244,  12011, 6489, 8099,  \n22968, 22971, 23364,  12464, 20221, 16064,  1774, 12846, 1775,  \n17872, 872, 20659,  22516, 22742, 23366,  19065, 14576, 19502,  \n16024, 17466, 11718,  5670, 9173, 4205,  13180, 22655, 12323,  \n18210, 7657, 8373,  391, 21388, 4660,  22747, 22522, 22970,  \n23367, 3407, 22144,  9278, 6726, 6725,  23157, 15057, 12230,  \n7254, 14534, 3478,  3537, 17401, 19040,  20658, 17066, 718,  \n23368, 22522, 22756,  6832, 1651, 4097,  1715, 3023, 1713,  \n2221, 9678, 12021,  4972, 15561, 15560,  12670, 17773, 5815,  \n8527, 5711, 11272,  13077, 3036, 15161,  2879, 7803, 3321,  \n21501, 21747, 17940,  23369, 22749, 22751,  11588, 5987, 22295,  \n1423, 15416, 14743,  15789, 13769, 5172,  19340, 19392, 19388,  \n17084, 17471, 13509,  6604, 10440, 5702,  6355, 15295, 4797,  \n4005, 4004, 11432,  23187, 22973, 22523,  1757, 14918, 14974,  \n22528, 22758, 23373,  18172, 13471, 15494,  22758, 23374, 23373,  \n9345, 10444, 491,  10894, 5240, 2785,  22530, 22762, 23188,  \n6438, 22017, 2165,  22978, 22976, 23375,  15505, 21142, 1493,  \n14323, 6529, 8761,  20121, 8048, 19946,  17470, 3564, 14933,  \n14083, 1379, 4110,  11071, 16548, 11072,  6828, 4249, 22324,  \n4300, 6880, 6882,  2564, 8185, 14814,  22762, 23195, 23376,  \n3973, 6799, 6798,  22766, 23192, 22761,  6502, 7413, 6759,  \n22296, 22619, 10635,  3266, 8310, 295,  7400, 19491, 14569,  \n10937, 1118, 11861,  15604, 887, 19212,  22764, 23191, 22536,  \n1247, 15152, 12316,  22762, 22985, 23195,  1118, 10937, 11166,  \n1595, 7021, 7022,  6284, 22869, 9276,  22985, 23530, 23195,  \n22307, 22982, 23197,  21228, 4991, 3711,  10446, 10445, 19438,  \n7149, 4700, 1647,  16724, 3725, 18941,  6958, 15062, 13565,  \n22767, 22310, 22986,  14600, 12955, 471,  23198, 22768, 22984,  \n7378, 9894, 15995,  21456, 23379, 7883,  1605, 5684, 17186,  \n6424, 4330, 10558,  11583, 718, 11584,  23198, 23380, 22768,  \n16922, 4328, 5156,  15714, 6230, 9132,  20312, 11932, 22612,  \n1815, 22980, 8280,  12010, 5128, 13230,  14282, 8049, 14283,  \n6696, 16735, 4715,  12748, 18710, 9488,  5207, 2827, 2828,  \n22322, 22987, 23202,  9175, 2114, 2113,  21478, 17614, 18918,  \n7753, 1472, 693,  12663, 560, 8014,  23385, 22772, 22991,  \n22272, 14876, 21449,  16759, 20734, 16760,  6257, 6258, 9820,  \n23204, 22326, 22060,  9825, 707, 17881,  14213, 4496, 22981,  \n23206, 22999, 22552,  14639, 18446, 18447,  18781, 10542, 15617,  \n3103, 11679, 21887,  23208, 22995, 22546,  18692, 12653, 11287,  \n22772, 23385, 22998,  4900, 703, 3510,  21211, 6162, 15293,  \n9309, 4414, 9310,  12222, 9050, 23390,  4247, 4248, 16879,  \n22597, 22596, 19132,  22777, 22559, 23209,  9201, 7019, 4902,  \n22879, 6597, 5197,  22558, 22998, 23212,  22774, 23000, 23208,  \n16393, 13711, 15474,  10648, 578, 12772,  23389, 22564, 22555,  \n22555, 22999, 23389,  18832, 16023, 18833,  10739, 12925, 4089,  \n6065, 10367, 12571,  23391, 23211, 22566,  6181, 1416, 4785,  \n23389, 23391, 22564,  5518, 21424, 1106,  19932, 4155, 4374,  \n23002, 22073, 23003,  11488, 2302, 11487,  23393, 22783, 22562,  \n3080, 12595, 3081,  8453, 4211, 4210,  7090, 13502, 7091,  \n13080, 5675, 11525,  23006, 22783, 23393,  19663, 11808, 5498,  \n7390, 11273, 7391,  5380, 19946, 8048,  22567, 23006, 23007,  \n13156, 3474, 2649,  15994, 16518, 9262,  23008, 22567, 23007,  \n2377, 10213, 9305,  23394, 23009, 22788,  23012, 22569, 23008,  \n23012, 23008, 23395,  12535, 12370, 9944,  4632, 10971, 8693,  \n14815, 6743, 14119,  13789, 16741, 3167,  1674, 5347, 5348,  \n6596, 18038, 22544,  5565, 11643, 16793,  23015, 23396, 23221,  \n7395, 2579, 3416,  1085, 4616, 3789,  21241, 12359, 2111,  \n23016, 23398, 23015,  7748, 1253, 10631,  23398, 23396, 23015,  \n22792, 23012, 23218,  23220, 23397, 23014,  9701, 9700, 4856,  \n5043, 10187, 6356,  2300, 11306, 11307,  6462, 6439, 11959,  \n1469, 9036, 14187,  23224, 23014, 23397,  3681, 20811, 16068,  \n23323, 11996, 11707,  14698, 1795, 10500,  11689, 2220, 17783,  \n22719, 16563, 16189,  7354, 9802, 7355,  23021, 23400, 23016,  \n23224, 23401, 23225,  4032, 7754, 12180,  9218, 19216, 13302,  \n17235, 628, 19935,  11470, 556, 14553,  15753, 7905, 10502,  \n14127, 17941, 599,  17666, 11418, 18529,  15384, 8884, 19034,  \n2757, 2955, 5440,  23021, 23226, 23400,  17095, 15521, 18512,  \n1853, 10773, 6170,  16303, 17393, 3185,  22811, 23402, 23228,  \n6838, 15873, 4823,  4842, 19904, 4841,  19478, 4142, 4144,  \n23231, 22808, 22803,  23403, 23404, 23017,  2582, 12842, 8905,  \n6941, 7780, 16199,  2422, 9162, 18229,  23027, 23032, 23230,  \n22096, 3770, 18531,  12191, 5500, 5502,  23032, 23405, 23230,  \n23406, 23405, 23032,  1964, 1963, 8969,  1051, 23407, 1052,  \n23403, 23017, 23028,  11751, 11750, 12778,  13993, 17229, 18640,  \n20576, 13682, 13385,  1679, 9725, 1581,  14528, 5067, 17720,  \n23032, 19855, 23406,  1819, 16077, 20139,  11237, 11693, 8244,  \n13799, 2008, 2159,  8918, 11797, 11796,  8648, 11254, 16603,  \n6093, 15751, 11898,  4524, 6568, 4525,  17635, 17934, 17464,  \n5344, 14606, 9218,  18599, 7085, 18600,  11954, 17729, 17730,  \n2464, 16353, 1458,  13624, 11287, 15341,  7511, 15469, 7510,  \n9291, 22635, 5461,  17362, 13184, 13185,  317, 3667, 19464,  \n13676, 23410, 4754,  12403, 13165, 2272,  2550, 2552, 13177,  \n19557, 16866, 1583,  23033, 22816, 23411,  16297, 17570, 11730,  \n763, 10328, 14538,  21235, 20592, 14671,  681, 7722, 7746,  \n22584, 23412, 22816,  22816, 23412, 23411,  6144, 7225, 19325,  \n14743, 9983, 1423,  7603, 20395, 15815,  22821, 23412, 22584,  \n5229, 8405, 6378,  22361, 23037, 23234,  18685, 726, 15509,  \n19259, 784, 877,  22360, 23040, 22821,  6041, 4736, 12662,  \n20441, 3921, 7466,  23041, 22361, 23234,  5973, 19346, 6411,  \n2585, 20968, 2584,  12786, 3762, 29337,  1132, 18455, 19150,  \n22113, 23238, 21432,  16870, 21501, 21502,  12004, 18827, 934,  \n892, 16611, 893,  23414, 10466, 6779,  901, 5184, 902,  \n7221, 15832, 13932,  14475, 6979, 11903,  15060, 14952, 15293,  \n11006, 9162, 20336,  14353, 20368, 16980,  18067, 12520, 6108,  \n23049, 23042, 22112,  6443, 5644, 9427,  22826, 22594, 23416,  \n2720, 15270, 2721,  18972, 3447, 1563,  20887, 16816, 2145,  \n7949, 12389, 16290,  16653, 5860, 15124,  5505, 6542, 5080,  \n9262, 11052, 15994,  5395, 4960, 3819,  23417, 22598, 23045,  \n14270, 20543, 22895,  22825, 23418, 22827,  5516, 17872, 737,  \n13552, 5447, 5448,  21563, 454, 15335,  22824, 22598, 23417,  \n22601, 22824, 23417,  22601, 23417, 23047,  2711, 15172, 10299,  \n15352, 11230, 9747,  23419, 23049, 22368,  23752, 23050, 22114,  \n23241, 23419, 22368,  11088, 1348, 14163,  23241, 22368, 22603,  \n22591, 7753, 6515,  23242, 23241, 23052,  12904, 10165, 10809,  \n1905, 5682, 5681,  22554, 14783, 22780,  8867, 18065, 15595,  \n1626, 12811, 1627,  20351, 11039, 9131,  8572, 8571, 20962,  \n23054, 23053, 23420,  23054, 23421, 23055,  7423, 18144, 18143,  \n23055, 23421, 23056,  10307, 7800, 14946,  23056, 23422, 22831,  \n13579, 7026, 13578,  8810, 1626, 3719,  12541, 10224, 10223,  \n4063, 4064, 10643,  3612, 3613, 12047,  22449, 11282, 5474,  \n20164, 21678, 21101,  7512, 11738, 2133,  18397, 1423, 1422,  \n5165, 14548, 3138,  4862, 9816, 10189,  8581, 14999, 12816,  \n23594, 23251, 23059,  10674, 14027, 10675,  1519, 19673, 14556,  \n9491, 16225, 6666,  1177, 21382, 1175,  6146, 6402, 19037,  \n23253, 23424, 23425,  23424, 23253, 23060,  12483, 12482, 9872,  \n747, 5404, 746,  23253, 23425, 23426,  10171, 9034, 16825,  \n23253, 23426, 23061,  4259, 656, 5503,  23062, 23061, 23426,  \n15434, 16565, 4123,  5998, 3406, 3407,  23254, 23062, 23427,  \n1562, 3934, 18971,  23428, 23254, 23427,  6980, 2035, 2034,  \n22383, 23256, 23063,  19315, 4866, 4710,  23252, 22136, 23429,  \n23255, 23430, 22618,  23255, 22618, 22616,  14557, 4890, 11863,  \n7766, 10222, 10221,  3319, 12205, 3320,  23428, 22617, 23258,  \n23254, 23258, 23257,  23254, 23428, 23258,  22618, 23430, 23065,  \n14825, 17015, 14826,  3138, 3137, 5165,  19830, 15252, 15369,  \n15174, 11887, 2160,  21093, 18535, 11738,  22044, 20324, 3082,  \n23065, 23430, 23259,  18651, 467, 466,  22849, 21807, 23431,  \n23431, 21807, 23767,  4143, 14444, 14713,  22570, 14110, 19659,  \n4385, 11330, 13124,  21000, 23432, 22387,  23434, 22625, 22626,  \n22142, 22625, 23068,  23433, 22855, 22390,  22855, 21816, 22390,  \n22359, 22573, 22454,  3744, 3745, 4876,  18690, 4489, 5003,  \n7430, 18902, 4093,  14952, 15060, 2064,  22611, 21052, 14577,  \n6253, 19944, 9149,  22855, 23435, 21479,  11687, 16551, 15410,  \n20189, 7001, 7000,  23435, 21482, 21479,  23435, 21825, 21482,  \n23263, 22856, 22395,  23265, 23263, 22395,  23264, 21484, 21825,  \n23300, 2105, 18801,  1999, 9991, 10996,  12211, 6802, 1041,  \n19884, 4874, 10198,  22396, 23076, 21025,  21624, 14597, 9693,  \n15696, 20305, 16211,  23437, 16448, 22531,  6994, 5261, 20472,  \n19567, 11984, 13691,  23270, 23605, 23607,  8570, 3977, 5790,  \n23605, 23270, 23436,  23436, 23269, 23439,  1610, 18632, 1609,  \n23436, 23270, 23077,  3974, 16335, 18594,  23268, 23436, 23077,  \n23436, 23268, 23269,  10208, 7928, 8236,  23608, 23270, 23607,  \n1080, 22425, 14318,  9354, 11082, 9353,  14427, 21235, 14428,  \n23273, 23440, 23269,  23271, 23270, 23608,  13387, 405, 404,  \n14528, 17720, 6384,  5254, 5253, 8959,  17385, 22489, 13909,  \n23274, 23271, 23610,  20184, 20511, 5744,  23085, 23275, 23442,  \n2293, 16257, 2292,  3634, 18509, 1429,  7301, 4399, 5362,  \n1209, 17622, 1210,  18570, 16739, 1716,  548, 18930, 16384,  \n23089, 23277, 23275,  23276, 23274, 23278,  23277, 23444, 23275,  \n18821, 21086, 2752,  17421, 14811, 15227,  20044, 12951, 12952,  \n10740, 4335, 4344,  2800, 8292, 4601,  23279, 23445, 23277,  \n23278, 23446, 23276,  23276, 23446, 23094,  6675, 3780, 9931,  \n23447, 23279, 23280,  2884, 7951, 7293,  7572, 11765, 10557,  \n23448, 23094, 23446,  23094, 23448, 23281,  23281, 23448, 23449,  \n23281, 23449, 23098,  12792, 1183, 1184,  23098, 23449, 23280,  \n11470, 9848, 4395,  23450, 23283, 14147,  16999, 11130, 18375,  \n16516, 17183, 22321,  9799, 7933, 21687,  22124, 19978, 8334,  \n18526, 22154, 23285,  18526, 20484, 22154,  23452, 22156, 23102,  \n4801, 452, 14132,  22156, 23452, 23104,  3142, 13344, 9141,  \n22979, 4498, 3976,  22864, 23454, 22401,  16046, 5249, 20595,  \n23454, 23456, 23105,  23105, 22401, 23454,  22157, 22636, 22639,  \n14728, 833, 3195,  18818, 1868, 5176,  23456, 23457, 23105,  \n15028, 19003, 15724,  1071, 7139, 20230,  23457, 23458, 23286,  \n23457, 23286, 23105,  17489, 21220, 12679,  21041, 19994, 23106,  \n18980, 17431, 5716,  23286, 23458, 23289,  14019, 14633, 16870,  \n13607, 1443, 3185,  6082, 20647, 18456,  21045, 22644, 23459,  \n9711, 14819, 15181,  23935, 22411, 23109,  23291, 23109, 22407,  \n12003, 7837, 17194,  20647, 6082, 22543,  22866, 23466, 23288,  \n2730, 2732, 6442,  18870, 12473, 4449,  17887, 17886, 7631,  \n22240, 24254, 18765,  22407, 22169, 23291,  22169, 22875, 23291,  \n11985, 4480, 11267,  20753, 18267, 7291,  23460, 23291, 22875,  \n22645, 23110, 22643,  23462, 23110, 23463,  20201, 12990, 14798,  \n12781, 12782, 19023,  21831, 22647, 23466,  22649, 22648, 23464,  \n23464, 22648, 23624,  22370, 4342, 16547,  23467, 18932, 14867,  \n6613, 4026, 23408,  22651, 22873, 23468,  8000, 1169, 17473,  \n14577, 9729, 11740,  3604, 3603, 5515,  23295, 22877, 22173,  \n22544, 16639, 12350,  17254, 23933, 6696,  12375, 6571, 4277,  \n4510, 4509, 1352,  3456, 1326, 16066,  10890, 12943, 18906,  \n6311, 22122, 13492,  22654, 22412, 23111,  501, 5842, 3730,  \n12569, 16368, 23336,  15682, 8008, 7646,  4924, 22579, 5147,  \n22665, 23298, 23304,  12823, 10996, 10997,  23470, 337, 338,  \n13782, 12900, 6918,  2513, 9401, 898,  17613, 17615, 19435,  \n22882, 22661, 22885,  22661, 21861, 22654,  23472, 22656, 23114,  \n4626, 15847, 14482,  23298, 22665, 23299,  21186, 15338, 16282,  \n23472, 23303, 22656,  22656, 23303, 22880,  2257, 1893, 21392,  \n15352, 1743, 11230,  1736, 23473, 5112,  3793, 5216, 22926,  \n22883, 22880, 23474,  5075, 7113, 13718,  15518, 7675, 17897,  \n21460, 17031, 10619,  9215, 23475, 4496,  5922, 20190, 5449,  \n14229, 12170, 17663,  23303, 23474, 22880,  19371, 6853, 20050,  \n6961, 3805, 10913,  23306, 23117, 23116,  9527, 2127, 7149,  \n7899, 7901, 16434,  19899, 23011, 10897,  14717, 19249, 16007,  \n12651, 11367, 11366,  11562, 12098, 12097,  22666, 23304, 23633,  \n23307, 3806, 20401,  4287, 18610, 22367,  8090, 6215, 6214,  \n12467, 21537, 6757,  23306, 23477, 23122,  22190, 23305, 21873,  \n9102, 11602, 15964,  21355, 12175, 13216,  23122, 23477, 23123,  \n22435, 22669, 23633,  11938, 4313, 18394,  456, 20728, 20727,  \n12952, 4327, 18204,  10912, 7183, 11673,  1607, 13896, 1608,  \n3493, 22793, 15436,  3667, 2124, 15106,  13728, 20247, 6920,  \n14466, 6117, 18730,  9738, 12635, 14891,  22193, 23125, 23643,  \n23126, 22193, 23643,  12327, 7020, 12328,  17532, 23479, 5729,  \n11282, 22449, 6772,  8721, 13039, 20563,  3713, 19316, 19665,  \n23128, 22668, 23126,  1603, 4829, 7137,  1573, 565, 23336,  \n21881, 23310, 23309,  2168, 8806, 4130,  23481, 23127, 21110,  \n7649, 4669, 10329,  23310, 21881, 22897,  13637, 7650, 11540,  \n4210, 20999, 9409,  5934, 1874, 5935,  21110, 22673, 23312,  \n23482, 22674, 23311,  23130, 23483, 22901,  23130, 23131, 23483,  \n22436, 23130, 22901,  23314, 22674, 23482,  7854, 447, 2106,  \n17469, 11726, 11963,  11024, 18535, 14981,  18817, 906, 5630,  \n4122, 13100, 1899,  3762, 12786, 8617,  22901, 23483, 23137,  \n11933, 13559, 19113,  9019, 14020, 4872,  21897, 23134, 22434,  \n11453, 21980, 6750,  1400, 357, 3158,  16305, 1630, 21048,  \n23314, 22678, 22904,  11408, 19022, 4825,  23319, 22442, 22672,  \n628, 627, 12246,  20771, 926, 18794,  14625, 22100, 8576,  \n10295, 5953, 6543,  22137, 10679, 20086,  23321, 23134, 21897,  \n14617, 14618, 5344,  4365, 10514, 4364,  6901, 1170, 12400,  \n23473, 5539, 18647,  16435, 18872, 16436,  11167, 11166, 10937,  \n15025, 11556, 19670,  22909, 22910, 23484,  22907, 23320, 23141,  \n23143, 23324, 23650,  2718, 17615, 3514,  23321, 23142, 23486,  \n3247, 15025, 3248,  23144, 22452, 23319,  23321, 22679, 23142,  \n5331, 2323, 8412,  8907, 18686, 5714,  860, 8983, 3429,  \n21989, 22299, 840,  20098, 5191, 2445,  23145, 22685, 23322,  \n14145, 1043, 7248,  11214, 12947, 2677,  6089, 22122, 6311,  \n3170, 6772, 22449,  23320, 23488, 23141,  22686, 23489, 23324,  \n13935, 7578, 1372,  6790, 15364, 1095,  16361, 14172, 16359,  \n22686, 23327, 23489,  3818, 12283, 8289,  22684, 22456, 23147,  \n3770, 13118, 1246,  22681, 23490, 22912,  23144, 23490, 22681,  \n3328, 9003, 20402,  22915, 23152, 23327,  7920, 23491, 4859,  \n1894, 5007, 21442,  23328, 23141, 23488,  15284, 10052, 9382,  \n23150, 23147, 22456,  17752, 8873, 16031,  17452, 9180, 7348,  \n1311, 16158, 13694,  13511, 12997, 12203,  22918, 23660, 22690,  \n8725, 12619, 17782,  2277, 11112, 11111,  11925, 5401, 10464,  \n11704, 9594, 11702,  8483, 14335, 15143,  7137, 9021, 7138,  \n22689, 22918, 22690,  11930, 15234, 11931,  12997, 2272, 12203,  \n23151, 23156, 23152,  19129, 11955, 13410,  4761, 14467, 22776,  \n22692, 22691, 23492,  8087, 16519, 6523,  22697, 23158, 22918,  \n23152, 23156, 23493,  23495, 23494, 23152,  23155, 23153, 23329,  \n7044, 7644, 11346,  22983, 14660, 12361,  22929, 23493, 23156,  \n8743, 12419, 359,  14769, 6017, 20619,  23331, 22921, 23328,  \n21666, 3343, 20190,  9015, 7885, 9016,  22927, 22916, 22921,  \n22693, 21927, 23333,  23496, 22693, 23333,  11540, 7650, 19975,  \n5651, 16386, 22453,  17075, 12070, 12069,  23497, 23154, 23155,  \n12603, 1252, 13079,  14644, 18737, 18600,  23498, 23495, 23159,  \n8466, 8091, 10504,  11222, 20350, 7669,  11743, 2677, 12244,  \n22461, 22928, 23333,  5439, 19349, 7705,  1806, 20853, 7782,  \n8886, 3498, 23039,  23158, 22235, 22468,  7608, 16403, 5006,  \n22927, 23335, 23161,  23498, 23159, 23338,  23843, 23158, 22468,  \n17494, 22288, 23499,  13982, 1017, 13981,  9582, 21387, 16811,  \n18961, 5246, 18055,  9142, 6280, 662,  4492, 2783, 13710,  \n8927, 6110, 6111,  22933, 22237, 23337,  22928, 21934, 23340,  \n15152, 6068, 18974,  11791, 7930, 2093,  12269, 12270, 16287,  \n7408, 11847, 5465,  1227, 11270, 3646,  1580, 8124, 20726,  \n23168, 23161, 23501,  18060, 18059, 12785,  22467, 22935, 22934,  \n22705, 23341, 22470,  16338, 17522, 9792,  15383, 14803, 10891,  \n17092, 11961, 8482,  14648, 2996, 5754,  4201, 10304, 15772,  \n22935, 23503, 23343,  10997, 12834, 12823,  19897, 8868, 8867,  \n22476, 23503, 22935,  23165, 23504, 23345,  4776, 1952, 15823,  \n23169, 23168, 23505,  17607, 3144, 3343,  10072, 16807, 10073,  \n4427, 483, 9261,  2447, 20771, 9092,  23507, 9515, 14359,  \n7511, 16904, 20679,  22944, 23166, 23506,  7231, 18093, 2420,  \n9554, 13202, 10986,  19144, 14290, 14289,  23173, 23169, 23505,  \n23509, 22710, 23351,  7003, 11660, 29627,  22710, 23509, 23171,  \n10434, 571, 9636,  2483, 14347, 16755,  4257, 739, 4258,  \n8076, 19221, 14318,  22947, 22485, 23350,  19600, 10697, 23510,  \n788, 17119, 20642,  14350, 23511, 4688,  19215, 12681, 4028,  \n10699, 22247, 20390,  23514, 23173, 23515,  23345, 23178, 22506,  \n8481, 11858, 12911,  20009, 6477, 20010,  23176, 23173, 23514,  \n22951, 23173, 23176,  1927, 16614, 3665,  12262, 3572, 3573,  \n7099, 12063, 11187,  11493, 3051, 18035,  14505, 16532, 13081,  \n21854, 19097, 11526,  23176, 23514, 23354,  11920, 6871, 7659,  \n20126, 20166, 9412,  22205, 15951, 17426,  8716, 4733, 15402,  \n10674, 8885, 14027,  8134, 8133, 20259,  1132, 16910, 12381,  \n9866, 11593, 3146,  22188, 17787, 22189,  22731, 23354, 23180,  \n3410, 20413, 6134,  22317, 9734, 7552,  13415, 10178, 14099,  \n9542, 10985, 19625,  11811, 19914, 11812,  8568, 8567, 13424,  \n2693, 4473, 14080,  16349, 16348, 9602,  2621, 21132, 498,  \n23363, 23359, 23358,  19585, 5812, 11152,  10786, 16011, 11671,  \n881, 3526, 882,  11752, 14741, 14740,  23362, 22967, 23364,  \n22960, 22969, 23179,  6591, 5447, 13552,  6704, 6703, 7804,  \n3240, 3241, 16839,  23519, 22743, 23363,  7893, 376, 375,  \n18965, 18966, 21540,  4930, 12912, 6400,  5044, 5809, 5808,  \n3436, 19995, 20395,  4977, 8539, 15868,  6840, 9627, 10963,  \n23184, 22743, 23519,  2554, 20208, 2948,  22970, 23368, 23183,  \n7672, 7671, 13773,  6234, 6235, 12213,  1122, 19418, 4618,  \n14233, 21842, 2705,  23185, 22516, 23366,  11341, 12659, 9267,  \n22970, 22522, 23368,  427, 21918, 9630,  11366, 6053, 9913,  \n20260, 8423, 2530,  17045, 8345, 5690,  21980, 6749, 6750,  \n8962, 14483, 7101,  6992, 10160, 12864,  22523, 22744, 23186,  \n21320, 5164, 4893,  12796, 22181, 19555,  10814, 14341, 3674,  \n18743, 14844, 20566,  22751, 23373, 23369,  22751, 22009, 23373,  \n22009, 22528, 23373,  2964, 2965, 9393,  11849, 6466, 14895,  \n23371, 22527, 22972,  6599, 5124, 21238,  10120, 7807, 6416,  \n15236, 11799, 11800,  22523, 23372, 23187,  2319, 13339, 1996,  \n23524, 23187, 23372,  3312, 3313, 5410,  17053, 17052, 7564,  \n19426, 9888, 8962,  12181, 4010, 7855,  18351, 1965, 19916,  \n22976, 22973, 23187,  845, 15315, 21466,  23526, 22976, 23187,  \n19892, 6716, 17908,  4407, 17791, 5400,  5559, 10212, 12511,  \n6507, 6769, 22231,  19802, 4525, 6568,  5977, 1187, 14117,  \n22759, 22974, 23189,  23167, 22181, 17038,  14110, 10436, 22608,  \n23192, 23527, 22761,  22976, 23526, 23375,  22978, 23375, 23191,  \n23188, 22762, 23376,  8110, 8109, 4817,  1354, 13564, 1355,  \n17389, 23529, 14150,  24009, 23191, 23375,  22537, 22759, 23189,  \n20269, 16003, 3254,  8965, 19931, 22854,  3089, 6672, 3090,  \n17078, 11840, 17413,  1432, 8413, 11232,  10801, 16006, 19313,  \n21101, 21678, 6559,  15935, 9557, 16907,  21123, 11526, 19097,  \n2364, 10621, 10622,  2245, 4181, 5484,  22536, 23191, 23196,  \n6874, 5866, 15838,  2368, 9221, 21186,  9230, 2032, 1731,  \n15755, 13683, 13682,  8272, 7171, 1738,  5117, 7896, 6066,  \n6069, 14963, 2365,  2869, 4874, 10378,  4196, 16080, 10363,  \n19817, 13379, 12375,  14600, 3382, 17024,  16401, 17200, 22486,  \n22984, 22536, 23196,  4836, 4835, 4945,  23530, 22985, 23199,  \n15091, 2740, 2739,  3464, 23533, 17923,  1642, 13973, 18220,  \n22987, 23197, 23532,  21092, 9396, 9517,  3148, 3688, 17362,  \n21421, 8305, 22249,  7884, 11185, 7883,  1789, 12005, 1790,  \n8986, 6358, 6833,  22768, 23380, 22769,  7526, 19825, 5775,  \n12609, 9986, 23536,  4066, 16190, 4065,  19374, 14058, 13296,  \n11732, 9585, 11733,  4616, 16889, 10060,  6308, 17108, 17063,  \n9253, 8092, 5021,  3768, 2382, 4507,  7739, 17020, 542,  \n17599, 17600, 11551,  23539, 1631, 17427,  23381, 22993, 23540,  \n22993, 22995, 23540,  22322, 23202, 23206,  7258, 12852, 8781,  \n2612, 8088, 3394,  16888, 4447, 9645,  18966, 1357, 21540,  \n507, 8609, 2556,  11611, 9372, 13064,  19394, 5730, 9418,  \n7609, 7610, 13335,  22995, 23208, 23543,  7896, 9516, 14272,  \n11887, 15174, 22727,  14049, 15937, 4595,  18501, 7768, 7064,  \n23385, 23388, 22998,  22999, 23544, 23389,  21875, 7923, 8446,  \n23212, 22998, 23388,  11392, 15871, 19046,  23209, 22559, 23875,  \n1172, 1174, 18585,  29503, 20199, 18689,  2782, 17868, 2783,  \n23545, 23391, 23389,  23213, 22561, 22779,  9943, 16007, 15679,  \n2597, 11623, 17515,  2708, 12052, 2709,  23545, 23211, 23391,  \n23391, 22566, 22564,  9956, 17797, 6893,  22779, 23002, 23214,  \n23002, 23003, 23211,  23547, 23002, 23211,  23213, 22779, 23214,  \n23212, 23546, 22562,  23000, 23004, 23548,  18645, 21235, 14427,  \n5859, 4589, 6473,  18751, 11836, 11835,  1173, 7072, 4503,  \n23551, 23004, 23215,  13087, 5662, 11744,  5357, 9467, 7319,  \n7447, 4606, 816,  10879, 20172, 7996,  22339, 5543, 5606,  \n11484, 2215, 14721,  23215, 23217, 23009,  3447, 10856, 1563,  \n23394, 23554, 23009,  15302, 5232, 9877,  9990, 8512, 12764,  \n1710, 11355, 8301,  2471, 2470, 13497,  776, 7081, 6062,  \n3512, 6685, 12229,  18820, 1681, 10403,  23221, 23556, 23220,  \n23557, 23220, 23556,  15530, 9397, 465,  23558, 23397, 23220,  \n23399, 23218, 23012,  23010, 23219, 23555,  23559, 23016, 23400,  \n1455, 11497, 1456,  23219, 22794, 23732,  22791, 22794, 23219,  \n15484, 15441, 5846,  3137, 21016, 15712,  21539, 1085, 1086,  \n7333, 11672, 21329,  23529, 9739, 14150,  10523, 16657, 7264,  \n10033, 3187, 3979,  6368, 6367, 7782,  17107, 15186, 17108,  \n9394, 15045, 9395,  2109, 14440, 5943,  10469, 10354, 10470,  \n23019, 22792, 23218,  5302, 8457, 18782,  17243, 6369, 19226,  \n14173, 531, 532,  22811, 23230, 23402,  23404, 23561, 22794,  \n2460, 7300, 1440,  23227, 23225, 23401,  19789, 11293, 20493,  \n23402, 23226, 23228,  7880, 3894, 1257,  23017, 23404, 22794,  \n7859, 1083, 20066,  23563, 23230, 23405,  10362, 11262, 5619,  \n7618, 9455, 2405,  4214, 13116, 19802,  1698, 15239, 5988,  \n9840, 15239, 1698,  23565, 23232, 23564,  23227, 23564, 23232,  \n14359, 14991, 2765,  7063, 6376, 2539,  7810, 20344, 17804,  \n12626, 23566, 6305,  16631, 12402, 14692,  527, 968, 2285,  \n4332, 4333, 12833,  23406, 23567, 23405,  10305, 10304, 8555,  \n6997, 15206, 20526,  14393, 23249, 14394,  23232, 23409, 23233,  \n23232, 23565, 23409,  336, 16489, 335,  11399, 10523, 11398,  \n20673, 6829, 7056,  23568, 23029, 23033,  13338, 14391, 19576,  \n19855, 23567, 23406,  3556, 14009, 13720,  8597, 9444, 6777,  \n7870, 10996, 12823,  23570, 23030, 23233,  23233, 23409, 23570,  \n21768, 22588, 19855,  22588, 23567, 19855,  9023, 10323, 18092,  \n13794, 4111, 21392,  23571, 23567, 22588,  10009, 6379, 6380,  \n23570, 23234, 23030,  2389, 22197, 19164,  19916, 894, 18351,  \n2566, 18646, 13941,  13055, 14978, 1300,  18158, 18689, 19965,  \n15014, 23317, 19329,  6958, 1655, 1697,  23234, 23570, 23574,  \n1289, 8811, 11085,  22587, 23571, 22588,  14056, 8285, 3869,  \n662, 1667, 18211,  23237, 24192, 22356,  8798, 6851, 6284,  \n21834, 18639, 6912,  23411, 23412, 23573,  2853, 15779, 1929,  \n15969, 6135, 15970,  18964, 1247, 10991,  9427, 2526, 3859,  \n23238, 23571, 22587,  21432, 23238, 22587,  4722, 22298, 19771,  \n429, 430, 2336,  22821, 23040, 23575,  14151, 9198, 17845,  \n22619, 13224, 3606,  9694, 21202, 15518,  23576, 23238, 23042,  \n13224, 18899, 3606,  4880, 11733, 7998,  6678, 16748, 4536,  \n22589, 23577, 23413,  22590, 22589, 23413,  18812, 20028, 13883,  \n22590, 23413, 23239,  11251, 15702, 7046,  23049, 23579, 23042,  \n23578, 22593, 22827,  21989, 5786, 22299,  22594, 23043, 23415,  \n15819, 22765, 15062,  22365, 22826, 23416,  23418, 22825, 23240,  \n1229, 18502, 16593,  6558, 9944, 12370,  680, 4454, 2023,  \n22602, 23044, 23752,  23579, 23049, 23419,  18925, 12711, 17941,  \n11784, 3687, 11213,  11838, 12998, 7323,  19384, 19383, 23580,  \n23045, 22365, 23416,  23045, 23416, 23581,  23582, 23419, 23241,  \n4960, 2487, 3819,  13328, 4797, 15295,  22829, 22371, 23584,  \n22829, 23585, 22372,  22829, 22372, 22118,  22372, 23585, 22373,  \n19785, 5018, 19091,  11131, 5803, 7377,  23052, 23244, 23586,  \n13135, 12576, 18851,  12955, 7928, 471,  2609, 679, 6039,  \n18579, 5290, 2591,  23588, 23586, 23244,  23422, 23589, 22831,  \n23588, 23244, 23251,  23251, 23244, 23059,  12918, 19527, 12916,  \n2634, 10544, 2269,  7130, 16677, 17675,  6930, 3709, 3874,  \n9824, 17499, 17695,  23246, 23057, 23590,  15099, 4471, 14016,  \n23057, 23245, 23590,  6503, 14539, 17663,  22835, 23246, 23247,  \n4884, 20137, 11807,  13446, 13559, 13560,  23247, 23246, 23248,  \n2602, 2604, 20227,  645, 15999, 7712,  23115, 17712, 16505,  \n4848, 10108, 14057,  16128, 1403, 1405,  7546, 4431, 2110,  \n23424, 23250, 23593,  22615, 11149, 5999,  23059, 22838, 23594,  \n6775, 6943, 14416,  22838, 22380, 23594,  789, 20642, 20641,  \n789, 788, 20642,  22380, 23252, 23594,  18394, 9043, 18395,  \n8288, 22585, 5890,  12143, 11296, 2424,  7751, 7750, 7088,  \n936, 9300, 16819,  23062, 23598, 23427,  23426, 23598, 23062,  \n4229, 11328, 11329,  23599, 23252, 23429,  18049, 18048, 3674,  \n23063, 23600, 23255,  18054, 13676, 11302,  23764, 23428, 23427,  \n13182, 15856, 15687,  7760, 7763, 21876,  23601, 23256, 22617,  \n23601, 22617, 23764,  23764, 22617, 23428,  2692, 16203, 2693,  \n22425, 21366, 21486,  15055, 1659, 21360,  5547, 23262, 22153,  \n5546, 18966, 18965,  13670, 20126, 3103,  10862, 7748, 10631,  \n23602, 22853, 23259,  11494, 10372, 11033,  16724, 20644, 3725,  \n22519, 16329, 12452,  16032, 16073, 4425,  14713, 14444, 12146,  \n23602, 23433, 22390,  23432, 23069, 22387,  23434, 23068, 22625,  \n23603, 22855, 23433,  23260, 23434, 22626,  15410, 14097, 11687,  \n12145, 12144, 17570,  9296, 14970, 16119,  2722, 18655, 19944,  \n16181, 12948, 8647,  7511, 8759, 15469,  3765, 9961, 10449,  \n964, 10284, 18915,  22858, 19884, 10198,  22629, 23604, 22396,  \n23264, 23604, 22629,  5998, 14634, 3406,  15719, 9011, 9010,  \n2712, 15711, 5217,  1375, 781, 14332,  12469, 6268, 589,  \n10808, 16032, 3971,  16139, 19274, 10844,  14332, 6101, 6100,  \n4103, 18517, 18012,  5279, 21454, 21328,  11738, 13630, 21093,  \n18469, 5632, 4732,  16643, 12289, 20111,  23438, 23606, 23605,  \n23605, 23921, 23607,  17833, 13154, 23223,  7632, 17586, 21177,  \n16130, 14705, 20351,  23605, 23436, 23438,  12872, 14819, 9711,  \n8435, 14592, 18666,  22709, 10122, 18920,  10504, 14170, 10505,  \n23438, 23436, 23439,  9239, 20931, 10426,  23439, 23269, 23440,  \n14467, 945, 19131,  5013, 3949, 15261,  21013, 7131, 4208,  \n5835, 7372, 10751,  8877, 8876, 13247,  23271, 23608, 23610,  \n23273, 23611, 23440,  14374, 17590, 11776,  23442, 23611, 23273,  \n2554, 10913, 20208,  8259, 6327, 18487,  3418, 3417, 10613,  \n6854, 12458, 9798,  17963, 8622, 4879,  23612, 23274, 23610,  \n17159, 6042, 10054,  21176, 11034, 11035,  23444, 23442, 23275,  \n21845, 1075, 3568,  861, 552, 14487,  23613, 23274, 23612,  \n15986, 20579, 18484,  11426, 8941, 9032,  23613, 23278, 23274,  \n8943, 11527, 11135,  5012, 5013, 15261,  17160, 21297, 10480,  \n23444, 23277, 23614,  18125, 12010, 8344,  10685, 17815, 20638,  \n13190, 13708, 4183,  23445, 23614, 23277,  9175, 11982, 9176,  \n23445, 23279, 23447,  23616, 23447, 23280,  23449, 23616, 23280,  \n5465, 11847, 9317,  21882, 2766, 2149,  16858, 17772, 21766,  \n18741, 1939, 16654,  7978, 15306, 12577,  4527, 14693, 9692,  \n8700, 14769, 22488,  13518, 12351, 1412,  13034, 7505, 7932,  \n7257, 12946, 12265,  9964, 9883, 12358,  15512, 15511, 900,  \n23285, 22154, 22866,  6199, 20931, 6200,  22194, 14949, 3476,  \n10797, 9202, 12392,  1934, 7708, 3962,  23453, 22866, 23288,  \n1136, 4269, 13152,  15899, 705, 4749,  4931, 11646, 19493,  \n23457, 23619, 23620,  23458, 23457, 23620,  5350, 3735, 8242,  \n10188, 18005, 22035,  2884, 7292, 2328,  23621, 23289, 23458,  \n22870, 22639, 23107,  6603, 11019, 7314,  13825, 15494, 16330,  \n16227, 20340, 8582,  23107, 23108, 22870,  10127, 10128, 12051,  \n22642, 22411, 23623,  23623, 22411, 23935,  7620, 22255, 7619,  \n11896, 12615, 1206,  21596, 9774, 9773,  8527, 5363, 22064,  \n8527, 5364, 5363,  6200, 9239, 14516,  6781, 11324, 9017,  \n23108, 23107, 23625,  14615, 13418, 11808,  14385, 13007, 15159,  \n3119, 2876, 17513,  22644, 22643, 23110,  23624, 22648, 22642,  \n23460, 22875, 23465,  17105, 21627, 14698,  7648, 7668, 16834,  \n23110, 23293, 23463,  23110, 22645, 23293,  23463, 23293, 23108,  \n3628, 15015, 11234,  22108, 4986, 17635,  1874, 5277, 3890,  \n23290, 23468, 22873,  10797, 1297, 1296,  10955, 6905, 20842,  \n7797, 17753, 19896,  23466, 22647, 23627,  23628, 23294, 22651,  \n11637, 17946, 14924,  23629, 2408, 17637,  17902, 5770, 14750,  \n15679, 12533, 12535,  19265, 15667, 8569,  16191, 10414, 20194,  \n13442, 8562, 12303,  17278, 11435, 14105,  12285, 19051, 19042,  \n8841, 12369, 2669,  6308, 12348, 6309,  22878, 23297, 23295,  \n23627, 22647, 22660,  6216, 18426, 3351,  23631, 22885, 22661,  \n17722, 22043, 11045,  1773, 18955, 3817,  8304, 8654, 16151,  \n2937, 17322, 21328,  17632, 11996, 23073,  23636, 23120, 23635,  \n19128, 19129, 13410,  23114, 23113, 23632,  10023, 15626, 10022,  \n12771, 3043, 18863,  19322, 10419, 6438,  12082, 19866, 19456,  \n8600, 9227, 18937,  21008, 8936, 18097,  21286, 9869, 14881,  \n4028, 12091, 12654,  22818, 8727, 3442,  6844, 16540, 1273,  \n1379, 5022, 9600,  23639, 23303, 23637,  23639, 23474, 23303,  \n21232, 13517, 14286,  23638, 23306, 23116,  18109, 1237, 9808,  \n17304, 15179, 3759,  2670, 15153, 1595,  9166, 11448, 13494,  \n13216, 12175, 11127,  9145, 5964, 15580,  22190, 23124, 23640,  \n17615, 17614, 18506,  23306, 23641, 23477,  6947, 1658, 5083,  \n23308, 23123, 23477,  8447, 14590, 1183,  5034, 11880, 3790,  \n23642, 23121, 22185,  7231, 17920, 21690,  4188, 5516, 13781,  \n23123, 23308, 22667,  17850, 868, 19141,  7249, 7759, 5493,  \n23124, 22196, 23127,  4966, 8604, 12746,  1385, 9300, 19024,  \n16198, 14837, 14838,  9948, 12714, 4449,  6890, 14284, 6663,  \n5868, 2912, 2911,  22672, 22435, 23478,  7653, 2220, 12246,  \n15532, 1382, 10138,  9816, 3420, 10053,  14229, 14226, 19786,  \n23644, 22896, 23309,  23644, 23131, 22896,  23128, 23126, 23645,  \n7137, 15444, 1603,  19814, 19815, 547,  12926, 12925, 13683,  \n23312, 23481, 21110,  23128, 23645, 23311,  1348, 1347, 1688,  \n23646, 6051, 5135,  11698, 12473, 301,  5612, 4362, 17123,  \n23315, 22672, 23647,  17396, 12056, 15755,  19838, 5012, 18604,  \n23313, 23481, 23312,  16944, 14761, 17539,  6678, 10320, 15742,  \n17105, 10500, 4318,  10018, 8333, 16244,  23483, 23649, 23137,  \n2411, 18430, 14194,  13066, 3463, 3464,  23313, 23316, 23648,  \n5575, 859, 1760,  1023, 964, 1275,  6473, 4589, 3806,  \n22898, 23650, 23651,  19650, 761, 20326,  23319, 22672, 23315,  \n23648, 23316, 22909,  2542, 4529, 6139,  23650, 22898, 22441,  \n16429, 6430, 11792,  1594, 4727, 1595,  22909, 23484, 23648,  \n23145, 23484, 22910,  2430, 7438, 7440,  19518, 9713, 10155,  \n23320, 23318, 23487,  17545, 2817, 15213,  703, 1637, 18176,  \n20938, 11595, 15550,  11032, 21561, 8234,  15189, 10763, 2895,  \n11203, 2129, 2956,  4521, 13912, 3373,  6584, 2518, 6585,  \n22683, 22678, 23654,  9052, 1167, 13788,  16147, 6071, 19593,  \n3644, 2146, 23132,  13472, 11490, 11491,  6733, 21520, 18229,  \n14760, 14761, 16943,  23099, 17550, 23655,  7805, 7804, 8259,  \n9838, 9837, 15278,  22691, 22683, 23654,  3413, 8287, 14271,  \n10148, 3176, 3177,  15936, 5283, 5284,  16907, 5052, 5053,  \n23487, 23488, 23320,  5947, 5948, 7762,  1391, 12126, 18362,  \n22353, 17440, 22658,  23488, 23487, 23657,  20063, 19970, 17735,  \n22912, 23490, 23658,  8092, 9253, 8773,  15955, 4543, 12426,  \n23659, 23327, 23152,  5524, 4988, 4989,  23658, 23329, 22912,  \n425, 3074, 424,  6749, 8815, 16364,  4988, 5525, 14646,  \n782, 5051, 4383,  3010, 11974, 3566,  1563, 18971, 18972,  \n7006, 7005, 2347,  11469, 2082, 20007,  20667, 16488, 6181,  \n8307, 21514, 8308,  23495, 23152, 23493,  12780, 6633, 6634,  \n23661, 572, 21250,  21940, 7466, 2863,  21922, 22693, 23662,  \n23328, 23488, 23331,  3022, 12873, 10849,  13582, 6771, 16319,  \n23488, 23663, 23331,  14080, 2494, 14364,  23329, 23664, 23155,  \n9931, 12857, 9325,  1217, 1152, 1153,  18016, 19212, 9766,  \n2583, 16842, 6730,  15273, 10338, 5951,  9057, 14862, 4412,  \n16122, 13356, 7974,  2991, 2656, 4421,  12742, 14769, 20619,  \n23493, 23159, 23495,  16098, 16838, 3352,  8012, 20242, 8013,  \n14336, 3860, 8575,  21541, 17599, 3945,  19886, 11345, 13207,  \n14281, 9172, 9171,  3901, 18460, 21369,  22695, 23665, 23162,  \n14561, 22129, 10353,  2542, 6139, 16126,  18184, 21127, 21126,  \n10023, 10022, 23667,  17163, 14379, 6124,  21893, 15944, 8841,  \n9217, 8503, 20986,  4195, 4194, 21472,  23160, 23154, 23500,  \n2294, 2289, 22577,  7020, 6620, 18318,  732, 20843, 10413,  \n12337, 12336, 16932,  16687, 10841, 3507,  20153, 2034, 1033,  \n22468, 22470, 23670,  1128, 1326, 3456,  7458, 6379, 10009,  \n23161, 23335, 23501,  23165, 23160, 23504,  23160, 23500, 23504,  \n23670, 22470, 23341,  23340, 22467, 22934,  23148, 13594, 13597,  \n11240, 22620, 11239,  5927, 8693, 10971,  22717, 23174, 23342,  \n23342, 23174, 23672,  21297, 7174, 10480,  10849, 20940, 3022,  \n11361, 998, 13021,  392, 2632, 22923,  23673, 22705, 23344,  \n22705, 23673, 23341,  6010, 18630, 20431,  2191, 8671, 20866,  \n9232, 2400, 1887,  18973, 16565, 13772,  6093, 20356, 6094,  \n5050, 14807, 8132,  2663, 9565, 10999,  22707, 22943, 23344,  \n21407, 8668, 3601,  22707, 22492, 22943,  8504, 19041, 16973,  \n16130, 8978, 13178,  5453, 9077, 20458,  23171, 23503, 22476,  \n9248, 8084, 4147,  6856, 20923, 1284,  8342, 19140, 18921,  \n23506, 23166, 22936,  23509, 23503, 23171,  22498, 23175, 22943,  \n18220, 13973, 16141,  4036, 3850, 4037,  22944, 23506, 23349,  \n6704, 7805, 6025,  8280, 22980, 3294,  19478, 4144, 18927,  \n16613, 4256, 19507,  17651, 8825, 8824,  23173, 23505, 23513,  \n22729, 23352, 23175,  23677, 22947, 23350,  13885, 15230, 8300,  \n22736, 5598, 9963,  23177, 23508, 23174,  2491, 13835, 13117,  \n13975, 16148, 13974,  23345, 23512, 23178,  1336, 19266, 19267,  \n8506, 8505, 21449,  23177, 23355, 23508,  23173, 23513, 23515,  \n13511, 5434, 13366,  10061, 17858, 10062,  14327, 15437, 13960,  \n16433, 22715, 20792,  9077, 13456, 9078,  6059, 25698, 17948,  \n7546, 1646, 4431,  3647, 7540, 17713,  22061, 4024, 11033,  \n11982, 20400, 19581,  18245, 21950, 7456,  23681, 23354, 23514,  \n10381, 10380, 12263,  4301, 6882, 8166,  2111, 5459, 21241,  \n4870, 16607, 17993,  21729, 17218, 17852,  17391, 21547, 1971,  \n23358, 23180, 23354,  9756, 16003, 20269,  12560, 18375, 11130,  \n23516, 22956, 22506,  17595, 17594, 21084,  23179, 23517, 23352,  \n23517, 23857, 23352,  22506, 23178, 23516,  9494, 15685, 15686,  \n22967, 23686, 22963,  13424, 8567, 14153,  8765, 14737, 4649,  \n3443, 8872, 8895,  2125, 5081, 9811,  4147, 23689, 17445,  \n4378, 2723, 10079,  23360, 23361, 14652,  23687, 22964, 22956,  \n13124, 21886, 21856,  23690, 22964, 23687,  1118, 1117, 11861,  \n21153, 17617, 5047,  15480, 16140, 14022,  11309, 6601, 13334,  \n346, 18631, 347,  23179, 22969, 23518,  18873, 20443, 16887,  \n22054, 9397, 1052,  19868, 19867, 12868,  22743, 23359, 23363,  \n4284, 6786, 16831,  22923, 2632, 1313,  23364, 22971, 23520,  \n19139, 11075, 6153,  5047, 13686, 4599,  1667, 14066, 14065,  \n9915, 11066, 15568,  7799, 7167, 13922,  23183, 23368, 23863,  \n13912, 4521, 20300,  16184, 22161, 9314,  1935, 1934, 3962,  \n7063, 18329, 23693,  23694, 13512, 10534,  18756, 13949, 6657,  \n22111, 23695, 23696,  22971, 22749, 23369,  22756, 23523, 23368,  \n8238, 5040, 10660,  22744, 23184, 23186,  3810, 19622, 3276,  \n10834, 6429, 10633,  9887, 20165, 4261,  18945, 3365, 5964,  \n15246, 15245, 16000,  14725, 11966, 14724,  22523, 23186, 23372,  \n16190, 14008, 14009,  4585, 6962, 14955,  2388, 15900, 4713,  \n22756, 22527, 23371,  22746, 23185, 23697,  10755, 16085, 19150,  \n23374, 23698, 23373,  4477, 4478, 7514,  20753, 20752, 1548,  \n14364, 16209, 18791,  1083, 4604, 18199,  20853, 1806, 12372,  \n2834, 15491, 2833,  15524, 7605, 9008,  23700, 23188, 23528,  \n23700, 22972, 23188,  22758, 22761, 23374,  22761, 23527, 23374,  \n14974, 18863, 3043,  7479, 11215, 7480,  23192, 24151, 23527,  \n23525, 23189, 22974,  18019, 15482, 17690,  23701, 23188, 23376,  \n19893, 5520, 411,  7324, 6130, 11359,  8431, 14069, 8475,  \n21889, 5532, 4647,  14787, 22016, 6002,  8253, 19806, 5212,  \n23702, 23375, 23526,  9349, 2558, 19136,  21747, 7912, 3371,  \n9350, 1829, 3710,  5381, 21844, 20759,  8381, 8380, 8506,  \n23375, 23702, 24009,  1248, 8363, 4672,  6718, 12796, 19555,  \n9501, 5048, 4390,  7727, 9258, 7728,  17128, 14486, 3178,  \n23376, 23195, 23530,  23198, 23196, 23531,  23706, 16108, 18152,  \n23197, 22982, 23532,  5103, 1035, 3684,  4113, 5535, 1430,  \n673, 16031, 8872,  23198, 22984, 23196,  804, 13126, 16637,  \n12720, 12719, 7802,  627, 18155, 18154,  6126, 16413, 9507,  \n9263, 16549, 5745,  7269, 15038, 6198,  23198, 23710, 23380,  \n22986, 22988, 23534,  1754, 12346, 1474,  585, 18171, 2151,  \n8800, 14390, 14389,  17380, 10140, 19258,  3280, 13504, 12360,  \n12622, 18463, 3800,  12525, 10681, 10680,  22769, 23380, 23535,  \n23229, 13984, 8411,  15984, 11643, 7521,  754, 6011, 755,  \n22987, 23712, 23713,  23199, 22771, 23381,  22987, 23532, 23712,  \n6182, 17189, 6183,  1992, 8570, 7740,  22771, 22993, 23381,  \n22987, 23713, 23202,  19567, 7848, 18587,  22084, 22083, 394,  \n14891, 20919, 20386,  22991, 22769, 23535,  20633, 9880, 21106,  \n23539, 17427, 17426,  21798, 3076, 22728,  15028, 15724, 11572,  \n14295, 465, 7201,  23714, 23381, 23540,  23385, 22991, 23716,  \n7776, 2030, 4854,  3341, 3340, 12074,  8554, 3937, 5669,  \n384, 6534, 385,  13254, 19121, 5930,  1115, 985, 1116,  \n6871, 1137, 7659,  23540, 22995, 23718,  16685, 16684, 19921,  \n13453, 14744, 21568,  23717, 22999, 23202,  23206, 23202, 22999,  \n14668, 6099, 22493,  23718, 22995, 23543,  9300, 5027, 12024,  \n14548, 1579, 3138,  10205, 16752, 10206,  13739, 6669, 9992,  \n13623, 14107, 16769,  13660, 20474, 2150,  1312, 13362, 5640,  \n23212, 23388, 23546,  11204, 8156, 6592,  2915, 12247, 6792,  \n3776, 8403, 3232,  23547, 23211, 23545,  1089, 19993, 13542,  \n23208, 23000, 23550,  23543, 23208, 23550,  14255, 16620, 11890,  \n11454, 14655, 12984,  23000, 23548, 23550,  14137, 613, 14136,  \n23722, 22562, 23546,  430, 13123, 12033,  14753, 22865, 6606,  \n23722, 23393, 22562,  23004, 23551, 23548,  20795, 14478, 14611,  \n23723, 23551, 23724,  23006, 23393, 23552,  23724, 23551, 23215,  \n23552, 23007, 23006,  8279, 2476, 19539,  23726, 23007, 23552,  \n2364, 6070, 2365,  22304, 719, 16569,  23007, 23395, 23008,  \n3809, 3808, 4890,  7345, 13828, 16473,  22788, 23010, 23555,  \n22788, 23555, 23394,  23399, 23012, 23395,  21160, 505, 21593,  \n23727, 23394, 23555,  17492, 21078, 23728,  23556, 23221, 23396,  \n23398, 23729, 23396,  12228, 6060, 10989,  6917, 4373, 13333,  \n23558, 23220, 23557,  2494, 2495, 18769,  13771, 2257, 4111,  \n11637, 14923, 21731,  23559, 23729, 23398,  23016, 23559, 23398,  \n23730, 12493, 18202,  3783, 1520, 5905,  12639, 12522, 17665,  \n21541, 3945, 17760,  23731, 23224, 23397,  17405, 21506, 12747,  \n15307, 16578, 15308,  23224, 23562, 23401,  4153, 14153, 4406,  \n18911, 18181, 17321,  1917, 1916, 17302,  16482, 3297, 23537,  \n6489, 10572, 15696,  23402, 23400, 23226,  8111, 10161, 5723,  \n692, 19812, 6127,  20143, 19069, 23734,  18804, 7377, 11273,  \n15557, 13387, 14044,  23227, 23401, 23735,  23402, 23230, 23563,  \n558, 14915, 3979,  22224, 15198, 8150,  17326, 22379, 5740,  \n13431, 12642, 18175,  6842, 2889, 10227,  5667, 5668, 702,  \n23227, 23735, 23564,  11619, 7314, 3135,  22803, 23019, 23231,  \n11473, 21835, 18004,  23231, 23019, 23736,  23737, 23404, 23403,  \n7995, 1093, 1092,  8558, 8557, 11118,  2160, 11887, 2161,  \n12988, 8523, 10482,  6175, 4961, 4963,  15244, 7107, 20046,  \n23565, 23564, 23738,  15224, 14799, 1849,  13040, 20574, 7982,  \n10829, 10093, 4165,  23568, 23028, 23029,  22242, 7229, 9827,  \n10727, 6248, 10728,  9795, 5966, 13372,  15388, 8107, 4081,  \n23409, 23565, 23739,  23739, 23740, 23409,  12034, 12035, 8297,  \n3376, 14677, 5242,  20851, 15492, 20852,  2367, 18539, 767,  \n7000, 7001, 7717,  23741, 23567, 23571,  13404, 11240, 11239,  \n6667, 6389, 10216,  23743, 22815, 23569,  2113, 5779, 11982,  \n22815, 23743, 22586,  5088, 19511, 7197,  23745, 23409, 23740,  \n16469, 14095, 10481,  23744, 23033, 23411,  17486, 1967, 11103,  \n11103, 1967, 11104,  23409, 23745, 23570,  21687, 7934, 8964,  \n23570, 23745, 23574,  15728, 15730, 13471,  23580, 17763, 19384,  \n23491, 7920, 15722,  18423, 1588, 9371,  23238, 23576, 23571,  \n20421, 5522, 2645,  23041, 23234, 23574,  23576, 23746, 23571,  \n22356, 24192, 23038,  23412, 22821, 23575,  16587, 17562, 16291,  \n4679, 4680, 11378,  8228, 17578, 8227,  5972, 15700, 19346,  \n6631, 3498, 3497,  4967, 16612, 2596,  726, 725, 18765,  \n20732, 16717, 9716,  21575, 16277, 4767,  23040, 23749, 23575,  \n15322, 10430, 22205,  10405, 12395, 12394,  12458, 6853, 19371,  \n16402, 4885, 19266,  4884, 4885, 16402,  2352, 15862, 23750,  \n23749, 23040, 23578,  9061, 10185, 12158,  12227, 8993, 16471,  \n5095, 6847, 12759,  9674, 9675, 4114,  19018, 21811, 20367,  \n7306, 5473, 11282,  23753, 22594, 23415,  23416, 22594, 23753,  \n23418, 23751, 22827,  12306, 19033, 8291,  15855, 1566, 1565,  \n23240, 23047, 23755,  8273, 13271, 21571,  19973, 5241, 16183,  \n23581, 23756, 23045,  23417, 23045, 23756,  23242, 23757, 23241,  \n521, 8302, 22022,  20031, 14723, 18897,  22184, 5832, 5831,  \n4726, 865, 4724,  3265, 1951, 12784,  23053, 22373, 23759,  \n6775, 17766, 11629,  23054, 22830, 23053,  23056, 23421, 23587,  \n23056, 23587, 23422,  19599, 21425, 16072,  23589, 23245, 22831,  \n4657, 4656, 8925,  343, 21894, 344,  14271, 20543, 14270,  \n18574, 9824, 17695,  630, 13732, 629,  23423, 23594, 23591,  \n1479, 4824, 1303,  17035, 3150, 11604,  23593, 23250, 23248,  \n7644, 13881, 7718,  3047, 12262, 16777,  20480, 9546, 8632,  \n5391, 16750, 9857,  1509, 12645, 1749,  3880, 10591, 3881,  \n16750, 3823, 9857,  7948, 2660, 2661,  6468, 13178, 22324,  \n23424, 23593, 23425,  21514, 4299, 854,  23425, 23761, 23426,  \n23597, 23594, 23252,  10670, 10669, 9404,  9401, 13908, 9400,  \n20163, 3437, 7603,  12421, 3851, 14742,  23763, 23598, 23426,  \n10537, 5787, 4548,  23764, 23427, 23598,  19666, 10321, 6364,  \n11423, 2987, 4667,  894, 11469, 20007,  23765, 23063, 23256,  \n13255, 4929, 14616,  23766, 23599, 23429,  8805, 12412, 18702,  \n23766, 22136, 23431,  23766, 23429, 22136,  23430, 23910, 23259,  \n2842, 9421, 2843,  23431, 22136, 22849,  21299, 8053, 14623,  \n18138, 16463, 8534,  15433, 22924, 10881,  18691, 22591, 15192,  \n6182, 16243, 17189,  23768, 23767, 23069,  8168, 10186, 17580,  \n12800, 12130, 6335,  9640, 21314, 17009,  21000, 23068, 23432,  \n13554, 20388, 4446,  11501, 9723, 11562,  13075, 14020, 14970,  \n23770, 3608, 1039,  15895, 15183, 15182,  7497, 2337, 17243,  \n20946, 4162, 21488,  23261, 23263, 23916,  1396, 5962, 7303,  \n5324, 1905, 1049,  1399, 17808, 6598,  5250, 16046, 17336,  \n5122, 9679, 7170,  23265, 23266, 23771,  7431, 7430, 5354,  \n1535, 1534, 342,  23772, 22631, 23773,  22859, 22631, 23772,  \n22396, 23773, 23076,  11943, 14909, 17893,  23076, 23773, 22631,  \n18305, 21145, 1611,  23605, 23774, 23920,  23606, 23775, 23774,  \n23605, 23606, 23774,  20154, 1599, 1601,  23921, 23605, 23920,  \n12245, 8532, 18938,  23776, 23775, 23606,  6866, 5980, 6562,  \n23776, 23606, 23438,  5451, 5895, 4762,  12275, 9418, 6661,  \n23777, 23776, 23438,  430, 3690, 13123,  14539, 13685, 8064,  \n2285, 18634, 527,  23439, 23777, 23438,  1886, 3271, 8462,  \n16573, 16520, 2779,  23607, 23921, 23608,  23440, 23778, 23439,  \n4807, 20980, 5178,  23609, 23778, 23440,  8619, 15773, 15339,  \n23611, 23609, 23440,  7804, 18326, 8259,  8142, 1638, 8143,  \n1805, 15747, 3472,  19579, 898, 9732,  13130, 2155, 2156,  \n15364, 17797, 7660,  23442, 23779, 23611,  22278, 13774, 4943,  \n12125, 12124, 16807,  16444, 17468, 17467,  6170, 10773, 22556,  \n23442, 23780, 23779,  13726, 9491, 6666,  9145, 20612, 2021,  \n23444, 23780, 23442,  4985, 4971, 4970,  23781, 23780, 23444,  \n23782, 23783, 23613,  4666, 9074, 14197,  23613, 23783, 23278,  \n1060, 6187, 870,  23444, 23614, 23781,  1136, 11612, 11349,  \n23783, 23784, 23278,  13259, 13260, 1645,  15779, 11452, 1929,  \n5109, 15344, 5108,  23278, 23784, 23446,  23784, 23615, 23446,  \n23445, 23928, 23614,  23615, 23784, 23785,  6617, 13610, 20756,  \n23445, 23786, 23928,  672, 17580, 15637,  23788, 23786, 23447,  \n23447, 23786, 23445,  23446, 23615, 23448,  23615, 23789, 23448,  \n5759, 23790, 12127,  8801, 9316, 8802,  11745, 2727, 2728,  \n23788, 23447, 23616,  23449, 23448, 23789,  23449, 23789, 23616,  \n4849, 1100, 4734,  4821, 13032, 13397,  19242, 17320, 2569,  \n1917, 6554, 16728,  15785, 8901, 14989,  10373, 22340, 23792,  \n2788, 9934, 14447,  23618, 21032, 22633,  1764, 16673, 21559,  \n17528, 17868, 2053,  16069, 9587, 9586,  13154, 7637, 23223,  \n2273, 4347, 15237,  6768, 11471, 10052,  3802, 7892, 3803,  \n20094, 3115, 6612,  22864, 22637, 23797,  21495, 23797, 22637,  \n11524, 12691, 21575,  19631, 5991, 7276,  23456, 23454, 23796,  \n1135, 5967, 19564,  22636, 23104, 23798,  14554, 17991, 20343,  \n10441, 12296, 3369,  23457, 23456, 23619,  23619, 23456, 23799,  \n1669, 6455, 17131,  21040, 21041, 23800,  7510, 15469, 5665,  \n23801, 22636, 23798,  11628, 12251, 6971,  10805, 13374, 20487,  \n3302, 11333, 3303,  17895, 2940, 14931,  19426, 14783, 3205,  \n1472, 6954, 693,  18752, 20609, 12032,  23621, 23458, 23620,  \n22636, 23801, 22639,  5113, 6379, 7458,  19152, 5759, 20058,  \n5391, 13635, 23384,  2792, 13060, 22425,  5132, 16263, 5131,  \n14507, 19357, 15635,  23621, 24080, 23802,  10452, 3127, 11458,  \n18088, 23330, 8513,  10620, 10273, 10274,  23290, 23289, 23621,  \n15278, 6150, 14522,  6554, 469, 470,  3775, 9693, 9694,  \n23465, 23803, 23460,  20310, 3588, 3323,  23290, 23621, 23802,  \n23461, 22644, 23110,  23805, 23288, 23466,  11535, 1130, 4094,  \n10590, 9383, 2143,  19696, 2978, 5641,  23468, 23290, 23802,  \n1234, 5361, 1232,  2992, 15764, 5814,  22877, 23803, 23465,  \n23468, 23802, 23628,  22877, 23295, 23803,  23468, 23628, 22651,  \n5631, 19169, 11570,  23469, 22650, 22649,  14161, 4460, 4459,  \n11625, 5650, 5540,  23807, 3947, 10253,  23808, 23111, 22650,  \n7229, 17118, 16729,  23294, 23628, 23113,  13888, 3983, 15546,  \n23298, 23299, 23810,  1795, 9932, 3576,  2965, 12967, 3833,  \n2293, 15622, 15623,  23809, 23304, 23810,  23810, 23304, 23298,  \n18478, 5493, 8022,  13173, 20031, 13172,  20111, 12289, 3252,  \n7773, 11171, 7772,  9175, 9176, 6021,  16462, 11932, 19113,  \n11945, 7385, 18622,  19996, 21975, 14329,  393, 6461, 11366,  \n17783, 2220, 14578,  8521, 5736, 4049,  1364, 3251, 3252,  \n8647, 15303, 8646,  2783, 2643, 11289,  9965, 3085, 3084,  \n7247, 14145, 7248,  2589, 824, 4804,  9415, 9416, 13818,  \n23635, 22885, 23631,  22661, 22654, 23631,  13570, 15797, 20478,  \n22654, 23111, 23631,  23627, 22660, 23121,  23120, 22885, 23635,  \n16545, 16546, 11031,  2755, 3813, 10024,  23472, 23114, 23632,  \n13758, 20376, 11846,  23472, 23632, 23812,  21221, 29152, 14936,  \n7207, 10391, 10392,  23303, 23472, 23637,  9735, 9736, 5659,  \n23472, 23812, 23637,  5511, 6594, 6078,  12011, 18026, 2038,  \n23476, 22883, 23474,  23116, 22883, 23476,  4834, 4836, 16508,  \n22704, 16607, 4870,  17151, 5522, 17152,  7976, 17009, 7977,  \n2579, 3631, 12893,  18800, 20989, 10930,  18715, 19295, 4338,  \n21280, 22408, 6551,  18825, 18642, 9328,  16415, 1945, 18105,  \n12942, 15116, 14263,  23642, 22185, 22427,  18970, 12063, 2383,  \n16243, 8042, 8043,  23813, 23477, 23641,  23477, 23813, 23308,  \n9335, 17603, 1655,  7670, 20677, 15445,  23308, 23813, 23815,  \n22667, 23308, 23816,  13453, 15265, 14744,  23642, 22427, 22670,  \n11444, 12108, 21095,  2120, 661, 4312,  23124, 23127, 23818,  \n23478, 23647, 22672,  23642, 22670, 23819,  13453, 366, 5933,  \n18121, 16125, 12967,  22898, 23819, 22670,  23309, 23821, 23644,  \n398, 6915, 6993,  14315, 20278, 14316,  23310, 23821, 23309,  \n10135, 11432, 4004,  12662, 4637, 4636,  19109, 8458, 8457,  \n23822, 23311, 23645,  16396, 14007, 21226,  16396, 21226, 16395,  \n6051, 15203, 5135,  23823, 23131, 23644,  9445, 23824, 7458,  \n23131, 23823, 23483,  2895, 18829, 19524,  1424, 1314, 17540,  \n23825, 23482, 23822,  23482, 23311, 23822,  7334, 13274, 11447,  \n23313, 23959, 23481,  23826, 23959, 23313,  13544, 3245, 12600,  \n19783, 17835, 21086,  23649, 23483, 23823,  23819, 22898, 23651,  \n19177, 14536, 14524,  23826, 23313, 23648,  14349, 4688, 14549,  \n16665, 16664, 19565,  5237, 19679, 3756,  5432, 21992, 5433,  \n23134, 22897, 22434,  17802, 8571, 19971,  7167, 7800, 10306,  \n23339, 6090, 9355,  20418, 23828, 10263,  23074, 20800, 5736,  \n24574, 6394, 6395,  8706, 11635, 8707,  19313, 7384, 3090,  \n23318, 23649, 23827,  23137, 23649, 23318,  6910, 14581, 6911,  \n15325, 9005, 15267,  23315, 23830, 23831,  15157, 16909, 14559,  \n12758, 8488, 17747,  24435, 23832, 23314,  9063, 1235, 18868,  \n20362, 7218, 19827,  23827, 23829, 23318,  1649, 11704, 16973,  \n23318, 23829, 23487,  9445, 22954, 9800,  4594, 7922, 13800,  \n15216, 5944, 375,  15216, 375, 5506,  23652, 23650, 23324,  \n585, 2151, 586,  18389, 12180, 18390,  23833, 23321, 23486,  \n23489, 23652, 23324,  23489, 23971, 23652,  23653, 23145, 23322,  \n9354, 9353, 10824,  23829, 23834, 23487,  19675, 6250, 6249,  \n4293, 11209, 5970,  9244, 16541, 17072,  2588, 12252, 13269,  \n20424, 17732, 10327,  22684, 23835, 23142,  23835, 23486, 23142,  \n3587, 13906, 2154,  21538, 6757, 21537,  19204, 21677, 1633,  \n2131, 14887, 2132,  20980, 12625, 19709,  23144, 23656, 23490,  \n22690, 23322, 22685,  10858, 1303, 11697,  17450, 11821, 17451,  \n8463, 15616, 8464,  23834, 23657, 23487,  14957, 16026, 17637,  \n2789, 4962, 582,  18470, 16005, 3800,  23840, 23657, 23834,  \n6388, 1204, 17896,  23654, 23838, 23492,  23654, 23492, 22691,  \n7398, 21845, 4683,  336, 6294, 19416,  14309, 14734, 4681,  \n20565, 3390, 712,  22819, 1194, 12828,  10407, 18149, 16793,  \n12114, 22652, 20412,  12194, 5492, 9446,  23329, 23658, 23664,  \n23488, 23657, 23840,  3297, 14941, 5434,  22117, 18365, 17611,  \n21473, 13187, 594,  9046, 18722, 7401,  23150, 21922, 23662,  \n23488, 23840, 23663,  20544, 7192, 8343,  14425, 19748, 3168,  \n21440, 3278, 15672,  16553, 4393, 2090,  23158, 23841, 22918,  \n1870, 865, 4726,  22693, 23496, 23662,  23332, 23331, 23663,  \n6131, 7256, 15523,  23332, 23663, 23666,  23497, 23155, 23842,  \n9248, 23377, 8084,  6361, 11210, 11662,  20082, 12110, 12109,  \n7467, 4993, 16832,  20200, 20085, 8081,  5154, 9579, 16636,  \n17492, 17494, 17493,  14648, 5754, 15581,  12857, 23671, 23392,  \n6867, 346, 348,  14287, 22161, 19408,  18817, 12254, 8549,  \n23332, 23666, 23844,  23335, 22921, 23332,  4926, 14717, 6848,  \n23498, 23338, 23980,  23337, 23162, 23845,  23669, 23333, 22928,  \n23338, 23342, 23980,  22468, 23670, 23843,  4521, 3373, 12864,  \n22928, 23340, 23669,  19421, 3164, 13897,  5583, 5024, 5023,  \n6735, 8794, 2756,  10060, 15266, 15991,  11020, 7267, 7266,  \n20335, 10957, 21483,  5684, 5685, 16096,  23980, 23342, 23672,  \n19132, 20839, 493,  9032, 23848, 23849,  2038, 5720, 8724,  \n8863, 8862, 8928,  2347, 7005, 20819,  18807, 1312, 18808,  \n8550, 9809, 17587,  15192, 15191, 18691,  23675, 23501, 23502,  \n6075, 8026, 7729,  23168, 23501, 23675,  2911, 2912, 22098,  \n8423, 18861, 2528,  3784, 3783, 5905,  23851, 7445, 5658,  \n17593, 8632, 535,  23672, 23508, 23985,  10264, 21156, 18018,  \n1421, 657, 1752,  22943, 23853, 23344,  22936, 22933, 23987,  \n12018, 18607, 22095,  18503, 6590, 6589,  23672, 23174, 23508,  \n23852, 23345, 23504,  9404, 10669, 9405,  21286, 11025, 9870,  \n23345, 23852, 23512,  7376, 19988, 6567,  18987, 14737, 8765,  \n23675, 23513, 23505,  18112, 16808, 13005,  10142, 21563, 15335,  \n6316, 18484, 18844,  21338, 2761, 6119,  5999, 11300, 6000,  \n13396, 8828, 14362,  20420, 793, 669,  3341, 12074, 12073,  \n10667, 11831, 18103,  3361, 3360, 13150,  16976, 14483, 10646,  \n17207, 17208, 10598,  11460, 21744, 19528,  18481, 15953, 16122,  \n17229, 2614, 2615,  12443, 21213, 2601,  10805, 11995, 8660,  \n6551, 6552, 9666,  3310, 13783, 16369,  19622, 4376, 4295,  \n4936, 9698, 4937,  5385, 5387, 13921,  22344, 11102, 9378,  \n23514, 23515, 23681,  16324, 12172, 12173,  15134, 6330, 9213,  \n4290, 7864, 7865,  11300, 6189, 6000,  23854, 23352, 23683,  \n13096, 565, 566,  14460, 9352, 9351,  15933, 13490, 18758,  \n10619, 17031, 17030,  23855, 23516, 23178,  16547, 10884, 1283,  \n23683, 23352, 23857,  14975, 17016, 9480,  23356, 22963, 23686,  \n23516, 23687, 22956,  12515, 5297, 5298,  3855, 12313, 15129,  \n7293, 7952, 18524,  3921, 19094, 17978,  3767, 3795, 19685,  \n23686, 22967, 23362,  14497, 14404, 22491,  23692, 23358, 23688,  \n23518, 23517, 23179,  7652, 17640, 7653,  6614, 5009, 4608,  \n23692, 23363, 23358,  23520, 23362, 23364,  12383, 1974, 2043,  \n22964, 23690, 23859,  627, 6216, 18155,  23518, 22969, 23183,  \n23183, 23860, 23518,  2388, 4713, 299,  13380, 16109, 18861,  \n16785, 10644, 13399,  22742, 22964, 23859,  12533, 2178, 12534,  \n8564, 8563, 14877,  684, 12317, 16979,  9486, 5201, 11829,  \n14506, 4772, 7128,  4694, 15956, 1327,  6928, 1818, 13487,  \n22742, 23859, 23366,  9754, 9753, 14930,  5971, 4707, 23437,  \n23184, 23519, 23862,  7997, 9273, 4229,  23523, 23863, 23368,  \n8380, 8381, 14667,  5648, 1983, 14733,  22971, 23369, 23864,  \n18466, 3899, 3900,  23864, 23369, 23698,  10848, 4470, 16841,  \n20561, 15361, 11862,  23523, 22756, 23371,  23136, 7995, 1092,  \n23698, 23369, 23373,  8422, 19954, 8420,  15825, 5295, 11422,  \n17060, 16832, 4994,  7107, 16303, 1443,  2594, 3480, 3481,  \n16352, 5116, 14242,  23371, 22972, 23700,  9774, 17994, 896,  \n22746, 23697, 22754,  13798, 16366, 4869,  829, 12913, 14705,  \n8135, 8720, 13314,  16084, 10525, 7212,  3229, 2930, 10818,  \n23701, 23528, 23188,  20575, 10929, 19082,  23526, 23187, 23867,  \n11072, 6283, 6282,  13952, 15251, 8261,  7789, 10327, 3150,  \n24154, 23701, 23376,  24151, 23192, 23704,  23703, 23189, 23525,  \n1491, 17500, 3307,  21648, 8111, 9656,  8417, 14756, 733,  \n15249, 1331, 17333,  22537, 23703, 22982,  10844, 16122, 7974,  \n22537, 23189, 23703,  20670, 23370, 17397,  9481, 9480, 17016,  \n4118, 4117, 11381,  23704, 23192, 22767,  8439, 19108, 14933,  \n3460, 1475, 3461,  14204, 17032, 19592,  8039, 9550, 6900,  \n14570, 17065, 2785,  16124, 12635, 12634,  23532, 23868, 23709,  \n6844, 3383, 21107,  23530, 23199, 23708,  20537, 17709, 17707,  \n9633, 16799, 9634,  2171, 14165, 20172,  19134, 5360, 22189,  \n5510, 5511, 17504,  20013, 4083, 9704,  14889, 15738, 7039,  \n23532, 23709, 23870,  3801, 19338, 21010,  1922, 6672, 3089,  \n23712, 23532, 23870,  23872, 23199, 23714,  23871, 23535, 23380,  \n23199, 23381, 23714,  13182, 15687, 1576,  5650, 14580, 5540,  \n5162, 7165, 7164,  5544, 20510, 13915,  5700, 9040, 19554,  \n5732, 18233, 9752,  8706, 8707, 9453,  5749, 10912, 2423,  \n14933, 795, 8439,  14236, 17883, 3303,  18797, 7568, 395,  \n23713, 23712, 23717,  20830, 1513, 3702,  17834, 17618, 17079,  \n23873, 23717, 23712,  23713, 23717, 23202,  23540, 23715, 23714,  \n23716, 22991, 23535,  22992, 23204, 23386,  2249, 13178, 8978,  \n19789, 13716, 11293,  22061, 18349, 4025,  21188, 7701, 13430,  \n9279, 9960, 15563,  14605, 18471, 15365,  6085, 6068, 15152,  \n17192, 7029, 11144,  14243, 29546, 4894,  6453, 6452, 7970,  \n15542, 15541, 6673,  23544, 22999, 23717,  23719, 23204, 23209,  \n18552, 1185, 22930,  22302, 10751, 19298,  16593, 4969, 6019,  \n6109, 14959, 2594,  18248, 4391, 4392,  1231, 19708, 1229,  \n11651, 2135, 19924,  5695, 6271, 12959,  23214, 23002, 23547,  \n21744, 11460, 18401,  11766, 11206, 20921,  23721, 23550, 23548,  \n19440, 13355, 9936,  613, 21330, 14136,  21329, 3932, 7333,  \n7186, 8588, 7187,  17413, 16971, 14869,  1670, 5747, 20385,  \n12668, 6564, 4488,  12803, 16229, 21894,  23215, 23009, 23725,  \n4749, 705, 12608,  13249, 5868, 13248,  20908, 5086, 12695,  \n9039, 19804, 16267,  23726, 23877, 23007,  6828, 22324, 15489,  \n12241, 8031, 15238,  21331, 9713, 9714,  23727, 23878, 23394,  \n1518, 13016, 844,  23556, 23396, 23879,  23880, 23396, 23729,  \n23880, 23879, 23396,  8088, 4493, 3394,  2874, 5511, 6078,  \n24022, 23729, 23881,  6545, 3595, 18036,  4019, 3183, 350,  \n4924, 17485, 22579,  18866, 7652, 10190,  23729, 23559, 23881,  \n10405, 12394, 4552,  11711, 18459, 14871,  21174, 14810, 18292,  \n23882, 23399, 23395,  11898, 1961, 3799,  23555, 23219, 23727,  \n18202, 12493, 12038,  23731, 23397, 23558,  4315, 2017, 4316,  \n23219, 23732, 23884,  10042, 2705, 21842,  1671, 2713, 5643,  \n23731, 23562, 23224,  23559, 23400, 23733,  23881, 23559, 23733,  \n23560, 23218, 23399,  21167, 11935, 14086,  6856, 1284, 12235,  \n8508, 14658, 10714,  5451, 14325, 22942,  3106, 10577, 13423,  \n23561, 23888, 22794,  8701, 6017, 8700,  11915, 10109, 15930,  \n3171, 19142, 16763,  2878, 11172, 22018,  6408, 5336, 5977,  \n18609, 13751, 15437,  7225, 8492, 1134,  13541, 8608, 19374,  \n12084, 18343, 22289,  23888, 23732, 22794,  18747, 8553, 2928,  \n23562, 23885, 23401,  23400, 23402, 23886,  19354, 20426, 2056,  \n23889, 23735, 23401,  5466, 13551, 5834,  2617, 466, 467,  \n4268, 4269, 13642,  21384, 3406, 14634,  4517, 4518, 5600,  \n23402, 23563, 23892,  23218, 23887, 23019,  1420, 17994, 21596,  \n23561, 23404, 23888,  1247, 12316, 13574,  12514, 23583, 21211,  \n23735, 23891, 23738,  23564, 23735, 23738,  10330, 5475, 8118,  \n4978, 1777, 1776,  650, 1249, 606,  11169, 11168, 15860,  \n23737, 23403, 23893,  2375, 5756, 6797,  23563, 23405, 23567,  \n23892, 23563, 23567,  4156, 7728, 16026,  1513, 6728, 3702,  \n23028, 23568, 23403,  23894, 23565, 23738,  23895, 23231, 23736,  \n18921, 21079, 14368,  23893, 23403, 23896,  16314, 10260, 5365,  \n22808, 23231, 23895,  3682, 6778, 3683,  7263, 21349, 10367,  \n1049, 1905, 1907,  23892, 23567, 23741,  15431, 5114, 3867,  \n17088, 7042, 7041,  14125, 5570, 5569,  7758, 12228, 16779,  \n3275, 4151, 4150,  23569, 22815, 23895,  6815, 20150, 16828,  \n14221, 6833, 11232,  22815, 22808, 23895,  8876, 19405, 3709,  \n18159, 10859, 11334,  1476, 2386, 1435,  7714, 8478, 7713,  \n23033, 23744, 23568,  5132, 17219, 16263,  9895, 5772, 2798,  \n20575, 6496, 10929,  3084, 3085, 2545,  7198, 3302, 3645,  \n23741, 23571, 23897,  7397, 621, 620,  23898, 23744, 23411,  \n8754, 2028, 2027,  23897, 23571, 23746,  23743, 23237, 22586,  \n2922, 6325, 2923,  15444, 12885, 6581,  13663, 10086, 5260,  \n3921, 3920, 7466,  21690, 12353, 12355,  22760, 19332, 15206,  \n19982, 12974, 4220,  23576, 23899, 23746,  23038, 24192, 23577,  \n23044, 23041, 23574,  17542, 21832, 4517,  22102, 2758, 5812,  \n12170, 18341, 1902,  15155, 10528, 13966,  14792, 20196, 16566,  \n23042, 23579, 23576,  23579, 23899, 23576,  23579, 23900, 23899,  \n23577, 23747, 23413,  19644, 3831, 18848,  3445, 15139, 10408,  \n6103, 9286, 9285,  15756, 9172, 16703,  23578, 22827, 23751,  \n4853, 5588, 14617,  23749, 23578, 23751,  23419, 23900, 23579,  \n20216, 23901, 13713,  8578, 3398, 4572,  22321, 17183, 11581,  \n21180, 12769, 3608,  23582, 23900, 23419,  5541, 14580, 13649,  \n23416, 23754, 23581,  3277, 17697, 15451,  7753, 9771, 1472,  \n23755, 23047, 23903,  15794, 12475, 21815,  23584, 22371, 23050,  \n22981, 4496, 22325,  2183, 4403, 4402,  7449, 10906, 16856,  \n17166, 6290, 7341,  22829, 23584, 23585,  1481, 2248, 8598,  \n14279, 6766, 23904,  23242, 23052, 23586,  23759, 22373, 23585,  \n23759, 23420, 23053,  16027, 15221, 10383,  12582, 13423, 320,  \n23588, 23760, 23586,  5287, 17044, 17045,  11621, 11620, 1356,  \n18123, 15119, 7489,  23245, 23906, 23590,  23588, 23251, 23423,  \n11323, 17287, 5685,  5986, 22295, 5987,  11396, 6417, 716,  \n15638, 12614, 20874,  24050, 23248, 23246,  23423, 23251, 23594,  \n12987, 3182, 3181,  18757, 19596, 13821,  11471, 15863, 8869,  \n17701, 15827, 8301,  23425, 23593, 23907,  23443, 3896, 17096,  \n23425, 23907, 23761,  20529, 9409, 20999,  23591, 23594, 23597,  \n16898, 7689, 3924,  21923, 5450, 5449,  19496, 9904, 19495,  \n23761, 23763, 23426,  19983, 19703, 19982,  4383, 5051, 13553,  \n5673, 7494, 20141,  12323, 20392, 15808,  23252, 23599, 23597,  \n11885, 3133, 683,  23908, 23765, 23601,  23598, 23601, 23764,  \n23598, 23908, 23601,  15395, 6027, 2023,  23765, 23600, 23063,  \n23765, 23256, 23601,  23909, 23910, 23430,  23600, 23909, 23430,  \n23600, 23430, 23255,  10222, 9890, 10221,  7885, 7887, 9016,  \n23910, 23911, 23259,  2507, 12215, 12028,  21542, 20867, 21541,  \n23767, 22386, 23069,  745, 21747, 14633,  3696, 9020, 16604,  \n23912, 23432, 23068,  23434, 23769, 23068,  23769, 23434, 23914,  \n15960, 16337, 13391,  23914, 23434, 23260,  23915, 23260, 23072,  \n15960, 13391, 13392,  23916, 23915, 23072,  23435, 22855, 23603,  \n23072, 23261, 23916,  3172, 2338, 6703,  23917, 23916, 23263,  \n18058, 1861, 11281,  21760, 14277, 14904,  23771, 23917, 23265,  \n23917, 23263, 23265,  22153, 17971, 12460,  20415, 12013, 19712,  \n22859, 23771, 23266,  10894, 4296, 5240,  9967, 10393, 1124,  \n23772, 23771, 22859,  16039, 3637, 3636,  11206, 8520, 11207,  \n23919, 16677, 19391,  13404, 1692, 11897,  24059, 23920, 23774,  \n19461, 17261, 17175,  17160, 9551, 3670,  16316, 13811, 15370,  \n7471, 22082, 22526,  7489, 6870, 11919,  5847, 172, 15522,  \n11801, 4393, 12664,  23777, 23922, 23776,  20196, 14793, 13387,  \n16163, 8778, 2968,  23439, 23778, 23777,  1602, 4829, 1603,  \n7536, 730, 1705,  14731, 6542, 1080,  5310, 13043, 17601,  \n1348, 22189, 1349,  8326, 5786, 21989,  24063, 23608, 23924,  \n17830, 8846, 1200,  23925, 23778, 23609,  23925, 23923, 23778,  \n2277, 19978, 11112,  19211, 4336, 8404,  6242, 1638, 8142,  \n24063, 23610, 23608,  13770, 2107, 1766,  11857, 21278, 18067,  \n11449, 10081, 8690,  23611, 23779, 24064,  17146, 16309, 1608,  \n23610, 24065, 23612,  10804, 19696, 3478,  20140, 14111, 9573,  \n5104, 5103, 15508,  23779, 23780, 23926,  19010, 18725, 10540,  \n7084, 18600, 7085,  7032, 5844, 7033,  23781, 23927, 23780,  \n23928, 23781, 23614,  1136, 11349, 1135,  10493, 4664, 1763,  \n12001, 11752, 17122,  19079, 10813, 8638,  23616, 23929, 23788,  \n23789, 23615, 23787,  23789, 23929, 23616,  20202, 19616, 13251,  \n22737, 4846, 4845,  5029, 10130, 22663,  13039, 4783, 20563,  \n21032, 23618, 23793,  2059, 2736, 2254,  14469, 4511, 14470,  \n23795, 18522, 23285,  15950, 663, 20241,  23102, 21032, 23794,  \n10733, 6729, 6728,  11057, 11248, 8887,  2594, 3481, 6382,  \n23285, 22866, 23453,  22864, 23797, 23454,  23796, 23454, 23930,  \n18181, 600, 17321,  4835, 11465, 20941,  13070, 1866, 1867,  \n4835, 20941, 4945,  23619, 23931, 23932,  23799, 23931, 23619,  \n11991, 13446, 15098,  23619, 23932, 23620,  17359, 16331, 5196,  \n16834, 22573, 6966,  6068, 6085, 22187,  734, 5271, 735,  \n12703, 21695, 8946,  23937, 23109, 23291,  23620, 23932, 23621,  \n8804, 5871, 9581,  23801, 23107, 22639,  8151, 8554, 5669,  \n1047, 6246, 14557,  23460, 23937, 23291,  13845, 365, 15243,  \n21307, 8244, 18323,  23106, 21045, 23459,  5127, 12555, 3359,  \n16839, 3241, 9998,  288, 18144, 5982,  23942, 23460, 23803,  \n23932, 24080, 23621,  23205, 9869, 4443,  16435, 17300, 18872,  \n22671, 17691, 356,  19696, 5641, 7747,  23463, 23108, 23625,  \n24836, 23464, 23804,  15698, 10051, 13462,  2436, 6402, 2437,  \n23461, 23110, 23462,  4138, 14519, 8559,  6800, 6799, 1079,  \n8580, 2097, 2231,  23295, 23945, 23803,  1771, 14843, 19120,  \n16562, 16561, 8936,  23469, 22649, 23464,  21492, 17763, 23580,  \n17042, 22740, 16937,  15211, 15210, 10113,  23946, 23810, 24083,  \n23299, 24083, 23810,  10668, 17069, 11675,  22650, 23469, 23808,  \n23304, 23809, 23811,  22329, 23947, 22419,  13693, 23948, 18034,  \n13272, 9692, 7971,  2965, 2511, 12967,  19213, 19214, 17060,  \n18442, 6624, 10330,  1180, 9035, 8568,  13818, 9416, 16464,  \n15884, 17411, 11337,  14654, 7753, 22591,  17951, 5164, 14897,  \n20191, 6187, 11599,  23808, 23949, 23631,  18071, 5348, 11426,  \n10167, 7306, 7307,  23301, 23119, 23120,  23301, 23120, 23634,  \n23120, 23636, 23634,  20401, 3806, 15788,  23811, 23633, 23304,  \n15093, 15983, 15982,  23636, 23635, 23951,  8374, 8373, 7657,  \n23951, 23635, 23631,  19551, 19478, 19479,  965, 1216, 18382,  \n23952, 22711, 13950,  23953, 22435, 23633,  18350, 11340, 2506,  \n11203, 784, 19259,  21306, 11429, 21307,  2542, 4530, 4529,  \n11843, 20341, 7211,  2068, 16350, 13861,  16235, 13534, 13552,  \n15234, 7470, 15235,  8230, 1868, 13381,  10231, 9696, 766,  \n10063, 20267, 5709,  10659, 12818, 10660,  23474, 23639, 23476,  \n4987, 15807, 23325,  3887, 4054, 12752,  21038, 6867, 14360,  \n23638, 23641, 23306,  14785, 8530, 8286,  10762, 4203, 12605,  \n23641, 23814, 23813,  20797, 2716, 2715,  23813, 23814, 23815,  \n3223, 7087, 14892,  10518, 3226, 3227,  23815, 23816, 23308,  \n22667, 23816, 23125,  1782, 10081, 10855,  23125, 23816, 23817,  \n5003, 15703, 11347,  23817, 23816, 23957,  4762, 4763, 14325,  \n23958, 23642, 23819,  23817, 23643, 23125,  23820, 23643, 23817,  \n6240, 7172, 13850,  6464, 6631, 3497,  23960, 23126, 23643,  \n16743, 12560, 8625,  23126, 23960, 23645,  21167, 5865, 19515,  \n17123, 4056, 11268,  23961, 23315, 23647,  16587, 358, 2173,  \n8454, 3611, 7130,  23310, 23963, 23821,  8805, 18702, 1810,  \n840, 11558, 8179,  23310, 22897, 23966,  13131, 11795, 8231,  \n15081, 15504, 3044,  22897, 23134, 23966,  20094, 6612, 13274,  \n23823, 23965, 23649,  4775, 8633, 3631,  23482, 23967, 23314,  \n10307, 21876, 10306,  16564, 12151, 14269,  23965, 23827, 23649,  \n23826, 23648, 23484,  11251, 22339, 20719,  14706, 9615, 3401,  \n24103, 23968, 23827,  23965, 24103, 23827,  5496, 9629, 5820,  \n1225, 4732, 15339,  10983, 7484, 21204,  8203, 13937, 4474,  \n23968, 23829, 23827,  23650, 23969, 23651,  23654, 22678, 23832,  \n12444, 11140, 12572,  5360, 5819, 13103,  6451, 17739, 5601,  \n17720, 15076, 17195,  16976, 10646, 7308,  23319, 23315, 23831,  \n23832, 22678, 23314,  10948, 10947, 13961,  11063, 12566, 11064,  \n23969, 23650, 23652,  8388, 5810, 14107,  10276, 6141, 10275,  \n13706, 9117, 13872,  23652, 23971, 23969,  2246, 9174, 9182,  \n2325, 2324, 10679,  22724, 6166, 6165,  23144, 23831, 23656,  \n5014, 12505, 9649,  1060, 1062, 18142,  4394, 20842, 6905,  \n15652, 19562, 16085,  8364, 11686, 5224,  14469, 6969, 6171,  \n16981, 3699, 10232,  1992, 22979, 3977,  1954, 14574, 15232,  \n7277, 22931, 11035,  6585, 6064, 18890,  3474, 3989, 2649,  \n23653, 23322, 23837,  18449, 6757, 21538,  1349, 5360, 13103,  \n5361, 10603, 1232,  11615, 4871, 17925,  17122, 19772, 16697,  \n12425, 11605, 3174,  23489, 23327, 23659,  15386, 16983, 2898,  \n23837, 23322, 22690,  1675, 7758, 5199,  10436, 23972, 22608,  \n22684, 23147, 23835,  24111, 23835, 23147,  13319, 13182, 12221,  \n15689, 13880, 15690,  3027, 13742, 7941,  24108, 23152, 23494,  \n23839, 23837, 22690,  24445, 23837, 23839,  5534, 6207, 6208,  \n14513, 17064, 19035,  23973, 23840, 23834,  19295, 4583, 4584,  \n10326, 10060, 15992,  864, 17802, 3012,  6345, 8594, 21154,  \n20671, 20672, 21645,  2130, 19259, 20125,  5447, 6591, 13202,  \n10113, 15210, 21709,  19505, 21024, 6156,  14661, 17646, 6094,  \n22690, 23660, 23839,  17301, 16543, 14363,  5370, 8274, 21644,  \n12094, 20215, 16847,  22789, 6578, 16040,  10211, 13231, 7284,  \n325, 14659, 18323,  23658, 23976, 23664,  13007, 14385, 18374,  \n17365, 9326, 1453,  5748, 5749, 6693,  5545, 10799, 20570,  \n9836, 14250, 9837,  22918, 23841, 23660,  18716, 8728, 5346,  \n22692, 23492, 23665,  1679, 1581, 22611,  4197, 14309, 17008,  \n23978, 23840, 23977,  23663, 23840, 23978,  23155, 23664, 23842,  \n22695, 22692, 23665,  5590, 22399, 17526,  5302, 8121, 8457,  \n1770, 1769, 674,  23979, 14678, 20390,  9184, 811, 9287,  \n5807, 2119, 2120,  4113, 14860, 6065,  11651, 10566, 8833,  \n9470, 20421, 5852,  18727, 1221, 13664,  22406, 22018, 20156,  \n20163, 13505, 3437,  2812, 6888, 2810,  4013, 10596, 2264,  \n6819, 6578, 6577,  4860, 6436, 18935,  1399, 1400, 3158,  \n11754, 11755, 20173,  10358, 12185, 3021,  12303, 9026, 9995,  \n1504, 21138, 16222,  1850, 1849, 12990,  23845, 23162, 23665,  \n5106, 8495, 5107,  7542, 3653, 11097,  23500, 23497, 23846,  \n23154, 23497, 23500,  11138, 11708, 22863,  11155, 23940, 20714,  \n23982, 23669, 23983,  4720, 5064, 4923,  14865, 3454, 18297,  \n4739, 11863, 3892,  23984, 23843, 23670,  11487, 3725, 3724,  \n2842, 12667, 9421,  23850, 23669, 23340,  23852, 23500, 23846,  \n17818, 16979, 3784,  14895, 21207, 2729,  10040, 557, 20192,  \n23504, 23500, 23852,  10645, 22733, 13348,  21058, 16080, 14847,  \n16782, 13349, 14124,  23340, 24299, 23850,  22914, 21936, 7058,  \n23986, 23670, 23341,  13072, 20111, 3252,  15934, 2562, 10477,  \n22016, 19106, 6002,  2260, 1531, 11386,  494, 493, 16063,  \n21506, 10920, 12747,  22249, 4908, 12055,  23673, 23344, 23853,  \n13087, 16565, 18973,  19931, 21254, 17162,  7845, 14487, 11479,  \n22943, 23175, 23853,  23505, 23168, 23675,  22936, 23987, 23988,  \n1857, 7309, 19612,  15458, 9104, 13796,  20342, 20326, 761,  \n3557, 20200, 10467,  22936, 23988, 23506,  23513, 23990, 23515,  \n23512, 23852, 23991,  23990, 23675, 23989,  23149, 13477, 6855,  \n23506, 23993, 23349,  23990, 23513, 23675,  1736, 5113, 1737,  \n23351, 23994, 23509,  6121, 16746, 6120,  12305, 8968, 17072,  \n17993, 5884, 5883,  23995, 23175, 23352,  10440, 6398, 21721,  \n21433, 13936, 20880,  9137, 1552, 8914,  9340, 13397, 15694,  \n13214, 12645, 9660,  15076, 19267, 15077,  7631, 1993, 19162,  \n12668, 6440, 6564,  23996, 23515, 23990,  16783, 14123, 16234,  \n23351, 22947, 23677,  1653, 16276, 12411,  1756, 15002, 15001,  \n23995, 23352, 23854,  10689, 16001, 9756,  16200, 7450, 10541,  \n23856, 8521, 7832,  6483, 6482, 10426,  8876, 11042, 19405,  \n4293, 17900, 3077,  23355, 23356, 23680,  10207, 18222, 14226,  \n19884, 12042, 10378,  23178, 23512, 23855,  23681, 23684, 23354,  \n19192, 19801, 16765,  14973, 20163, 7603,  14707, 2186, 15276,  \n21534, 1570, 8886,  5341, 18822, 12553,  759, 13456, 592,  \n28419, 20113, 2764,  23358, 23354, 23684,  3617, 9960, 18008,  \n9163, 488, 3443,  18821, 2752, 4498,  3094, 15569, 13762,  \n20437, 16896, 7424,  23855, 23687, 23516,  23688, 23684, 23998,  \n23358, 23684, 23688,  16685, 19921, 19025,  5888, 22852, 5887,  \n7854, 2240, 2239,  20578, 15941, 15942,  11021, 2595, 10658,  \n1625, 10236, 2787,  21347, 16337, 18488,  17162, 7232, 20938,  \n11944, 17893, 5676,  6692, 3890, 4409,  1124, 14941, 16481,  \n11884, 23148, 16408,  7437, 9991, 15151,  7105, 18197, 14194,  \n23363, 23692, 23862,  19094, 3411, 16523,  4189, 4188, 1395,  \n3127, 13004, 11458,  14866, 15312, 15311,  23519, 23363, 23862,  \n13966, 19580, 15706,  5708, 16613, 851,  17155, 16448, 4707,  \n13015, 10512, 11783,  6361, 13429, 23913,  5191, 13658, 721,  \n11292, 11293, 7114,  16438, 18357, 18358,  19325, 7225, 17328,  \n20714, 23940, 4140,  22733, 5766, 21474,  15091, 20657, 3712,  \n1296, 16509, 11906,  18244, 21865, 18539,  5478, 14216, 1426,  \n7304, 16830, 10388,  19204, 20661, 15958,  15621, 1771, 19120,  \n6159, 6158, 11394,  23185, 24002, 24003,  24003, 23697, 23185,  \n14319, 13422, 14320,  24003, 24002, 24004,  23371, 23865, 23523,  \n11272, 15330, 2964,  22289, 21319, 12643,  14372, 1802, 15052,  \n3481, 14902, 2419,  23865, 23371, 23700,  8086, 6095, 2709,  \n12625, 1106, 19709,  23372, 23186, 23524,  15360, 8089, 6214,  \n382, 15130, 14833,  7520, 21314, 13526,  3029, 23115, 16505,  \n19117, 14916, 18004,  8948, 19375, 2846,  579, 12406, 14305,  \n3101, 17752, 7797,  9211, 5061, 16791,  23374, 23527, 24151,  \n7659, 1137, 21818,  23525, 22974, 24006,  18172, 13824, 8044,  \n9765, 13468, 10069,  1363, 1362, 1644,  10733, 6863, 6729,  \n19108, 8517, 8659,  19362, 8282, 15457,  23867, 23702, 23526,  \n24008, 23702, 23867,  9040, 11133, 13992,  23702, 24008, 24009,  \n6449, 13211, 13210,  10657, 6052, 6460,  23868, 22982, 23703,  \n17141, 6732, 17928,  23191, 24009, 23196,  13758, 7899, 16734,  \n23376, 23707, 24154,  22493, 19603, 14668,  23376, 23530, 23708,  \n22982, 23868, 23532,  23376, 23708, 23707,  18564, 3560, 12621,  \n14728, 4901, 7019,  14090, 13350, 7567,  9949, 3530, 16378,  \n17421, 9281, 3582,  23869, 22986, 23534,  12597, 8169, 18438,  \n23708, 23199, 23872,  19948, 15569, 19711,  17259, 11131, 7377,  \n985, 8586, 986,  4693, 1327, 22894,  1655, 9849, 10467,  \n11915, 15930, 744,  11619, 3135, 6128,  8328, 19785, 20313,  \n2331, 22781, 7416,  11366, 6461, 6053,  23872, 23714, 24010,  \n21842, 5196, 2244,  6693, 16842, 2583,  3516, 3316, 17518,  \n23873, 23712, 24011,  24013, 17826, 2089,  24014, 22992, 23386,  \n1327, 15956, 20554,  4473, 18741, 17686,  23540, 23718, 23715,  \n7353, 12574, 6204,  457, 2828, 2827,  7465, 2179, 5914,  \n22001, 4079, 16362,  24015, 23388, 23385,  23873, 23544, 23717,  \n2392, 1959, 2686,  23718, 23874, 24016,  23389, 23544, 23545,  \n19732, 22765, 18295,  23874, 23718, 23543,  7311, 698, 641,  \n19631, 20964, 19849,  3493, 5041, 5491,  9064, 6236, 19679,  \n709, 9702, 6451,  12855, 16424, 3351,  17627, 16057, 5928,  \n19900, 16660, 21382,  12441, 4591, 16554,  5812, 2757, 4920,  \n23543, 23550, 23874,  11717, 15972, 8078,  10179, 16612, 4968,  \n24017, 23874, 23550,  17314, 12191, 17315,  3920, 3921, 17978,  \n23550, 23721, 24017,  13997, 3730, 9204,  16853, 435, 9456,  \n23548, 23551, 23721,  14351, 10443, 20985,  1573, 15066, 20671,  \n6626, 21569, 8354,  23723, 23721, 23551,  11361, 3358, 997,  \n1640, 18397, 3761,  15981, 15063, 21475,  23009, 23554, 23725,  \n8752, 6887, 9562,  11345, 19886, 16843,  23878, 23554, 23394,  \n24020, 23554, 23878,  16010, 24021, 4639,  24023, 23880, 24022,  \n23395, 23007, 23877,  1546, 1545, 6400,  23880, 24023, 23879,  \n16083, 12248, 4222,  23556, 23879, 24025,  24022, 23880, 23729,  \n24022, 23881, 24024,  6840, 21549, 6841,  24174, 24022, 24024,  \n16729, 7994, 16730,  4284, 15783, 17238,  23557, 24025, 24027,  \n23557, 23556, 24025,  6436, 7894, 7858,  23557, 24027, 23558,  \n11825, 20858, 21214,  24027, 23731, 23558,  23071, 13799, 20124,  \n12772, 1466, 8902,  24024, 23881, 23733,  14043, 17256, 12906,  \n24028, 23562, 23731,  23733, 23400, 23886,  6369, 17243, 2337,  \n23885, 23562, 24028,  23887, 23218, 23560,  12294, 12696, 5174,  \n3963, 21550, 6124,  20617, 23668, 16826,  8698, 967, 12376,  \n23401, 23885, 23889,  9881, 305, 6469,  24029, 21390, 3218,  \n6062, 7081, 7080,  10265, 18018, 20469,  15756, 18367, 9172,  \n23402, 23892, 23886,  13678, 18343, 13235,  23890, 23735, 23889,  \n13095, 566, 7706,  19682, 4300, 3819,  23888, 23404, 23737,  \n23735, 23890, 23891,  15534, 16156, 10196,  8697, 20265, 15554,  \n23736, 23019, 24334,  13249, 13248, 4159,  21838, 23378, 5834,  \n23887, 24334, 23019,  3391, 13961, 3718,  10068, 14803, 6492,  \n15662, 7085, 15658,  11428, 7010, 2957,  2394, 18986, 1358,  \n2042, 12383, 2043,  24031, 23894, 23738,  23891, 24031, 23738,  \n4897, 3341, 12073,  3588, 3587, 19847,  9867, 22958, 17002,  \n20116, 17518, 3316,  17803, 15823, 14612,  2161, 11998, 4617,  \n23892, 23741, 24032,  1453, 7324, 3482,  22344, 20428, 23140,  \n10818, 22750, 7960,  24033, 23565, 23894,  15705, 795, 14934,  \n23896, 23403, 23568,  1761, 21318, 2175,  24033, 23739, 23565,  \n3978, 7196, 14356,  17891, 15996, 10574,  23897, 24032, 23741,  \n6122, 12441, 12442,  12487, 5802, 5814,  6959, 13907, 8098,  \n3648, 8416, 9896,  18556, 909, 7473,  12295, 5267, 7914,  \n13773, 13774, 6754,  3532, 5905, 1519,  17241, 22869, 20501,  \n20078, 23235, 8545,  11884, 9249, 23148,  7166, 7105, 11570,  \n11574, 7115, 8566,  22620, 11240, 11897,  5694, 16878, 5695,  \n14924, 7390, 11124,  11993, 21678, 16575,  10449, 10448, 16106,  \n23574, 23745, 24035,  12814, 22152, 12812,  24035, 23902, 23574,  \n24036, 23412, 23575,  1346, 15463, 12536,  23044, 23574, 23902,  \n24037, 24038, 23900,  24038, 23899, 23900,  23272, 21221, 13347,  \n24040, 23413, 23747,  15459, 10636, 8025,  23239, 23413, 24040,  \n10342, 4653, 4654,  15311, 15340, 14662,  23752, 23044, 23902,  \n4513, 4063, 2231,  9714, 22415, 21331,  450, 12741, 448,  \n23415, 23043, 23239,  8637, 8638, 7362,  23582, 24194, 23900,  \n23900, 24194, 24037,  16859, 9210, 16308,  23418, 23240, 24043,  \n3873, 3874, 11042,  2428, 4401, 453,  14660, 3624, 3623,  \n23903, 23047, 23417,  19607, 6950, 11681,  23902, 24044, 24045,  \n16274, 4820, 4819,  23241, 23757, 23582,  23752, 23902, 24045,  \n6372, 2582, 6730,  9791, 14602, 15708,  23752, 24045, 23584,  \n9001, 5840, 14762,  23758, 23757, 23242,  13429, 11662, 11211,  \n3643, 14180, 17096,  23584, 24046, 23585,  1576, 6509, 18961,  \n6559, 7625, 21102,  23242, 23586, 23760,  23760, 23758, 23242,  \n20712, 15163, 15582,  23421, 23054, 23420,  17160, 17218, 21297,  \n13857, 8500, 8499,  24047, 23587, 23421,  2534, 10866, 19318,  \n11462, 11463, 3544,  17370, 23392, 20872,  4085, 4084, 15314,  \n23422, 23587, 24048,  14232, 17223, 1967,  9162, 13557, 1097,  \n23589, 24049, 23245,  10425, 10643, 4946,  3200, 3199, 6126,  \n23590, 24050, 23246,  23592, 23423, 23591,  23593, 23248, 24050,  \n22471, 12898, 16595,  1327, 1328, 22894,  10603, 19771, 10604,  \n14875, 12994, 11819,  5660, 2308, 12581,  23762, 23591, 23597,  \n7541, 6288, 3653,  458, 7015, 10310,  16877, 13404, 11239,  \n10709, 7913, 5267,  10373, 16245, 22340,  23919, 4483, 18395,  \n3529, 5359, 5238,  24212, 23598, 23763,  23762, 23597, 24052,  \n23908, 23598, 24212,  14129, 4603, 14127,  23765, 23908, 23600,  \n15415, 19126, 21815,  16894, 6035, 16895,  23597, 23599, 24052,  \n9944, 15679, 12535,  20177, 9629, 5496,  13817, 14673, 18175,  \n8874, 464, 15926,  5633, 3993, 16444,  21552, 21553, 16515,  \n19659, 22608, 14225,  23911, 23602, 23259,  24053, 24054, 23768,  \n13075, 20143, 15947,  438, 1527, 1526,  8393, 6923, 11195,  \n23912, 23068, 23769,  23433, 24056, 23603,  3746, 9284, 15656,  \n23914, 23260, 23915,  21725, 3059, 3061,  14416, 5562, 17766,  \n10440, 6604, 6398,  5473, 13623, 8460,  2890, 13597, 4001,  \n23918, 23264, 23435,  19502, 14904, 14277,  6228, 13129, 13016,  \n21747, 15170, 17940,  21825, 23435, 23264,  14931, 7968, 10219,  \n3415, 17421, 3582,  1301, 14978, 3086,  19036, 7309, 1857,  \n13374, 18487, 6328,  2621, 4294, 14898,  5906, 13838, 13837,  \n21601, 16752, 11503,  2093, 17925, 19917,  6524, 15813, 24060,  \n24058, 24059, 23774,  23775, 24058, 23774,  15696, 10572, 6671,  \n23292, 16004, 10838,  23775, 24061, 24058,  23776, 24061, 23775,  \n15806, 20793, 23325,  22889, 3865, 12282,  23776, 23922, 24061,  \n16627, 7408, 5464,  3773, 11804, 17140,  10616, 16865, 1928,  \n22611, 3317, 21052,  2667, 21376, 13162,  14054, 6428, 19233,  \n15714, 23938, 18064,  23778, 23923, 23777,  13919, 5207, 4615,  \n14255, 11890, 6677,  23924, 23608, 23921,  11391, 7929, 21271,  \n23609, 24064, 23925,  23611, 24064, 23609,  24065, 23610, 24063,  \n7678, 15496, 14338,  4617, 11998, 12668,  15498, 10143, 4022,  \n3187, 7640, 10218,  17667, 15542, 6673,  24066, 24064, 23779,  \n8534, 7605, 18138,  11543, 18069, 9594,  24065, 24067, 23612,  \n20058, 3985, 4601,  23926, 24066, 23779,  21929, 20109, 10802,  \n23612, 24067, 23613,  2042, 11311, 18011,  17573, 7495, 17574,  \n17574, 7495, 17673,  6469, 305, 19927,  7406, 1539, 7407,  \n23926, 23780, 23927,  6848, 4927, 4926,  24068, 23783, 23782,  \n23927, 23781, 23928,  24233, 23927, 23928,  24069, 24233, 23928,  \n12330, 12331, 16813,  23615, 23785, 23787,  10718, 19744, 22413,  \n23786, 24069, 23928,  23786, 23788, 24069,  7061, 2047, 7062,  \n24070, 23789, 23787,  23929, 23789, 24070,  10718, 10847, 19744,  \n1587, 10918, 11994,  15137, 4974, 7963,  4677, 11371, 22977,  \n9509, 5437, 11069,  6825, 4434, 4433,  8478, 15523, 4796,  \n8113, 10270, 2967,  2175, 9125, 6397,  2133, 11738, 18535,  \n743, 744, 15930,  1191, 10605, 17265,  23452, 23102, 24071,  \n23795, 23285, 23453,  23795, 23453, 24072,  23797, 24074, 23454,  \n24075, 23797, 23455,  5372, 1196, 1197,  13786, 10607, 20467,  \n21251, 21400, 4292,  24076, 24077, 23931,  24076, 23931, 24078,  \n706, 20133, 16365,  24078, 23931, 23799,  23456, 23796, 23799,  \n24079, 23799, 23930,  23796, 23930, 23799,  24080, 23932, 24077,  \n23932, 23931, 24077,  7866, 14328, 2274,  8755, 12795, 13877,  \n19523, 14820, 18534,  15288, 4341, 11913,  2990, 9314, 2988,  \n13483, 20195, 12233,  7846, 5353, 14727,  21643, 3621, 3620,  \n23935, 23109, 24248,  13355, 17455, 19825,  10141, 17380, 11582,  \n6590, 17677, 9740,  24248, 23109, 23937,  14108, 15159, 15307,  \n23942, 23937, 23460,  22642, 23623, 23941,  19609, 10680, 12950,  \n23943, 23942, 23803,  23803, 23945, 23943,  6061, 7007, 29287,  \n18809, 7109, 10911,  4562, 15694, 1596,  19979, 6374, 2270,  \n23459, 22644, 23461,  21731, 14923, 15054,  4340, 4339, 20775,  \n24081, 23945, 23295,  24082, 23628, 23802,  2855, 1539, 2854,  \n13635, 19055, 6745,  23808, 23469, 24084,  13385, 13957, 13956,  \n8784, 19201, 8384,  17628, 974, 20297,  9558, 14474, 3158,  \n4046, 1427, 15000,  24083, 23299, 23301,  10051, 10663, 13461,  \n845, 8714, 846,  23628, 24085, 23113,  20542, 11224, 3122,  \n3340, 4098, 4099,  11717, 2189, 2242,  506, 10302, 3602,  \n13015, 22343, 10512,  12048, 4467, 16353,  9210, 1476, 1435,  \n17874, 13412, 9762,  5223, 2423, 8364,  13509, 24089, 17084,  \n23949, 23951, 23631,  23111, 23808, 23631,  6575, 5666, 9563,  \n24085, 23632, 23113,  18390, 13796, 24090,  512, 14756, 8417,  \n21299, 6716, 10976,  18318, 19029, 14728,  24085, 24091, 23632,  \n24092, 23627, 24093,  23627, 23121, 24093,  23955, 23478, 22435,  \n14284, 12941, 5109,  23812, 24094, 23637,  23953, 23955, 22435,  \n12481, 773, 774,  24094, 24095, 23637,  3068, 23847, 22219,  \n23637, 24095, 23639,  18771, 20990, 14765,  19384, 17763, 710,  \n4659, 15295, 6355,  24096, 23638, 23476,  23116, 23476, 23638,  \n20090, 17763, 21492,  21178, 3353, 1960,  8422, 15543, 19954,  \n23478, 23955, 23647,  18818, 9045, 22612,  1510, 1511, 13337,  \n1439, 6455, 11892,  8429, 16609, 11663,  11902, 14475, 11903,  \n23956, 23638, 24096,  23956, 23641, 23638,  23642, 23954, 23121,  \n13570, 18349, 22061,  10755, 23997, 21549,  23641, 23956, 23814,  \n5391, 23384, 18520,  23954, 23642, 23958,  3448, 2960, 16829,  \n18999, 5988, 20433,  23815, 24099, 23816,  4439, 19626, 21308,  \n1176, 24100, 10264,  9785, 1741, 2064,  9127, 9128, 12861,  \n22181, 8755, 17038,  16614, 4853, 3665,  23818, 23127, 24101,  \n20692, 11065, 2207,  23481, 24102, 24101,  15146, 8996, 15610,  \n21547, 15525, 10181,  23958, 23819, 23651,  23959, 24102, 23481,  \n23822, 23645, 23960,  736, 12523, 1398,  1186, 16816, 1185,  \n23959, 23826, 24102,  21671, 14584, 15792,  4036, 15081, 17738,  \n23821, 23964, 23965,  23823, 23644, 23965,  12699, 4028, 12380,  \n7292, 7293, 9129,  19620, 19274, 15801,  21649, 4582, 3539,  \n23966, 23963, 23310,  23964, 23821, 23963,  6628, 2515, 16205,  \n23644, 23821, 23965,  16487, 22359, 4867,  16957, 13806, 23243,  \n5924, 9677, 23193,  23964, 24103, 23965,  8974, 9529, 9528,  \n15247, 5193, 20197,  16558, 16568, 12055,  11251, 20719, 11656,  \n23482, 23825, 23967,  23705, 20497, 1988,  11684, 4661, 4663,  \n16244, 18425, 10018,  23484, 23970, 23826,  4139, 20329, 16223,  \n23134, 24104, 23966,  13030, 3761, 7719,  6837, 8774, 18197,  \n24103, 24105, 23968,  7874, 16358, 2334,  23134, 23833, 24104,  \n12617, 4803, 4802,  336, 6643, 6294,  20121, 9048, 17453,  \n20040, 21229, 20039,  23144, 23319, 23831,  23484, 23653, 23970,  \n16129, 3422, 16198,  23833, 23134, 23321,  15167, 11035, 8141,  \n11261, 14997, 1434,  23653, 23484, 23145,  14318, 22425, 13060,  \n23829, 23968, 24107,  5037, 19523, 18534,  17412, 19934, 14808,  \n23834, 23829, 24107,  23971, 23489, 23659,  9082, 7714, 20645,  \n23971, 23659, 24108,  9708, 3009, 13592,  12003, 15030, 7837,  \n23838, 23654, 23832,  12823, 12834, 14232,  10856, 3447, 14844,  \n18743, 10856, 14844,  23834, 24107, 24109,  22876, 6268, 2216,  \n10618, 10274, 20983,  14493, 19068, 4230,  20467, 12179, 3094,  \n24110, 2238, 13921,  6135, 22248, 19304,  17014, 4058, 21105,  \n3234, 3236, 22276,  2215, 19604, 10518,  7695, 3129, 2425,  \n23659, 23152, 24108,  1390, 19190, 2445,  23834, 24109, 23973,  \n23975, 24444, 23494,  9457, 15748, 20276,  23658, 23490, 24112,  \n23302, 4263, 5092,  13292, 6052, 10657,  23207, 23235, 20078,  \n5487, 20849, 14493,  19745, 17045, 5690,  2526, 5644, 8633,  \n18588, 19896, 18405,  23840, 23973, 23977,  6025, 2772, 16598,  \n15679, 15872, 12533,  7302, 11479, 1396,  7119, 18146, 7117,  \n23975, 23494, 23495,  1030, 9963, 5598,  10519, 6177, 19319,  \n23495, 24115, 23975,  18122, 9357, 4232,  23841, 24280, 23660,  \n23492, 24114, 23665,  1082, 18253, 1269,  3928, 19865, 8112,  \n4833, 23536, 9986,  18332, 7752, 18245,  8774, 6837, 3364,  \n3382, 20106, 17024,  24115, 23495, 23498,  3053, 3054, 11456,  \n994, 11100, 3655,  23977, 24119, 23978,  17678, 617, 12666,  \n23843, 23841, 23158,  16742, 416, 8820,  23978, 24121, 23663,  \n7604, 6418, 8646,  23663, 24121, 23666,  20514, 17685, 17686,  \n344, 11225, 345,  22459, 3369, 12296,  23666, 24121, 23844,  \n24122, 23980, 23672,  29615, 20103, 14588,  14149, 6888, 16406,  \n23982, 23333, 23669,  23190, 16454, 17647,  10951, 4488, 6960,  \n6445, 12575, 5259,  9593, 14791, 15215,  13493, 12621, 6086,  \n23850, 23983, 23669,  13059, 21587, 21324,  13173, 12923, 1909,  \n23844, 23501, 23335,  13638, 15038, 6930,  21538, 7587, 5925,  \n23335, 23332, 23844,  14263, 10178, 13415,  23986, 23984, 23670,  \n23502, 23501, 23844,  5660, 5368, 10297,  23987, 23337, 24125,  \n22933, 23337, 23987,  13151, 6195, 6577,  15795, 16898, 3924,  \n523, 9027, 11153,  23343, 22934, 22935,  7384, 19313, 19134,  \n24126, 23341, 23673,  17387, 17388, 22930,  3932, 21329, 6827,  \n21581, 11793, 11792,  10395, 14733, 1982,  5647, 15306, 7978,  \n8715, 5635, 5634,  23989, 23675, 23502,  14975, 4878, 708,  \n7167, 5387, 13922,  10714, 686, 5063,  24127, 23343, 23503,  \n4218, 5962, 1396,  9388, 10037, 11002,  8986, 14221, 8985,  \n4642, 4643, 11752,  23853, 23175, 23995,  20657, 10046, 3712,  \n18870, 4449, 17424,  1797, 10777, 1798,  846, 20640, 17718,  \n23992, 23503, 23509,  15246, 16000, 1260,  2364, 14604, 10621,  \n20298, 14384, 4443,  5422, 1612, 8378,  23677, 23350, 24129,  \n23350, 23349, 24129,  9363, 8757, 16370,  23351, 24130, 24131,  \n23355, 23680, 24128,  16278, 16279, 1345,  1209, 1930, 5149,  \n11121, 17705, 11120,  5304, 1462, 6141,  24132, 23681, 23515,  \n14944, 8899, 11789,  765, 764, 17005,  20877, 10514, 3580,  \n20028, 1495, 9668,  9177, 9178, 12801,  17531, 7478, 9748,  \n23684, 23681, 24132,  532, 531, 15120,  8058, 8057, 4876,  \n10618, 21460, 10619,  21549, 912, 6841,  14742, 11173, 12421,  \n17127, 8709, 8708,  8830, 1516, 21770,  14854, 785, 24135,  \n14173, 23521, 18582,  3439, 22422, 3438,  14401, 8062, 15294,  \n24136, 23686, 23362,  8365, 8177, 8178,  23687, 24137, 24139,  \n23999, 23517, 23518,  1619, 29569, 11483,  5959, 3878, 3877,  \n5473, 7306, 13623,  12226, 26285, 14321,  16336, 5101, 5100,  \n4338, 4584, 1896,  24140, 23860, 23183,  4363, 4362, 15874,  \n17120, 8366, 6792,  12876, 12884, 10746,  8251, 14851, 8600,  \n12955, 13976, 7705,  9332, 11036, 3457,  20696, 22336, 21252,  \n7642, 3044, 3264,  13475, 12803, 15203,  23520, 22971, 24141,  \n3000, 8547, 15929,  10724, 2489, 2039,  10039, 7930, 9465,  \n10762, 12605, 18784,  24001, 23366, 23859,  7851, 940, 939,  \n16582, 2189, 16132,  24142, 23862, 24000,  24142, 23184, 23862,  \n18105, 17584, 16415,  11770, 1793, 20452,  19931, 8965, 15988,  \n12020, 10867, 1053,  23185, 23366, 24002,  1692, 13404, 18997,  \n7398, 17023, 7921,  1916, 1917, 16728,  23186, 23184, 24142,  \n24144, 24143, 23865,  23186, 24142, 24145,  21624, 17035, 11604,  \n23865, 23700, 24144,  23071, 20124, 9022,  23524, 23186, 24145,  \n18986, 7621, 16903,  13859, 18256, 19680,  24006, 22754, 23697,  \n17385, 13909, 22036,  23698, 23374, 24146,  19935, 20207, 5672,  \n13207, 11345, 20164,  3430, 1117, 14636,  21192, 4963, 18212,  \n9585, 3768, 9586,  23524, 24147, 24148,  17700, 16402, 4781,  \n23187, 23524, 24148,  14155, 1140, 5798,  12188, 10163, 9354,  \n7722, 17502, 7746,  15164, 10323, 4324,  23701, 24149, 23528,  \n20030, 15493, 3460,  23867, 24148, 24150,  23867, 23187, 24148,  \n8322, 8321, 14402,  21483, 10957, 10958,  23525, 24006, 24152,  \n13633, 17625, 18124,  23703, 23525, 24152,  12186, 2212, 12187,  \n14539, 6503, 13685,  10051, 10052, 10663,  12742, 20619, 10114,  \n762, 12137, 13282,  3592, 12621, 13493,  23704, 22767, 22986,  \n23704, 22986, 23869,  23710, 23198, 24157,  9879, 20924, 19774,  \n22852, 1938, 5887,  24156, 23709, 23868,  12946, 2847, 4501,  \n847, 12073, 10309,  1686, 6480, 6130,  1920, 2367, 1921,  \n23870, 23709, 24160,  5324, 9320, 9855,  24161, 23871, 23710,  \n23871, 23380, 23710,  22990, 23534, 22988,  14089, 5345, 9777,  \n16070, 17211, 20477,  9564, 18379, 13715,  14256, 6464, 12804,  \n23716, 23535, 23871,  8604, 18080, 18079,  23716, 23871, 24012,  \n20798, 2850, 14017,  24010, 23714, 23715,  11418, 16459, 18529,  \n23035, 2838, 18697,  22065, 17884, 7027,  1895, 22218, 1894,  \n13368, 9654, 4747,  23719, 23386, 23204,  9327, 9639, 9638,  \n24165, 23873, 24011,  22095, 7082, 19761,  23718, 24016, 23715,  \n6485, 13282, 17904,  23209, 23875, 23719,  23544, 23873, 24165,  \n14960, 10009, 1441,  15042, 9030, 9031,  17177, 3310, 16159,  \n4280, 14383, 20298,  24169, 24016, 23874,  22561, 23875, 22559,  \n6822, 18558, 11477,  23875, 22561, 23213,  12882, 4630, 16664,  \n14876, 22272, 6945,  24167, 23547, 23545,  3161, 2635, 1932,  \n12959, 18222, 2980,  23876, 23213, 23214,  7934, 20431, 18630,  \n5245, 2474, 10057,  23546, 23388, 23542,  24168, 24169, 24017,  \n12453, 15746, 3061,  4426, 16601, 4427,  6120, 8006, 13704,  \n15044, 3025, 14787,  2801, 8291, 2800,  23722, 23546, 24018,  \n10471, 5079, 18092,  7788, 2267, 9729,  10467, 9335, 1655,  \n7655, 13870, 19621,  24170, 23721, 23723,  13514, 13432, 13431,  \n1750, 15339, 5632,  7136, 8954, 8953,  14038, 22082, 4697,  \n13456, 759, 10368,  18407, 2934, 13372,  23393, 23722, 23552,  \n8473, 17279, 899,  23215, 23725, 23724,  20589, 16452, 7829,  \n23552, 24019, 23726,  14976, 4678, 6636,  935, 4540, 12875,  \n5673, 17090, 4865,  24024, 24175, 24174,  9340, 9620, 4212,  \n15425, 11776, 19119,  6624, 13088, 5475,  17567, 14159, 14205,  \n24173, 24022, 24174,  3978, 14356, 18061,  10383, 10382, 16027,  \n14122, 18728, 3641,  13281, 18373, 13349,  2312, 7500, 6767,  \n13729, 6920, 6919,  488, 10465, 16670,  15713, 2627, 15411,  \n24023, 24178, 23879,  12006, 8720, 9650,  24178, 24025, 23879,  \n19132, 22596, 20839,  23878, 23727, 24026,  430, 17205, 3690,  \n23877, 23882, 23395,  24025, 24180, 24027,  23731, 24027, 24181,  \n24026, 23727, 23883,  24177, 24024, 23733,  2441, 3909, 13127,  \n1740, 6587, 4410,  23399, 23882, 23560,  18456, 20647, 14938,  \n15117, 3492, 3491,  18655, 23292, 10838,  23883, 23727, 23219,  \n24177, 23733, 23886,  4654, 11433, 9514,  3154, 15241, 19207,  \n24182, 24177, 23886,  11268, 2504, 21237,  20562, 4244, 13484,  \n20719, 22339, 5606,  13184, 12644, 6850,  2179, 3701, 2180,  \n24184, 23890, 23889,  21157, 20418, 10263,  19889, 14693, 9691,  \n23886, 23892, 24030,  7700, 18148, 18262,  24183, 23886, 24030,  \n23300, 18801, 3273,  20709, 15371, 4129,  24030, 23892, 24032,  \n18638, 22094, 21328,  8346, 2907, 2908,  8479, 2452, 6902,  \n9733, 5345, 4821,  12907, 9805, 6456,  2956, 22149, 21588,  \n3844, 9361, 9360,  14934, 16115, 15705,  21579, 602, 1470,  \n9875, 16415, 3742,  15595, 22763, 6456,  14745, 4761, 20551,  \n3573, 3572, 9635,  9263, 5745, 7817,  417, 8820, 416,  \n24033, 23894, 24186,  23668, 20618, 3593,  12002, 6581, 12885,  \n13324, 2469, 9970,  11297, 11168, 1506,  6658, 15388, 6897,  \n4088, 22162, 20029,  7545, 4767, 4766,  17611, 18365, 15201,  \n19500, 6405, 13899,  13564, 13173, 13172,  5176, 9045, 18818,  \n14910, 20657, 15091,  13916, 11829, 5201,  17919, 17611, 15201,  \n5770, 5133, 4315,  6049, 11525, 14326,  23743, 23569, 24034,  \n23745, 23740, 23739,  8895, 8872, 24188,  23745, 23739, 24189,  \n16160, 17474, 16955,  8803, 5175, 1465,  15198, 10245, 17737,  \n2055, 2056, 20426,  23746, 23899, 24038,  24192, 23237, 23743,  \n10211, 19045, 11627,  10520, 10381, 5741,  18651, 5262, 12908,  \n2508, 9207, 2509,  24190, 23412, 24036,  22247, 10699, 21477,  \n4111, 2257, 21392,  23749, 24036, 23575,  24035, 24195, 23902,  \n12782, 4436, 21171,  6933, 5990, 12019,  22369, 7198, 486,  \n3792, 3753, 5743,  24042, 23415, 23239,  16725, 11941, 4878,  \n2871, 2872, 16513,  23751, 23418, 24193,  4015, 7283, 9811,  \n12949, 22834, 12950,  23749, 23751, 24193,  3410, 6134, 14166,  \n15769, 19716, 15135,  24044, 24195, 24200,  525, 526, 12209,  \n24196, 24194, 23582,  19858, 9881, 10119,  23416, 23753, 23754,  \n23581, 23754, 24198,  23756, 23581, 24199,  24195, 24044, 23902,  \n23757, 24196, 23582,  9056, 10196, 17454,  24201, 24044, 24200,  \n10867, 5657, 1053,  23050, 23752, 23584,  23441, 6737, 5460,  \n24045, 24044, 24203,  24045, 24204, 23584,  9494, 10199, 9612,  \n2454, 8016, 10396,  10961, 18651, 675,  3700, 16981, 11768,  \n10775, 16938, 9522,  23584, 24204, 24046,  5861, 20321, 3661,  \n23585, 24046, 23759,  13189, 10286, 13188,  24205, 23758, 23760,  \n16312, 21473, 20699,  21992, 18323, 21065,  23420, 24047, 23421,  \n2061, 18418, 13067,  23588, 24206, 23760,  9938, 19649, 19968,  \n22398, 8018, 3108,  12655, 6332, 11351,  23422, 24048, 24207,  \n23589, 23422, 24207,  16940, 16739, 19683,  23589, 24207, 24049,  \n3057, 2593, 13727,  22953, 12089, 5025,  11523, 19638, 23026,  \n9030, 15042, 10336,  24208, 23588, 23423,  11813, 6565, 11814,  \n24050, 23590, 24209,  24208, 23423, 23592,  14065, 14064, 21826,  \n24051, 23592, 23591,  19608, 21789, 5717,  16700, 14299, 13008,  \n21835, 21834, 15470,  3001, 11499, 6482,  20144, 18451, 22295,  \n23761, 23907, 24210,  14238, 10785, 7157,  15058, 4804, 824,  \n23763, 23761, 24211,  15029, 13745, 7556,  23600, 23908, 24213,  \n1506, 23770, 1039,  24213, 23908, 24212,  2985, 15963, 1061,  \n5460, 6737, 5461,  10716, 990, 15403,  19349, 12955, 7705,  \n23910, 23909, 24215,  16196, 10868, 21142,  6153, 472, 20411,  \n24054, 23767, 23768,  24054, 23431, 23767,  23433, 23602, 24217,  \n1545, 7743, 551,  12158, 10185, 18267,  7779, 443, 10742,  \n23432, 23768, 23069,  5169, 21044, 12786,  12774, 23361, 2925,  \n10794, 9197, 9199,  16006, 13788, 4154,  13609, 4488, 14410,  \n23603, 24056, 24057,  24218, 23769, 23914,  5912, 2742, 22298,  \n23914, 23915, 24218,  24219, 23915, 23916,  23603, 24057, 23435,  \n24057, 24220, 23435,  13623, 16769, 8460,  3385, 5441, 11480,  \n23918, 23435, 24220,  9230, 11468, 2032,  23917, 24221, 23916,  \n3110, 19387, 21819,  1741, 1742, 2064,  18593, 5027, 11150,  \n3438, 1104, 22366,  23604, 23264, 24222,  23604, 24223, 22396,  \n23604, 24224, 24223,  15046, 4473, 2693,  1781, 15816, 1782,  \n23771, 23772, 24225,  1449, 1448, 7941,  9280, 18041, 5404,  \n2062, 6857, 21143,  17289, 11830, 9707,  17678, 16094, 14227,  \n24058, 24226, 24059,  23920, 24059, 24380,  24226, 24227, 24059,  \n10813, 9127, 13448,  16815, 16814, 10427,  6926, 2869, 3649,  \n2899, 11241, 11191,  15825, 15296, 10206,  24062, 23920, 24379,  \n2682, 6189, 2683,  24061, 23922, 24228,  21324, 22150, 6889,  \n24229, 24228, 23922,  23921, 23920, 24062,  4185, 15953, 7530,  \n13300, 4126, 4125,  10266, 4635, 21427,  12045, 20540, 13632,  \n23777, 24230, 23922,  14048, 15131, 4845,  5453, 20458, 8434,  \n23923, 24230, 23777,  6987, 11496, 6986,  23924, 23921, 24062,  \n23923, 23925, 24230,  13942, 13943, 10368,  5329, 1246, 16716,  \n17084, 24089, 23470,  5335, 15840, 12588,  21264, 12363, 11463,  \n24231, 7956, 21731,  20847, 11923, 23510,  9375, 17854, 9376,  \n3200, 7666, 15014,  6545, 1372, 3595,  2646, 18678, 2647,  \n10453, 438, 437,  8064, 323, 8065,  24066, 24232, 24064,  \n9815, 4145, 18308,  22340, 10854, 23792,  23782, 23613, 24067,  \n17978, 16523, 18106,  4958, 1542, 1543,  23927, 24066, 23926,  \n15041, 576, 575,  1925, 7750, 12204,  10829, 2121, 4422,  \n22818, 3442, 3441,  19491, 8336, 14569,  24068, 23784, 23783,  \n9825, 17881, 2474,  15800, 12928, 11422,  8011, 514, 9215,  \n10408, 9446, 3445,  24069, 24235, 24233,  23784, 24234, 23785,  \n13572, 7329, 19566,  24069, 24238, 24235,  23787, 23785, 24237,  \n24237, 24070, 23787,  13321, 10235, 9026,  3446, 9549, 13129,  \n23788, 24239, 24238,  24238, 24069, 23788,  6847, 11576, 651,  \n20712, 1705, 14235,  24070, 24239, 23929,  23929, 24239, 23788,  \n1662, 7813, 7812,  4988, 5524, 5525,  14568, 3359, 6679,  \n2083, 16246, 894,  14476, 12058, 4649,  3439, 22724, 22422,  \n16525, 19666, 7179,  1308, 9418, 12275,  7900, 8266, 13546,  \n17067, 10275, 7381,  24240, 23618, 6758,  6456, 22763, 12907,  \n6509, 5247, 5246,  737, 2230, 13191,  23794, 21032, 23793,  \n13806, 17971, 23243,  21090, 12367, 4056,  6035, 6034, 16895,  \n5633, 16444, 17467,  5181, 7839, 5182,  24071, 23102, 23794,  \n7563, 2098, 16507,  20153, 1033, 9949,  5798, 3002, 7607,  \n24244, 24242, 24245,  24244, 24245, 24246,  24076, 24246, 24245,  \n23454, 24074, 23930,  22160, 22159, 8977,  23104, 23452, 23798,  \n1270, 9035, 1859,  18543, 16719, 21683,  24246, 24076, 24078,  \n24078, 24247, 24246,  11164, 10622, 10621,  9628, 16808, 4348,  \n13289, 10826, 14415,  23799, 24247, 24078,  24247, 23799, 24079,  \n19488, 21040, 23800,  10656, 19786, 15394,  15322, 22205, 15321,  \n11212, 22205, 10430,  24245, 24242, 24077,  24077, 24076, 24245,  \n15476, 5518, 19963,  23934, 23453, 23288,  14774, 9524, 20234,  \n8118, 5475, 4940,  22099, 1707, 1708,  8118, 4940, 7817,  \n24249, 24250, 23942,  24242, 24400, 24077,  22132, 11405, 18770,  \n11544, 11545, 877,  23801, 23798, 23939,  23934, 24072, 23453,  \n4809, 1713, 2634,  24250, 23937, 23942,  24249, 23942, 23943,  \n15147, 5733, 11725,  24400, 24080, 24077,  945, 18327, 790,  \n24251, 23107, 23801,  20112, 24252, 18301,  3916, 3375, 670,  \n2222, 22889, 2427,  24253, 24080, 24400,  9756, 20269, 9755,  \n23804, 23464, 23624,  9964, 9963, 19441,  13908, 19381, 18338,  \n5633, 17467, 21640,  24082, 24080, 24253,  8551, 14600, 17024,  \n23944, 23463, 23625,  19772, 15290, 18828,  23462, 23463, 23944,  \n24082, 23802, 24080,  15703, 2626, 18127,  24255, 23469, 23464,  \n7043, 8696, 7041,  18061, 10653, 9493,  364, 11371, 19568,  \n18795, 22404, 9721,  24256, 23628, 24082,  23805, 23466, 23627,  \n6664, 17453, 19162,  7830, 18060, 20589,  5673, 20141, 17090,  \n22979, 12083, 4498,  9510, 6044, 11845,  16885, 17341, 16048,  \n507, 2556, 5151,  3056, 14532, 13267,  2861, 1242, 17151,  \n23628, 24256, 24085,  14589, 14590, 6517,  1576, 1468, 14774,  \n23811, 23953, 23633,  21092, 9517, 4289,  5313, 5314, 7435,  \n4425, 16073, 6446,  24081, 23295, 23297,  24088, 24081, 23297,  \n8033, 2437, 16933,  10365, 20922, 2451,  988, 536, 537,  \n4883, 14108, 15308,  23951, 23634, 23636,  21488, 7777, 10754,  \n15788, 4589, 8821,  21567, 20561, 11862,  4843, 15479, 6667,  \n12081, 13401, 15917,  18158, 18807, 18689,  24087, 24088, 23297,  \n10134, 10133, 1310,  14614, 5077, 14613,  8316, 8315, 644,  \n8627, 6038, 7654,  15940, 4091, 16572,  24259, 24087, 23297,  \n8531, 17330, 7569,  5888, 1272, 18753,  3489, 7286, 2694,  \n23133, 23361, 12774,  14533, 15354, 17287,  24091, 23812, 23632,  \n20342, 16161, 20326,  3808, 3809, 21256,  11691, 19781, 19907,  \n18417, 18416, 12892,  23954, 24093, 23121,  8032, 20965, 11446,  \n6325, 12061, 2923,  20121, 1446, 8048,  7092, 17887, 21400,  \n14243, 1074, 1073,  3487, 11074, 20506,  10890, 5902, 10296,  \n4809, 18751, 4810,  23818, 23640, 23124,  23639, 24095, 24261,  \n5789, 16813, 6072,  23639, 24261, 23476,  29546, 14243, 1073,  \n23730, 18202, 13654,  10591, 10592, 19790,  24263, 23814, 23956,  \n24097, 23815, 23814,  24097, 24099, 23815,  24097, 24098, 24099,  \n24099, 24265, 23816,  17371, 18667, 18650,  9626, 14200, 14199,  \n24101, 23127, 23481,  20204, 6225, 20901,  23820, 23817, 24267,  \n10350, 3968, 11783,  544, 10277, 545,  16657, 4546, 7264,  \n18783, 23390, 4351,  458, 10310, 15642,  23820, 24269, 23643,  \n23643, 24269, 23960,  24270, 23958, 23651,  10349, 12159, 12160,  \n24268, 24102, 23826,  17751, 17750, 14946,  20006, 5472, 19248,  \n7800, 7799, 14945,  22518, 15657, 7995,  5255, 24272, 20653,  \n24273, 23964, 23963,  23315, 23961, 23830,  24103, 23964, 24273,  \n5141, 6313, 8211,  23966, 24273, 23963,  14252, 6041, 6042,  \n8914, 18603, 10952,  10708, 10244, 18674,  11249, 20203, 2715,  \n7472, 7471, 4332,  24104, 24273, 23966,  11721, 16645, 9898,  \n7954, 8222, 13968,  14072, 2313, 15655,  5329, 8742, 12362,  \n21981, 18841, 1193,  9230, 17678, 689,  16009, 5711, 3687,  \n24435, 23314, 23967,  16438, 18358, 11898,  17822, 390, 2763,  \n24105, 24433, 24107,  23971, 24275, 23969,  14439, 14440, 18063,  \n18726, 20478, 15797,  19496, 5010, 19244,  20370, 10204, 16383,  \n20075, 8210, 11906,  21867, 11664, 15867,  16627, 5464, 5926,  \n24108, 24275, 23971,  17666, 16345, 17240,  15453, 8106, 8105,  \n18974, 22074, 15152,  24107, 23968, 24105,  6153, 14872, 15305,  \n14616, 7187, 8588,  8908, 4343, 11368,  21232, 14286, 16730,  \n23486, 24276, 23833,  10805, 8660, 13374,  9827, 3358, 2953,  \n20553, 23348, 7325,  15477, 9593, 6203,  6949, 21729, 17852,  \n23838, 23832, 24106,  17412, 14808, 10490,  2395, 13242, 3584,  \n23835, 24276, 23486,  16162, 5755, 13242,  2303, 9778, 1190,  \n2830, 2829, 15829,  12239, 4484, 12298,  16573, 12355, 11613,  \n11971, 11970, 11888,  10880, 8743, 16291,  24277, 24444, 23975,  \n10825, 8807, 3211,  6063, 20333, 16705,  8889, 16079, 4468,  \n12272, 12508, 16045,  2609, 6039, 11489,  23658, 24112, 23976,  \n11931, 19423, 17060,  24117, 23973, 24278,  12115, 12116, 11055,  \n23147, 24113, 24111,  14077, 8772, 14078,  24109, 24278, 23973,  \n6371, 11372, 11374,  22923, 22924, 392,  16162, 21007, 19650,  \n14683, 13805, 14682,  5593, 8835, 3851,  24277, 23975, 24115,  \n24134, 16174, 19829,  7323, 12998, 17034,  8796, 415, 6282,  \n24113, 23147, 23150,  18890, 18474, 6585,  23977, 23973, 24117,  \n22220, 17484, 4825,  23664, 23976, 24118,  24113, 23150, 24281,  \n10331, 15735, 20021,  16734, 10102, 14956,  4284, 12232, 15783,  \n19719, 19685, 12039,  24119, 23977, 24117,  15777, 14034, 16424,  \n14015, 15099, 14016,  14593, 20304, 10589,  16152, 9255, 8304,  \n11755, 797, 20173,  23498, 23980, 24115,  350, 9698, 6850,  \n1726, 11713, 11712,  14813, 15481, 7801,  3645, 22065, 8273,  \n8049, 6161, 18268,  23980, 24122, 24115,  16200, 19812, 692,  \n10063, 1650, 4755,  7299, 12860, 2597,  23496, 23333, 23982,  \n24284, 24119, 24283,  24284, 23978, 24119,  24121, 23978, 24284,  \n23497, 23842, 24285,  564, 20297, 562,  21693, 9549, 5583,  \n23845, 23665, 24120,  6357, 5809, 5044,  3516, 15427, 26391,  \n19545, 18742, 589,  9230, 21863, 17678,  3836, 13210, 18790,  \n24122, 23672, 23985,  23846, 23497, 24285,  24124, 23982, 23983,  \n12920, 12921, 17673,  7967, 5998, 3407,  10214, 16296, 18538,  \n13703, 19641, 7156,  24125, 23337, 23845,  23844, 24121, 24288,  \n6225, 20204, 962,  2101, 12845, 12439,  15569, 19948, 20527,  \n5590, 4397, 11553,  13717, 5075, 19412,  24292, 23984, 23986,  \n23850, 24293, 23983,  20334, 4489, 2448,  13812, 11865, 15079,  \n3617, 18008, 3522,  12686, 18310, 8375,  18422, 1863, 22965,  \n24294, 23986, 23341,  22934, 23343, 24299,  24299, 23340, 22934,  \n23502, 23844, 24295,  24294, 23341, 24126,  9095, 431, 9096,  \n23502, 24295, 24296,  23853, 24126, 23673,  3796, 14770, 1537,  \n9629, 13894, 20719,  13987, 12728, 20492,  1113, 12592, 9028,  \n8738, 15695, 14446,  14852, 17479, 13539,  23343, 24127, 24299,  \n4008, 17969, 4009,  12990, 20201, 1850,  23853, 23995, 24126,  \n16291, 358, 16587,  7973, 19815, 18909,  21188, 21187, 19070,  \n14740, 4642, 11752,  24301, 24126, 23995,  2318, 2320, 2344,  \n2275, 2274, 14583,  8151, 8152, 9763,  24454, 23508, 24128,  \n17601, 13132, 6142,  24300, 23991, 23852,  968, 2284, 2285,  \n10840, 10377, 10841,  5453, 8434, 5454,  19911, 17020, 7842,  \n23506, 23988, 24302,  5516, 3279, 872,  23508, 23355, 24128,  \n22863, 15145, 15146,  13645, 16308, 13151,  23351, 23677, 24130,  \n15231, 10898, 24303,  10125, 11795, 13131,  8161, 10578, 8159,  \n20494, 6684, 20469,  1132, 17428, 14203,  10027, 10026, 24304,  \n17393, 16303, 3003,  20455, 8850, 8488,  24132, 23515, 23996,  \n13785, 10608, 13786,  3915, 12390, 3916,  23512, 23991, 23855,  \n21839, 21675, 10780,  23356, 23686, 23680,  3637, 1438, 353,  \n4228, 4227, 3673,  5466, 13080, 13551,  7857, 14999, 11181,  \n3349, 2724, 2726,  14311, 19910, 7413,  22016, 20965, 19106,  \n18722, 9046, 11151,  6390, 16737, 10216,  11655, 9929, 5468,  \n623, 10020, 10021,  23855, 24137, 23687,  18502, 6329, 4102,  \n17433, 7179, 6364,  7581, 7582, 15027,  16389, 10162, 11922,  \n16849, 9899, 11968,  6932, 18569, 7081,  9982, 9851, 7661,  \n11087, 4811, 15577,  23518, 24138, 23999,  5359, 11020, 5238,  \n2086, 15866, 2087,  23690, 23687, 24139,  8177, 21084, 15367,  \n23860, 24138, 23518,  13037, 17951, 5599,  24465, 23362, 23520,  \n13419, 6124, 8735,  6532, 10066, 10067,  2230, 2229, 14689,  \n12349, 16638, 1824,  23692, 23691, 24000,  10241, 13376, 3372,  \n2065, 1116, 985,  13877, 14568, 6679,  4362, 5612, 15874,  \n6672, 21918, 427,  4616, 1085, 16889,  15573, 2200, 9317,  \n23058, 21969, 8335,  5284, 16301, 15936,  5793, 10462, 15544,  \n24309, 23183, 23863,  20157, 3546, 4529,  16664, 19732, 12882,  \n9259, 5254, 4463,  23366, 24001, 24002,  19057, 16408, 19643,  \n8507, 17244, 6623,  3906, 5913, 1038,  12412, 18701, 18702,  \n6115, 6886, 6960,  5489, 5488, 19461,  6538, 19932, 6537,  \n4339, 3170, 22449,  1304, 15030, 5291,  2660, 11122, 2661,  \n13450, 13277, 21095,  10262, 13123, 3691,  1304, 5892, 21812,  \n5624, 2460, 16723,  22255, 20871, 20872,  24144, 23700, 23528,  \n17142, 23480, 20569,  23528, 24311, 24144,  4631, 2904, 10871,  \n10841, 10377, 3507,  1949, 1948, 15807,  6906, 4394, 6905,  \n11485, 8003, 20879,  23374, 24151, 24146,  1066, 14540, 18264,  \n10187, 17085, 16467,  12469, 9433, 5278,  21574, 4930, 15477,  \n14735, 29717, 21171,  11096, 11271, 17634,  3560, 18564, 3561,  \n22615, 11867, 11149,  5518, 2449, 21424,  2951, 2950, 18768,  \n889, 888, 13014,  14937, 22102, 19585,  15762, 13420, 20079,  \n24009, 24008, 24155,  10159, 1445, 9825,  16312, 20699, 19262,  \n23703, 24152, 24312,  14428, 21235, 14671,  24313, 24009, 24155,  \n3377, 13365, 660,  1189, 15301, 2016,  23868, 23703, 24312,  \n23531, 23196, 24009,  9599, 22318, 9600,  5953, 10911, 4433,  \n23198, 23531, 24157,  23534, 24316, 23869,  23707, 23872, 24159,  \n24158, 23710, 24157,  15129, 8922, 8923,  24316, 23534, 22990,  \n4116, 3679, 1786,  11262, 5620, 5619,  22990, 24162, 24316,  \n11159, 1895, 21442,  24011, 23870, 24160,  844, 16802, 1518,  \n3267, 9668, 10486,  22992, 24014, 22990,  24014, 24162, 22990,  \n11934, 5703, 11179,  23235, 17319, 5815,  23712, 23870, 24011,  \n15117, 16120, 6089,  6851, 14242, 5116,  10874, 2558, 8686,  \n4293, 3077, 5456,  14507, 683, 7145,  538, 6669, 16479,  \n1248, 11636, 1249,  23719, 24164, 23386,  24319, 24165, 24011,  \n18851, 12576, 7263,  24320, 22627, 23136,  23715, 24016, 24163,  \n23385, 23716, 24015,  24163, 24016, 24169,  24321, 23545, 23544,  \n1001, 18388, 9126,  703, 18176, 1965,  11817, 10496, 10495,  \n24321, 24167, 23545,  12904, 367, 12523,  15536, 12268, 4925,  \n23876, 23214, 23547,  23876, 23547, 24167,  16990, 22278, 17454,  \n12933, 17958, 14850,  14677, 15647, 15397,  24323, 24018, 23546,  \n22874, 17958, 4027,  24324, 24017, 23721,  24018, 24323, 24325,  \n4721, 19771, 10338,  24170, 24324, 23721,  15580, 5964, 3365,  \n20175, 4329, 10627,  24171, 23723, 23724,  15923, 15922, 2938,  \n9337, 3328, 9336,  23552, 23722, 24018,  12097, 21694, 14101,  \n14377, 18420, 14131,  24171, 23724, 23725,  4051, 569, 11635,  \n18066, 815, 814,  24174, 24326, 24173,  24022, 24173, 24176,  \n6687, 3364, 6688,  1981, 8857, 21229,  23725, 23554, 24172,  \n8119, 8120, 2475,  7544, 5733, 5586,  19686, 20825, 11252,  \n21182, 3367, 14518,  23222, 7197, 2139,  24022, 24176, 24023,  \n8598, 2248, 2249,  23554, 24020, 24172,  24176, 24327, 24023,  \n13427, 19599, 392,  24023, 24327, 24178,  24020, 23878, 24026,  \n24175, 24024, 24177,  16816, 20887, 1837,  22733, 21474, 14124,  \n4755, 23410, 6031,  24328, 24025, 24178,  3130, 10274, 6990,  \n8237, 8590, 13108,  7651, 12246, 22078,  23882, 23877, 24488,  \n12145, 18730, 18731,  14484, 2718, 3514,  11682, 407, 15650,  \n24027, 24180, 24181,  2906, 5830, 16367,  22790, 7203, 19468,  \n24028, 23731, 24181,  18408, 2243, 423,  24183, 24182, 23886,  \n23883, 23219, 23884,  23885, 24028, 24329,  3458, 18994, 6266,  \n7564, 17052, 11205,  15894, 13778, 10953,  14667, 15443, 8380,  \n6283, 6394, 19818,  9182, 2247, 2246,  319, 19363, 21278,  \n24330, 23887, 23560,  7384, 17787, 1332,  11751, 14533, 19070,  \n785, 2236, 14203,  4334, 22836, 17650,  6732, 12430, 17928,  \n23890, 24184, 24331,  4640, 12296, 10925,  21375, 21851, 12835,  \n23884, 23732, 24332,  23732, 23888, 24332,  18981, 18983, 1255,  \n24331, 24333, 23890,  22109, 15901, 21457,  7566, 13147, 14732,  \n24333, 23891, 23890,  15698, 18499, 4577,  14129, 7742, 3292,  \n24031, 24336, 23894,  465, 9397, 22054,  15966, 6115, 17567,  \n7426, 7427, 5202,  24337, 23894, 24336,  24338, 23736, 24334,  \n24339, 23893, 23896,  23893, 24339, 24335,  24186, 23894, 24337,  \n5147, 22579, 9496,  24187, 23895, 23736,  19557, 1583, 23529,  \n9450, 15654, 9449,  15407, 17627, 2473,  9045, 8060, 22612,  \n23569, 23895, 24187,  7480, 10730, 9748,  22579, 17485, 7573,  \n21331, 20707, 9940,  11532, 4797, 14401,  12480, 1684, 15072,  \n23568, 23744, 23896,  2513, 18145, 12447,  23898, 23896, 23744,  \n16453, 9767, 21085,  7051, 17304, 5362,  1512, 10953, 9981,  \n23897, 23746, 24038,  24033, 24189, 23739,  24341, 23898, 23411,  \n20879, 8003, 17855,  15207, 18506, 20118,  10942, 4068, 3723,  \n23573, 23412, 24190,  3883, 16949, 4298,  23411, 23573, 24190,  \n7967, 3121, 16722,  24034, 24192, 23743,  15157, 15439, 15158,  \n24035, 23745, 24189,  17407, 15489, 16051,  24343, 1139, 972,  \n6232, 16306, 2641,  431, 9806, 10078,  24344, 24190, 24036,  \n13685, 6503, 15012,  5731, 3411, 4928,  5974, 5975, 7529,  \n24192, 24345, 23577,  24348, 24195, 24035,  18604, 2115, 11109,  \n23747, 23577, 24345,  24036, 23749, 24346,  24040, 23747, 24347,  \n6253, 7514, 2722,  15736, 18103, 17477,  11384, 2399, 21326,  \n23239, 24040, 24042,  24348, 24350, 24195,  8190, 6113, 20926,  \n15641, 5761, 1238,  4115, 18059, 20711,  24350, 24200, 24195,  \n7944, 7943, 11692,  23240, 23755, 24197,  19446, 13187, 21473,  \n11646, 22106, 12167,  23903, 23417, 23756,  18627, 9010, 23622,  \n10881, 22923, 1313,  24352, 24353, 24350,  24352, 24350, 24351,  \n24200, 24350, 24353,  20633, 22397, 9880,  24353, 24352, 24354,  \n24353, 24201, 24200,  8890, 9286, 6103,  18841, 9731, 4232,  \n4961, 4764, 11496,  24353, 24354, 24355,  24045, 24203, 24204,  \n24202, 23757, 23758,  14696, 14346, 19101,  24356, 24201, 24353,  \n24044, 24201, 24356,  2401, 1530, 12895,  24205, 24652, 23758,  \n1948, 1949, 10617,  12993, 11918, 19584,  24357, 24204, 24203,  \n24357, 24046, 24204,  23420, 23759, 24357,  23759, 24046, 24357,  \n11078, 8335, 12594,  3985, 6103, 4601,  24047, 23420, 24358,  \n17637, 17523, 14822,  6611, 5713, 7698,  24359, 23587, 24047,  \n21123, 9737, 11526,  3914, 19311, 835,  24361, 23245, 24049,  \n23245, 24361, 23906,  21561, 10815, 8234,  24799, 23590, 23906,  \n13044, 22517, 2130,  24209, 23590, 24799,  13868, 12310, 9839,  \n23592, 24513, 24208,  15651, 15970, 9264,  1223, 1225, 16412,  \n7128, 7129, 8324,  20709, 4129, 12184,  15974, 16511, 19945,  \n11508, 5692, 17376,  23593, 24363, 23907,  7707, 6984, 5203,  \n4264, 7596, 20683,  24210, 23907, 24363,  19420, 12582, 320,  \n24364, 23761, 24210,  24051, 23591, 23762,  3459, 3458, 6266,  \n24051, 23762, 24365,  7942, 2241, 2242,  24365, 24214, 24366,  \n24213, 24212, 24211,  23763, 24211, 24212,  13884, 17431, 13963,  \n18921, 19140, 13294,  24369, 23909, 23600,  24214, 24052, 23599,  \n17717, 14410, 14621,  24215, 24370, 23910,  24370, 23911, 23910,  \n14463, 14462, 19412,  23766, 23431, 24054,  24217, 23602, 23911,  \n16280, 3791, 10888,  23912, 23768, 23432,  24053, 23768, 24373,  \n12146, 14444, 16247,  20317, 15996, 7012,  1988, 4161, 20946,  \n14112, 5640, 7841,  23769, 24374, 23912,  23769, 24218, 24374,  \n16676, 3028, 3030,  24219, 24218, 23915,  24219, 23916, 24375,  \n6944, 15403, 12896,  24057, 24376, 24220,  24375, 23916, 24221,  \n18375, 815, 16999,  23917, 23771, 24221,  1705, 730, 1706,  \n3976, 19912, 5790,  1728, 21031, 9955,  11813, 4790, 6565,  \n20173, 797, 2590,  22396, 24223, 23773,  23773, 24223, 23772,  \n10360, 6197, 15818,  24377, 24227, 24378,  24226, 24378, 24227,  \n7404, 3889, 17900,  1641, 14451, 13972,  7325, 4787, 3673,  \n24226, 24058, 24381,  8857, 1980, 8858,  11637, 3146, 3145,  \n24059, 24227, 24380,  24381, 24058, 24061,  14827, 1822, 4953,  \n5880, 11132, 17259,  23920, 24380, 24379,  5595, 14489, 5880,  \n24229, 24382, 24228,  8712, 1718, 17430,  24230, 24229, 23922,  \n24383, 23924, 24062,  9526, 9387, 6346,  13894, 13895, 11656,  \n12856, 1523, 11308,  11184, 738, 4331,  9181, 9575, 17622,  \n24386, 24230, 23925,  1742, 9044, 12288,  1705, 1706, 14235,  \n9468, 1040, 9469,  13776, 12995, 5303,  24063, 23924, 24385,  \n10428, 3173, 15881,  10674, 14217, 8101,  10146, 19943, 4782,  \n20054, 14717, 10703,  508, 2540, 17474,  24064, 24386, 23925,  \n6077, 13124, 21856,  22954, 9801, 9800,  18325, 13928, 6521,  \n5304, 5305, 14823,  2146, 3644, 3643,  20680, 18212, 21021,  \n2248, 13178, 2249,  7841, 5640, 17213,  2335, 14919, 14530,  \n24388, 24066, 23927,  24068, 24067, 24387,  23782, 24067, 24068,  \n24233, 24388, 23927,  4335, 10740, 5596,  16868, 2117, 2116,  \n7153, 13333, 19078,  4511, 16135, 15574,  9283, 9282, 7517,  \n1346, 3788, 15463,  19057, 515, 16408,  24235, 24527, 24233,  \n10180, 893, 16611,  24529, 24527, 24235,  24234, 24237, 23785,  \n24529, 24235, 24389,  18629, 10515, 14831,  24238, 24239, 24389,  \n24389, 24235, 24238,  12099, 12100, 11419,  14842, 19783, 12762,  \n2202, 2203, 9841,  1978, 14963, 9276,  15690, 9694, 9693,  \n1687, 20844, 10512,  7602, 23282, 12545,  11112, 17481, 11113,  \n17940, 15170, 16364,  6848, 9942, 4927,  9942, 6558, 11993,  \n8326, 21989, 435,  507, 5151, 7947,  19467, 18522, 24532,  \n24392, 24532, 18522,  10062, 12929, 8375,  18522, 23795, 24392,  \n8884, 8885, 8101,  8228, 8227, 3935,  1648, 17890, 13425,  \n13904, 9464, 11609,  16095, 13012, 19803,  24242, 24393, 24394,  \n1760, 18620, 17374,  24395, 24393, 24242,  24395, 24242, 24244,  \n24244, 24397, 24395,  6995, 16081, 20128,  2957, 9291, 18489,  \n8456, 6808, 8455,  24242, 24394, 24243,  24397, 24244, 24246,  \n14526, 4996, 15491,  24246, 24398, 24397,  7112, 17861, 9133,  \n5866, 3326, 15838,  11986, 4068, 4067,  23452, 24399, 23798,  \n15700, 9489, 9490,  23795, 24072, 24073,  24400, 24242, 24243,  \n24246, 24401, 24398,  24247, 24401, 24246,  10342, 14134, 13357,  \n10592, 11086, 14873,  16448, 10521, 16029,  14052, 10370, 7682,  \n11382, 20010, 8672,  5645, 5647, 20114,  24402, 24403, 23935,  \n24248, 24402, 23935,  24248, 23937, 24250,  16109, 10145, 18200,  \n8580, 2282, 2573,  15208, 18904, 3194,  15241, 12101, 19207,  \n1437, 1628, 11983,  18928, 11709, 17404,  2041, 14058, 19374,  \n11203, 24135, 784,  12666, 16313, 12667,  1112, 22363, 24405,  \n23624, 22642, 23941,  11947, 11949, 8824,  3418, 10613, 18616,  \n16472, 16239, 18488,  4372, 4472, 3221,  21876, 7763, 10306,  \n13529, 13425, 17890,  8704, 978, 1091,  13560, 13559, 21379,  \n1431, 1430, 13188,  24253, 24400, 24404,  15569, 6660, 19711,  \n19318, 10866, 4221,  23934, 23288, 23805,  16889, 1811, 6702,  \n8906, 7379, 5304,  16533, 18972, 13386,  3202, 13174, 18010,  \n7568, 14558, 742,  12994, 19839, 14097,  18856, 11548, 8753,  \n6174, 5787, 10942,  24255, 23464, 24836,  17073, 5006, 16403,  \n23809, 24408, 23811,  9192, 2004, 9193,  16584, 21167, 14086,  \n4247, 16879, 15771,  24253, 24256, 24082,  24257, 23805, 23627,  \n23809, 23810, 24409,  17989, 18056, 3990,  1215, 9252, 1739,  \n24083, 23301, 24411,  23301, 24550, 24411,  24412, 24550, 23301,  \n24084, 23469, 24255,  2758, 9436, 2757,  6997, 20526, 16058,  \n13848, 11452, 15779,  14026, 23378, 21838,  1973, 13040, 7982,  \n18076, 501, 13553,  5410, 21776, 3312,  8129, 7077, 7076,  \n24092, 24257, 23627,  9043, 8568, 9035,  24414, 24092, 24415,  \n24556, 23953, 23811,  5754, 2996, 7513,  8072, 4417, 8071,  \n24554, 24417, 23949,  23808, 24084, 23949,  24084, 24554, 23949,  \n24085, 24256, 24418,  8008, 15682, 9060,  10559, 9062, 6420,  \n12464, 19692, 5791,  498, 3834, 2621,  19487, 16453, 21085,  \n19487, 1401, 16453,  12307, 15347, 11476,  1519, 15982, 12225,  \n20784, 15870, 13081,  23305, 24259, 23297,  24415, 24092, 24093,  \n24419, 14651, 14652,  20111, 16642, 16643,  23640, 23305, 22190,  \n19614, 2424, 9689,  24420, 24415, 24093,  4935, 9388, 13289,  \n17163, 6124, 13420,  19416, 13061, 14993,  23812, 24260, 24094,  \n4611, 16346, 15400,  23954, 24420, 24093,  24260, 24095, 24094,  \n11777, 11091, 17913,  17645, 5808, 22955,  24420, 23954, 23958,  \n24421, 24261, 24095,  23476, 24261, 24096,  24261, 24262, 24096,  \n18605, 12163, 7203,  24262, 24263, 24096,  18893, 3253, 16003,  \n13555, 1902, 18341,  9086, 2945, 5330,  598, 22293, 17543,  \n24097, 23814, 24263,  23200, 13902, 10474,  23961, 23647, 24424,  \n14034, 1873, 4346,  2639, 18553, 22930,  24097, 24425, 24098,  \n24099, 24098, 24264,  24264, 24265, 24099,  23958, 24426, 24420,  \n3321, 20146, 18625,  23816, 24265, 23957,  24265, 24266, 23957,  \n8011, 9215, 4497,  24270, 24426, 23958,  23817, 23957, 24267,  \n9403, 7654, 5555,  10679, 2324, 15069,  16013, 16401, 7929,  \n23960, 24269, 24431,  23822, 23960, 24431,  24270, 23651, 23969,  \n24428, 23830, 23961,  5784, 373, 5782,  23825, 23822, 24431,  \n18039, 13993, 986,  1293, 15304, 1292,  1481, 17407, 2248,  \n16013, 1907, 16401,  12943, 1978, 9276,  23969, 24275, 24432,  \n7314, 3385, 6603,  24105, 24103, 24433,  9147, 7597, 9148,  \n24440, 24268, 23826,  16147, 10355, 11716,  4076, 10579, 11944,  \n22950, 18928, 19223,  24103, 24273, 24433,  4842, 3311, 3652,  \n18650, 17372, 17983,  23830, 24434, 23831,  24435, 23967, 24436,  \n5226, 17921, 9589,  24273, 24104, 24437,  20434, 24438, 24439,  \n16396, 5894, 10831,  15945, 12190, 19698,  13924, 11227, 21250,  \n8806, 17641, 4130,  8402, 21475, 15063,  4399, 664, 665,  \n2775, 9869, 23205,  13648, 2859, 9669,  24276, 24104, 23833,  \n24276, 24437, 24104,  24433, 24273, 24437,  5382, 16053, 3290,  \n6597, 13488, 5197,  17028, 16053, 17490,  10677, 10630, 9122,  \n19152, 1571, 1478,  2151, 2147, 2148,  8878, 17431, 1026,  \n23656, 23831, 24441,  24440, 23653, 23837,  4227, 20553, 7325,  \n24107, 24433, 24443,  23494, 24444, 24108,  24446, 24276, 23835,  \n24109, 24107, 24443,  4792, 4984, 19636,  23656, 24441, 24112,  \n4055, 3180, 17507,  326, 5696, 5611,  10628, 15138, 15137,  \n20409, 10424, 10423,  5890, 19228, 16655,  12695, 5086, 23357,  \n23835, 24111, 24446,  24112, 23490, 23656,  10815, 18752, 12032,  \n24443, 24278, 24109,  15356, 2088, 9367,  8012, 18354, 20242,  \n24443, 24447, 24278,  21814, 16629, 11451,  631, 17363, 11197,  \n24448, 23976, 24112,  24280, 24720, 23839,  24113, 24279, 24111,  \n967, 11870, 19494,  24280, 23839, 23660,  5128, 5129, 9591,  \n12918, 6371, 11374,  18374, 11560, 16440,  15479, 6389, 6667,  \n3379, 3244, 5273,  13858, 9380, 9430,  23838, 24114, 23492,  \n6308, 17063, 13575,  9861, 9860, 16615,  24279, 24113, 24281,  \n11784, 13041, 16009,  9478, 18054, 13308,  12050, 11875, 11876,  \n20195, 2877, 12233,  21818, 14495, 21819,  19101, 8813, 4160,  \n18045, 3237, 6267,  24117, 24278, 24449,  14511, 3244, 3433,  \n24282, 24280, 23841,  22399, 22220, 1755,  24449, 24450, 24117,  \n19453, 17134, 4059,  24281, 23150, 23662,  14955, 9971, 13454,  \n8155, 11604, 13141,  13296, 14058, 13297,  14088, 10034, 315,  \n389, 1928, 2007,  23664, 24118, 23842,  24119, 24117, 24450,  \n14571, 17378, 22044,  24453, 23662, 23496,  24283, 24119, 24450,  \n1377, 2123, 13916,  23981, 23841, 23843,  10213, 2797, 664,  \n15539, 14188, 3025,  4810, 2055, 1714,  23507, 9514, 9515,  \n673, 22232, 15120,  10697, 2279, 19549,  15649, 5644, 6443,  \n18677, 20901, 20451,  24123, 24453, 23982,  20975, 16545, 4033,  \n2308, 9046, 2309,  23843, 23984, 23981,  15390, 15389, 14627,  \n24287, 23845, 24120,  2638, 14799, 16294,  5616, 6809, 7122,  \n24288, 24121, 24286,  2146, 2627, 15713,  11913, 5120, 18698,  \n15309, 12949, 9864,  24121, 24284, 24286,  24287, 24289, 23845,  \n7909, 18415, 618,  23985, 24454, 24122,  6643, 1415, 10371,  \n24125, 23845, 24289,  7089, 9697, 7090,  14890, 9892, 15683,  \n5837, 12808, 5838,  2183, 7990, 3902,  10818, 2930, 22750,  \n12611, 8924, 20606,  8742, 5329, 14251,  9311, 21210, 1241,  \n7344, 15644, 16537,  18834, 7540, 3647,  21126, 21127, 3329,  \n913, 17392, 16322,  24299, 24293, 23850,  18056, 1881, 19268,  \n14263, 22059, 5085,  24294, 24455, 23986,  14911, 14912, 22248,  \n8286, 13805, 14683,  3371, 7912, 22518,  24298, 23987, 24125,  \n11102, 18683, 11103,  10314, 13138, 6117,  17797, 15364, 6893,  \n722, 5683, 15688,  8019, 6374, 19979,  20994, 1761, 6396,  \n24296, 23989, 23502,  18210, 8373, 11909,  14261, 13476, 19079,  \n15739, 8738, 21358,  2159, 16396, 10830,  14155, 5798, 7606,  \n16458, 16723, 7579,  2741, 1459, 3818,  22748, 19144, 14289,  \n15422, 2944, 15287,  14702, 7609, 13335,  5486, 5330, 20849,  \n20772, 19112, 22489,  9492, 15627, 15628,  24302, 23993, 23506,  \n14340, 23347, 19600,  17248, 9990, 12764,  8973, 14534, 19518,  \n23993, 24129, 23349,  7851, 22004, 16288,  24130, 23677, 24129,  \n13917, 3844, 9360,  9472, 14313, 12648,  11316, 11076, 2263,  \n24130, 24129, 24457,  24305, 23996, 24458,  5766, 10654, 16142,  \n1011, 14207, 13408,  11678, 11677, 6234,  1703, 9013, 6508,  \n12841, 19992, 2167,  8017, 7901, 13546,  23855, 23991, 24459,  \n4227, 7325, 3673,  6791, 6792, 8366,  9868, 13785, 22958,  \n1191, 10075, 10605,  9717, 16633, 9718,  7329, 18788, 19477,  \n23998, 23684, 24132,  6939, 9994, 11370,  2014, 16422, 2015,  \n13080, 5466, 19123,  24305, 24307, 24132,  24135, 785, 784,  \n17491, 17492, 16860,  24307, 23998, 24132,  23517, 24461, 23857,  \n496, 9393, 497,  24464, 23998, 24307,  24133, 1408, 12641,  \n23855, 24460, 24137,  13320, 4783, 21911,  15193, 5874, 14443,  \n10099, 16648, 16737,  9531, 24462, 15598,  8082, 12506, 17188,  \n743, 15930, 9455,  8482, 19062, 16030,  12172, 22077, 13247,  \n23692, 24464, 23691,  22101, 14327, 13960,  4939, 10822, 21945,  \n8400, 399, 3184,  3803, 13884, 10172,  3768, 11732, 7533,  \n15539, 3026, 4954,  489, 3126, 732,  4005, 13838, 5906,  \n502, 18517, 4103,  11076, 11078, 12399,  7809, 19284, 7810,  \n23859, 24139, 24308,  24140, 23183, 24309,  23862, 23692, 24000,  \n15682, 5590, 9060,  14354, 3129, 7695,  2821, 6843, 19451,  \n23523, 24466, 23863,  24467, 24142, 24000,  21215, 5623, 21749,  \n3159, 20989, 10348,  14350, 7163, 23511,  3337, 13159, 10499,  \n11318, 3644, 1862,  11882, 8598, 9116,  8996, 15146, 8994,  \n18981, 1255, 13853,  24466, 23523, 23865,  10434, 14059, 946,  \n17984, 19124, 877,  20466, 7809, 22466,  2349, 2348, 3468,  \n16781, 4731, 18072,  6985, 5203, 6984,  18697, 8296, 23035,  \n6141, 9284, 8906,  24143, 24144, 24310,  13564, 1354, 12674,  \n18179, 11629, 12510,  24469, 23698, 24146,  5039, 22106, 22107,  \n15014, 7666, 18404,  24145, 24468, 23524,  23697, 24003, 24470,  \n24310, 24144, 24311,  18037, 22077, 16324,  21209, 4937, 14703,  \n8054, 18049, 8055,  10379, 10520, 15605,  24311, 23528, 24149,  \n11117, 14912, 12639,  3697, 7927, 9615,  7770, 7146, 2543,  \n456, 455, 14964,  18422, 4108, 12981,  24149, 23701, 24154,  \n6841, 9627, 6840,  5726, 9879, 19086,  9193, 19324, 19325,  \n24473, 23704, 23869,  24154, 23707, 24472,  19611, 15829, 4338,  \n6418, 11669, 8646,  7069, 10654, 10644,  24473, 23869, 24314,  \n24157, 23531, 24313,  23287, 611, 5830,  23707, 23708, 23872,  \n23709, 24156, 24317,  21407, 20968, 8668,  11395, 11394, 11987,  \n16660, 16659, 7405,  11484, 10568, 2215,  12147, 4478, 4477,  \n20795, 14611, 14612,  16755, 14347, 18819,  24316, 24162, 24474,  \n5452, 22942, 2432,  12605, 17251, 18785,  9332, 3457, 4516,  \n11449, 1429, 12103,  7674, 18443, 19986,  19261, 3567, 5102,  \n3749, 3748, 13454,  24475, 24014, 23386,  22001, 16362, 17997,  \n10694, 6919, 4285,  15213, 18134, 10622,  12645, 13214, 1749,  \n5037, 18534, 8171,  13709, 17717, 7240,  5614, 5615, 3134,  \n8650, 24315, 8649,  3875, 17905, 12986,  302, 19402, 15522,  \n2058, 6710, 6712,  23544, 24165, 24321,  24166, 23875, 23213,  \n23213, 23876, 24166,  415, 11071, 6282,  12286, 2140, 3153,  \n20407, 20040, 20039,  23542, 23388, 24015,  20812, 20313, 16783,  \n5679, 3060, 5677,  24323, 23546, 23542,  23874, 24017, 24169,  \n19108, 9406, 14933,  18760, 7182, 4570,  24017, 24324, 24168,  \n3340, 1373, 4098,  13021, 21095, 11360,  511, 15276, 512,  \n537, 6641, 1821,  8314, 8323, 7771,  9680, 21058, 9679,  \n21485, 16924, 15145,  24622, 24478, 24173,  12039, 8795, 8794,  \n24479, 24173, 24326,  24176, 24173, 24478,  3655, 6935, 15315,  \n24326, 24174, 24480,  3537, 2657, 17401,  24176, 24478, 24481,  \n17349, 12014, 21764,  24480, 24174, 24175,  24176, 24481, 24327,  \n22077, 14682, 8877,  24019, 24483, 23726,  940, 7851, 16288,  \n11923, 20847, 11924,  18397, 1639, 1423,  11091, 11777, 908,  \n11525, 17789, 17350,  3148, 13930, 3688,  18804, 17946, 2397,  \n22084, 11367, 19534,  24175, 24177, 24182,  3562, 4023, 10143,  \n339, 7360, 12476,  24327, 24328, 24178,  2772, 11995, 9041,  \n24485, 24020, 24026,  3946, 12841, 3947,  24025, 24486, 24180,  \n29206, 5246, 19547,  24180, 24486, 24487,  6199, 4273, 20931,  \n7111, 13957, 10739,  7706, 566, 13307,  7744, 21974, 7745,  \n24180, 24487, 24181,  24489, 23882, 24488,  12929, 18822, 5341,  \n24485, 24026, 23883,  24182, 24183, 24490,  11214, 18033, 4323,  \n11642, 9367, 2025,  23073, 23323, 8498,  24429, 4402, 12884,  \n5281, 1318, 12941,  24489, 23560, 23882,  24181, 24491, 24028,  \n20527, 19948, 4245,  23883, 23884, 24492,  23889, 23885, 24329,  \n24490, 24183, 24030,  16928, 4676, 17867,  6699, 21627, 6698,  \n24490, 24030, 24185,  24184, 24493, 24331,  16360, 16359, 641,  \n18096, 6120, 16746,  794, 16803, 14983,  24331, 24637, 24333,  \n7549, 18029, 22680,  17902, 17775, 5133,  6517, 1253, 821,  \n713, 13232, 712,  24060, 15813, 11182,  18476, 2912, 18559,  \n24031, 23891, 24333,  24030, 24032, 24185,  2724, 9079, 19364,  \n24185, 24032, 24495,  23737, 24332, 23888,  4418, 4789, 4419,  \n6052, 13292, 15405,  1927, 2031, 17400,  7140, 3077, 7141,  \n24031, 24642, 24336,  12796, 4190, 8199,  24335, 23737, 23893,  \n6453, 20648, 6452,  9389, 5758, 2482,  17203, 17293, 12777,  \n8849, 8850, 11580,  6475, 19667, 7862,  9393, 2965, 497,  \n16141, 18221, 18220,  429, 10076, 430,  20562, 13484, 2791,  \n20752, 7290, 1547,  5759, 5758, 23790,  24340, 24339, 23896,  \n16562, 5054, 6493,  13513, 13432, 13514,  24496, 24339, 24340,  \n1444, 1445, 10159,  12245, 3785, 3055,  2690, 8973, 4622,  \n15724, 21458, 13055,  24189, 24033, 24186,  23898, 24340, 23896,  \n5863, 8480, 8481,  13853, 1254, 23538,  23897, 24038, 24342,  \n18964, 15744, 1247,  13435, 7250, 7249,  24498, 24034, 23569,  \n21193, 17919, 14388,  18090, 5589, 11553,  6831, 3250, 637,  \n19803, 14865, 18297,  19648, 19968, 19649,  12104, 1429, 15678,  \n15970, 9371, 9264,  24034, 24345, 24192,  18614, 2236, 785,  \n19152, 20058, 1571,  5693, 15248, 18610,  13551, 6049, 10422,  \n10857, 18571, 13878,  5763, 16930, 14536,  16441, 9804, 2509,  \n6921, 20881, 22696,  24194, 24500, 24037,  6020, 15042, 4981,  \n4559, 18032, 15684,  398, 6993, 9294,  24348, 24499, 24350,  \n24502, 24194, 24196,  9223, 9724, 8439,  19569, 10350, 7964,  \n20813, 14394, 19504,  5874, 17749, 12231,  24351, 24350, 24501,  \n11640, 13370, 15387,  747, 11841, 21258,  7816, 7099, 5112,  \n10961, 675, 674,  23415, 24042, 23753,  24193, 23418, 24349,  \n24503, 24351, 24501,  5094, 3289, 10105,  24504, 23753, 24042,  \n24043, 23240, 24197,  18666, 14592, 9194,  12312, 8110, 12212,  \n23755, 23903, 24505,  21660, 14843, 3008,  24352, 24351, 24506,  \n15796, 13816, 15704,  8474, 8473, 477,  21385, 21384, 11047,  \n24652, 24202, 23758,  16910, 14203, 2236,  17106, 12826, 18221,  \n4556, 9965, 3084,  24507, 24203, 24044,  13483, 6796, 6795,  \n10712, 11182, 14894,  2188, 436, 438,  24044, 24356, 24507,  \n20971, 14677, 3376,  20261, 18766, 8423,  14602, 9791, 13120,  \n3517, 21127, 15350,  18178, 359, 18177,  24203, 24507, 24357,  \n6669, 538, 9992,  9909, 15220, 15221,  17363, 10380, 17790,  \n14213, 22997, 8920,  24356, 24358, 24357,  17164, 14544, 3584,  \n24507, 24356, 24357,  11029, 1614, 11030,  24358, 23420, 24357,  \n23760, 24206, 24205,  12754, 13147, 19117,  11789, 19728, 5576,  \n24359, 24048, 23587,  2316, 13457, 21098,  24048, 24510, 24207,  \n1516, 8831, 22067,  20165, 22479, 21042,  3962, 3231, 6037,  \n23588, 24208, 24206,  19830, 12043, 536,  5517, 4764, 12476,  \n14321, 9854, 20595,  23593, 24050, 24362,  24363, 23593, 24362,  \n18957, 12329, 4178,  24515, 24514, 23592,  24515, 23592, 24051,  \n5790, 607, 13603,  17080, 16044, 4738,  16164, 9706, 7365,  \n17630, 9870, 13273,  23761, 24364, 24211,  5100, 10687, 3274,  \n23762, 24052, 24365,  24365, 24052, 24214,  23600, 24213, 24369,  \n16449, 803, 8182,  9742, 9743, 11037,  4826, 13853, 23538,  \n19384, 16531, 14505,  23909, 24369, 24215,  2523, 3843, 5517,  \n23599, 24216, 24214,  23599, 23766, 24216,  24216, 23766, 24054,  \n5137, 12880, 11633,  19913, 15906, 15130,  24517, 24216, 24053,  \n19919, 14684, 8844,  24373, 23768, 23912,  1554, 13054, 13592,  \n24217, 24056, 23433,  1015, 6046, 12483,  24374, 24518, 23912,  \n24056, 24519, 24057,  24218, 24219, 24520,  24520, 24219, 24375,  \n6595, 408, 10783,  7366, 9971, 10538,  12135, 18294, 15890,  \n5894, 5885, 18281,  298, 7362, 9770,  12683, 15688, 5683,  \n10987, 2406, 11388,  23604, 24222, 24224,  18003, 9370, 9374,  \n24225, 23772, 24521,  10202, 2869, 2409,  11078, 12593, 12399,  \n3222, 18745, 4322,  14041, 14513, 19035,  16134, 14008, 4066,  \n24381, 24378, 24226,  11915, 743, 14771,  24522, 24379, 24380,  \n473, 11517, 472,  8480, 12227, 8481,  3472, 10070, 10069,  \n2269, 10544, 10543,  3057, 9792, 4440,  4131, 5066, 17633,  \n24228, 24381, 24061,  8619, 10695, 8618,  19828, 20876, 19429,  \n19322, 2166, 9575,  7456, 8085, 23377,  24062, 24379, 24383,  \n22881, 3494, 11115,  24230, 24382, 24229,  21982, 8053, 9950,  \n11541, 8395, 8858,  24383, 24671, 23924,  15290, 15291, 16280,  \n7364, 16164, 7365,  24385, 23924, 24523,  12900, 4769, 5983,  \n20970, 5323, 14019,  1248, 3492, 8363,  3338, 19374, 570,  \n21563, 11443, 6830,  9381, 8679, 9430,  24675, 24063, 24385,  \n8374, 17237, 4106,  24232, 24524, 24386,  24064, 24232, 24386,  \n24065, 24063, 24675,  24067, 24065, 24675,  3343, 3144, 12890,  \n16527, 6219, 12064,  8181, 1787, 10445,  24526, 24677, 24387,  \n24066, 24388, 24232,  24526, 24387, 24067,  13745, 2314, 7557,  \n5398, 6406, 22291,  10727, 18664, 6248,  21251, 4292, 21042,  \n7128, 4772, 7129,  8642, 12984, 22755,  23617, 6366, 14471,  \n24527, 24388, 24233,  1351, 17338, 20346,  24068, 24387, 23784,  \n5019, 3401, 9615,  10459, 18733, 18073,  622, 19916, 1965,  \n11583, 11584, 11809,  24234, 24530, 24237,  14505, 15181, 19383,  \n8260, 14054, 19233,  24531, 24070, 24237,  24531, 24237, 24530,  \n1623, 1625, 2787,  24070, 24531, 24389,  24070, 24389, 24239,  \n7030, 2848, 7070,  20964, 17591, 14563,  21449, 8505, 4665,  \n23262, 5547, 24533,  15465, 12518, 12389,  7052, 360, 14170,  \n7089, 7091, 20971,  24395, 24535, 24393,  10831, 5894, 18356,  \n24536, 24395, 24397,  3872, 7333, 3931,  10242, 8182, 9054,  \n14980, 2386, 22752,  17105, 4319, 13801,  19073, 14032, 20618,  \n24537, 24536, 24398,  24398, 24536, 24397,  24071, 24399, 23452,  \n24394, 24538, 24243,  18207, 1227, 22445,  10382, 12647, 16027,  \n2536, 4171, 983,  10854, 22540, 14014,  24074, 23797, 24075,  \n23797, 21495, 23455,  17024, 20106, 7983,  24539, 24402, 24250,  \n9173, 7402, 2531,  24401, 24537, 24398,  24247, 24079, 24401,  \n23935, 24403, 23623,  835, 18023, 19191,  15526, 22540, 19875,  \n15755, 12926, 13683,  24541, 24400, 24243,  20658, 23947, 17066,  \n24243, 24538, 24541,  17524, 1462, 14823,  24827, 24249, 23943,  \n3274, 10687, 3275,  15643, 13339, 7060,  3565, 15709, 16012,  \n5494, 24315, 8650,  23943, 23945, 24542,  24400, 24541, 24543,  \n17772, 16858, 17773,  24543, 24404, 24400,  16866, 12532, 1583,  \n24251, 23801, 23939,  11897, 11755, 9676,  19610, 9988, 19947,  \n603, 17353, 15093,  12868, 10641, 16897,  24406, 23934, 23805,  \n12629, 16180, 9430,  14056, 887, 8285,  13479, 11556, 21215,  \n24543, 24545, 24404,  11417, 21543, 5377,  29259, 11794, 6658,  \n5552, 4030, 4031,  24547, 23461, 23462,  24546, 24547, 23462,  \n15984, 17927, 11643,  19705, 22304, 16569,  1656, 4186, 1486,  \n7353, 8586, 12574,  24409, 23810, 23946,  6985, 6984, 18733,  \n24549, 23946, 24083,  9532, 15693, 7648,  24408, 23809, 24409,  \n8541, 22274, 1815,  5746, 6330, 19603,  24411, 24549, 24083,  \n24549, 24411, 24550,  8920, 22997, 20019,  24551, 24552, 24553,  \n24545, 24253, 24404,  11846, 4114, 4857,  17107, 17033, 2847,  \n23950, 24413, 24412,  13029, 2561, 6064,  6523, 3448, 16829,  \n9959, 11594, 19247,  1866, 7863, 1212,  6783, 20195, 12254,  \n11025, 1359, 18070,  24412, 23301, 23950,  7429, 7428, 18834,  \n24554, 24084, 24255,  11768, 19409, 10755,  16837, 14420, 14666,  \n24545, 24555, 24253,  2281, 2468, 21513,  18319, 1568, 1367,  \n24256, 24253, 24555,  3083, 14663, 15476,  23950, 23634, 24258,  \n13364, 983, 3503,  24258, 23634, 23951,  4250, 15222, 21724,  \n4133, 16871, 1532,  13578, 7026, 14414,  8321, 21787, 1552,  \n4142, 23678, 4143,  14675, 8631, 16203,  23951, 23949, 24417,  \n8465, 8464, 22417,  24256, 24555, 24418,  24415, 24557, 24414,  \n4032, 20975, 4033,  24558, 24091, 24418,  23955, 23953, 24559,  \n739, 1536, 10346,  3930, 18124, 21546,  2865, 10589, 4037,  \n23305, 24560, 24259,  23640, 24560, 23305,  8803, 1465, 6306,  \n24091, 24561, 23812,  8129, 1724, 7077,  17727, 12626, 18545,  \n24561, 24260, 23812,  4548, 3569, 9564,  24424, 23955, 24559,  \n24562, 24260, 24561,  15090, 12373, 895,  5814, 6671, 6816,  \n7444, 21187, 15277,  12828, 4601, 8292,  8890, 3986, 17598,  \n24261, 24423, 24262,  23956, 24096, 24263,  16003, 3253, 3254,  \n1140, 24343, 29659,  24263, 24425, 24097,  20209, 6277, 6276,  \n15883, 5275, 18776,  8195, 14565, 8196,  24425, 24565, 24098,  \n24565, 24264, 24098,  24566, 24264, 24565,  21361, 9675, 9674,  \n5390, 4508, 16711,  24266, 24430, 24267,  23957, 24266, 24267,  \n23961, 24424, 24428,  17431, 13884, 17430,  14479, 18521, 16229,  \n23820, 24267, 24430,  23820, 24430, 24269,  13853, 4826, 18981,  \n4631, 4630, 2904,  24431, 24269, 24568,  24270, 23969, 24432,  \n8015, 23070, 9544,  19904, 4012, 4841,  5128, 13193, 17869,  \n11274, 4324, 10323,  10794, 1706, 6875,  22306, 2008, 1807,  \n5157, 5156, 12825,  24431, 24569, 23825,  24570, 24268, 24440,  \n23825, 24569, 23967,  12776, 11797, 1091,  5365, 10260, 1256,  \n23967, 24569, 24436,  24567, 24432, 24275,  17840, 10186, 6477,  \n12689, 4967, 17515,  13367, 3767, 19685,  3177, 16845, 16329,  \n14566, 12767, 9459,  24106, 23832, 24435,  16108, 3816, 3817,  \n9909, 9908, 2659,  23970, 23653, 24440,  12593, 11078, 12594,  \n24108, 24444, 24275,  15443, 802, 475,  24567, 24275, 24444,  \n10623, 15402, 4733,  23837, 24571, 24440,  24573, 24572, 24437,  \n15399, 10752, 22302,  5701, 22459, 24574,  4388, 4387, 1144,  \n14101, 21694, 14102,  24573, 24437, 24276,  24433, 24437, 24443,  \n18510, 16741, 4395,  16016, 13411, 2333,  21531, 21229, 20040,  \n24573, 24276, 24446,  18510, 14849, 16741,  23837, 24445, 24442,  \n20686, 1434, 3455,  23838, 24106, 24577,  3516, 13315, 15427,  \n14299, 12810, 13008,  24576, 24437, 24572,  24443, 24437, 24576,  \n24572, 24573, 24578,  636, 16589, 14219,  1846, 5422, 8378,  \n9983, 14743, 13914,  24573, 24446, 24111,  19960, 11135, 9331,  \n24447, 24443, 24576,  24572, 24580, 24576,  11214, 10759, 2932,  \n24572, 24578, 24580,  10135, 3258, 3260,  24279, 24573, 24111,  \n8486, 11023, 12255,  24580, 24447, 24576,  18301, 10111, 1816,  \n6992, 6991, 10160,  12404, 6921, 6714,  5151, 2556, 5150,  \n10650, 5845, 13662,  1284, 19812, 16200,  18688, 7218, 7219,  \n22242, 13062, 7229,  9674, 21115, 15203,  24279, 24581, 24573,  \n20177, 16358, 13895,  1019, 12786, 4234,  24581, 24279, 24583,  \n24278, 24447, 24582,  15245, 3379, 5273,  3726, 1547, 17270,  \n5218, 15711, 16935,  1550, 13488, 6476,  9870, 15090, 13273,  \n24278, 24582, 24449,  1688, 1689, 8599,  10677, 9122, 9121,  \n11362, 7357, 6743,  24584, 24279, 24281,  5381, 9553, 7023,  \n20759, 9553, 5381,  4354, 18159, 11334,  20506, 17179, 15775,  \n7879, 4420, 4421,  9838, 15278, 13977,  24452, 23841, 23981,  \n1112, 1111, 22363,  24452, 24282, 23841,  24115, 24122, 24585,  \n22583, 17760, 3944,  23665, 24114, 24120,  7978, 12577, 11688,  \n21760, 3466, 5296,  3413, 12787, 5272,  1927, 24586, 16614,  \n4265, 12528, 14477,  24285, 23842, 24118,  18541, 16181, 17229,  \n2616, 14223, 1199,  24283, 24590, 24591,  20526, 19332, 16059,  \n599, 598, 7742,  24453, 23496, 23982,  1341, 18165, 13205,  \n5748, 2582, 7183,  4029, 4028, 12681,  24283, 24591, 24284,  \n18207, 3728, 3727,  11180, 17159, 10056,  16874, 21552, 7840,  \n7333, 3932, 3931,  24588, 24122, 24454,  2987, 21532, 10010,  \n18482, 21094, 15939,  9754, 11799, 21225,  24592, 23981, 23984,  \n24594, 24288, 24286,  2704, 14233, 2705,  13626, 10318, 21289,  \n21366, 918, 11027,  4131, 4559, 5066,  16738, 3738, 19316,  \n18493, 11245, 19032,  15928, 22109, 10594,  6463, 750, 6439,  \n2713, 6354, 2714,  4404, 4405, 19390,  24288, 24295, 23844,  \n6662, 19406, 18695,  24455, 24292, 23986,  21572, 13622, 17274,  \n2710, 18511, 9971,  24295, 24288, 24594,  24454, 23985, 23508,  \n23852, 23846, 24595,  8282, 9710, 8283,  11894, 18083, 11893,  \n521, 16699, 8302,  2023, 6121, 15395,  10239, 16762, 20563,  \n18320, 5213, 18319,  3629, 20370, 20705,  2868, 10513, 22343,  \n9360, 13038, 13917,  11210, 6361, 16127,  18035, 3051, 5756,  \n13983, 22834, 16461,  10523, 7264, 5654,  10536, 10535, 13753,  \n12962, 22007, 1863,  17068, 10667, 18103,  7449, 3684, 18043,  \n24596, 1418, 5326,  13644, 2280, 18674,  13962, 2910, 11756,  \n23992, 24127, 23503,  22548, 7894, 6436,  17589, 17588, 15809,  \n13103, 2458, 1347,  4931, 1900, 4932,  16105, 3766, 3765,  \n23991, 24300, 24456,  2903, 19419, 15274,  3625, 6411, 19346,  \n3668, 13197, 20082,  21131, 9167, 12280,  332, 5815, 17319,  \n23992, 23509, 24597,  23995, 23854, 24301,  2353, 2354, 9510,  \n19121, 11494, 11032,  5123, 19390, 6652,  20748, 10116, 9800,  \n21818, 21819, 19387,  15941, 8893, 18292,  19252, 18367, 10600,  \n14218, 16589, 10078,  14689, 14765, 13191,  15941, 13767, 8893,  \n8720, 8719, 9650,  23210, 12408, 4191,  6039, 7267, 21015,  \n19592, 367, 8197,  14626, 19064, 21258,  24458, 23996, 23990,  \n7210, 7209, 9192,  22543, 18764, 15804,  6730, 2582, 2583,  \n24132, 23996, 24305,  16718, 17571, 18449,  18028, 17407, 1481,  \n21751, 8394, 19031,  18449, 17571, 6756,  3841, 12727, 2194,  \n21376, 8785, 14412,  13253, 636, 8041,  886, 10403, 11764,  \n2604, 549, 550,  11110, 793, 9346,  21078, 17492, 17493,  \n24137, 24460, 24603,  24461, 23517, 23999,  7265, 307, 6645,  \n355, 14090, 1798,  18716, 10828, 9972,  19927, 9394, 9395,  \n1914, 4843, 6667,  23688, 24464, 23692,  23688, 23998, 24464,  \n7505, 13034, 7504,  17315, 12191, 5502,  6491, 16942, 10919,  \n22417, 8464, 8816,  11191, 15887, 19826,  24110, 13921, 7168,  \n24138, 23860, 24140,  4050, 16989, 20630,  22454, 16834, 22058,  \n11640, 9731, 13364,  20511, 2403, 19227,  23859, 23690, 24139,  \n17645, 5043, 5044,  6509, 5246, 18961,  2682, 14342, 23022,  \n11209, 21336, 5970,  3230, 3229, 10818,  24465, 23520, 24141,  \n12795, 22181, 12796,  24001, 23859, 24308,  24309, 23863, 24466,  \n7598, 22248, 6135,  2724, 19364, 12957,  10605, 10074, 17440,  \n19820, 9531, 9530,  1145, 5426, 15844,  10527, 10528, 8232,  \n8767, 17129, 8768,  19563, 18888, 9190,  3754, 3753, 8717,  \n11917, 10211, 8421,  24145, 24142, 24467,  2399, 6629, 21326,  \n24145, 24467, 24468,  4748, 9654, 10761,  2638, 14798, 14799,  \n9023, 7689, 10323,  22409, 21636, 5708,  10324, 546, 547,  \n10927, 5836, 10928,  1054, 1553, 8624,  22861, 22379, 20462,  \n23972, 17178, 2387,  7371, 1262, 14795,  7993, 23972, 2387,  \n15184, 19459, 15584,  4359, 9059, 13198,  5616, 7122, 22945,  \n18420, 15153, 14131,  22240, 13860, 9277,  14721, 2215, 16881,  \n18853, 7036, 1670,  18815, 21962, 4416,  24470, 24152, 24006,  \n18337, 21944, 6622,  24152, 24470, 24153,  2542, 7771, 2543,  \n12276, 1908, 20219,  4083, 4085, 9704,  15225, 5804, 15596,  \n17431, 13441, 5716,  24149, 24154, 24471,  16700, 10401, 10400,  \n19975, 2593, 19626,  24151, 23704, 24607,  5749, 2423, 1151,  \n24360, 7673, 20571,  24152, 24153, 24608,  24609, 24154, 24472,  \n17548, 10559, 10560,  15741, 6678, 15742,  8738, 2346, 21358,  \n21199, 7836, 14752,  20433, 6010, 20431,  8339, 10516, 8338,  \n7799, 5386, 14945,  24156, 23868, 24312,  11961, 17092, 7327,  \n9884, 21235, 3370,  20141, 4145, 9815,  23869, 24316, 24314,  \n15554, 17302, 17301,  11972, 20480, 5996,  4629, 2886, 2885,  \n7838, 15038, 16701,  7932, 13042, 7931,  4351, 15543, 17679,  \n22575, 1157, 24612,  9285, 9286, 7033,  13301, 19512, 313,  \n24161, 23710, 24613,  1470, 602, 11325,  23709, 24317, 24160,  \n24159, 23872, 24010,  20423, 5743, 3754,  16038, 10777, 9871,  \n10481, 10048, 3886,  24012, 23871, 24161,  6087, 17548, 20066,  \n8557, 7124, 7387,  9963, 9965, 22736,  19287, 19018, 5444,  \n24010, 23715, 24318,  24614, 24319, 24011,  23715, 24163, 24616,  \n24015, 23716, 24012,  12679, 21220, 8290,  24615, 24164, 23719,  \n24165, 24319, 24321,  3880, 17983, 17371,  20858, 17955, 10490,  \n14644, 19294, 19635,  7607, 7606, 5798,  23876, 24167, 24322,  \n5101, 10687, 5100,  6936, 16655, 6937,  13170, 14603, 13120,  \n1085, 8805, 1811,  1831, 19485, 14773,  22214, 15253, 8529,  \n317, 318, 2124,  1165, 1166, 21289,  22620, 10904, 11239,  \n24619, 24620, 24624,  5313, 7435, 13348,  15998, 12794, 3358,  \n1045, 13515, 2867,  14189, 11228, 15086,  24624, 24620, 24479,  \n19927, 9395, 12223,  2219, 2665, 2220,  4211, 2211, 7454,  \n10634, 4448, 22330,  24326, 24624, 24479,  24326, 24626, 24624,  \n24480, 24626, 24326,  15630, 11648, 21968,  14168, 12488, 14887,  \n24622, 24623, 24478,  24173, 24620, 24622,  4033, 4682, 20404,  \n2332, 20573, 5331,  14049, 8144, 5642,  8977, 8976, 20756,  \n20626, 1021, 13604,  22443, 15184, 15584,  14347, 4340, 15177,  \n3099, 3526, 3043,  24620, 24173, 24479,  13861, 9975, 9977,  \n19947, 14247, 15910,  24481, 24478, 24623,  22188, 22189, 1348,  \n20086, 15069, 13231,  24018, 24325, 24628,  7489, 11919, 22624,  \n15669, 5122, 21280,  24175, 24627, 24480,  4727, 7021, 1595,  \n14898, 8420, 16391,  16237, 16236, 21494,  18540, 18541, 18644,  \n24171, 23725, 24172,  22763, 18065, 12907,  24629, 24019, 24018,  \n24019, 23552, 24018,  15244, 15243, 16303,  940, 16288, 24631,  \n19206, 16126, 4037,  15035, 4661, 4915,  24484, 24175, 24182,  \n6916, 3026, 21783,  18804, 11273, 17946,  14041, 19035, 14040,  \n23726, 24483, 23877,  8109, 12313, 3855,  13222, 13784, 17177,  \n10682, 7515, 19524,  5838, 830, 10928,  19226, 18025, 17333,  \n24488, 23877, 25074,  14456, 17792, 14457,  15371, 3555, 15372,  \n24025, 24328, 24486,  4522, 16632, 4523,  17275, 9854, 14321,  \n18951, 18952, 489,  24484, 24182, 24490,  2590, 21104, 20173,  \n9669, 2859, 2858,  18033, 15520, 4323,  24181, 24487, 24491,  \n5591, 19664, 5592,  7268, 924, 8692,  7685, 15660, 23847,  \n24491, 24329, 24028,  15754, 13617, 20525,  1567, 1568, 19806,  \n8410, 20010, 15260,  24633, 24634, 24635,  24636, 24633, 24637,  \n4965, 18931, 7459,  24634, 24633, 24636,  24638, 24637, 24633,  \n4782, 19943, 13730,  24639, 24636, 24493,  24184, 24640, 24493,  \n6789, 6790, 4235,  7421, 6555, 6556,  10926, 8327, 8328,  \n3750, 3749, 8154,  24493, 24636, 24637,  20926, 10500, 1794,  \n22787, 15554, 17301,  3703, 2360, 3702,  20924, 14796, 18409,  \n24637, 24331, 24493,  441, 442, 18326,  24638, 24633, 24635,  \n10361, 14658, 8684,  9535, 8010, 10036,  2149, 6506, 6494,  \n1364, 17137, 3251,  23884, 24332, 24641,  24637, 24494, 24333,  \n24637, 24638, 24494,  3826, 21444, 13708,  10366, 8552, 8551,  \n9565, 8563, 10999,  5944, 5943, 14439,  24031, 24333, 24494,  \n11089, 11090, 13643,  23887, 24330, 24334,  17470, 14933, 9406,  \n2566, 10793, 5346,  4083, 7731, 4084,  24031, 24494, 24642,  \n24332, 23737, 24335,  2872, 6429, 10834,  21314, 13527, 13526,  \n2031, 14996, 7615,  7421, 3201, 10413,  2600, 3037, 15503,  \n20732, 5151, 5150,  24643, 24032, 23897,  8606, 12320, 12321,  \n24337, 24336, 24642,  11476, 17289, 17288,  24187, 23736, 24338,  \n11310, 13251, 8954,  8363, 3492, 8910,  5893, 7826, 5291,  \n19785, 9543, 9068,  419, 16705, 16706,  12472, 12474, 20500,  \n24643, 23897, 24342,  7123, 6552, 6551,  9573, 7455, 1499,  \n7595, 7596, 4264,  24189, 24186, 24645,  6877, 5863, 1660,  \n15017, 8093, 5968,  23569, 24497, 24498,  24646, 23898, 24341,  \n20091, 4831, 5219,  24341, 23411, 24190,  24645, 24035, 24189,  \n13076, 15215, 3036,  9151, 6008, 3548,  24647, 24348, 24035,  \n17280, 16558, 12055,  8637, 14261, 19079,  16094, 19055, 14227,  \n24038, 24037, 24500,  11430, 11429, 21306,  21454, 18638, 21328,  \n14598, 15662, 15661,  11858, 8481, 12227,  5261, 1391, 20472,  \n842, 7106, 10757,  23747, 24345, 24347,  21454, 13113, 18638,  \n24350, 24499, 24648,  24502, 24500, 24194,  23749, 24193, 24346,  \n24350, 24648, 24501,  8637, 7362, 298,  14147, 13510, 18024,  \n11298, 14231, 16756,  17594, 596, 12066,  16937, 10299, 17042,  \n7446, 2067, 20093,  15409, 8157, 1947,  10773, 2883, 22556,  \n18402, 14457, 19408,  14272, 9516, 189,  3204, 19426, 3205,  \n20146, 3321, 7802,  22699, 22254, 22426,  24650, 24503, 24501,  \n18829, 4583, 10683,  1206, 19809, 11896,  11807, 1933, 4885,  \n7740, 8301, 15827,  14349, 8023, 14350,  517, 340, 12954,  \n24197, 23755, 24505,  24506, 24351, 24503,  8617, 2872, 11098,  \n24202, 24196, 23757,  24651, 24352, 24506,  24652, 24502, 24196,  \n5060, 16786, 12792,  5379, 14003, 12956,  24354, 24352, 24651,  \n6451, 9702, 6896,  24653, 24354, 24651,  11495, 7443, 2606,  \n3701, 11010, 11973,  20215, 22893, 9619,  21744, 4444, 19528,  \n16076, 9307, 14195,  16390, 15179, 3677,  24353, 24655, 24356,  \n24353, 24355, 24655,  24356, 24655, 24358,  14084, 22013, 8951,  \n24508, 24205, 24206,  24358, 24656, 24509,  24358, 24655, 24656,  \n13904, 6779, 3209,  24509, 24047, 24358,  14156, 22418, 10988,  \n24509, 24359, 24047,  24359, 24511, 24048,  7099, 18647, 2383,  \n24512, 24508, 24206,  24510, 24048, 24511,  13420, 6124, 13419,  \n23101, 22496, 22495,  24049, 24657, 24361,  24206, 24208, 24512,  \n6011, 10999, 18839,  12968, 13927, 10935,  19219, 15488, 20409,  \n24658, 24513, 24514,  13205, 18165, 20854,  18165, 1799, 20854,  \n16124, 8745, 6020,  15993, 7889, 1127,  7764, 8847, 14863,  \n24514, 24515, 24658,  10546, 10548, 6188,  24363, 24659, 24210,  \n10429, 10027, 24304,  24515, 24051, 24516,  11585, 10973, 9957,  \n24051, 24365, 24516,  3237, 3459, 6266,  24660, 24516, 24365,  \n11768, 15757, 19409,  24662, 24211, 24364,  24660, 24365, 24366,  \n24662, 24213, 24211,  24368, 24366, 24214,  7498, 561, 9776,  \n24368, 24216, 24517,  23911, 24370, 24371,  24216, 24054, 24053,  \n10585, 10584, 13062,  412, 11901, 11900,  4597, 18252, 15073,  \n2135, 6478, 2136,  2372, 903, 8702,  12076, 9051, 11233,  \n24373, 23912, 24372,  21818, 1137, 14495,  19118, 14046, 15566,  \n14549, 8940, 8941,  14334, 6292, 20223,  3660, 4675, 9902,  \n2491, 14257, 15601,  24218, 24520, 24664,  24665, 24520, 24375,  \n24665, 24375, 24221,  24222, 23264, 23918,  11735, 16746, 4454,  \n23771, 24665, 24221,  24665, 23771, 24225,  4806, 1748, 7766,  \n5695, 8997, 6271,  17803, 19032, 4775,  21233, 7994, 2387,  \n18898, 20043, 6673,  19218, 9936, 10356,  23772, 24223, 24521,  \n24380, 24227, 24667,  5268, 2311, 2310,  24227, 24377, 24667,  \n16362, 4079, 9633,  19312, 20921, 11206,  13341, 1088, 16017,  \n1140, 29659, 5799,  24668, 24377, 24378,  24669, 24668, 24378,  \n16982, 357, 1400,  24667, 24522, 24380,  13257, 6324, 22734,  \n20003, 13950, 5140,  7608, 6721, 17361,  24669, 24378, 24381,  \n7690, 3280, 14619,  18694, 1320, 8217,  10063, 4097, 1650,  \n13764, 20189, 7000,  24381, 24228, 24670,  3038, 374, 5319,  \n18100, 8525, 2618,  24230, 24672, 24382,  4306, 923, 5827,  \n24673, 24672, 24230,  10841, 10371, 10840,  24674, 24673, 24386,  \n24386, 24673, 24230,  6694, 6695, 3219,  24524, 24674, 24386,  \n23203, 20150, 6815,  24676, 24524, 24232,  23203, 8754, 20150,  \n13276, 5426, 5425,  24526, 24675, 24525,  11470, 9571, 556,  \n24675, 24526, 24067,  24676, 24232, 24678,  24388, 24678, 24232,  \n5529, 5530, 2091,  19745, 5691, 20070,  22284, 10883, 10424,  \n7151, 20495, 21105,  16735, 11807, 20137,  9174, 503, 502,  \n19112, 17693, 10513,  7794, 16371, 4628,  24680, 24387, 24528,  \n1632, 1631, 10353,  24681, 24682, 24680,  5088, 7197, 1456,  \n23784, 24387, 24680,  24234, 23784, 24680,  17044, 5497, 12499,  \n5897, 13723, 10529,  24529, 24679, 24527,  24682, 24683, 24680,  \n3502, 4171, 16536,  24680, 24683, 24234,  24234, 24683, 24530,  \n24683, 24685, 24530,  19742, 12924, 17231,  17276, 16603, 13154,  \n24531, 24530, 24685,  24389, 24531, 24684,  10409, 10411, 1684,  \n24389, 24684, 24529,  9873, 10229, 22752,  21089, 504, 916,  \n10195, 3599, 1042,  8979, 24686, 8980,  18952, 11320, 12217,  \n4326, 17623, 10008,  16547, 4342, 5179,  10993, 21251, 22479,  \n5960, 19610, 19947,  14825, 2765, 2764,  4234, 21044, 18150,  \n21187, 21188, 15277,  6063, 11435, 11437,  20584, 17219, 20236,  \n23793, 24534, 23794,  11547, 16687, 12589,  8438, 8508, 10714,  \n3065, 6913, 6914,  24395, 24536, 24535,  4624, 17205, 13726,  \n4560, 6928, 11586,  20066, 13493, 6087,  24393, 24535, 24689,  \n24689, 24394, 24393,  10790, 14092, 2193,  10150, 8512, 9618,  \n693, 6954, 5459,  24688, 23795, 24073,  8519, 13965, 8518,  \n1895, 4224, 11753,  9422, 2514, 3856,  15229, 15228, 5264,  \n24690, 24538, 24394,  24540, 23930, 24074,  7021, 10973, 14767,  \n18358, 18049, 14341,  24248, 24250, 24402,  10878, 11871, 14140,  \n21779, 4714, 5011,  10934, 8735, 8736,  1377, 11814, 1376,  \n24540, 24401, 24079,  24692, 24401, 24540,  24693, 24540, 24074,  \n24540, 24079, 23930,  24539, 24250, 24249,  15541, 6666, 20902,  \n16647, 13510, 24694,  23455, 19488, 23800,  20009, 20010, 8410,  \n22634, 4502, 14709,  14769, 12742, 22488,  23934, 24406, 24072,  \n23074, 8522, 13203,  4241, 15485, 13816,  21041, 23106, 24697,  \n13479, 10823, 8834,  9225, 10146, 8879,  5111, 16940, 5110,  \n14981, 11147, 11146,  1847, 2778, 7473,  3983, 433, 12345,  \n23804, 23624, 24696,  15274, 2556, 17926,  23943, 24542, 24698,  \n944, 20978, 20297,  13945, 18864, 3386,  24541, 24699, 24543,  \n18238, 10040, 18236,  23625, 23107, 24251,  6132, 6131, 9082,  \n7299, 3486, 7298,  3745, 1411, 21576,  24409, 24702, 24408,  \n24549, 24409, 23946,  7158, 21966, 6502,  11580, 5890, 8854,  \n3763, 8617, 16912,  10795, 15627, 9492,  3578, 17411, 3579,  \n24251, 24705, 23944,  24257, 24406, 23805,  9286, 8890, 17598,  \n24257, 24407, 24406,  24408, 24702, 23811,  5025, 12089, 5026,  \n16565, 13087, 11744,  19614, 5512, 5513,  24704, 24550, 24412,  \n1212, 3105, 1866,  11954, 8116, 16843,  11640, 13364, 13370,  \n3905, 16728, 470,  24544, 24701, 24081,  24701, 23945, 24081,  \n24545, 24543, 24706,  24699, 24706, 24543,  11223, 19485, 15473,  \n13623, 7306, 10167,  9673, 9672, 9819,  7221, 13932, 10955,  \n24703, 24549, 24550,  9185, 12291, 9184,  6679, 3359, 6680,  \n9697, 4208, 7090,  5107, 10045, 6278,  5485, 10688, 5484,  \n16373, 5917, 13436,  15505, 16196, 21142,  21787, 7389, 12750,  \n9792, 632, 4440,  3328, 14073, 9336,  5281, 12941, 17684,  \n13881, 2937, 7718,  7428, 11663, 18834,  8838, 8837, 2527,  \n23950, 23301, 23634,  10247, 11718, 17466,  17686, 6805, 18889,  \n24707, 24414, 24557,  24707, 24257, 24414,  22384, 6557, 6780,  \n24416, 24258, 23951,  7184, 16166, 7297,  10122, 15251, 3274,  \n24416, 23951, 24417,  9798, 19372, 10700,  7399, 5497, 18196,  \n24414, 24257, 24092,  23953, 24556, 24709,  14544, 19368, 10198,  \n5138, 1457, 5074,  12866, 7577, 6813,  24710, 24418, 24551,  \n14299, 10400, 17113,  23953, 24709, 24559,  17385, 2930, 20772,  \n24091, 24085, 24418,  13545, 7564, 11205,  13718, 14994, 10263,  \n4933, 3760, 16390,  16079, 2574, 4468,  7408, 4499, 10693,  \n23640, 24422, 24560,  6364, 15382, 17433,  10055, 10337, 17034,  \n2395, 10202, 2409,  3425, 15493, 20030,  3430, 16000, 15245,  \n7311, 13990, 6959,  4248, 14407, 1677,  4647, 8218, 21889,  \n24711, 24415, 24420,  12373, 14452, 4438,  23647, 23955, 24424,  \n23640, 23818, 24422,  15034, 5408, 652,  24260, 24421, 24095,  \n24423, 24712, 24262,  24262, 24563, 24263,  23818, 24564, 24422,  \n9352, 21914, 1535,  24261, 24421, 24423,  15640, 6583, 2161,  \n9041, 11707, 11996,  18408, 17325, 2243,  8871, 712, 13232,  \n24566, 24265, 24264,  24566, 24713, 24265,  19052, 3679, 17216,  \n24714, 24564, 24101,  24713, 24266, 24265,  6039, 21015, 12260,  \n24266, 24713, 24427,  11267, 8641, 14701,  24266, 24427, 24430,  \n4633, 9683, 9684,  11279, 20924, 11280,  10177, 13568, 12930,  \n24568, 24715, 24431,  6876, 10794, 6875,  5804, 5803, 22184,  \n24431, 24715, 24569,  23830, 24428, 24434,  12473, 2341, 4449,  \n5845, 10086, 13662,  16756, 8866, 11298,  15410, 16551, 11101,  \n4362, 21147, 21090,  23826, 23970, 24440,  24716, 24436, 24717,  \n24571, 24570, 24440,  24716, 24435, 24436,  1050, 10802, 20109,  \n3120, 3121, 6695,  8709, 17143, 7215,  11314, 8397, 9529,  \n24441, 23831, 24718,  2606, 14376, 9251,  17081, 667, 12433,  \n24444, 24719, 24567,  12037, 5338, 2737,  15676, 1406, 23682,  \n14170, 20341, 10505,  5262, 466, 17278,  24571, 23837, 24442,  \n5018, 19785, 19336,  24445, 24575, 24442,  7286, 7285, 14035,  \n24444, 24277, 24719,  24448, 24112, 24441,  15658, 2936, 15659,  \n24579, 24719, 24277,  18052, 7956, 12275,  668, 631, 11197,  \n501, 3730, 13997,  18155, 21652, 18154,  16488, 3893, 6735,  \n3573, 704, 705,  11415, 20688, 11416,  13343, 21498, 853,  \n24445, 23839, 24720,  24721, 23838, 24577,  13732, 630, 2934,  \n1703, 15879, 1702,  24578, 24573, 24581,  740, 5462, 2975,  \n9592, 13672, 22043,  8929, 9560, 13723,  24580, 24578, 24722,  \n24282, 24720, 24280,  24114, 23838, 24721,  24582, 24447, 24580,  \n17468, 12814, 12813,  24583, 24722, 24581,  24578, 24581, 24722,  \n18752, 21292, 20609,  5218, 5217, 15711,  5940, 14717, 15878,  \n24115, 24585, 24277,  11336, 11670, 9094,  13192, 3393, 4839,  \n2216, 6162, 6154,  805, 20166, 3141,  24118, 23976, 24726,  \n24584, 24727, 24279,  24727, 24583, 24279,  21960, 10470, 1921,  \n24449, 24582, 24728,  14366, 2455, 14367,  7165, 6688, 6837,  \n21185, 6887, 6886,  13081, 16532, 12656,  23662, 24453, 24281,  \n17590, 1758, 19119,  4367, 8696, 15060,  24453, 24729, 24281,  \n24449, 24730, 24450,  24587, 24585, 24122,  1518, 16864, 6228,  \n6399, 952, 16678,  6466, 6465, 6497,  24590, 24450, 24730,  \n14871, 14973, 15815,  3966, 7790, 7789,  21187, 11750, 19070,  \n16573, 11613, 11234,  5542, 8626, 14745,  24729, 24453, 24123,  \n13738, 11181, 13737,  24283, 24450, 24590,  8416, 19647, 9896,  \n5495, 5496, 5216,  8877, 14682, 3590,  10141, 4851, 10142,  \n24284, 24591, 24593,  11552, 10087, 2434,  14691, 5070, 5069,  \n24123, 23982, 24124,  17806, 21247, 20522,  17635, 4986, 19539,  \n18126, 17369, 9327,  12515, 11351, 6332,  24286, 24284, 24593,  \n15274, 17926, 10871,  16739, 19684, 19683,  24290, 23846, 24285,  \n8242, 3734, 2563,  15224, 16294, 14799,  24594, 24286, 24731,  \n24592, 23984, 24291,  9587, 19367, 433,  13430, 3960, 3138,  \n6858, 11915, 14771,  13824, 18172, 13825,  24732, 24292, 24455,  \n2719, 14484, 22773,  18331, 18332, 7456,  21168, 15963, 1693,  \n13201, 14151, 17968,  18773, 1957, 13598,  24300, 23852, 24595,  \n22152, 16842, 6693,  17079, 17618, 17313,  7986, 2950, 9004,  \n16999, 5948, 16050,  24296, 24295, 24734,  23987, 24298, 24733,  \n2599, 5392, 19791,  1759, 908, 16920,  21514, 15639, 8308,  \n23988, 23987, 24733,  19297, 2202, 17734,  2439, 19213, 19423,  \n23989, 24296, 24735,  6754, 17379, 20482,  11584, 17282, 7144,  \n1458, 14892, 14069,  24735, 24296, 24736,  17581, 1419, 1005,  \n24126, 24301, 24737,  15778, 7997, 4229,  17609, 17229, 18039,  \n7187, 17148, 19704,  22247, 18918, 6986,  23990, 23989, 24735,  \n9115, 11039, 22787,  6608, 10437, 21659,  10389, 10390, 314,  \n8468, 16101, 12479,  23680, 24598, 24128,  15916, 13490, 6288,  \n932, 931, 7663,  23509, 23994, 24597,  9836, 19189, 8056,  \n23994, 23351, 24131,  5664, 10594, 23236,  24599, 24597, 23994,  \n18612, 18137, 18611,  16315, 18382, 6269,  1746, 9750, 1747,  \n1807, 4250, 15804,  23357, 1216, 965,  7406, 16043, 4982,  \n10670, 13736, 10669,  22017, 20154, 1601,  24460, 23855, 24459,  \n2197, 7750, 1925,  19371, 21478, 19372,  12245, 14003, 5379,  \n4741, 4740, 6036,  18310, 12686, 12323,  2315, 18827, 12004,  \n16205, 2517, 16759,  6119, 519, 521,  11121, 17910, 17705,  \n4558, 12459, 19205,  11343, 10984, 13964,  8608, 17449, 12989,  \n8264, 1545, 551,  13679, 15606, 22289,  24461, 23999, 24138,  \n24463, 24137, 24603,  10122, 3275, 4150,  24139, 24137, 24463,  \n1588, 3320, 1589,  7602, 12601, 6724,  17461, 4355, 22962,  \n4822, 4898, 20629,  14688, 4742, 7494,  320, 13971, 7460,  \n10148, 3177, 12451,  3177, 22519, 12451,  24464, 24885, 23691,  \n13878, 4316, 13487,  19382, 2788, 14447,  18844, 18484, 20579,  \n23691, 24885, 24741,  18172, 8045, 15728,  11658, 1324, 10718,  \n4519, 3442, 8727,  24604, 24000, 23691,  13325, 8479, 12958,  \n14675, 6444, 8631,  17393, 10649, 3186,  623, 10021, 624,  \n24141, 22971, 23864,  15075, 17898, 14726,  9611, 11278, 11280,  \n24000, 25048, 24467,  10634, 22330, 574,  2739, 17848, 16138,  \n19878, 13014, 17338,  14997, 4477, 12266,  24743, 24466, 23865,  \n21731, 9866, 11637,  24744, 24001, 24745,  10505, 20341, 11843,  \n2673, 2672, 16921,  11537, 10635, 3605,  15399, 3717, 9522,  \n1392, 9210, 1435,  24002, 24001, 24744,  24002, 24744, 24004,  \n7724, 641, 16359,  23865, 24143, 24743,  16159, 21493, 13223,  \n23864, 23698, 24469,  10005, 15031, 15253,  15709, 3566, 8715,  \n10584, 17118, 13062,  18782, 8457, 8737,  7472, 4697, 22082,  \n24146, 24605, 24469,  23035, 8296, 8295,  11092, 6215, 9307,  \n21889, 8256, 6157,  6970, 15365, 1642,  6430, 21581, 11792,  \n24746, 24470, 24003,  24310, 24311, 24749,  12621, 12620, 6086,  \n24606, 24605, 24146,  24006, 23697, 24470,  18820, 17317, 6007,  \n24311, 24748, 24749,  6869, 20328, 17299,  14723, 1909, 1908,  \n9967, 7327, 12021,  24148, 24147, 24150,  7660, 6197, 15364,  \n18003, 11192, 8952,  24750, 24146, 24607,  11478, 7302, 11644,  \n24151, 24607, 24146,  12873, 7986, 17954,  18477, 10098, 6194,  \n16379, 19327, 11110,  24754, 24607, 24473,  17028, 2411, 8774,  \n23704, 24473, 24607,  24154, 24609, 24471,  14175, 3934, 1562,  \n18925, 19183, 12711,  15223, 7626, 18161,  24312, 24152, 24610,  \n24609, 24472, 24753,  16746, 2023, 4454,  24314, 24754, 24473,  \n24472, 23707, 24753,  24156, 24312, 24610,  23531, 24009, 24313,  \n12515, 6332, 7782,  23707, 24159, 24755,  24316, 24611, 24314,  \n21137, 2735, 13755,  2921, 13483, 6795,  12813, 12812, 20231,  \n23549, 21013, 1502,  16830, 3824, 3825,  17776, 20797, 2715,  \n24317, 24614, 24160,  24162, 24014, 24757,  2137, 2138, 7888,  \n15512, 900, 20641,  24159, 24010, 24318,  22895, 20543, 6946,  \n18759, 11587, 4066,  24614, 24011, 24160,  24475, 23386, 24164,  \n9310, 4414, 6907,  9054, 8209, 10294,  13293, 6088, 21667,  \n18150, 17945, 6302,  24616, 24318, 23715,  5785, 19819, 7947,  \n16392, 9829, 7730,  5415, 3053, 11456,  24012, 24758, 24015,  \n2158, 15102, 5090,  24476, 24616, 24163,  24322, 24167, 24321,  \n732, 10414, 12895,  16713, 17068, 15736,  9998, 3241, 8808,  \n24615, 23719, 23875,  24166, 24618, 23875,  24384, 2076, 24760,  \n5893, 1147, 5892,  6405, 1589, 13899,  5262, 3639, 5263,  \n8786, 3739, 2959,  24477, 23876, 24322,  18127, 4990, 15703,  \n24763, 24764, 24762,  21518, 21044, 20255,  23542, 24015, 24617,  \n22197, 15766, 19164,  14619, 7635, 7690,  7733, 19810, 7731,  \n24761, 24163, 24169,  4384, 13997, 19500,  5398, 22291, 10640,  \n18043, 14795, 10906,  17302, 15554, 7409,  24763, 24762, 24766,  \n14169, 14168, 14887,  24763, 24766, 24622,  4211, 8453, 2211,  \n24764, 24763, 24619,  10573, 12243, 2676,  1169, 8000, 10655,  \n22177, 16118, 20414,  24323, 23542, 24617,  24619, 24763, 24620,  \n2480, 21462, 15957,  24764, 24619, 24621,  1512, 9981, 1513,  \n24763, 24622, 24620,  24325, 24323, 24617,  8317, 13907, 12251,  \n24906, 24623, 24622,  24621, 24619, 24624,  24626, 24621, 24624,  \n15568, 16320, 6607,  4721, 10338, 15273,  3934, 13841, 13687,  \n22422, 6165, 8601,  338, 11940, 20995,  6142, 13132, 11566,  \n20169, 23858, 8267,  24625, 24168, 24324,  926, 9140, 6337,  \n18400, 15303, 18540,  24480, 24627, 24768,  24626, 24480, 24768,  \n9009, 23622, 9010,  10075, 1192, 10076,  18037, 16324, 3064,  \n24623, 24769, 24770,  7881, 24771, 23475,  24481, 24623, 24770,  \n13825, 16330, 16845,  24482, 24170, 23723,  24482, 23723, 24171,  \n19714, 8958, 632,  9407, 15627, 15374,  24481, 24770, 24630,  \n3304, 3479, 12820,  4018, 7515, 11511,  15076, 17720, 18858,  \n8096, 6478, 7335,  24482, 24171, 24172,  6280, 9142, 546,  \n9488, 9487, 5936,  4297, 3501, 17047,  24772, 24627, 24484,  \n5046, 19219, 5045,  11038, 21520, 11322,  4283, 9835, 7410,  \n13459, 9190, 14335,  2839, 17491, 16860,  24627, 24175, 24484,  \n24772, 24484, 24773,  22857, 8068, 22858,  20518, 5084, 17479,  \n10285, 10286, 2880,  1283, 17920, 17170,  24774, 24481, 24630,  \n2998, 2640, 2999,  24328, 24327, 24774,  15120, 22232, 532,  \n20931, 6385, 10426,  4703, 1201, 1203,  5240, 13552, 2784,  \n7723, 6075, 7068,  24775, 24484, 24490,  2001, 8316, 1999,  \n17641, 4559, 4131,  24776, 24486, 24328,  15385, 13794, 16759,  \n18827, 13405, 13521,  24486, 24777, 24487,  19013, 5557, 9018,  \n24485, 23883, 24632,  24491, 24487, 24777,  2801, 5383, 8291,  \n12195, 10602, 16911,  24634, 24636, 24780,  24778, 24780, 24636,  \n24778, 24636, 24639,  3962, 6238, 3231,  15008, 7681, 17081,  \n1753, 16155, 17910,  5772, 9895, 5403,  7797, 17752, 17753,  \n24632, 23883, 24492,  24635, 24634, 24781,  24780, 24779, 24634,  \n4522, 12930, 12931,  19512, 13301, 5807,  23889, 24329, 24184,  \n24329, 24640, 24184,  11147, 12434, 6719,  8424, 12744, 1602,  \n13320, 20563, 4783,  24495, 24490, 24185,  12439, 9889, 8866,  \n11924, 12363, 21264,  20008, 2475, 6104,  24492, 23884, 24641,  \n24781, 24783, 24635,  24784, 24641, 24332,  24785, 24638, 24635,  \n24783, 24785, 24635,  24638, 24785, 24494,  4067, 10942, 12335,  \n10401, 16700, 13616,  12410, 17639, 21796,  3172, 6703, 3171,  \n20205, 7932, 7505,  24495, 24032, 24643,  8539, 4977, 8540,  \n2223, 4262, 5705,  12937, 7725, 8163,  24785, 24642, 24494,  \n11719, 18844, 19418,  22980, 12169, 3294,  807, 23539, 15951,  \n9189, 4765, 7245,  10689, 14150, 6861,  16560, 4112, 4111,  \n9828, 22433, 19059,  20370, 7017, 20705,  12059, 3862, 8678,  \n3866, 12282, 3865,  6526, 1415, 6643,  24005, 9884, 16550,  \n7031, 7030, 5181,  1640, 19404, 1639,  6745, 23384, 13635,  \n24187, 24497, 23569,  16222, 17365, 20825,  5673, 9085, 7493,  \n5181, 7030, 7070,  20201, 21813, 1850,  23898, 24789, 24340,  \n24186, 24337, 24644,  4403, 3902, 21369,  24644, 24645, 24186,  \n9702, 15763, 6896,  23898, 24646, 24789,  3524, 18456, 21476,  \n354, 4705, 355,  2742, 5912, 2741,  9203, 13023, 18530,  \n16650, 9344, 2366,  2500, 13099, 10488,  24497, 24790, 24498,  \n9268, 16478, 15429,  7936, 1858, 15035,  14596, 9768, 13450,  \n24647, 24035, 24645,  9932, 8190, 3576,  6780, 8624, 22384,  \n16481, 3297, 16482,  8099, 5720, 18026,  24348, 24647, 24499,  \n19695, 14269, 6136,  3690, 7185, 3691,  10570, 12101, 6256,  \n13678, 15226, 13679,  1892, 9005, 8360,  5869, 14738, 20956,  \n18022, 13547, 8392,  16186, 6813, 7577,  24499, 24792, 24648,  \n9297, 21513, 2468,  2689, 10370, 11301,  11263, 5958, 16157,  \n4138, 8984, 8364,  12091, 4029, 7351,  20451, 20894, 18677,  \n24649, 24040, 24347,  12144, 18726, 17570,  19612, 7309, 2666,  \n13234, 22606, 20567,  24346, 24193, 24349,  1618, 16989, 1617,  \n24650, 24501, 24648,  18690, 16311, 4620,  24042, 24040, 24649,  \n2397, 327, 3700,  18357, 16438, 3798,  7429, 12032, 16049,  \n7314, 5563, 3385,  23418, 24043, 24794,  7844, 11331, 8999,  \n10656, 21730, 19786,  4995, 14636, 5368,  4838, 3396, 11581,  \n16268, 17443, 14113,  14891, 4981, 20919,  11838, 757, 16316,  \n24349, 23418, 24794,  24198, 23754, 24795,  24199, 23581, 24198,  \n468, 8448, 452,  3756, 11502, 2849,  23903, 23756, 24199,  \n24505, 23903, 24796,  6842, 1969, 2889,  24652, 24196, 24202,  \n22433, 13398, 21953,  8139, 2695, 14837,  16459, 9841, 2203,  \n13080, 19123, 5675,  12363, 11924, 19612,  6445, 3708, 4252,  \n14731, 16825, 6542,  16693, 20262, 8641,  24656, 24655, 24797,  \n24359, 24509, 24511,  4613, 5652, 11315,  12127, 3986, 3985,  \n24798, 24207, 24510,  10527, 17439, 10528,  24657, 24049, 24207,  \n5802, 14496, 1551,  9051, 14915, 558,  20419, 2237, 2238,  \n23906, 24361, 24799,  18129, 8588, 7186,  24513, 24512, 24208,  \n17642, 13095, 7680,  24513, 23592, 24514,  24050, 24209, 24362,  \n20428, 12736, 12737,  16941, 6201, 13102,  15457, 18287, 18286,  \n9191, 14139, 15292,  24210, 24659, 24364,  24364, 24801, 24662,  \n10969, 17676, 13702,  24369, 24213, 24662,  6186, 21250, 11455,  \n7169, 4413, 2806,  8999, 14702, 13335,  7420, 10516, 8173,  \n15651, 14767, 3895,  9667, 7617, 847,  24803, 24802, 24957,  \n24662, 24802, 24369,  11585, 9097, 3895,  24215, 24369, 24802,  \n6717, 7915, 5942,  24215, 24803, 24370,  24215, 24802, 24803,  \n24368, 24214, 24216,  24805, 24370, 24803,  24805, 24371, 24370,  \n2727, 17869, 2728,  15148, 10780, 23249,  9885, 18490, 13369,  \n24373, 24517, 24053,  4351, 16422, 18783,  24517, 24373, 24372,  \n16625, 2372, 8702,  22321, 10041, 1333,  23828, 5075, 1176,  \n3239, 2382, 7532,  12563, 5129, 17869,  24372, 23912, 24518,  \n24057, 24519, 24376,  24664, 24374, 24218,  24664, 24808, 24374,  \n1462, 7316, 6141,  24664, 24520, 24810,  4384, 12205, 4383,  \n24810, 24520, 24665,  20113, 15760, 8233,  6922, 6921, 22696,  \n14763, 864, 9859,  3918, 12524, 16602,  7255, 12747, 21146,  \n24223, 24224, 24666,  17095, 20724, 14629,  24521, 24223, 24811,  \n12562, 16207, 481,  18963, 5141, 8211,  5772, 5403, 5402,  \n10632, 21696, 11070,  24812, 24667, 24377,  24812, 24377, 24668,  \n3128, 18112, 13004,  15884, 19618, 18956,  10247, 10246, 11718,  \n21824, 15416, 2019,  24379, 24522, 24813,  14150, 10689, 9755,  \n12054, 16724, 18940,  19021, 10418, 7203,  5137, 15786, 9833,  \n3997, 3999, 16606,  2755, 8538, 3813,  20147, 13038, 15172,  \n13120, 14603, 14602,  8231, 16658, 16968,  8702, 903, 8958,  \n3046, 2807, 8725,  24670, 24669, 24381,  20010, 14515, 15260,  \n24813, 24383, 24379,  1546, 11178, 7743,  700, 9055, 9056,  \n700, 3421, 9055,  24228, 24814, 24670,  24814, 24228, 24382,  \n24815, 24814, 24382,  13861, 10901, 2068,  8822, 17558, 11323,  \n1476, 9210, 9873,  23924, 24671, 24523,  20407, 2078, 20481,  \n15794, 19126, 2763,  17477, 20021, 15735,  24385, 24523, 24675,  \n3000, 12118, 16719,  8931, 20622, 9613,  1552, 1551, 14496,  \n2879, 16089, 17988,  19002, 12082, 19456,  19013, 14782, 5557,  \n15361, 18071, 11426,  12905, 12906, 3681,  448, 3678, 449,  \n6873, 11594, 1436,  16740, 12031, 4006,  15015, 20823, 22955,  \n4298, 16949, 19692,  12543, 1876, 1875,  24679, 24684, 24816,  \n24684, 24679, 24529,  19670, 14958, 15025,  8465, 10344, 8463,  \n2393, 15824, 19453,  24531, 24685, 24817,  24817, 24684, 24531,  \n14240, 4505, 21508,  11306, 8329, 14737,  14534, 11968, 9899,  \n18951, 11320, 18952,  22081, 16762, 10239,  14810, 15012, 15011,  \n24532, 24818, 19467,  3501, 22127, 10300,  24532, 24819, 24818,  \n8711, 4542, 9636,  1044, 10248, 1043,  9477, 7903, 6030,  \n24240, 23793, 23618,  23904, 6765, 24821,  24392, 24819, 24532,  \n1389, 22397, 5886,  24822, 24535, 24536,  24071, 23794, 24534,  \n24392, 23795, 24688,  9737, 9738, 21854,  24822, 24689, 24535,  \n24536, 24823, 24822,  11656, 13895, 7873,  24537, 24823, 24536,  \n24402, 24824, 24825,  24689, 24690, 24394,  24537, 24826, 24823,  \n728, 10652, 14356,  23595, 15873, 9974,  12192, 11683, 21020,  \n1540, 3583, 2664,  10142, 15335, 10140,  24827, 24539, 24249,  \n15938, 9472, 17507,  24828, 24826, 24537,  23623, 24403, 24691,  \n6609, 3854, 17354,  24829, 24538, 24690,  24828, 24537, 24401,  \n24828, 24401, 24692,  24306, 20202, 11310,  24830, 24692, 24540,  \n2319, 1996, 2320,  12245, 3055, 8532,  4263, 23302, 18123,  \n2498, 13668, 13737,  24072, 24831, 24073,  7934, 7933, 20431,  \n24752, 18137, 18612,  3179, 3178, 16381,  24832, 24831, 24072,  \n14809, 1319, 1320,  2149, 5793, 15556,  23941, 23623, 24691,  \n24406, 24832, 24072,  12226, 4864, 10382,  24827, 23943, 24698,  \n16930, 3917, 15868,  20518, 5083, 5084,  3463, 20361, 3464,  \n24695, 23939, 23798,  11948, 11520, 11949,  24696, 23624, 23941,  \n14360, 22600, 21038,  24538, 24829, 24541,  24829, 24834, 24541,  \n16521, 5072, 12897,  23804, 24696, 24836,  17517, 9783, 9782,  \n7177, 1395, 1394,  16158, 1311, 7980,  24407, 24837, 24832,  \n7148, 7147, 6861,  24542, 23945, 24701,  24541, 24834, 24699,  \n24840, 24699, 24834,  17350, 3958, 18609,  24841, 24839, 24409,  \n24841, 24409, 24703,  9099, 18258, 9098,  1934, 1645, 22524,  \n24839, 24702, 24409,  21312, 19879, 12664,  24409, 24549, 24703,  \n6344, 9913, 6053,  24703, 24704, 24841,  8679, 20069, 11955,  \n24704, 24703, 24550,  24841, 24704, 24842,  24843, 24704, 24412,  \n19005, 17810, 2337,  516, 19643, 16571,  19216, 8249, 8250,  \n19742, 9007, 6276,  13179, 12230, 15555,  8691, 15452, 3634,  \n21966, 7413, 6502,  19945, 19619, 18742,  18204, 16009, 12952,  \n12694, 8591, 7014,  23461, 24547, 23459,  24547, 24844, 23459,  \n23625, 24251, 23944,  4133, 2260, 12646,  2634, 4225, 4809,  \n10321, 6365, 6364,  24840, 24552, 24699,  11933, 20312, 9136,  \n22218, 5493, 14273,  24556, 23811, 24702,  18053, 695, 13085,  \n18161, 2205, 15223,  5193, 15908, 13701,  24413, 23950, 24258,  \n10605, 15108, 8791,  24846, 24413, 24258,  24699, 24552, 24706,  \n24407, 24257, 24707,  9971, 7366, 13454,  20644, 1547, 3726,  \n5402, 2962, 2961,  13667, 9123, 2576,  19042, 3696, 13550,  \n5527, 1569, 2190,  13277, 11028, 11360,  2008, 22306, 14006,  \n16833, 19214, 14438,  20092, 1469, 3610,  6671, 20305, 15696,  \n20983, 14354, 13139,  20124, 2774, 19542,  20114, 5357, 5645,  \n24554, 24847, 24417,  1967, 17223, 11104,  24544, 24081, 24088,  \n24555, 24545, 24706,  24706, 24551, 24418,  24555, 24706, 24418,  \n24708, 24417, 24847,  5728, 5729, 20043,  4584, 14372, 21777,  \n15667, 8236, 19349,  19976, 18590, 18325,  4100, 7332, 2182,  \n8548, 19979, 13114,  24544, 24088, 24848,  24848, 24088, 24087,  \n10828, 23541, 19351,  6570, 3547, 7173,  6435, 6717, 5942,  \n24558, 24418, 24710,  24850, 24557, 24415,  13873, 13176, 10847,  \n7814, 19643, 14893,  16148, 21721, 6398,  13687, 13841, 4600,  \n20873, 20874, 2178,  13442, 12303, 9995,  14332, 12976, 14331,  \n6924, 8687, 6923,  7964, 10349, 7965,  17676, 10968, 3556,  \n24850, 24415, 24711,  6789, 4235, 4236,  15650, 6708, 11682,  \n21677, 4945, 20941,  24558, 24561, 24091,  3163, 5558, 3164,  \n3916, 671, 8501,  24561, 24851, 24562,  6262, 4450, 6263,  \n24562, 24852, 24260,  24260, 24852, 24421,  2371, 8267, 23858,  \n24712, 24563, 24262,  24420, 24426, 24711,  24852, 24854, 24421,  \n24423, 24421, 24854,  11280, 20924, 18409,  24425, 24263, 24563,  \n9424, 18374, 13098,  9293, 12089, 9294,  11252, 20825, 3483,  \n8445, 19274, 12590,  24566, 24565, 24855,  24566, 24855, 24856,  \n24566, 24856, 24713,  4830, 12744, 1809,  24564, 23818, 24101,  \n21579, 4900, 602,  7220, 4960, 5856,  24857, 24101, 24102,  \n16364, 15170, 9292,  3187, 10218, 3979,  24432, 24858, 24270,  \n24268, 24857, 24102,  24857, 24714, 24101,  2741, 3818, 15737,  \n24860, 24430, 24859,  24430, 24861, 24269,  24860, 24861, 24430,  \n24862, 24432, 24567,  24568, 24269, 24861,  11961, 7327, 16482,  \n13923, 16060, 20338,  25162, 24268, 24570,  5575, 15008, 1783,  \n21177, 837, 20895,  3177, 16329, 22519,  23831, 24434, 24718,  \n24106, 24435, 24863,  16497, 15043, 9031,  8631, 6444, 5822,  \n11874, 930, 20501,  19019, 18975, 18976,  17952, 5833, 3333,  \n18919, 18238, 18237,  13348, 22733, 14124,  18212, 3191, 21192,  \n3713, 19665, 11736,  10821, 4575, 16019,  8473, 8474, 17279,  \n12841, 7948, 3947,  3973, 15289, 12626,  6108, 18673, 9968,  \n24720, 24575, 24445,  5364, 2964, 9393,  24448, 24441, 24864,  \n2962, 3402, 2440,  12156, 10827, 14899,  18268, 6161, 6590,  \n811, 9184, 12291,  3015, 6133, 3014,  24114, 24721, 24867,  \n24580, 24722, 24725,  24580, 24725, 24582,  5075, 10265, 20469,  \n24725, 24728, 24582,  4420, 1288, 7057,  6166, 9101, 6165,  \n14237, 23553, 3600,  24866, 24583, 24727,  4849, 4734, 3575,  \n24725, 24722, 24583,  7445, 20364, 8048,  17237, 22240, 9277,  \n14567, 3400, 7769,  24583, 24865, 24725,  7379, 21636, 22409,  \n22108, 23695, 22111,  18582, 23521, 20991,  3092, 20522, 3093,  \n24865, 24583, 24866,  17256, 17308, 12906,  7716, 9052, 13788,  \n16846, 20707, 16849,  24729, 24584, 24281,  17486, 15486, 14232,  \n24730, 24449, 24728,  9753, 9202, 14930,  22611, 17755, 1679,  \n20058, 12127, 3985,  10308, 17175, 9020,  24452, 23981, 24592,  \n7969, 13246, 5439,  11444, 13021, 17188,  11793, 11439, 11438,  \n18500, 8030, 8032,  24587, 24122, 24589,  480, 12563, 12562,  \n5108, 15344, 21995,  18460, 3901, 7364,  3867, 21864, 18389,  \n2311, 12408, 2310,  8366, 8178, 1931,  9694, 15518, 17897,  \n24287, 24120, 24871,  12633, 6342, 6343,  12755, 11041, 21325,  \n7796, 5000, 12660,  24593, 24731, 24286,  16448, 10531, 10521,  \n5033, 22385, 22959,  16391, 2621, 14898,  6227, 13024, 11365,  \n6843, 592, 19451,  18109, 6229, 1237,  20312, 1741, 9136,  \n23983, 24293, 24124,  24595, 23846, 24290,  24291, 23984, 24292,  \n21940, 2863, 6446,  4101, 3801, 9958,  24125, 24289, 24874,  \n20989, 18800, 10348,  24595, 24290, 24875,  10238, 432, 18811,  \n24126, 25037, 24294,  11690, 14949, 10388,  14411, 8462, 6530,  \n11640, 15387, 8655,  8282, 18572, 10930,  24127, 24293, 24299,  \n9241, 15193, 14443,  14088, 5345, 14089,  7353, 6204, 22024,  \n5863, 564, 563,  24595, 24876, 24456,  2483, 18174, 14347,  \n14014, 14013, 24877,  24879, 24128, 24598,  8203, 2592, 12504,  \n7429, 16049, 7428,  10338, 10603, 5950,  24878, 24127, 23992,  \n24296, 24734, 24736,  21244, 20169, 21013,  21148, 16253, 21090,  \n13665, 11544, 877,  6796, 12233, 3119,  15415, 2763, 19126,  \n13888, 11733, 9587,  23680, 23686, 24600,  3318, 19396, 8485,  \n17190, 8043, 2769,  13724, 14862, 16651,  14922, 17162, 16465,  \n23993, 24302, 24880,  16180, 13858, 9430,  24598, 23680, 24600,  \n5578, 9113, 10181,  19579, 22486, 20674,  24129, 23993, 24880,  \n16522, 5709, 20267,  7480, 11402, 10730,  11140, 7627, 12572,  \n8971, 4918, 21629,  11226, 7388, 11119,  24301, 23854, 23683,  \n24457, 24129, 24880,  11810, 7226, 12470,  7415, 4540, 4542,  \n7346, 22680, 15018,  8990, 15991, 21769,  25044, 23683, 23857,  \n24305, 24881, 24601,  24600, 23686, 24136,  22653, 2453, 2455,  \n14298, 12436, 4400,  4377, 5248, 23553,  24739, 24307, 24601,  \n22204, 11607, 15028,  23362, 24883, 24136,  15933, 21739, 15932,  \n4483, 23919, 11939,  4585, 14955, 3748,  10882, 12322, 2559,  \n5424, 9111, 16524,  22288, 18249, 24884,  5310, 5309, 13043,  \n10481, 14095, 15733,  14838, 2695, 12387,  189, 169, 14272,  \n11542, 1313, 8395,  24464, 24307, 24739,  2926, 15412, 12575,  \n24885, 24464, 24739,  24140, 24886, 24138,  15062, 20120, 13565,  \n17802, 21336, 3012,  11168, 1591, 15860,  18639, 14821, 995,  \n11451, 20095, 10188,  7996, 6286, 21717,  24140, 24742, 24887,  \n24741, 24604, 23691,  15030, 23522, 7837,  10366, 7983, 9592,  \n354, 14916, 19117,  2371, 16625, 8267,  4442, 20104, 8968,  \n24140, 24309, 24742,  16151, 16152, 8304,  16264, 17668, 19363,  \n2372, 16625, 2371,  15285, 18378, 8293,  24743, 24309, 24466,  \n24604, 25048, 24000,  24001, 24308, 24745,  7357, 6325, 6743,  \n12000, 4896, 14741,  17256, 16477, 17308,  8840, 8425, 2776,  \n3376, 14704, 20971,  1407, 12641, 1408,  4809, 1714, 1713,  \n3943, 12505, 14415,  18651, 22305, 467,  4289, 4288, 7834,  \n18642, 15556, 12779,  24743, 24143, 25185,  2931, 7717, 14343,  \n11359, 14879, 3483,  29627, 29727, 7003,  1081, 5968, 4344,  \n20796, 21338, 6119,  15180, 12397, 12398,  24004, 24746, 24003,  \n24303, 2671, 15231,  20106, 4087, 7983,  24470, 24746, 24747,  \n8873, 8872, 16031,  19884, 10378, 4874,  2535, 10886, 4337,  \n19012, 8975, 7469,  24311, 24751, 24748,  24751, 24149, 24471,  \n24470, 24747, 24153,  24751, 24311, 24149,  15455, 14107, 5810,  \n5344, 2947, 14606,  13105, 8442, 16517,  6564, 15189, 4017,  \n9625, 4379, 12129,  3907, 12768, 12769,  8841, 1289, 8842,  \n23867, 24150, 24008,  8678, 8679, 9381,  17412, 6700, 19934,  \n14660, 22983, 16152,  2185, 22489, 4095,  24008, 24889, 24155,  \n24611, 24890, 24754,  8628, 20796, 6119,  12762, 21086, 18821,  \n24754, 24314, 24611,  5001, 845, 5000,  15958, 4945, 21677,  \n6410, 373, 5784,  24753, 23707, 24755,  24158, 24157, 24313,  \n11107, 1703, 1702,  24474, 24611, 24316,  24159, 24756, 24755,  \n18500, 8032, 18501,  20180, 19803, 18297,  20060, 10505, 21864,  \n2908, 7711, 2750,  1502, 21013, 4208,  6635, 5504, 3685,  \n1302, 1303, 10858,  3464, 13065, 13066,  19015, 10339, 1886,  \n3550, 18980, 5715,  24159, 24895, 24756,  11980, 3981, 11979,  \n24895, 24159, 24318,  2277, 11111, 19351,  494, 3978, 492,  \n24757, 24014, 24475,  3080, 8088, 9658,  17621, 9064, 8639,  \n5105, 8501, 8502,  8212, 7163, 14350,  2466, 4035, 22989,  \n24897, 24319, 24614,  11419, 6004, 12099,  2915, 6792, 6791,  \n1562, 12914, 14175,  24758, 24759, 24015,  10843, 1501, 9029,  \n9813, 7849, 10209,  446, 5299, 447,  24902, 24477, 24322,  \n21018, 9793, 21017,  9251, 16688, 11495,  24762, 24901, 24900,  \n16953, 8514, 13992,  19289, 24533, 5547,  1170, 19902, 12400,  \n567, 4003, 23549,  24762, 24900, 24899,  24762, 24899, 24766,  \n6935, 21466, 15315,  24904, 24617, 24015,  10379, 13278, 10380,  \n24764, 24901, 24762,  13210, 13211, 11515,  320, 7460, 9921,  \n21285, 23200, 16316,  10051, 15698, 6768,  20961, 7877, 1442,  \n15961, 7665, 9096,  6298, 4668, 6299,  17524, 14823, 14822,  \n24765, 24901, 24764,  24169, 24905, 24761,  17064, 11755, 1692,  \n24622, 24766, 24906,  17622, 2771, 9180,  24907, 24765, 24621,  \n21474, 5766, 16143,  24908, 24907, 24621,  23583, 6162, 21211,  \n5588, 4852, 23132,  16217, 3342, 21923,  24905, 24169, 24168,  \n24905, 24168, 24909,  23553, 14238, 4377,  24768, 24908, 24626,  \n24908, 24621, 24626,  2895, 2894, 1803,  16617, 609, 10144,  \n5756, 2375, 18035,  9826, 10234, 10233,  1762, 14270, 16626,  \n24909, 24168, 24625,  24623, 24906, 24767,  24769, 24623, 24767,  \n16849, 11968, 16882,  19688, 2162, 2164,  9888, 11266, 8896,  \n18868, 1237, 14595,  13845, 15243, 3117,  25207, 24768, 24910,  \n1629, 5414, 10057,  1743, 24911, 11230,  13361, 13362, 1312,  \n5651, 16349, 5652,  7204, 1564, 10242,  24768, 24627, 24772,  \n7381, 11566, 11590,  6721, 7608, 19956,  9520, 845, 21466,  \n22854, 13351, 16673,  24629, 24018, 24628,  8882, 13481, 1636,  \n11267, 16694, 8641,  2658, 2657, 4356,  8978, 16130, 20351,  \n1097, 6733, 9162,  2132, 1924, 7143,  6571, 12375, 3547,  \n24327, 24481, 24774,  24773, 24484, 24775,  5443, 15877, 5444,  \n21929, 9540, 9072,  15452, 10082, 7710,  24913, 24172, 24020,  \n21145, 10903, 21276,  24020, 24485, 24913,  20196, 13387, 404,  \n24914, 24913, 24485,  7141, 16195, 16196,  15579, 13053, 10175,  \n4286, 16338, 9792,  24328, 24774, 24776,  23728, 21078, 24917,  \n24775, 24490, 24916,  24490, 24495, 24916,  22724, 6165, 22422,  \n24329, 24491, 24777,  7743, 11178, 552,  8436, 13475, 6050,  \n24919, 24782, 24640,  24640, 24329, 24919,  11328, 13023, 10532,  \n24782, 24778, 24639,  10559, 6419, 10560,  23262, 24533, 5778,  \n15071, 19573, 10257,  24489, 24920, 23560,  14646, 24921, 4988,  \n24634, 24779, 24781,  24782, 24639, 24640,  24639, 24493, 24640,  \n18079, 7171, 8038,  24492, 24922, 24632,  5900, 13149, 13411,  \n1622, 13690, 1290,  24492, 24641, 24922,  11628, 7177, 1394,  \n4564, 3370, 4565,  22753, 6962, 4585,  24783, 24781, 24923,  \n19134, 17787, 7384,  22127, 19684, 6170,  8557, 11226, 11118,  \n8142, 10690, 6242,  24641, 24784, 24924,  2143, 4619, 4620,  \n5134, 10977, 12284,  4108, 16194, 20779,  24925, 24785, 24783,  \n9034, 4168, 16825,  16391, 23390, 9050,  11623, 12688, 17515,  \n5259, 12774, 2925,  4970, 12729, 14643,  24495, 24643, 24926,  \n24784, 24332, 24335,  24927, 24784, 24335,  17688, 17690, 23948,  \n24928, 24642, 24785,  22167, 13395, 9728,  24926, 24643, 24929,  \n896, 17994, 7245,  13600, 6036, 5371,  16611, 892, 18355,  \n24337, 24642, 24928,  9011, 15719, 9014,  13604, 18709, 20626,  \n9080, 23539, 807,  2329, 16093, 8593,  24787, 24338, 24334,  \n8049, 4921, 4922,  24335, 24339, 24930,  4973, 15561, 4972,  \n24496, 24930, 24339,  19607, 10235, 18704,  22266, 18975, 16036,  \n24789, 24496, 24340,  7383, 4999, 7382,  11496, 6987, 4962,  \n24933, 24643, 24342,  24337, 24934, 24644,  21540, 7365, 15560,  \n20933, 4199, 17671,  21855, 11962, 6505,  24645, 24644, 24647,  \n23536, 3154, 3500,  6982, 5862, 5847,  12210, 10273, 10620,  \n4288, 6326, 4304,  12192, 6233, 18952,  11284, 4114, 9675,  \n24344, 24935, 24190,  24499, 24936, 24792,  8910, 15117, 6089,  \n23383, 11308, 8954,  14625, 15040, 4656,  24500, 24502, 24937,  \n1086, 1085, 1345,  24938, 24036, 24346,  24344, 24036, 24938,  \n2833, 15781, 2834,  4950, 4952, 9606,  16527, 533, 3564,  \n24347, 24940, 24649,  4993, 4994, 16832,  11933, 19113, 11932,  \n6189, 2682, 22624,  24939, 24650, 24648,  6413, 19116, 13476,  \n19956, 7608, 5006,  10127, 1171, 10128,  5893, 5291, 5292,  \n363, 16615, 18672,  24942, 24650, 24939,  22445, 14024, 14025,  \n22547, 9134, 4453,  13712, 7106, 21599,  2125, 9811, 9810,  \n2920, 526, 1923,  8122, 6740, 13485,  24943, 24503, 24650,  \n23754, 23753, 24795,  25092, 24197, 24505,  14427, 18667, 5822,  \n24943, 24506, 24503,  15844, 20445, 4515,  10764, 9689, 2424,  \n15496, 18911, 17321,  24945, 24502, 24652,  12852, 7258, 22722,  \n15536, 9432, 12268,  1710, 7591, 10855,  22887, 13537, 17533,  \n1756, 15001, 10185,  24653, 24651, 24946,  13188, 10286, 1431,  \n24354, 24947, 24355,  24354, 24653, 24947,  22329, 22419, 21880,  \n19023, 16171, 12781,  24797, 24355, 24948,  24655, 24355, 24797,  \n16798, 10818, 331,  5259, 3708, 6445,  19931, 13351, 22854,  \n9104, 7721, 13393,  18111, 13160, 12537,  22635, 9291, 7337,  \n427, 13636, 426,  6612, 4026, 6613,  24207, 24798, 24657,  \n24510, 24950, 24798,  11890, 4627, 9548,  24800, 24361, 24657,  \n7328, 7327, 17092,  9012, 9013, 11976,  11185, 7884, 10672,  \n5765, 20452, 20911,  10351, 23913, 17996,  3825, 10774, 13830,  \n6819, 18949, 6578,  16833, 15975, 5375,  11848, 13643, 13027,  \n19249, 12018, 7282,  18114, 9746, 4773,  18471, 14451, 1641,  \n14272, 169, 11826,  24658, 24515, 24952,  24516, 24952, 24515,  \n9687, 14249, 5631,  17522, 16338, 4010,  1945, 12112, 23048,  \n24953, 24364, 24659,  6782, 12798, 15697,  24364, 24954, 24801,  \n24364, 24953, 24954,  4685, 12287, 4686,  24957, 24954, 24956,  \n2449, 15475, 6179,  24802, 24954, 24957,  3947, 7948, 2661,  \n11789, 5576, 9322,  16937, 22740, 22389,  24802, 24801, 24954,  \n8730, 15288, 10200,  24802, 24662, 24801,  5793, 15544, 12779,  \n17658, 9695, 14211,  16299, 9808, 9807,  420, 421, 978,  \n8642, 5369, 7227,  5823, 21961, 13533,  24958, 24803, 24957,  \n9896, 11008, 9279,  9298, 22575, 18580,  14119, 8141, 14815,  \n17123, 21090, 4056,  24958, 24804, 24803,  24960, 24804, 24958,  \n24804, 24960, 24961,  7188, 20283, 2769,  14124, 14123, 16783,  \n16307, 11082, 10960,  24961, 24962, 24804,  24803, 24804, 24962,  \n24803, 24962, 24805,  24963, 24366, 24368,  24368, 24517, 24963,  \n12060, 19956, 14291,  10466, 6602, 11309,  3007, 22715, 16433,  \n15204, 7501, 18363,  24663, 24963, 24517,  23911, 24371, 24217,  \n24806, 24371, 24805,  24517, 24372, 24663,  24964, 24663, 24372,  \n7346, 12090, 5527,  12994, 10204, 19839,  24519, 24056, 24806,  \n24217, 24806, 24056,  842, 11513, 7106,  24372, 24518, 24965,  \n24376, 24519, 24807,  24518, 24374, 24808,  879, 11339, 1820,  \n14758, 14757, 20525,  23918, 24220, 24376,  6594, 3414, 7535,  \n24966, 24967, 24222,  11940, 6682, 7114,  24225, 24968, 24810,  \n24967, 24224, 24222,  24225, 24521, 24811,  23292, 13719, 6847,  \n16832, 17060, 16833,  13465, 1884, 2250,  22551, 10443, 17504,  \n19586, 12594, 17502,  20684, 19251, 13084,  2829, 961, 9348,  \n5347, 14349, 5348,  24666, 24811, 24223,  11420, 21644, 20538,  \n17252, 12057, 14210,  8157, 19795, 20307,  10459, 6985, 18733,  \n16323, 8974, 18575,  15467, 11946, 9564,  20119, 11488, 12650,  \n6659, 15368, 2283,  1336, 1337, 349,  24969, 24668, 24669,  \n1296, 8210, 11799,  24970, 24813, 24522,  7661, 15818, 7660,  \n12475, 2523, 12476,  18352, 20209, 6276,  3839, 4875, 19449,  \n11625, 1777, 5650,  13605, 1355, 15035,  24971, 24669, 24670,  \n3460, 1473, 1475,  10336, 18025, 9030,  24971, 24670, 24814,  \n17714, 21999, 22062,  24383, 24813, 25254,  14767, 15651, 9139,  \n24383, 25254, 24671,  14937, 14936, 2758,  8583, 14070, 7055,  \n24672, 24815, 24382,  24523, 24671, 24972,  24973, 24672, 24673,  \n14063, 1276, 9835,  11061, 19288, 9917,  4579, 16455, 16449,  \n24974, 24523, 24972,  17513, 2375, 3119,  530, 3251, 18622,  \n9521, 9520, 23742,  11232, 8413, 8985,  15645, 11914, 12492,  \n24675, 24523, 24975,  25116, 24674, 24524,  24977, 24524, 24676,  \n8506, 21449, 14861,  24977, 24676, 24678,  20306, 2659, 16342,  \n19906, 4595, 15937,  13608, 1031, 1032,  8490, 2827, 9839,  \n24388, 24978, 24678,  3376, 17977, 14432,  24978, 24388, 24527,  \n24679, 24978, 24527,  24387, 24677, 24528,  24677, 24979, 24528,  \n329, 4444, 4445,  6424, 11184, 4330,  24981, 24679, 24816,  \n4137, 4736, 11785,  8826, 939, 938,  16188, 6465, 13938,  \n5573, 18336, 5572,  24816, 24817, 24983,  7169, 7170, 4413,  \n24817, 24816, 24684,  24682, 24984, 24683,  24983, 24685, 24683,  \n24983, 24683, 24984,  24983, 24817, 24685,  5046, 7601, 6831,  \n4428, 4427, 9261,  4930, 3814, 15477,  1732, 6063, 15588,  \n18526, 20485, 20484,  17017, 19977, 22151,  18988, 14147, 23283,  \n5909, 15613, 5908,  24818, 24819, 24986,  21644, 8274, 20538,  \n3970, 7054, 20937,  13096, 23336, 565,  15930, 7326, 7325,  \n9036, 9043, 9035,  8457, 14901, 19109,  8076, 14318, 13060,  \n23646, 8874, 15926,  15309, 9864, 2147,  23793, 24820, 24534,  \n14000, 13042, 8108,  9021, 7137, 4830,  10230, 15662, 17408,  \n414, 8796, 27026,  24688, 24073, 24987,  24689, 24822, 24988,  \n24988, 24822, 24823,  6809, 4203, 10762,  15214, 15213, 10622,  \n24989, 24990, 24987,  21079, 16321, 15568,  9740, 6588, 6590,  \n24988, 24690, 24689,  24992, 24823, 24826,  5594, 13250, 6289,  \n5902, 20743, 6751,  11477, 18363, 11921,  6835, 9558, 4272,  \n1336, 16402, 19266,  23387, 10634, 574,  24539, 24824, 24402,  \n24824, 24539, 24991,  24827, 24991, 24539,  24988, 24993, 24690,  \n5832, 11132, 16240,  390, 14772, 11724,  16746, 6121, 2023,  \n24993, 24829, 24690,  8702, 8958, 15555,  12901, 13535, 9390,  \n16117, 14784, 9240,  5804, 5831, 15596,  24827, 24698, 25130,  \n17968, 6940, 13201,  2148, 12261, 17211,  23800, 21041, 24697,  \n8636, 8505, 3451,  23798, 24399, 24695,  17881, 707, 2518,  \n24829, 24835, 24834,  5484, 10948, 5485,  16020, 3464, 20361,  \n6750, 23676, 14495,  24542, 25130, 24698,  1291, 3666, 13176,  \n5164, 4666, 14897,  24406, 24407, 24832,  19924, 2136, 8095,  \n1923, 2132, 2920,  1339, 12391, 5188,  24995, 24834, 24835,  \n20956, 20340, 16227,  22557, 2209, 4643,  19827, 11064, 20362,  \n9858, 13635, 5391,  14684, 8845, 8844,  2628, 5373, 17716,  \n24996, 24702, 24839,  2953, 3358, 11361,  2594, 14959, 3480,  \n24841, 24838, 24839,  13122, 4212, 9620,  21842, 19281, 5196,  \n2697, 8966, 15882,  24995, 24840, 24834,  4643, 17122, 11752,  \n19493, 15434, 4123,  7859, 20066, 17548,  11940, 4891, 12292,  \n15766, 22197, 13807,  2432, 20657, 14909,  7482, 7068, 16079,  \n24999, 24842, 24704,  24843, 24999, 24704,  20511, 19278, 8057,  \n18942, 12517, 16445,  20453, 8753, 11548,  25000, 23106, 23459,  \n9353, 9459, 12767,  10426, 11499, 9239,  10847, 10846, 19744,  \n9998, 20880, 16839,  651, 652, 22376,  10336, 15042, 6020,  \n24707, 24837, 24407,  9778, 2303, 19211,  18292, 18656, 21174,  \n5768, 2083, 14911,  13100, 1900, 1899,  8728, 10957, 5346,  \n7665, 3658, 2297,  24533, 19289, 3954,  24843, 24412, 24413,  \n24845, 24413, 24846,  12372, 5816, 11706,  4187, 16154, 16153,  \n7526, 5775, 7525,  24546, 23462, 23944,  12336, 4325, 16932,  \n25001, 24707, 25003,  8791, 15108, 8792,  2167, 19939, 8806,  \n25004, 24553, 24840,  25003, 24707, 25005,  11512, 21105, 20495,  \n12052, 2447, 2709,  834, 7439, 7438,  25006, 24416, 24417,  \n24554, 25008, 24847,  2472, 15407, 2473,  17288, 10280, 12305,  \n11105, 5007, 1894,  4551, 21338, 13099,  25006, 24417, 24708,  \n12475, 2522, 2523,  15188, 2644, 17529,  24706, 24552, 24551,  \n25005, 24707, 24557,  4387, 5285, 15600,  4541, 9636, 4542,  \n9895, 2731, 2730,  18124, 3929, 14193,  20369, 6967, 5538,  \n10438, 21393, 2886,  24553, 25009, 24551,  10335, 13631, 13632,  \n16292, 8462, 3271,  25009, 24710, 24551,  3502, 13370, 3503,  \n9951, 21008, 9326,  7376, 6567, 6568,  24848, 24087, 24259,  \n24849, 24558, 24710,  11113, 21011, 11111,  12820, 2678, 3305,  \n11175, 11997, 4880,  16830, 12309, 11690,  19466, 7602, 4696,  \n1376, 6565, 21071,  24851, 24561, 24558,  24560, 24422, 25010,  \n9109, 1685, 16561,  11387, 7293, 18524,  18353, 3142, 17607,  \n24424, 24559, 25011,  7162, 8500, 11214,  20072, 915, 17677,  \n16435, 8497, 17300,  24851, 24852, 24562,  25013, 25291, 24564,  \n2783, 2644, 2643,  2890, 1194, 8269,  24712, 24853, 24563,  \n17989, 3990, 19767,  25014, 24563, 24853,  18833, 10801, 19313,  \n24852, 25016, 24854,  13135, 19438, 17721,  21072, 14665, 7599,  \n8626, 6239, 13850,  24563, 25014, 24425,  9446, 8758, 3445,  \n24856, 24855, 25018,  24856, 25018, 25019,  616, 2867, 2898,  \n25019, 24713, 24856,  25019, 25020, 24713,  8776, 12974, 19982,  \n16652, 5765, 12794,  11324, 23365, 14864,  24714, 25013, 24564,  \n8124, 11243, 20726,  24425, 25014, 24565,  24565, 25014, 24855,  \n14242, 247, 16352,  24713, 25020, 24427,  23933, 20565, 712,  \n24270, 24858, 24426,  4881, 13374, 6328,  3702, 17798, 21709,  \n1671, 6354, 2713,  24862, 24858, 24432,  5087, 5750, 15265,  \n24430, 24427, 24859,  1748, 12731, 1746,  2206, 7571, 15223,  \n5037, 8171, 5036,  24861, 25021, 24568,  25021, 24715, 24568,  \n4598, 4672, 15867,  24715, 25022, 24569,  2397, 2398, 18804,  \n6990, 4562, 4563,  15386, 3922, 16983,  12542, 15663, 12543,  \n6072, 16813, 6073,  24863, 24435, 24716,  10328, 22219, 5621,  \n12414, 10736, 1016,  9826, 6276, 12045,  11131, 17259, 11132,  \n24442, 24575, 25023,  24442, 25023, 24571,  1255, 2830, 18663,  \n4493, 9448, 7393,  8993, 5863, 563,  7198, 3645, 486,  \n4201, 15772, 8383,  24720, 25026, 24575,  1379, 14083, 1380,  \n19612, 2666, 3544,  19688, 6866, 2162,  4735, 3905, 470,  \n8752, 6960, 6887,  24277, 24585, 24579,  3866, 8482, 16030,  \n3454, 5224, 11686,  24720, 24282, 25026,  16313, 16901, 9985,  \n5444, 19018, 5443,  20617, 16826, 14506,  12987, 3181, 13270,  \n7819, 15536, 15535,  3534, 9511, 9512,  16072, 9705, 16164,  \n11244, 8124, 5032,  24725, 25027, 24728,  25028, 24727, 24584,  \n24865, 24866, 24868,  24869, 24728, 25027,  24730, 24728, 24869,  \n14579, 9414, 5581,  24729, 25028, 24584,  4624, 4452, 17205,  \n24868, 24866, 24727,  1060, 18142, 6187,  3823, 7296, 6752,  \n15188, 3675, 4134,  20601, 10633, 15864,  21490, 10657, 12709,  \n24285, 24118, 25577,  24871, 24120, 24114,  24122, 24588, 24589,  \n1079, 21829, 6800,  11272, 4327, 15330,  16819, 19183, 18925,  \n24591, 24590, 25029,  5733, 7544, 11725,  25035, 24287, 24871,  \n24731, 24593, 25030,  25031, 24588, 24454,  9427, 4060, 20050,  \n24289, 24287, 25035,  24124, 25034, 25032,  23962, 14476, 8329,  \n24289, 25035, 24874,  24292, 24873, 24291,  10060, 15991, 15992,  \n9863, 9862, 14593,  10175, 7115, 15579,  4788, 7534, 9852,  \n21163, 12894, 11563,  11078, 19978, 22124,  24595, 24875, 24876,  \n7894, 14458, 18402,  24874, 24298, 24125,  591, 1672, 3835,  \n1172, 5265, 18787,  25036, 25038, 24594,  8627, 774, 6038,  \n16501, 19800, 2446,  24734, 24295, 24594,  24734, 24594, 25038,  \n18520, 14252, 6042,  24737, 25037, 24126,  1975, 2193, 14092,  \n24736, 24734, 25038,  12034, 12658, 3682,  1818, 4675, 1816,  \n739, 4257, 740,  3821, 20860, 8257,  14333, 2057, 6712,  \n13638, 16701, 15038,  15759, 12360, 13504,  4689, 3083, 15476,  \n17459, 10809, 10166,  2105, 2104, 6868,  967, 3419, 11870,  \n16914, 4302, 3782,  884, 6352, 22696,  17637, 16026, 23629,  \n10290, 13611, 21900,  24302, 23988, 24733,  6035, 23630, 1618,  \n9645, 11489, 9646,  14182, 19578, 8840,  24878, 23992, 25321,  \n10366, 15271, 8552,  10738, 12925, 10739,  15291, 3753, 16280,  \n24459, 24456, 25042,  14233, 2704, 1461,  14690, 10225, 7017,  \n11691, 11237, 19780,  23994, 24131, 24599,  24735, 25043, 24458,  \n23990, 24735, 24458,  24458, 25043, 24881,  21504, 8039, 6900,  \n24459, 23991, 24456,  15581, 5754, 16429,  24882, 24131, 24130,  \n10294, 924, 7204,  12499, 13281, 931,  24301, 23683, 25044,  \n1945, 23048, 18105,  20117, 20441, 7466,  24458, 24881, 24305,  \n1608, 13896, 15544,  25044, 23857, 24461,  25045, 24601, 24881,  \n4991, 21228, 11015,  24602, 24460, 24459,  20735, 20365, 22570,  \n3711, 4991, 4990,  1785, 11379, 4117,  24307, 24305, 24601,  \n4397, 7647, 4398,  2516, 2515, 18985,  14700, 10017, 18080,  \n24603, 24460, 24602,  3474, 13156, 5599,  7447, 7446, 20454,  \n24883, 23362, 24465,  3243, 15382, 3244,  13294, 1943, 15061,  \n13128, 12739, 2780,  16585, 19499, 20260,  6769, 16761, 6770,  \n18527, 21132, 18528,  24139, 24463, 24308,  20801, 6168, 16348,  \n24741, 25048, 24604,  794, 15705, 16803,  15129, 9422, 3855,  \n13957, 13385, 10738,  24742, 24309, 24743,  11826, 21564, 14272,  \n15164, 4324, 12336,  10650, 5984, 12182,  9481, 13673, 13674,  \n4207, 4206, 1917,  4256, 1835, 9476,  609, 13289, 6810,  \n17432, 6237, 9107,  14988, 23070, 13900,  1886, 8462, 18243,  \n13837, 3355, 2976,  24746, 24004, 24744,  3896, 16447, 19888,  \n969, 11081, 17004,  23524, 24468, 24147,  1787, 19438, 10445,  \n24146, 24750, 24606,  12368, 6741, 8961,  15517, 8150, 7501,  \n21308, 3057, 4440,  7388, 11226, 7387,  15311, 14662, 12157,  \n24747, 25050, 24153,  7668, 7648, 14079,  19165, 19166, 1034,  \n2355, 5946, 15132,  15217, 21887, 12477,  20083, 16679, 16680,  \n6526, 312, 5560,  417, 9966, 8820,  24610, 24152, 24608,  \n8520, 13829, 11207,  13800, 7922, 7223,  12366, 2217, 2413,  \n5822, 4644, 14427,  11540, 19975, 24297,  24156, 24610, 24891,  \n24313, 24155, 24893,  24654, 18605, 18606,  21451, 4070, 4069,  \n24892, 24156, 24891,  24317, 24156, 24892,  24893, 24158, 24313,  \n4625, 1614, 2804,  24756, 24894, 24755,  4771, 13642, 9167,  \n591, 7127, 4769,  16219, 5521, 20810,  19409, 18266, 17392,  \n23710, 24158, 24613,  13203, 22903, 23074,  10748, 1351, 20346,  \n19262, 18179, 16312,  1176, 5075, 13716,  11771, 12084, 12085,  \n24317, 25052, 25055,  9928, 1947, 15758,  11341, 12101, 500,  \n15319, 3389, 3390,  24614, 24317, 24896,  20341, 14170, 14169,  \n5588, 23132, 1940,  13837, 15572, 10692,  24758, 24012, 24161,  \n24895, 24318, 24616,  792, 12744, 8424,  21293, 13503, 5437,  \n12366, 13768, 2217,  19670, 18758, 15466,  4780, 13263, 1879,  \n13006, 16841, 6198,  17441, 22926, 5820,  24897, 24614, 24896,  \n2562, 4594, 10477,  24475, 24164, 24615,  3210, 3209, 6779,  \n12655, 11351, 2821,  2987, 9801, 21532,  7209, 7210, 21893,  \n25056, 24616, 24476,  24438, 16617, 13380,  4934, 3760, 4933,  \n7110, 11639, 8703,  7752, 6627, 6626,  21565, 23572, 6572,  \n25200, 24900, 24901,  25059, 25200, 24901,  24615, 23875, 24618,  \n24321, 24319, 24897,  24899, 25057, 25058,  8412, 2323, 5607,  \n2178, 12614, 12534,  15549, 21941, 10456,  2503, 1787, 9994,  \n462, 12791, 12792,  22736, 5961, 5598,  25060, 24322, 24321,  \n24476, 24761, 25061,  2134, 10836, 13595,  24899, 24900, 25057,  \n21081, 19272, 8308,  11463, 19612, 3544,  1631, 1632, 17997,  \n24904, 24015, 24759,  14331, 12976, 2267,  24903, 24166, 23876,  \n24903, 23876, 24477,  12318, 6408, 22211,  23193, 9677, 21104,  \n9968, 9969, 12461,  24476, 24163, 24761,  24899, 25058, 25063,  \n24764, 24621, 24765,  5921, 7385, 11945,  23200, 10442, 16316,  \n24766, 24899, 25065,  15072, 10411, 15073,  7646, 12393, 7647,  \n14239, 12111, 14240,  24766, 25065, 24906,  2347, 17806, 20522,  \n8254, 5301, 19866,  25065, 25063, 25066,  10275, 17067, 18529,  \n24086, 19617, 10584,  5624, 7222, 14960,  24906, 25065, 24767,  \n18529, 17067, 16345,  15887, 16231, 8817,  25065, 25066, 24767,  \n11923, 11924, 21264,  24617, 25067, 24325,  19500, 18213, 6334,  \n24767, 25066, 24769,  21300, 20823, 3628,  5319, 3597, 18748,  \n2725, 11974, 2726,  4940, 5475, 13089,  8862, 16097, 6280,  \n9699, 1974, 9700,  24770, 24769, 25208,  4855, 12384, 17070,  \n6855, 13477, 16521,  24910, 24768, 24772,  17008, 4784, 4197,  \n12517, 5649, 20378,  25208, 25068, 24770,  7137, 7139, 15444,  \n24324, 24170, 24482,  14849, 8139, 14837,  5056, 17618, 17834,  \n11437, 13158, 20333,  22893, 13122, 9620,  25069, 12642, 20799,  \n4927, 9942, 11993,  5078, 19200, 14545,  4632, 8693, 2353,  \n10999, 8563, 3882,  13666, 5956, 6070,  24019, 25072, 24483,  \n3202, 14839, 7206,  24913, 24912, 24172,  11160, 8519, 10959,  \n24773, 24775, 25071,  7211, 14169, 14887,  11516, 5914, 5915,  \n8503, 8645, 8333,  21326, 15973, 15264,  4057, 13606, 7151,  \n13052, 10175, 13053,  24775, 24916, 25071,  15761, 575, 15760,  \n18238, 7930, 10039,  4741, 15699, 4740,  24777, 24486, 24776,  \n24780, 25077, 25078,  6869, 2154, 20328,  14396, 1723, 16366,  \n21889, 6157, 14103,  24778, 24782, 24918,  19690, 8803, 879,  \n10066, 12684, 11107,  24329, 24777, 24919,  6645, 1002, 9606,  \n25077, 24780, 24778,  13962, 15509, 2910,  1731, 21863, 9230,  \n5741, 8622, 8621,  16240, 14489, 17076,  15870, 20784, 18159,  \n24779, 24780, 25078,  24916, 24495, 25076,  16339, 8207, 8206,  \n5923, 19807, 10158,  22544, 16272, 6596,  24923, 24781, 25080,  \n21098, 13457, 11021,  24781, 24779, 25360,  373, 11094, 11854,  \n24330, 23560, 24920,  19108, 8659, 9406,  5777, 3860, 3861,  \n7737, 11308, 20483,  3465, 10161, 3740,  11268, 4056, 1381,  \n24783, 24923, 25082,  13040, 3372, 13376,  19576, 14022, 20065,  \n7191, 3282, 3993,  20139, 1820, 1819,  24925, 24928, 24785,  \n19390, 4405, 6652,  7824, 15070, 3217,  12559, 23936, 10729,  \n13432, 12643, 12642,  6734, 10784, 7172,  18997, 13404, 16877,  \n24930, 25083, 24335,  635, 391, 5908,  12646, 14949, 22194,  \n20686, 18739, 8573,  19209, 17772, 5098,  2181, 4402, 24429,  \n19559, 6702, 18450,  24788, 24338, 24787,  24643, 24933, 24929,  \n17058, 3797, 2122,  24930, 24496, 24789,  10998, 23443, 17096,  \n2047, 14644, 7062,  3269, 13809, 19027,  17270, 7290, 17114,  \n23792, 2631, 1290,  6214, 10850, 14883,  17141, 20108, 21672,  \n4444, 1435, 2386,  20895, 19473, 21055,  6308, 13575, 12348,  \n25084, 24933, 24038,  24499, 24647, 24936,  14526, 15491, 2834,  \n24933, 24342, 24038,  25085, 24498, 24790,  6330, 5746, 14389,  \n21139, 15088, 25086,  13846, 1959, 2393,  13959, 9750, 18917,  \n8149, 15665, 2818,  24793, 24345, 24034,  15922, 15923, 13462,  \n6074, 19527, 20992,  24648, 24792, 25087,  24347, 24345, 24793,  \n2632, 2633, 8395,  14791, 17952, 2457,  24940, 24347, 24793,  \n14664, 14666, 14420,  2146, 15713, 11760,  25088, 25089, 25090,  \n7954, 14943, 17181,  10024, 11922, 3225,  11884, 16408, 515,  \n11842, 12787, 3413,  17076, 14489, 17166,  24943, 24650, 24942,  \n24089, 17326, 12321,  3755, 9402, 18986,  20561, 1442, 18071,  \n24089, 13509, 17326,  14651, 17040, 23133,  19191, 9952, 17041,  \n10404, 10611, 7159,  24795, 23753, 24504,  1243, 5522, 17151,  \n25092, 24043, 24197,  6502, 16273, 20517,  1556, 523, 10873,  \n23903, 24199, 24944,  1316, 19193, 12184,  25093, 25094, 24506,  \n24651, 25094, 24946,  25094, 24651, 24506,  12727, 12716, 11891,  \n16531, 16532, 14505,  24946, 25235, 24653,  3974, 9969, 16335,  \n24653, 25235, 25095,  17059, 1674, 18071,  12714, 9947, 7687,  \n25095, 24947, 24653,  1964, 21843, 15621,  12491, 14556, 19673,  \n15093, 13970, 603,  11980, 11696, 4673,  9683, 17357, 11872,  \n10428, 4528, 1168,  24949, 24205, 24508,  16456, 1737, 23824,  \n16093, 2329, 13775,  20063, 17735, 2202,  6012, 6104, 2475,  \n25096, 24509, 24656,  10443, 12986, 20985,  14384, 14383, 8930,  \n24797, 25096, 24656,  1346, 12537, 13160,  10924, 19958, 12869,  \n25096, 24511, 24509,  24512, 25097, 24508,  24798, 24950, 25098,  \n1613, 2051, 22242,  8364, 5224, 5223,  1666, 8238, 13534,  \n24657, 25099, 24800,  25385, 24800, 25099,  24361, 24800, 25100,  \n24951, 24512, 24513,  25100, 24799, 24361,  24799, 25100, 25239,  \n3567, 10287, 21069,  4600, 13841, 16045,  8038, 8039, 21504,  \n1631, 16362, 15951,  8493, 1289, 11084,  13112, 14503, 18825,  \n20838, 13689, 1966,  24659, 24362, 25101,  6198, 15038, 7838,  \n3169, 18174, 10398,  3971, 16032, 4425,  16294, 535, 2638,  \n24953, 24956, 24954,  14397, 21335, 13324,  15451, 13667, 3277,  \n16103, 13240, 13322,  1287, 1286, 3559,  4624, 389, 4452,  \n9719, 5261, 1228,  8240, 7181, 2384,  20231, 17702, 8490,  \n17398, 3221, 3222,  24135, 13486, 14854,  24957, 24956, 25103,  \n24957, 25103, 24958,  1199, 15254, 23207,  3904, 4735, 18436,  \n3542, 7915, 3543,  10364, 18476, 16868,  1750, 3967, 8619,  \n6440, 16034, 10763,  3706, 2564, 7801,  24806, 24217, 24371,  \n17144, 2052, 12836,  24663, 24964, 25104,  24372, 24965, 24964,  \n14382, 19363, 319,  1283, 10884, 14290,  12877, 5560, 335,  \n16683, 12391, 1339,  2928, 14540, 1066,  14821, 11046, 7034,  \n6923, 17383, 6924,  24965, 24518, 24808,  6576, 22820, 4504,  \n12672, 22890, 447,  13476, 19116, 9589,  7341, 6876, 17167,  \n14948, 22309, 15973,  24966, 23918, 24376,  24966, 24376, 25105,  \n19086, 5727, 5726,  3414, 3415, 7535,  25106, 24664, 24968,  \n24664, 24810, 24968,  24222, 23918, 24966,  24810, 24665, 24225,  \n19501, 14185, 18572,  24968, 24225, 24811,  21123, 15249, 9737,  \n6293, 16264, 11983,  24967, 24666, 24224,  14394, 20813, 5780,  \n15198, 17737, 18363,  1744, 1743, 15352,  3260, 3354, 11432,  \n8729, 8730, 3232,  817, 816, 6178,  15286, 14050, 2779,  \n24667, 24812, 25107,  24812, 25108, 25107,  9903, 19244, 17700,  \n15333, 9022, 20124,  2138, 2137, 7526,  25109, 25108, 24812,  \n24812, 24668, 25109,  25110, 24970, 24522,  3845, 10810, 15439,  \n24969, 25109, 24668,  14082, 16441, 2509,  9526, 6346, 9402,  \n4724, 15018, 4725,  5646, 5645, 15351,  24971, 24969, 24669,  \n15364, 6197, 1095,  1141, 17309, 21761,  25111, 24671, 25254,  \n24671, 25111, 24972,  13324, 9970, 10800,  18640, 2615, 1779,  \n23101, 22495, 25113,  3546, 20157, 2866,  1367, 22818, 3441,  \n24673, 24976, 24973,  24975, 24523, 24974,  15434, 22034, 12509,  \n24674, 24976, 24673,  25114, 25115, 24975,  25116, 24976, 24674,  \n8688, 17579, 16818,  2884, 7293, 7292,  24525, 24975, 25115,  \n552, 11569, 1396,  24675, 24975, 24525,  12378, 21391, 2825,  \n24524, 24977, 25116,  25257, 24526, 24525,  17597, 9286, 17598,  \n24677, 24526, 25257,  1134, 1721, 8880,  12255, 11023, 996,  \n24977, 24678, 24978,  13117, 13835, 8688,  960, 962, 20204,  \n24981, 24978, 24679,  24528, 25118, 24982,  24982, 24681, 24680,  \n24528, 24982, 24680,  24981, 24816, 25119,  4956, 15341, 12653,  \n24984, 25121, 24983,  1316, 1317, 19193,  25120, 24682, 24681,  \n24682, 25120, 24984,  1071, 1072, 7139,  12071, 10095, 21149,  \n12071, 21149, 3208,  17718, 20640, 20227,  5524, 5818, 5525,  \n24661, 22592, 3078,  20578, 12019, 19215,  24985, 25123, 24240,  \n20483, 11308, 20439,  608, 23806, 4935,  6203, 21574, 15477,  \n1410, 6293, 11983,  11382, 14515, 20010,  3780, 1109, 11377,  \n5447, 13202, 9555,  949, 4207, 12832,  23793, 24240, 24820,  \n24820, 24240, 25123,  16874, 6507, 21552,  25125, 17841, 10111,  \n18459, 14973, 14871,  14941, 3297, 16481,  6622, 6623, 11391,  \n24534, 24820, 24687,  9584, 3187, 10033,  24392, 25124, 24819,  \n8173, 10516, 21492,  20804, 9022, 4830,  24990, 24392, 24688,  \n414, 27026, 25126,  25127, 24071, 24534,  3654, 14322, 11271,  \n13416, 5556, 20826,  25127, 24534, 24687,  22099, 1708, 8576,  \n15957, 10039, 10220,  24990, 24688, 24987,  4195, 1615, 5550,  \n24402, 24825, 24403,  2002, 2004, 9192,  2778, 9910, 7473,  \n25128, 24074, 25129,  20139, 16077, 6208,  8055, 9987, 2805,  \n13137, 13138, 19536,  24993, 24988, 25131,  25131, 24823, 24992,  \n24988, 24823, 25131,  16376, 7959, 15585,  9128, 21935, 12861,  \n24987, 24073, 24831,  2005, 3250, 21122,  2929, 396, 2096,  \n24075, 23455, 25133,  17021, 9413, 17022,  1247, 6218, 15152,  \n5259, 2926, 3708,  24835, 24829, 24993,  25134, 24835, 24993,  \n25134, 24993, 25131,  23170, 5614, 5887,  25135, 24826, 24828,  \n20965, 8125, 11446,  5226, 4265, 17921,  24832, 25136, 24831,  \n24987, 24831, 25136,  6697, 6814, 16507,  2665, 14578, 2220,  \n24697, 23106, 25139,  19209, 13897, 21766,  22388, 3537, 3536,  \n24837, 25136, 24832,  9718, 16633, 16563,  8673, 8672, 20010,  \n13018, 7578, 13935,  24995, 24835, 25134,  9002, 6218, 6085,  \n25140, 24996, 24839,  25140, 24839, 24838,  24838, 24998, 25142,  \n15897, 3325, 3326,  24998, 24841, 24842,  24701, 25137, 24542,  \n25000, 25139, 23106,  9134, 22547, 16112,  24695, 24700, 23939,  \n14018, 11502, 11503,  288, 13622, 21572,  5715, 18980, 5716,  \n24700, 24251, 23939,  10352, 10351, 17996,  17571, 6768, 15698,  \n4215, 4217, 16361,  24843, 24845, 24999,  11801, 2089, 4393,  \n11522, 13131, 16968,  5256, 18916, 5257,  8003, 6501, 9376,  \n10137, 820, 14541,  4812, 14162, 4184,  1293, 1292, 4978,  \n11122, 17196, 2661,  19015, 1969, 9928,  8117, 6033, 14714,  \n12378, 18137, 12712,  24556, 24702, 25002,  24413, 24845, 24843,  \n20543, 14271, 1480,  5301, 15877, 10083,  24700, 24705, 24251,  \n20443, 13026, 9780,  9477, 6030, 6032,  12510, 19446, 21473,  \n2609, 5286, 9645,  12831, 6835, 949,  24840, 24995, 25004,  \n20684, 19533, 16757,  18644, 12771, 18863,  20601, 10834, 10633,  \n16240, 16241, 5832,  19207, 15041, 3500,  2001, 8315, 8316,  \n24258, 24416, 24846,  1094, 20004, 4261,  25006, 25145, 24416,  \n24553, 24552, 24840,  12255, 14162, 8486,  4860, 1065, 22548,  \n9900, 4433, 13864,  4843, 1914, 4214,  9596, 5786, 8326,  \n16029, 9489, 22531,  8728, 9972, 13987,  11731, 14774, 20234,  \n12598, 12693, 9823,  25007, 24708, 24847,  1824, 7776, 12349,  \n1890, 15948, 1889,  6175, 3936, 7878,  25004, 25009, 24553,  \n6234, 11677, 22704,  7918, 6744, 306,  15181, 14505, 11139,  \n7767, 7768, 11446,  7736, 12664, 14177,  11262, 10362, 10363,  \n3110, 16054, 3111,  25009, 25146, 24710,  25147, 25005, 24850,  \n24850, 25005, 24557,  7125, 16662, 17290,  25148, 4696, 25149,  \n15870, 11139, 13081,  16010, 21975, 15817,  18308, 17344, 11576,  \n9673, 14361, 11739,  25150, 24559, 24709,  4989, 4988, 24921,  \n8276, 14312, 4239,  10529, 12213, 6235,  12012, 993, 992,  \n8836, 8838, 7635,  24851, 24558, 24849,  13758, 11846, 11667,  \n5573, 29426, 5198,  17273, 8135, 13314,  24424, 25011, 25012,  \n17782, 12618, 11727,  16030, 19062, 9150,  21154, 10483, 6345,  \n25153, 5440, 20123,  25151, 25154, 24852,  24851, 25151, 24852,  \n17124, 5993, 4161,  25157, 24853, 25155,  25152, 24711, 24426,  \n3257, 20142, 2156,  25291, 24422, 24564,  13505, 11583, 11809,  \n3437, 13505, 11809,  14777, 17583, 3335,  24712, 25155, 24853,  \n9916, 22437, 6210,  16381, 2467, 21661,  25018, 25294, 25019,  \n25160, 25019, 25161,  580, 9025, 12407,  3753, 3792, 3791,  \n24854, 25295, 24423,  24423, 25295, 24712,  25014, 25159, 24855,  \n19278, 4875, 4876,  24855, 25159, 25018,  752, 19602, 2703,  \n2797, 6512, 2796,  19133, 492, 29449,  16006, 4154, 19134,  \n14896, 15781, 2833,  13789, 3093, 10267,  2236, 18614, 16910,  \n2639, 22930, 17388,  15879, 11873, 10449,  25162, 25163, 24714,  \n24428, 25012, 25164,  24428, 24424, 25012,  24714, 24857, 25162,  \n4000, 4457, 20162,  2785, 2784, 12079,  5294, 17756, 781,  \n9291, 9290, 18489,  11776, 8920, 20019,  14809, 1320, 7329,  \n24857, 24268, 25162,  24861, 24860, 25165,  25165, 25166, 24861,  \n12293, 12294, 13133,  25166, 25021, 24861,  4749, 12608, 6826,  \n842, 844, 13016,  1483, 8394, 12981,  3168, 6028, 7877,  \n2382, 7533, 7532,  12002, 12885, 1072,  14866, 12157, 20356,  \n25022, 25167, 24436,  25022, 24436, 24569,  18345, 5278, 9433,  \n12254, 18817, 5630,  1433, 6018, 24760,  24567, 25024, 24862,  \n6195, 9959, 19247,  25024, 24567, 24719,  25023, 24570, 24571,  \n10545, 426, 5523,  4125, 12461, 12462,  10918, 12412, 8652,  \n25023, 24575, 25168,  24106, 24863, 25025,  19019, 16036, 18975,  \n24577, 24106, 25025,  6493, 22894, 16562,  14022, 16140, 20065,  \n18269, 11561, 5785,  17051, 3577, 22140,  18010, 13174, 3633,  \n8502, 8501, 6347,  6761, 1520, 3783,  10495, 8578, 4572,  \n15966, 3772, 16403,  24864, 25169, 24448,  2830, 1255, 21076,  \n5261, 9719, 1391,  18419, 17137, 16232,  11511, 7515, 10682,  \n20372, 20437, 23172,  15945, 16048, 15946,  2985, 18099, 18306,  \n24867, 24721, 24577,  9573, 4905, 9574,  3534, 9512, 10885,  \n12480, 15074, 773,  23976, 25170, 24726,  11884, 3169, 11883,  \n12816, 7857, 19024,  15226, 5049, 13679,  20900, 12909, 19223,  \n14365, 9662, 9663,  16245, 10373, 13690,  8516, 1915, 22080,  \n24871, 24114, 24867,  595, 20699, 21473,  25027, 24725, 24865,  \n1656, 1486, 18133,  4092, 29502, 3404,  10735, 8547, 12037,  \n20975, 11843, 16545,  16312, 18179, 12510,  5318, 3266, 11645,  \n6392, 13944, 21761,  24590, 24730, 24869,  16459, 11418, 20929,  \n18053, 11593, 19653,  24729, 25173, 25028,  15945, 16041, 12190,  \n24729, 24123, 25173,  10840, 4426, 4428,  15810, 14576, 11120,  \n8223, 10331, 20021,  24123, 25032, 25173,  1218, 1152, 1217,  \n24588, 25031, 25174,  13568, 20652, 13567,  14172, 14173, 2897,  \n25175, 24592, 25033,  18006, 378, 6600,  7488, 8053, 21299,  \n10089, 16652, 14286,  2421, 2422, 18229,  24591, 25029, 24593,  \n13783, 19915, 11225,  5354, 7430, 4093,  16298, 19389, 7233,  \n25030, 24593, 25029,  3783, 3782, 4302,  15939, 21094, 16973,  \n11758, 17197, 11759,  10181, 9113, 10820,  7320, 6453, 12971,  \n24290, 24285, 24872,  1152, 3488, 9749,  4854, 2587, 6655,  \n24732, 24873, 24292,  9853, 19950, 21056,  16576, 12169, 22980,  \n24731, 25176, 25036,  25034, 24124, 24293,  25037, 24455, 24294,  \n524, 21863, 10873,  25177, 24454, 24128,  5244, 20072, 23940,  \n24293, 25039, 25034,  2942, 11193, 18322,  11144, 7029, 21775,  \n15705, 16804, 16803,  25039, 24293, 24127,  24456, 24300, 24595,  \n15692, 4332, 7471,  15076, 1337, 19267,  12067, 16154, 4187,  \n17245, 5984, 12133,  8328, 11866, 19785,  5834, 23378, 5467,  \n10746, 12884, 4402,  5947, 6587, 17410,  20413, 7598, 6135,  \n25178, 25039, 24127,  9055, 5468, 2875,  16699, 4423, 4424,  \n19705, 16569, 5891,  24598, 25040, 24879,  22160, 10288, 18785,  \n16417, 12065, 15714,  10829, 4165, 1155,  12669, 3459, 6957,  \n9654, 4748, 4747,  11741, 1973, 4942,  24598, 24600, 25040,  \n25321, 23992, 24597,  867, 14220, 23938,  24736, 25043, 24735,  \n25180, 24737, 25044,  13992, 12166, 16953,  24737, 24301, 25044,  \n13430, 3138, 3847,  7560, 9991, 15681,  11010, 6001, 13177,  \n8170, 11049, 15292,  13175, 12661, 1051,  18665, 2983, 18664,  \n16549, 8704, 20240,  16944, 17538, 5831,  10556, 10557, 3545,  \n22813, 5386, 25181,  429, 2336, 4528,  21324, 21587, 22150,  \n2854, 4982, 4981,  16558, 10905, 16568,  12206, 19932, 6917,  \n13726, 17205, 1192,  24138, 24886, 25046,  1957, 9185, 13599,  \n10122, 22709, 15251,  3587, 2154, 19847,  24886, 24140, 24887,  \n2866, 20217, 2864,  17750, 10307, 14946,  4667, 10010, 14960,  \n12371, 1499, 16892,  25183, 24465, 24141,  16871, 7058, 7059,  \n2677, 2676, 12243,  7507, 7251, 17224,  14871, 15815, 10924,  \n11606, 20651, 10427,  428, 425, 20079,  16309, 4120, 1606,  \n21537, 12467, 12466,  8134, 3031, 17911,  6796, 6797, 10749,  \n14062, 7226, 17631,  17734, 4127, 1267,  14697, 7060, 9932,  \n24467, 25048, 25049,  11883, 3169, 10398,  12710, 12888, 12711,  \n22996, 20949, 16916,  15242, 7637, 13154,  24141, 23864, 24888,  \n12731, 11484, 18917,  10355, 18574, 17695,  16230, 18009, 18162,  \n24888, 23864, 24469,  3485, 9906, 16974,  13801, 6698, 17105,  \n15193, 12178, 17749,  16193, 7003, 29727,  25186, 24468, 24467,  \n25188, 24143, 24310,  13705, 628, 12246,  24888, 24469, 24605,  \n18869, 19430, 5994,  2498, 1279, 1278,  13129, 11513, 13016,  \n8112, 19865, 17019,  5205, 5204, 2443,  3493, 15436, 9110,  \n14236, 5212, 17883,  11288, 6278, 10045,  951, 14862, 13724,  \n12914, 19535, 14048,  11440, 14096, 10567,  14005, 6913, 3065,  \n24419, 14652, 23361,  3020, 9628, 4348,  11227, 8467, 7100,  \n6888, 2812, 16406,  24607, 25191, 24750,  11951, 15578, 8715,  \n1500, 1501, 23791,  19460, 11275, 19466,  7161, 6410, 4255,  \n16181, 18540, 12948,  21130, 6344, 6053,  25193, 25595, 24751,  \n24008, 24150, 24889,  12782, 12800, 6335,  8161, 4648, 14820,  \n16464, 14639, 13818,  24471, 24609, 24751,  24890, 24607, 24754,  \n24609, 25051, 24751,  1399, 14474, 17808,  25194, 24610, 24608,  \n24609, 24753, 25051,  25195, 24155, 24889,  3609, 18502, 4102,  \n6569, 18955, 19744,  25196, 24753, 24755,  3647, 17713, 14024,  \n24155, 25195, 25197,  2267, 2266, 14331,  11986, 8533, 741,  \n16441, 14081, 5197,  3974, 18594, 15573,  15567, 22437, 9916,  \n24317, 24892, 25052,  9871, 12887, 9872,  24158, 24893, 24613,  \n15090, 9870, 11026,  24894, 24756, 25053,  3465, 3740, 2282,  \n24162, 24757, 25198,  11889, 13270, 11701,  24317, 25055, 24896,  \n2485, 18637, 2486,  15261, 2115, 18604,  802, 15443, 14667,  \n11521, 9664, 11522,  6841, 9867, 3831,  4209, 15954, 15057,  \n24900, 25200, 25199,  25199, 25057, 24900,  18129, 8491, 16961,  \n25058, 25201, 25202,  25057, 25201, 25058,  19249, 15005, 15679,  \n14565, 3838, 3281,  11599, 6187, 618,  14689, 18771, 14765,  \n14022, 14021, 15479,  931, 8344, 8345,  8583, 1599, 16227,  \n18365, 16556, 15201,  24897, 25060, 24321,  25056, 24476, 25061,  \n8361, 8360, 15325,  24615, 24618, 25203,  9741, 3572, 12262,  \n10086, 12182, 5354,  3610, 1498, 3611,  12646, 10388, 14949,  \n9838, 22628, 19189,  15226, 20688, 11415,  18429, 12340, 19253,  \n12272, 2351, 12508,  24765, 25059, 24901,  2744, 5899, 10031,  \n1632, 9525, 17997,  24902, 24903, 24477,  25202, 25204, 25058,  \n1267, 12761, 3747,  13257, 9986, 6324,  3066, 3065, 9077,  \n5336, 6408, 12318,  15231, 16950, 10898,  15430, 11504, 15410,  \n13921, 2237, 5385,  29542, 11652, 17110,  25063, 25058, 25204,  \n25065, 24899, 25063,  4158, 9758, 4486,  25063, 25204, 25066,  \n13713, 7146, 13714,  14074, 16939, 12978,  6452, 2088, 7970,  \n18921, 8343, 8342,  25204, 25206, 25066,  2638, 2637, 11196,  \n25208, 25066, 25209,  24769, 25066, 25208,  22264, 20193, 3880,  \n15117, 3491, 17724,  653, 12117, 2704,  333, 10815, 21561,  \n18404, 994, 18588,  4447, 16888, 6513,  23695, 21620, 25211,  \n8645, 8503, 18565,  18565, 11497, 8645,  2118, 4593, 386,  \n7308, 682, 16976,  13831, 10774, 14146,  2024, 18795, 14302,  \n24772, 25070, 24910,  19346, 15700, 15699,  24630, 24770, 25068,  \n22908, 16785, 13399,  24773, 25070, 24772,  24629, 24628, 25213,  \n11146, 11024, 14981,  17373, 596, 17596,  24172, 24912, 24482,  \n25070, 24773, 25071,  7148, 13940, 12606,  24629, 25213, 25072,  \n24629, 25072, 24019,  5443, 10084, 10083,  24630, 25068, 24774,  \n21992, 325, 18323,  17898, 18400, 18864,  24774, 25351, 24776,  \n11896, 7127, 10164,  15712, 416, 16742,  12733, 12734, 14190,  \n10788, 2975, 2974,  12006, 7757, 1198,  12559, 14198, 23936,  \n24485, 25075, 24914,  25075, 24485, 24632,  12325, 2430, 2851,  \n17763, 20090, 711,  762, 10328, 763,  25079, 25077, 24918,  \n10613, 3417, 10612,  25077, 24778, 24918,  25216, 24918, 24782,  \n24782, 24919, 25216,  17675, 23919, 18395,  9304, 10049, 9289,  \n7865, 12053, 13575,  20849, 5487, 5486,  24632, 25217, 25075,  \n19973, 18562, 5806,  6660, 15569, 3094,  25218, 24779, 25078,  \n24779, 25218, 25360,  25219, 24489, 24488,  25219, 24920, 24489,  \n25080, 24781, 25360,  8209, 9054, 1407,  4391, 18248, 22288,  \n25217, 24632, 24922,  24923, 25080, 25220,  4260, 16286, 9887,  \n17809, 18817, 17137,  6430, 1584, 21581,  9445, 10251, 22954,  \n7640, 6211, 10218,  14201, 14200, 19394,  4113, 6065, 18136,  \n20578, 15942, 13555,  1864, 21184, 22965,  7511, 5376, 5378,  \n15121, 15120, 4216,  24783, 25082, 24925,  5838, 12808, 5951,  \n10196, 2875, 12964,  22548, 1065, 1990,  19109, 14901, 11878,  \n613, 612, 12224,  14994, 13718, 21524,  2370, 7243, 18410,  \n16108, 19870, 3816,  24927, 24335, 25083,  18729, 5041, 5040,  \n24934, 24337, 24928,  24187, 24338, 24788,  1383, 15257, 15256,  \n24930, 24789, 25367,  3791, 3790, 16267,  10683, 10682, 19524,  \n7048, 15810, 7049,  24644, 24934, 24647,  24647, 24934, 25222,  \n25222, 24936, 24647,  21099, 19086, 23118,  24646, 24341, 24791,  \n25084, 24038, 24500,  10628, 10627, 4329,  17818, 14511, 16980,  \n15961, 10078, 10715,  16594, 17348, 554,  6488, 6487, 7538,  \n24936, 25222, 25223,  1498, 12631, 3611,  745, 7912, 21747,  \n24791, 24341, 24935,  1835, 7843, 7903,  14321, 7991, 7992,  \n14422, 24760, 6018,  25224, 24793, 24034,  11221, 11222, 7669,  \n22737, 17859, 6248,  22728, 14965, 8989,  25087, 24939, 24648,  \n10867, 12020, 15568,  25226, 24937, 24502,  19196, 23510, 10697,  \n21980, 21546, 6749,  24939, 25225, 24942,  5669, 20934, 13844,  \n2892, 22398, 8948,  12465, 19213, 2438,  16384, 18930, 22024,  \n12473, 12472, 15654,  24346, 24349, 25228,  17523, 16663, 19282,  \n509, 508, 17474,  24042, 24649, 25232,  13117, 4494, 2491,  \n4640, 10925, 14330,  20219, 9177, 12276,  24349, 24941, 25228,  \n25231, 24943, 24942,  24349, 24794, 24941,  2451, 20922, 10128,  \n2557, 7819, 15535,  24795, 24504, 25233,  18512, 17852, 17218,  \n3723, 4068, 741,  24794, 24043, 25092,  24943, 25093, 24506,  \n25233, 24198, 24795,  6403, 16455, 4580,  12814, 16355, 11227,  \n23903, 24944, 24796,  21332, 2317, 6006,  7294, 7295, 15217,  \n6806, 4706, 9919,  18645, 14427, 4644,  24355, 24947, 25236,  \n24652, 24205, 24949,  15744, 18964, 533,  24948, 25237, 24797,  \n25097, 24949, 24508,  23693, 18329, 4573,  16470, 378, 17731,  \n14568, 19717, 3359,  3741, 1257, 8275,  24511, 25382, 24510,  \n25382, 24511, 25096,  4706, 4817, 9919,  25238, 24798, 25098,  \n24657, 24798, 25099,  8944, 8943, 19960,  4925, 13495, 1937,  \n25097, 24512, 24951,  5861, 8713, 20321,  10897, 22150, 19899,  \n25385, 25100, 24800,  15516, 8774, 3364,  6492, 14803, 16632,  \n7416, 6800, 7417,  16354, 18934, 17147,  2628, 17716, 12186,  \n19192, 16765, 6406,  25240, 24513, 24658,  19814, 546, 9142,  \n25101, 24209, 25239,  24362, 24209, 25101,  6709, 10320, 17711,  \n18511, 4458, 10538,  24659, 24363, 24362,  12016, 17210, 4602,  \n25242, 24953, 24659,  24956, 24953, 25242,  24952, 24516, 25102,  \n639, 16634, 640,  21159, 1154, 13829,  10728, 15092, 1393,  \n25102, 24516, 24660,  16128, 10520, 1403,  11894, 2116, 14310,  \n2753, 2754, 14407,  24660, 24366, 24959,  24958, 25103, 24960,  \n11339, 11093, 1820,  13314, 8720, 12007,  18476, 10364, 10397,  \n16489, 336, 14993,  25243, 24961, 25392,  24962, 24961, 25243,  \n24962, 25243, 25245,  25246, 25244, 24963,  24962, 25245, 24805,  \n17567, 11127, 12174,  23748, 16637, 23836,  17144, 2053, 2052,  \n10743, 443, 6029,  4026, 21547, 23408,  24806, 25247, 24519,  \n17720, 17195, 6384,  11498, 7804, 2338,  24519, 25247, 24807,  \n29155, 680, 6027,  13318, 18387, 1566,  22188, 1348, 11088,  \n17854, 2049, 2050,  5490, 8739, 8311,  24809, 24376, 24807,  \n1018, 6891, 13145,  957, 9781, 9783,  24808, 24664, 25106,  \n25105, 24376, 24809,  24968, 25249, 25106,  19367, 12516, 6755,  \n25250, 25251, 24967,  20544, 8343, 14368,  22652, 22571, 20412,  \n25110, 25107, 25252,  4532, 1788, 9483,  2904, 953, 2903,  \n8021, 16723, 16458,  22852, 5888, 7611,  24522, 24667, 25110,  \n7991, 4865, 7992,  25107, 25110, 24667,  9903, 17700, 9904,  \n11158, 22404, 11157,  17458, 6061, 19438,  17121, 17512, 13621,  \n15952, 6908, 19063,  10848, 16841, 13563,  7773, 17864, 8982,  \n8215, 4727, 6648,  25254, 24813, 25255,  14001, 17213, 13362,  \n20445, 7773, 8982,  1512, 1513, 14855,  16837, 19120, 14842,  \n25111, 25254, 25256,  4826, 23538, 12259,  8551, 17024, 7983,  \n8273, 8274, 5369,  8484, 3010, 3565,  20566, 15514, 9918,  \n25402, 24814, 24815,  25112, 24815, 24672,  5370, 5369, 8274,  \n13826, 23617, 14471,  7458, 10251, 9445,  22735, 12299, 4484,  \n19222, 7255, 14662,  12649, 17388, 17387,  17583, 2754, 2753,  \n22094, 18638, 13113,  7919, 7921, 11369,  4761, 22776, 20551,  \n13457, 2316, 22996,  24877, 460, 10854,  17861, 9819, 9133,  \n7847, 7848, 12503,  7307, 3156, 10167,  10386, 9365, 16095,  \n25257, 25115, 25258,  973, 1139, 10988,  786, 10074, 10076,  \n16572, 17987, 9231,  17301, 3904, 12982,  15641, 7778, 5761,  \n16580, 11045, 11914,  8507, 8438, 17244,  13227, 3162, 17748,  \n1863, 22007, 1864,  1077, 22355, 16175,  11355, 1710, 1709,  \n24528, 24979, 25118,  11804, 16534, 17140,  25406, 25119, 25121,  \n5271, 4928, 4408,  7657, 18210, 13867,  20569, 21010, 19124,  \n3586, 9581, 5872,  6519, 17258, 4357,  25121, 25119, 24816,  \n25259, 25120, 24681,  14349, 5347, 8023,  25120, 25259, 25261,  \n25260, 24984, 25120,  25260, 25120, 25261,  15473, 10331, 8223,  \n25260, 25121, 24984,  25121, 24816, 24983,  1338, 16656, 17762,  \n16204, 4290, 17062,  25262, 25123, 24985,  11690, 13889, 3476,  \n24986, 25264, 25265,  25123, 25262, 25408,  16338, 16339, 4010,  \n24986, 24819, 25264,  9730, 2686, 2687,  6391, 18269, 7947,  \n3663, 14960, 16668,  11838, 7323, 757,  24819, 25124, 25264,  \n12472, 20500, 15406,  12609, 19928, 6323,  24990, 25124, 24392,  \n5648, 14733, 14732,  8153, 8154, 16853,  18109, 9808, 16299,  \n12486, 17709, 20537,  6950, 18704, 20979,  974, 17628, 2473,  \n4126, 13299, 21278,  9247, 13470, 9248,  3122, 19181, 13312,  \n21204, 18199, 4604,  24989, 24987, 25272,  11860, 8882, 540,  \n24827, 25130, 25271,  23941, 25132, 24696,  23941, 24691, 25132,  \n12832, 4207, 19175,  18286, 18287, 22451,  24830, 24540, 24693,  \n25133, 23455, 23800,  3626, 13600, 15114,  24987, 25136, 25272,  \n13248, 19101, 4160,  11318, 14180, 3643,  15125, 17491, 2251,  \n15355, 1892, 2257,  18728, 695, 18053,  25131, 24992, 25273,  \n25276, 25273, 24992,  25276, 24992, 25135,  25135, 24992, 24826,  \n4698, 2484, 16926,  25274, 25135, 24692,  25135, 24828, 24692,  \n25133, 23800, 24697,  7094, 18920, 21346,  19566, 19101, 13248,  \n6389, 14021, 6390,  4454, 23296, 4453,  25131, 25273, 25134,  \n17439, 9643, 10528,  3086, 10241, 3372,  3312, 19144, 22748,  \n18424, 14912, 11117,  22680, 21375, 15018,  7413, 19910, 10663,  \n9199, 1063, 1064,  21559, 16673, 13351,  14954, 14056, 3869,  \n24838, 24841, 24998,  2945, 2333, 5330,  20578, 13556, 12019,  \n19772, 18828, 19264,  24399, 24994, 24695,  25141, 25136, 24837,  \n16966, 15948, 1890,  16009, 20044, 12952,  7298, 16114, 5429,  \n24701, 26114, 25137,  25276, 25134, 25273,  17236, 8254, 19866,  \n15764, 2992, 5995,  5636, 20343, 17991,  7173, 21297, 21729,  \n24695, 25277, 24700,  24837, 25001, 25141,  25002, 24702, 25278,  \n25278, 24702, 24996,  12076, 11233, 18686,  25279, 24999, 24845,  \n11604, 11204, 21624,  13993, 18640, 1779,  13102, 13696, 6013,  \n4176, 7519, 7520,  24837, 24707, 25001,  16897, 16896, 17536,  \n6344, 21130, 19471,  1755, 4827, 12258,  9323, 2646, 9375,  \n15237, 15886, 19701,  9145, 21491, 20612,  10388, 14766, 11385,  \n12683, 5682, 14908,  24845, 24846, 24416,  21407, 16757, 19533,  \n2552, 21199, 14752,  11612, 14032, 11911,  12872, 12444, 11145,  \n13518, 3669, 9920,  18721, 15527, 18550,  17447, 17121, 17936,  \n25281, 23459, 24844,  5459, 5290, 21241,  2539, 9804, 16441,  \n9793, 24931, 21017,  14755, 3306, 4070,  25144, 24701, 24544,  \n14452, 11026, 18995,  10981, 19732, 16664,  11288, 10045, 12798,  \n10632, 3767, 13115,  14540, 2063, 3903,  8670, 10119, 12111,  \n19112, 4069, 4095,  13852, 19295, 2760,  25005, 25283, 25003,  \n4430, 3812, 25284,  1410, 5285, 4387,  14997, 13166, 13165,  \n520, 18235, 521,  17109, 3733, 23414,  15251, 5100, 3274,  \n9641, 9640, 1010,  25009, 25285, 25146,  17219, 14297, 16263,  \n9004, 17954, 7986,  20358, 13185, 645,  21547, 17391, 15525,  \n25286, 25683, 24560,  10485, 15182, 3558,  22801, 6511, 14184,  \n25683, 24259, 24560,  25146, 25287, 24710,  580, 12407, 579,  \n21416, 12410, 4294,  6305, 16475, 15433,  14733, 10395, 7566,  \n25287, 24849, 24710,  5427, 5426, 1145,  13667, 15451, 16745,  \n25288, 24849, 25287,  19701, 23947, 22329,  7971, 17619, 20492,  \n14728, 7019, 18318,  9457, 20276, 12739,  13620, 18399, 22133,  \n5881, 21378, 21154,  5041, 18729, 5491,  12099, 9614, 2493,  \n25288, 24851, 24849,  25288, 25289, 25290,  5190, 11149, 11867,  \n2183, 2182, 7990,  6603, 11481, 16117,  25159, 25014, 25157,  \n9311, 11218, 21803,  21790, 12993, 14744,  5887, 5614, 5888,  \n741, 4068, 11986,  25155, 25156, 25157,  3570, 6654, 5421,  \n24853, 25157, 25014,  14416, 3988, 5562,  25292, 25159, 25157,  \n19368, 14965, 14964,  25294, 25159, 25293,  25294, 25018, 25159,  \n24852, 25154, 25016,  22548, 14458, 7894,  2696, 20965, 22016,  \n25155, 25295, 25296,  14534, 7254, 11968,  10349, 10350, 18504,  \n21794, 3953, 20400,  25161, 25019, 25294,  24854, 25016, 25295,  \n3171, 16763, 3942,  12499, 13948, 13281,  8635, 2621, 3834,  \n4645, 3658, 3659,  6884, 6883, 5654,  25020, 24859, 24427,  \n25020, 25297, 24859,  12085, 12643, 13432,  5926, 20222, 16627,  \n5178, 5177, 4807,  17859, 382, 15092,  5724, 11061, 7294,  \n5240, 16235, 13552,  15725, 13994, 18950,  17545, 6911, 2817,  \n15166, 3796, 1537,  20585, 2092, 2091,  12883, 24870, 16351,  \n24859, 25298, 24860,  24860, 25298, 25165,  25021, 25022, 24715,  \n2853, 1210, 3575,  6343, 10637, 12633,  6962, 9971, 14955,  \n16282, 15338, 10932,  25024, 25299, 24862,  23287, 11434, 20664,  \n21563, 6830, 454,  21178, 9496, 9497,  25300, 24570, 25023,  \n14360, 11739, 14361,  4416, 4363, 15009,  2661, 11758, 11759,  \n24863, 24716, 24717,  4590, 13378, 13541,  6352, 884, 17249,  \n3375, 579, 14305,  12603, 16479, 11386,  17134, 15824, 5061,  \n18776, 11620, 981,  25026, 25693, 24575,  13540, 7523, 10825,  \n18482, 15939, 10053,  11609, 20014, 19828,  20150, 8754, 8753,  \n10186, 8673, 6477,  18949, 11524, 16040,  6139, 2865, 4037,  \n23471, 17767, 15585,  6680, 20042, 12554,  17315, 5502, 29712,  \n8563, 9565, 9566,  16683, 4943, 13773,  23976, 24448, 25170,  \n25302, 24867, 24577,  9258, 9257, 7728,  24451, 24282, 24452,  \n12613, 12612, 19164,  21898, 12485, 12486,  16582, 16132, 11259,  \n18928, 17403, 19223,  7919, 11369, 15723,  10281, 4930, 6400,  \n6131, 4290, 16204,  25577, 24118, 24726,  27347, 608, 609,  \n6544, 18678, 22140,  24865, 24868, 25172,  18921, 13294, 13979,  \n24865, 25172, 25027,  16457, 16456, 23824,  24869, 25027, 25305,  \n25305, 25027, 25304,  10884, 16547, 12060,  5173, 349, 1337,  \n1493, 484, 1413,  13680, 17264, 13681,  25306, 24727, 25028,  \n16137, 12779, 13896,  24868, 24727, 25171,  25172, 24868, 25171,  \n10398, 18174, 10399,  25304, 25027, 25172,  11636, 606, 1249,  \n25305, 24590, 24869,  11520, 20435, 19900,  13796, 9104, 24090,  \n25306, 25028, 25173,  2857, 4368, 2856,  2289, 4360, 22577,  \n12837, 3295, 3294,  14002, 10349, 12160,  2548, 8376, 2546,  \n24589, 24588, 25174,  11410, 19677, 11582,  25307, 24590, 25305,  \n9229, 10595, 9956,  5912, 17086, 9832,  23467, 22953, 11150,  \n24590, 25307, 25029,  24592, 24291, 25033,  24124, 25032, 24123,  \n20909, 17980, 9839,  6097, 14442, 1402,  4819, 16298, 7233,  \n25310, 25033, 24291,  9114, 3215, 18780,  18725, 4680, 663,  \n17207, 10598, 8086,  24873, 25310, 24291,  3216, 3215, 9114,  \n6618, 7102, 13855,  7778, 10684, 13862,  21382, 7405, 17899,  \n25311, 24732, 24455,  18325, 3898, 3897,  25311, 24455, 25037,  \n10446, 18851, 10445,  24731, 25036, 24594,  13297, 9813, 20934,  \n24128, 25313, 25177,  7802, 7803, 12720,  8556, 438, 1526,  \n24298, 24874, 25314,  15319, 3424, 3389,  18651, 10961, 22305,  \n24128, 24879, 25313,  14777, 4076, 1096,  14924, 770, 14923,  \n649, 9810, 11238,  25034, 25039, 25315,  12904, 2802, 10165,  \n6993, 13498, 9293,  14852, 14853, 12057,  24462, 10281, 15598,  \n13255, 14968, 6182,  8914, 10952, 9137,  13485, 21191, 13486,  \n14156, 14155, 7606,  4758, 16958, 10901,  17131, 17132, 17895,  \n4259, 4258, 656,  19781, 15142, 19356,  25313, 24879, 25040,  \n5424, 875, 9111,  5335, 12588, 10758,  5687, 5686, 19062,  \n20401, 15788, 18040,  12591, 6317, 11721,  22931, 21316, 14815,  \n12824, 23685, 2099,  9065, 10908, 19698,  8822, 11323, 5684,  \n6664, 2611, 17453,  4038, 4037, 10589,  8896, 18595, 10646,  \n11308, 23383, 12856,  25320, 25040, 25323,  1986, 1987, 7238,  \n25041, 24733, 25319,  25041, 24302, 24733,  24600, 25323, 25040,  \n360, 7052, 12836,  6808, 15421, 8455,  618, 6188, 12741,  \n6429, 1019, 22033,  3198, 4536, 16748,  7175, 21158, 11792,  \n24880, 24302, 25322,  14194, 18197, 8774,  18442, 17595, 6624,  \n1658, 6947, 21359,  25324, 24597, 24599,  16002, 22080, 12951,  \n1717, 1719, 16802,  12703, 18694, 8217,  3557, 3559, 20085,  \n24130, 24457, 24882,  18262, 20310, 3323,  19072, 324, 21992,  \n24600, 24136, 25323,  24459, 25042, 24602,  24883, 25323, 24136,  \n15484, 6449, 15441,  11814, 1377, 3475,  24601, 25045, 24739,  \n14311, 12604, 11466,  4523, 10176, 12930,  8447, 1183, 12791,  \n18525, 6582, 14491,  25325, 24883, 24465,  4225, 3389, 3424,  \n12687, 7873, 7874,  6387, 432, 18448,  13075, 14970, 9296,  \n299, 298, 10517,  20767, 17584, 2150,  24603, 25047, 24463,  \n4337, 10886, 23711,  2116, 2117, 12051,  10784, 16176, 18178,  \n9629, 11193, 5820,  11193, 9629, 18089,  24885, 25182, 25048,  \n3853, 21404, 2631,  8132, 17660, 18617,  3842, 16159, 3310,  \n6546, 13669, 13579,  7219, 20362, 4803,  25048, 24741, 24885,  \n2007, 3159, 389,  16871, 22914, 7058,  16238, 9334, 1119,  \n14631, 12345, 20771,  14532, 2584, 13268,  25185, 24742, 24743,  \n21966, 14311, 7413,  13551, 10422, 5834,  20570, 18966, 5546,  \n9409, 22236, 4210,  1115, 1114, 13927,  17987, 10129, 19208,  \n11290, 11222, 11221,  19375, 12265, 2846,  24310, 24749, 25188,  \n10254, 13002, 13003,  7028, 17192, 5710,  6922, 22696, 6353,  \n18494, 19869, 4251,  24468, 25189, 24147,  2768, 2730, 16643,  \n8687, 2397, 11769,  25332, 24747, 24746,  21289, 1166, 14411,  \n12203, 3298, 13511,  5807, 13301, 16343,  21090, 21147, 21148,  \n24747, 25332, 25050,  6011, 18157, 755,  19574, 5499, 13017,  \n15773, 11555, 15339,  13943, 20458, 9078,  17030, 12093, 16847,  \n15150, 19694, 21969,  1685, 1686, 9070,  3764, 15563, 9960,  \n5342, 16890, 16891,  24607, 24890, 25191,  24608, 24153, 25050,  \n24751, 25051, 25193,  9333, 12423, 9331,  12640, 2405, 3715,  \n16123, 20002, 1107,  13282, 4815, 762,  18295, 13975, 13974,  \n20466, 6817, 16064,  24891, 24610, 25194,  24893, 24155, 25197,  \n25196, 25051, 24753,  11675, 21444, 8261,  19113, 13559, 13446,  \n4817, 4706, 12212,  8390, 19618, 14525,  15896, 16665, 19565,  \n25334, 24611, 24474,  10000, 11159, 21442,  5982, 5981, 10001,  \n25334, 24474, 25198,  8373, 7808, 17239,  13374, 8660, 18487,  \n2661, 11759, 18342,  24474, 24162, 25198,  21476, 7320, 20315,  \n4402, 4403, 10746,  11002, 10029, 14138,  8101, 14217, 7492,  \n17040, 14651, 13136,  13244, 715, 20047,  2175, 1001, 9125,  \n24475, 25338, 24757,  10069, 13468, 1805,  14688, 1263, 4447,  \n25335, 25199, 25200,  8463, 10344, 5039,  10556, 1220, 10377,  \n9692, 13272, 4527,  25056, 25336, 24616,  11756, 11757, 7299,  \n20026, 21537, 12466,  11202, 8229, 5513,  14131, 9998, 7343,  \n12622, 17432, 813,  25336, 24895, 24616,  18714, 2777, 21790,  \n25057, 25199, 25340,  25057, 25340, 25201,  19600, 2279, 10697,  \n1473, 15493, 14030,  16156, 17454, 10196,  12211, 1041, 993,  \n25339, 25202, 25201,  2704, 12117, 5309,  11948, 11521, 11520,  \n13974, 16148, 6399,  14294, 3838, 14564,  14564, 3838, 14565,  \n4026, 3115, 22473,  1896, 4584, 21777,  24902, 24322, 25060,  \n7568, 4013, 14558,  25476, 25341, 25202,  25062, 25059, 24765,  \n18042, 2646, 3632,  24907, 25062, 24765,  14357, 8838, 2527,  \n25343, 24166, 24903,  2942, 3685, 655,  3522, 8542, 3617,  \n3541, 1821, 1786,  25202, 25341, 25204,  6953, 6546, 4328,  \n25061, 24761, 24905,  25347, 24907, 24908,  16745, 9123, 13667,  \n2200, 15573, 18594,  16724, 18941, 18940,  7467, 4148, 16160,  \n12139, 780, 13307,  22046, 17014, 11217,  4337, 8701, 4171,  \n9520, 3432, 23742,  3324, 6869, 13464,  25207, 25347, 24908,  \n10608, 9867, 16322,  25207, 24908, 24768,  25066, 25206, 25209,  \n25206, 25348, 25209,  6575, 691, 5666,  25067, 25210, 24325,  \n7789, 7791, 16554,  1360, 1359, 18281,  3020, 11265, 20839,  \n13827, 11321, 12033,  1935, 3962, 6037,  24628, 24325, 25210,  \n25068, 25208, 25350,  22931, 8141, 11035,  25349, 24910, 25070,  \n12515, 7782, 20853,  19379, 13499, 12397,  1487, 1717, 16802,  \n16189, 7913, 12417,  15147, 12920, 7495,  11088, 1332, 22188,  \n25068, 25350, 25351,  18729, 8238, 16228,  6242, 6233, 6232,  \n25068, 25351, 24774,  25074, 23877, 24483,  15591, 1611, 21145,  \n17876, 12195, 19299,  16926, 18480, 4698,  24483, 25072, 25074,  \n3638, 21150, 22872,  9488, 18710, 3672,  24913, 24914, 25214,  \n17235, 627, 628,  7025, 13579, 11849,  24776, 25355, 25073,  \n16132, 7349, 11259,  10754, 1988, 21488,  16154, 6909, 16961,  \n24777, 24776, 24919,  2850, 20798, 2849,  9492, 16224, 9491,  \n13576, 10991, 1247,  8836, 19004, 8837,  17002, 18848, 3831,  \n22022, 11788, 9361,  25357, 25078, 25077,  18652, 23348, 4763,  \n5908, 7503, 635,  21504, 19169, 7634,  19223, 17403, 19222,  \n18480, 16925, 5137,  25218, 25078, 25357,  8834, 8835, 11491,  \n22793, 18979, 8621,  4162, 13458, 21488,  3128, 3127, 12286,  \n22115, 11420, 11421,  5650, 1974, 9699,  19573, 15071, 7152,  \n6820, 19237, 2118,  25076, 24495, 24926,  14914, 1323, 13985,  \n770, 11123, 11439,  18234, 634, 16812,  25364, 24330, 24920,  \n24922, 24924, 25361,  24922, 24641, 24924,  2582, 8905, 11673,  \n25363, 24330, 25364,  24330, 25363, 24334,  24787, 24334, 25363,  \n10572, 6489, 19516,  5669, 13844, 8151,  5296, 14277, 21760,  \n14102, 4054, 4053,  22064, 3531, 491,  21335, 12998, 11837,  \n16658, 16660, 20435,  16391, 19954, 15543,  24929, 24933, 25221,  \n25367, 25366, 24930,  13953, 17232, 16135,  7407, 1539, 4917,  \n24497, 24187, 24788,  10502, 6661, 9418,  13247, 22077, 8877,  \n24497, 24788, 25368,  25122, 4696, 12544,  4349, 16307, 2541,  \n19712, 12013, 5979,  21147, 4362, 14063,  3348, 5551, 20552,  \n24936, 25223, 25371,  24341, 24190, 24935,  24500, 24937, 25226,  \n9236, 9238, 12933,  14584, 21671, 14582,  1309, 20521, 25372,  \n24939, 25087, 25225,  17252, 17479, 12057,  11737, 15781, 587,  \n14373, 3007, 9648,  10466, 20176, 6602,  21142, 484, 1493,  \n25225, 25373, 24942,  3237, 18045, 2192,  16460, 16459, 19297,  \n25373, 25231, 24942,  7345, 5274, 13828,  25229, 25226, 24502,  \n9715, 10928, 830,  11577, 20043, 5729,  8178, 8177, 6536,  \n25374, 25232, 25230,  25232, 25374, 25375,  24504, 24042, 25232,  \n1631, 23539, 14561,  3832, 4653, 19157,  25229, 24502, 24945,  \n12277, 25376, 21817,  24794, 25378, 24941,  25231, 25093, 24943,  \n20138, 16402, 17700,  8928, 8331, 5307,  6578, 18949, 16040,  \n25377, 25229, 24945,  8683, 3445, 8758,  686, 10714, 687,  \n25092, 24505, 25379,  15650, 22036, 13909,  3865, 22889, 7328,  \n25380, 24945, 24652,  9533, 3305, 12201,  13945, 14726, 17898,  \n18194, 5769, 10715,  21501, 16870, 14633,  24948, 24355, 25236,  \n24949, 25380, 24652,  11714, 8198, 8653,  25237, 25096, 24797,  \n25096, 25383, 25382,  8643, 8644, 2520,  24950, 24510, 25382,  \n25238, 25099, 24798,  8015, 5431, 8016,  16840, 16153, 16961,  \n14775, 826, 825,  12429, 17649, 6495,  9883, 17671, 3848,  \n20007, 2082, 2083,  24799, 25239, 24209,  10296, 12943, 10890,  \n8117, 7817, 5745,  25443, 6462, 5639,  5946, 22977, 18672,  \n24513, 25240, 24951,  15877, 9842, 5444,  25386, 25242, 24659,  \n19156, 16098, 10875,  24952, 25241, 24658,  25242, 25386, 24956,  \n25387, 3722, 19639,  15541, 19344, 6666,  16782, 14124, 16783,  \n10554, 12755, 540,  2603, 9521, 2604,  24254, 3846, 18765,  \n3751, 4064, 4063,  24959, 25389, 24660,  25390, 25391, 25103,  \n4048, 7832, 8521,  24961, 24960, 25391,  5351, 12754, 19117,  \n25392, 24961, 25391,  11831, 11833, 2196,  15918, 13591, 16074,  \n24959, 24366, 24963,  23646, 15926, 6051,  1163, 17428, 19562,  \n13842, 14175, 14047,  10087, 13688, 17927,  24806, 24805, 25245,  \n9340, 15694, 10273,  9209, 10215, 4903,  17935, 6419, 1757,  \n5306, 5307, 13190,  5041, 3493, 9110,  25247, 24806, 25245,  \n2719, 2718, 14484,  6105, 17422, 13034,  9479, 22044, 17378,  \n25247, 25248, 24807,  25248, 25393, 24807,  22053, 16662, 19047,  \n4176, 13171, 12561,  24809, 24807, 25393,  20315, 7320, 21071,  \n1382, 1044, 10138,  13451, 14120, 5325,  11427, 8234, 1158,  \n7541, 3653, 7542,  20663, 1394, 1393,  14632, 9289, 10049,  \n14159, 13709, 14205,  8392, 7620, 7619,  19268, 1881, 11182,  \n24967, 24966, 25250,  12059, 6346, 9387,  16176, 8859, 4512,  \n5960, 19947, 3878,  24666, 25397, 24811,  25396, 24811, 25397,  \n25249, 24968, 25396,  24968, 24811, 25396,  7519, 4176, 691,  \n11893, 18083, 16868,  25660, 25398, 25110,  25399, 25107, 25400,  \n23334, 13190, 4183,  1143, 1142, 5230,  1443, 16303, 3185,  \n25108, 25400, 25107,  19485, 1831, 18206,  15964, 11553, 6140,  \n2212, 12092, 20955,  10039, 557, 10040,  16975, 12579, 937,  \n3470, 9774, 5554,  24970, 25398, 25253,  25110, 25398, 24970,  \n2688, 6573, 5677,  24970, 25255, 24813,  25255, 24970, 25253,  \n24969, 25401, 25109,  11325, 602, 14592,  3969, 21522, 15704,  \n8428, 8954, 8427,  1626, 8809, 18396,  25402, 24815, 25112,  \n838, 16076, 14195,  810, 9442, 8601,  9573, 1499, 4596,  \n12538, 1556, 1730,  25403, 24672, 24973,  6890, 6663, 9893,  \n2171, 15079, 14165,  18471, 11870, 8797,  7234, 20607, 5657,  \n24973, 25404, 25403,  25404, 24973, 24976,  24410, 15194, 5256,  \n2198, 4074, 16851,  25114, 24975, 25405,  20166, 805, 9412,  \n19385, 13664, 16542,  459, 7015, 458,  3897, 7497, 13928,  \n25404, 24976, 25116,  437, 18063, 10453,  23408, 5082, 2125,  \n17224, 7251, 9321,  25114, 25258, 25115,  25257, 24525, 25115,  \n19012, 7469, 7470,  12110, 18116, 10574,  9164, 24188, 14616,  \n24978, 24981, 24977,  24979, 24677, 25257,  2712, 2711, 10299,  \n12300, 1616, 9569,  1030, 16376, 19441,  11229, 9748, 9747,  \n2641, 15400, 4533,  25407, 24982, 25118,  25407, 24681, 24982,  \n13640, 9574, 4905,  25260, 25261, 25121,  816, 12721, 13828,  \n3286, 548, 3287,  3007, 13238, 9648,  25064, 1523, 12856,  \n23791, 1501, 17320,  5539, 13047, 17231,  6859, 11916, 6858,  \n13573, 5868, 9216,  3897, 19005, 7497,  12611, 8612, 8924,  \n4059, 10702, 19453,  10086, 5845, 12182,  4056, 12367, 1382,  \n731, 14761, 730,  11073, 1271, 11886,  18307, 852, 1768,  \n21681, 12301, 19798,  25268, 24820, 25123,  25124, 25409, 25264,  \n5135, 15203, 21115,  13335, 7610, 14074,  24990, 25409, 25124,  \n24820, 25268, 24687,  10640, 22291, 9696,  24990, 25410, 25409,  \n7910, 15122, 14632,  24989, 25410, 24990,  8097, 15014, 19329,  \n4195, 5550, 4194,  24691, 24403, 24825,  25270, 24824, 24991,  \n25413, 25270, 24991,  24991, 24827, 25413,  25414, 25410, 25272,  \n25415, 25414, 25272,  14059, 10434, 4541,  6519, 4357, 5152,  \n25413, 24827, 25271,  11477, 11921, 6822,  24693, 24074, 25128,  \n3490, 23541, 9260,  25136, 25416, 25272,  3638, 22872, 18928,  \n25130, 24542, 25417,  25274, 24692, 24830,  3915, 3916, 8501,  \n25418, 24399, 24071,  25416, 25136, 25141,  5121, 6610, 20276,  \n14788, 9799, 9801,  19726, 16063, 11265,  25137, 25417, 24542,  \n25276, 25135, 25419,  25419, 25135, 25274,  9926, 13807, 13806,  \n15503, 9012, 6599,  24998, 24842, 24999,  17558, 13261, 16903,  \n19772, 19264, 16697,  11125, 1689, 1688,  6520, 1766, 7742,  \n9139, 20880, 2670,  20493, 20494, 13717,  12791, 1183, 12792,  \n25420, 24724, 7697,  25276, 24995, 25134,  25421, 24995, 25276,  \n12342, 11771, 15432,  14568, 19718, 19717,  12695, 6811, 20908,  \n25422, 5255, 23339,  25552, 24999, 25279,  25678, 25279, 25145,  \n25421, 25428, 24995,  12169, 9431, 12837,  23146, 24931, 24932,  \n9517, 10329, 4669,  4649, 1000, 12726,  6284, 4275, 22869,  \n25556, 25001, 25283,  9143, 12276, 10734,  16897, 17536, 12868,  \n4041, 10048, 15733,  25424, 13251, 25425,  9873, 1454, 10229,  \n5154, 9621, 9579,  7678, 14338, 7679,  18747, 2928, 18748,  \n25145, 24845, 24416,  13126, 13125, 16347,  25000, 23459, 25281,  \n25001, 25003, 25283,  10578, 14820, 19523,  11164, 1594, 10622,  \n16467, 17085, 21300,  24255, 24836, 25280,  1358, 9402, 9380,  \n6757, 4576, 15812,  24931, 23146, 22713,  22426, 8453, 22236,  \n24554, 25280, 25008,  24554, 24255, 25280,  13476, 14261, 6413,  \n7444, 15277, 10563,  5879, 17383, 5595,  14283, 8049, 18268,  \n13867, 19589, 3846,  18405, 4216, 4215,  25426, 24708, 25007,  \n24847, 25427, 25007,  662, 14066, 1667,  25428, 25004, 24995,  \n25429, 24556, 25002,  11170, 9779, 5636,  12217, 8063, 11683,  \n3292, 12330, 3293,  16011, 8911, 8471,  4551, 13099, 2500,  \n13508, 6683, 21584,  24556, 25429, 24709,  14770, 3796, 6974,  \n25009, 25004, 25285,  8432, 14801, 22719,  10255, 2142, 2143,  \n10363, 3542, 11262,  21812, 14136, 21330,  7044, 9421, 12667,  \n4865, 17090, 910,  2826, 1016, 13290,  17470, 9406, 6219,  \n15719, 19555, 9015,  25431, 25146, 25285,  24848, 24259, 25683,  \n25431, 25287, 25146,  25011, 24559, 25150,  10716, 15403, 6945,  \n23035, 13700, 2838,  11336, 13326, 11670,  24850, 24711, 25432,  \n25432, 24711, 25152,  25010, 24422, 25291,  4353, 10885, 4354,  \n2928, 8553, 4753,  24426, 24858, 25152,  2180, 11373, 11372,  \n25151, 24851, 25288,  18188, 2312, 15307,  9223, 8439, 795,  \n19688, 2164, 10221,  8272, 1738, 15350,  25292, 25293, 25159,  \n19440, 9936, 19218,  13640, 13641, 9574,  3812, 3387, 11313,  \n16512, 2871, 16513,  19503, 15613, 5909,  7591, 1782, 10855,  \n25155, 25296, 25433,  13880, 6592, 6892,  17807, 5771, 9695,  \n15000, 8421, 4046,  5030, 21093, 15745,  25294, 25293, 25161,  \n25160, 25161, 25568,  25154, 25295, 25016,  8686, 8432, 10874,  \n25155, 24712, 25295,  19272, 8307, 8308,  25160, 25020, 25019,  \n5469, 2880, 2875,  25163, 25013, 24714,  625, 11600, 21217,  \n12114, 19791, 22652,  23485, 5314, 18373,  2339, 20100, 11772,  \n16213, 3124, 3123,  6224, 12827, 19033,  16017, 17646, 13341,  \n7443, 10629, 4015,  25435, 24862, 25299,  682, 7308, 7722,  \n15722, 7920, 7919,  1405, 18979, 3493,  25298, 24859, 25297,  \n2697, 8964, 8966,  11914, 15645, 16915,  25436, 25166, 25165,  \n25166, 25439, 25021,  4376, 3810, 17674,  9344, 3035, 11274,  \n25439, 25022, 25021,  19242, 2568, 25266,  25438, 24434, 24428,  \n6450, 7204, 16933,  24434, 25438, 24718,  15018, 21375, 4725,  \n7906, 1585, 2508,  24436, 25167, 24717,  12609, 12215, 19928,  \n15514, 6846, 9918,  20208, 3892, 10268,  10121, 5530, 5531,  \n24441, 24718, 24864,  17688, 13125, 21327,  12684, 8371, 1703,  \n17141, 21672, 3982,  382, 14833, 15092,  24575, 25693, 25168,  \n372, 16162, 3779,  19952, 1770, 10595,  5705, 13274, 2223,  \n24719, 24579, 25440,  5014, 9649, 18200,  452, 10250, 468,  \n3166, 13352, 3016,  12129, 18776, 18017,  5375, 9807, 509,  \n20108, 17141, 6221,  15384, 6123, 4788,  6278, 25443, 5107,  \n1336, 349, 4781,  25026, 24282, 24451,  14763, 5199, 16780,  \n25302, 24577, 25445,  24579, 24585, 24587,  6750, 16364, 23676,  \n1861, 1862, 24586,  7271, 11588, 1813,  4953, 8320, 8322,  \n25444, 24451, 24452,  7347, 7252, 4570,  18074, 6480, 21970,  \n12235, 23149, 6856,  24452, 24592, 25303,  24871, 24867, 25446,  \n13973, 1642, 1641,  7166, 11570, 6899,  10795, 13726, 10796,  \n12035, 16306, 8297,  14975, 9480, 6149,  14074, 12978, 13335,  \n25304, 25172, 25171,  2552, 16375, 21199,  25171, 24727, 25306,  \n12833, 16834, 6966,  2698, 5347, 4501,  24872, 24285, 25577,  \n18032, 19939, 8162,  5843, 5844, 4814,  17750, 14859, 7760,  \n13405, 15960, 13521,  8005, 3711, 8004,  25448, 25306, 25173,  \n4926, 3766, 16105,  25033, 25449, 25175,  25032, 25450, 25173,  \n25450, 25448, 25173,  637, 21534, 8886,  2497, 13802, 3487,  \n25031, 25309, 25174,  22230, 12037, 12038,  25032, 25451, 25450,  \n25308, 25029, 25307,  10454, 17503, 15593,  18652, 13212, 20815,  \n25030, 25029, 25308,  14416, 10298, 3988,  4224, 10000, 19200,  \n24875, 24290, 24872,  10292, 10291, 14638,  15702, 11251, 11656,  \n1947, 9928, 15409,  3337, 5016, 3335,  25309, 25031, 25177,  \n25177, 25031, 24454,  20465, 446, 22890,  16932, 20503, 12337,  \n25032, 25034, 25312,  11257, 19294, 7083,  17753, 4216, 18405,  \n24874, 25035, 25452,  16461, 4322, 18745,  2063, 20082, 12109,  \n24874, 25452, 25314,  9383, 10590, 9382,  11751, 12777, 17293,  \n25036, 25453, 25038,  15539, 4954, 13317,  5054, 8936, 8935,  \n4555, 4556, 2653,  6293, 19985, 809,  12388, 15539, 13317,  \n25179, 24456, 24876,  24298, 25314, 25454,  25320, 25313, 25040,  \n14405, 3313, 17260,  25316, 25317, 25038,  25178, 24127, 24878,  \n23979, 22247, 11496,  5161, 21721, 16148,  24736, 25038, 25317,  \n6718, 9010, 18627,  13736, 2977, 2978,  15108, 9611, 8792,  \n3431, 9520, 21466,  20873, 18157, 21081,  7441, 12110, 20082,  \n8604, 9687, 8603,  5433, 21992, 21065,  12126, 1391, 20013,  \n25324, 25321, 24597,  10439, 5701, 5702,  16718, 18449, 3603,  \n11147, 6719, 9090,  3249, 14521, 13870,  25044, 24461, 25455,  \n16092, 3975, 11491,  25456, 25323, 24883,  10585, 21862, 18173,  \n18917, 11484, 4404,  14586, 2630, 1150,  25457, 24602, 25042,  \n19528, 4444, 7011,  25455, 24461, 25046,  24138, 25046, 24461,  \n19474, 13524, 9764,  25326, 24739, 25045,  14081, 17004, 4745,  \n15216, 5506, 4916,  5595, 5594, 14489,  14684, 6299, 5817,  \n25457, 24603, 24602,  2136, 6478, 8096,  25460, 25046, 24886,  \n16485, 12236, 11533,  25047, 24603, 25461,  7054, 3970, 15603,  \n19576, 14391, 14021,  25326, 25182, 24739,  3438, 18555, 3439,  \n12796, 6718, 4190,  24885, 24739, 25182,  4569, 17827, 7347,  \n18501, 7064, 4500,  11206, 11766, 8520,  1592, 22226, 1593,  \n19524, 18829, 10683,  16761, 21317, 6770,  3446, 6228, 16084,  \n8139, 14849, 18510,  10099, 1884, 1883,  15511, 15510, 14445,  \n4803, 20362, 4802,  25047, 25328, 24463,  17383, 5879, 6924,  \n24141, 25184, 25183,  24308, 24463, 25328,  9600, 4111, 4110,  \n24745, 24308, 25328,  24887, 24742, 25185,  25462, 4696, 25122,  \n333, 12670, 5815,  11097, 12081, 7542,  24888, 25184, 24141,  \n11018, 13518, 1412,  24254, 7658, 13867,  2942, 18322, 18621,  \n10341, 20403, 10340,  21047, 3435, 4702,  13683, 12925, 10738,  \n12442, 14775, 6123,  9409, 9198, 14151,  8042, 6908, 14800,  \n12978, 16939, 18259,  25188, 25185, 24143,  25331, 24744, 25463,  \n2821, 14471, 12655,  25190, 25464, 25188,  5321, 9758, 4158,  \n10814, 4787, 12216,  24749, 25190, 25188,  21735, 1384, 18386,  \n13214, 2710, 1749,  14735, 4436, 14736,  25330, 24888, 24605,  \n14384, 23205, 4443,  25330, 24605, 24606,  1023, 1024, 963,  \n13088, 17120, 12247,  25190, 24749, 24748,  24147, 25189, 25333,  \n25331, 25332, 24746,  16863, 9760, 16862,  24750, 25465, 24606,  \n17074, 14780, 15454,  16222, 6675, 9325,  24150, 24147, 25192,  \n25192, 24147, 25333,  14814, 14813, 7801,  25192, 24889, 24150,  \n2289, 4361, 4360,  8186, 8731, 12030,  1344, 18727, 15614,  \n5284, 11771, 12342,  6081, 8515, 11137,  7343, 6910, 7104,  \n11947, 9370, 13331,  9317, 2200, 9318,  14476, 25467, 12058,  \n19110, 11878, 20756,  10581, 10580, 21998,  25468, 25194, 24608,  \n14646, 2744, 2743,  25196, 25469, 25051,  9402, 1358, 18986,  \n15036, 14281, 3601,  4684, 4683, 18551,  25470, 24611, 25334,  \n8323, 21131, 7770,  20651, 8706, 9453,  3305, 3304, 12820,  \n9810, 649, 15281,  1735, 18180, 5007,  1593, 18579, 796,  \n13778, 21775, 18407,  5869, 21555, 14738,  10483, 12651, 6344,  \n20694, 7429, 18834,  14842, 21660, 19783,  20826, 5556, 18582,  \n25335, 25473, 25472,  20241, 7367, 14222,  25340, 25474, 25339,  \n12321, 17326, 21839,  25472, 25199, 25335,  22624, 11919, 11201,  \n24756, 24895, 25053,  25339, 25201, 25340,  8599, 11023, 1688,  \n25338, 25054, 24757,  24895, 25336, 25053,  21088, 17439, 10041,  \n20424, 10327, 7789,  4370, 25475, 4135,  10745, 2125, 12799,  \n25199, 25472, 25340,  14128, 599, 7742,  25335, 25059, 25478,  \n25200, 25059, 25335,  13386, 18972, 18971,  966, 1306, 1307,  \n25477, 25476, 25339,  8063, 21020, 11683,  14102, 2121, 10829,  \n18483, 2073, 23510,  6874, 3676, 3677,  573, 23387, 574,  \n1596, 315, 316,  25202, 25339, 25476,  25479, 24897, 24896,  \n4430, 3387, 3812,  968, 4431, 1646,  15488, 637, 8886,  \n25062, 25478, 25059,  19675, 13904, 3209,  11114, 4067, 12335,  \n7245, 17994, 9189,  13860, 725, 12434,  25483, 25062, 25484,  \n16034, 11935, 10763,  9781, 959, 17438,  7866, 4510, 14176,  \n25482, 25341, 25476,  25484, 25062, 24907,  6414, 4386, 4388,  \n935, 12875, 9385,  18635, 9168, 11128,  17571, 15698, 4577,  \n1955, 1011, 1904,  24166, 25485, 24618,  24166, 25343, 25485,  \n3650, 7484, 13128,  25204, 25341, 25345,  11060, 9383, 11471,  \n12322, 402, 2559,  14685, 2571, 9638,  6504, 15506, 18171,  \n989, 1786, 3679,  14417, 14084, 11767,  25204, 25486, 25206,  \n11052, 9599, 5022,  18594, 18547, 2200,  18481, 10844, 19274,  \n7177, 11628, 6971,  6705, 20033, 6706,  20583, 7315, 23905,  \n4844, 8987, 4845,  12475, 15794, 13733,  9315, 10012, 12279,  \n4778, 4779, 14796,  25207, 24910, 25488,  25209, 25348, 25613,  \n5517, 23979, 4764,  7664, 1123, 1122,  11983, 16264, 14382,  \n16522, 20267, 7902,  16130, 6468, 829,  4017, 6915, 14621,  \n13692, 25490, 23836,  25209, 25613, 25208,  11885, 683, 11839,  \n7106, 13712, 5335,  25212, 24625, 24324,  9742, 21588, 6193,  \n10150, 17741, 15864,  24324, 24482, 25212,  14063, 4363, 1276,  \n10895, 10896, 22270,  4413, 14847, 14656,  24912, 25212, 24482,  \n1091, 978, 421,  17062, 17063, 17108,  12210, 17030, 9619,  \n9540, 10802, 10798,  19423, 19213, 17060,  15471, 14965, 22728,  \n6263, 12894, 6262,  24776, 25351, 25355,  25071, 24916, 25354,  \n25073, 25493, 24919,  13601, 21229, 4100,  1106, 21424, 19709,  \n25073, 24919, 24776,  25354, 24916, 25215,  24919, 25493, 25216,  \n5568, 19420, 5854,  18413, 6422, 15846,  25356, 25077, 25079,  \n25494, 25079, 24918,  25494, 24918, 25216,  613, 12224, 15608,  \n25215, 24916, 25076,  14621, 398, 17717,  22133, 19991, 13621,  \n25217, 25359, 25075,  1333, 1402, 16516,  8789, 18324, 20305,  \n25495, 25360, 25218,  19701, 18280, 23947,  9824, 19593, 17376,  \n10233, 1388, 17442,  12088, 14867, 17437,  25215, 25076, 25362,  \n2142, 4619, 2143,  20756, 8976, 19110,  11492, 12541, 12540,  \n21661, 2258, 9364,  14013, 10267, 24877,  12144, 18731, 20478,  \n1005, 11664, 11665,  1449, 7941, 13742,  24923, 25496, 25497,  \n25076, 24926, 25362,  25329, 6177, 18007,  14800, 15952, 2770,  \n25082, 24923, 25497,  562, 20297, 974,  4517, 20063, 17542,  \n24926, 25221, 25362,  25084, 25362, 25221,  24926, 24929, 25221,  \n24924, 24784, 24927,  13887, 542, 21728,  3020, 4348, 11265,  \n20705, 10225, 20713,  14281, 9171, 19251,  8837, 19004, 14431,  \n24930, 25366, 25083,  14582, 2275, 14583,  25082, 24928, 24925,  \n25084, 25221, 24933,  24928, 25082, 25365,  18770, 18769, 22132,  \n12623, 17168, 25499,  24934, 24928, 25365,  15680, 518, 5202,  \n6678, 4536, 4537,  9835, 21147, 14063,  15487, 15486, 17486,  \n24934, 25500, 25222,  21812, 5892, 14136,  9233, 9234, 8434,  \n1245, 17777, 17778,  2810, 19993, 2811,  24792, 25371, 25087,  \n2317, 17949, 7713,  14352, 14353, 16980,  24792, 24936, 25371,  \n25084, 24500, 25226,  14443, 11362, 21316,  25224, 24034, 24498,  \n20297, 564, 944,  6648, 11163, 11162,  16359, 2896, 7724,  \n12910, 5160, 5161,  25502, 25225, 25087,  20428, 8050, 23140,  \n24793, 25224, 25503,  5053, 18467, 16907,  17660, 8153, 16853,  \n24344, 24938, 24791,  934, 18827, 13521,  3004, 17096, 3896,  \n2389, 19164, 12612,  11919, 6871, 11920,  25505, 25231, 25373,  \n18348, 10014, 16560,  24938, 24346, 25228,  11301, 10370, 22702,  \n24649, 24940, 25230,  21138, 13334, 3781,  24649, 25230, 25232,  \n4777, 3854, 18760,  16506, 18689, 18808,  25375, 24504, 25232,  \n14817, 7545, 14359,  11880, 7693, 9038,  7916, 6084, 1560,  \n4737, 5047, 4599,  15509, 5429, 18685,  1795, 14698, 14697,  \n3904, 1916, 3905,  2146, 3004, 2627,  2087, 11263, 12971,  \n3750, 17659, 15677,  17709, 836, 17707,  7249, 5493, 19990,  \n24944, 24199, 24198,  16577, 15918, 8296,  25377, 24945, 25380,  \n25507, 24796, 24944,  25379, 24796, 25234,  24505, 24796, 25379,  \n25510, 25235, 24946,  3384, 3385, 5563,  25095, 25511, 25512,  \n25510, 25509, 25235,  9812, 13668, 10379,  25095, 25235, 25511,  \n22084, 19534, 16651,  17504, 10443, 17505,  18622, 7385, 530,  \n17140, 4883, 4882,  1575, 395, 12913,  6914, 592, 13456,  \n18926, 18927, 12413,  25237, 25383, 25096,  20881, 12404, 19892,  \n6326, 17186, 16096,  15149, 19311, 3914,  8046, 5908, 391,  \n9134, 21993, 7112,  3938, 9101, 8790,  22479, 16286, 638,  \n14727, 9028, 9027,  15949, 7296, 10056,  4253, 18494, 4251,  \n21787, 8321, 11972,  24951, 25513, 25097,  12754, 16478, 9608,  \n25762, 25239, 25100,  23705, 1055, 3072,  16014, 10148, 4455,  \n13680, 15800, 15691,  2293, 8667, 6339,  1681, 18820, 22330,  \n1972, 13528, 16566,  6229, 6230, 11228,  473, 12723, 11517,  \n9094, 9105, 8448,  8293, 10969, 15285,  25386, 24659, 25101,  \n25240, 24658, 25241,  12085, 22289, 12643,  20611, 16877, 1668,  \n17800, 18830, 1207,  18590, 17783, 14578,  25103, 24956, 25388,  \n25103, 25388, 25515,  9520, 9521, 2603,  16023, 18832, 5581,  \n5416, 11456, 8718,  25515, 25390, 25103,  19580, 13966, 9644,  \n25391, 24960, 25103,  5904, 10456, 16135,  5104, 19908, 23595,  \n19329, 8098, 8097,  25389, 24959, 25516,  20015, 17186, 17187,  \n13529, 16635, 639,  11455, 6730, 16842,  24959, 24963, 25244,  \n17955, 12873, 17954,  22053, 8509, 16662,  25517, 25247, 25245,  \n25518, 25247, 25517,  17797, 9982, 7660,  5513, 8229, 19229,  \n18056, 17989, 1881,  20398, 20399, 5825,  25248, 25247, 25518,  \n16238, 1119, 16236,  10536, 13449, 1007,  22433, 21953, 9100,  \n2674, 20576, 7045,  16674, 11657, 16033,  25248, 25521, 25393,  \n18566, 10038, 10037,  24965, 25394, 24964,  22367, 20894, 18090,  \n13410, 4410, 5334,  10176, 10123, 10891,  4024, 22061, 4025,  \n1206, 16535, 2958,  553, 24179, 4254,  24808, 25106, 25395,  \n25395, 24965, 24808,  631, 8271, 16470,  25523, 25105, 24809,  \n19043, 14956, 10102,  25106, 25524, 25395,  25524, 25249, 25396,  \n16104, 6178, 7674,  25249, 25524, 25106,  5580, 5579, 2157,  \n25251, 24666, 24967,  14289, 5006, 17073,  15692, 22526, 11614,  \n21217, 19708, 18164,  698, 8098, 19329,  25110, 25252, 25660,  \n3304, 4759, 3479,  14793, 20196, 14792,  3178, 14486, 8934,  \n25399, 25252, 25107,  19162, 1993, 6665,  29709, 5733, 7495,  \n25525, 25108, 25109,  2665, 2822, 17894,  25109, 25401, 25525,  \n11280, 18409, 12086,  12114, 12599, 12112,  1204, 10295, 15454,  \n247, 249, 16352,  7859, 17548, 15571,  1892, 8360, 1893,  \n16643, 8769, 2768,  16106, 10448, 15316,  25526, 25111, 25256,  \n12378, 2825, 9912,  3006, 4364, 10514,  25402, 24971, 24814,  \n10872, 13312, 13586,  7609, 11154, 11155,  25403, 25112, 24672,  \n25111, 25527, 24972,  653, 23861, 12117,  15981, 1606, 4119,  \n25527, 24974, 24972,  1606, 4120, 4119,  22524, 7709, 7708,  \n25529, 16704, 21996,  24974, 25527, 25405,  8758, 14045, 3147,  \n1426, 5479, 5478,  1762, 19802, 19386,  4074, 3081, 16851,  \n6524, 1634, 15813,  24974, 25405, 24975,  11195, 6923, 11196,  \n3483, 14879, 11252,  17446, 17445, 6177,  8593, 6370, 6369,  \n17256, 14043, 11236,  25404, 25116, 24977,  8176, 2738, 11681,  \n25530, 24977, 24981,  25406, 24981, 25119,  10556, 10840, 7572,  \n25118, 25782, 25407,  25406, 25121, 25533,  11670, 13326, 14132,  \n16940, 19683, 4297,  25407, 25534, 24681,  1026, 18980, 3550,  \n2109, 5943, 15216,  24681, 25535, 25259,  25534, 25535, 24681,  \n25533, 25261, 25259,  25533, 25259, 25535,  25533, 25121, 25261,  \n2287, 10771, 10770,  7733, 6517, 821,  22152, 6186, 16842,  \n13544, 9183, 13545,  25262, 25536, 25408,  25264, 25538, 25265,  \n4890, 3808, 4249,  4400, 12435, 15625,  25538, 25264, 25409,  \n5945, 4629, 3943,  16358, 15507, 16856,  18955, 1773, 19744,  \n14745, 20551, 5543,  25123, 25539, 25268,  4252, 19869, 10964,  \n16358, 16856, 2334,  15844, 4515, 4514,  1335, 2302, 20119,  \n9121, 9122, 8447,  15127, 2554, 2948,  1432, 5110, 16940,  \n25540, 25409, 25410,  23734, 22975, 18451,  9749, 3488, 3489,  \n25543, 25540, 25410,  1952, 11818, 15823,  1766, 3292, 7742,  \n25544, 25269, 25270,  25545, 24297, 19975,  18825, 2767, 18642,  \n25414, 25543, 25410,  21211, 15293, 1742,  24691, 24825, 25132,  \n24825, 24824, 25270,  25269, 24825, 25270,  452, 11670, 14132,  \n25127, 24687, 25268,  6962, 1882, 1509,  8062, 5613, 15294,  \n25410, 24989, 25272,  17124, 1988, 20497,  15172, 9360, 890,  \n19882, 14708, 14709,  12146, 9373, 12413,  12883, 7345, 16473,  \n25415, 25272, 25416,  25415, 25416, 25547,  25271, 25130, 25417,  \n25128, 25546, 24693,  15265, 5750, 18714,  982, 1356, 9385,  \n3069, 17804, 20344,  25551, 24830, 25548,  24830, 24693, 25548,  \n1256, 1257, 3741,  25418, 24071, 25127,  15748, 5121, 20276,  \n3913, 748, 8241,  5662, 8407, 4122,  24998, 25552, 25550,  \n24998, 24999, 25552,  5013, 3948, 3949,  24830, 25551, 25274,  \n25551, 25554, 25274,  10082, 15452, 8691,  9697, 9698, 19845,  \n12505, 2885, 9649,  25554, 25276, 25419,  6050, 6051, 8436,  \n24994, 24399, 25418,  20811, 9157, 16068,  25556, 25555, 25001,  \n25555, 25141, 25001,  25553, 25279, 25678,  9990, 20532, 5689,  \n25421, 25276, 25554,  4396, 16741, 13789,  10203, 5171, 29754,  \n17433, 14556, 7179,  25279, 24845, 25145,  14436, 2517, 14437,  \n17910, 20973, 17705,  15616, 8463, 15615,  10816, 5184, 7949,  \n14678, 13955, 20390,  2413, 12489, 11551,  6995, 20128, 6994,  \n11549, 14126, 7419,  7823, 18766, 25557,  25277, 24994, 25558,  \n12360, 15759, 8487,  3402, 2962, 11440,  5646, 19935, 16281,  \n13818, 14639, 9415,  1600, 1599, 8583,  14995, 1273, 16540,  \n24708, 25559, 25006,  18828, 15290, 16280,  1016, 10736, 13290,  \n7473, 909, 9815,  9828, 5753, 22433,  7632, 17585, 17586,  \n23792, 10854, 2631,  14080, 17685, 2495,  4452, 3159, 7297,  \n13643, 11090, 22655,  23157, 15647, 8312,  16232, 10875, 18419,  \n8871, 16735, 6696,  18749, 12116, 1259,  1010, 10278, 9641,  \n2546, 9830, 2547,  20165, 21042, 4291,  24547, 25561, 24844,  \n1901, 15942, 15011,  11549, 15302, 10510,  5658, 19563, 9735,  \n10076, 16814, 786,  2729, 14605, 7026,  25427, 24847, 25008,  \n20029, 22162, 5068,  15593, 25562, 2047,  2505, 7148, 12606,  \n24546, 25282, 24547,  10077, 10532, 3607,  19819, 6742, 8610,  \n25004, 25428, 25285,  25564, 25285, 25428,  8848, 25138, 17006,  \n25430, 24544, 24848,  12702, 10199, 9895,  19259, 2130, 11203,  \n11189, 20359, 18294,  8364, 8984, 11686,  9531, 4799, 9530,  \n16710, 3542, 9680,  16036, 10507, 22266,  22162, 17152, 5068,  \n8063, 12217, 8056,  25147, 24850, 25432,  15488, 8886, 23039,  \n16714, 4077, 4078,  11219, 4633, 2112,  8553, 3136, 3135,  \n14893, 16372, 18121,  2000, 1999, 7869,  19683, 19684, 3501,  \n8214, 12892, 3441,  4035, 4034, 25565,  25289, 25288, 25287,  \n13625, 13360, 9398,  6724, 16704, 7602,  15474, 13710, 22490,  \n2970, 4916, 8076,  21070, 9123, 13652,  25156, 25566, 25157,  \n16984, 16737, 4726,  23485, 7551, 5314,  10221, 2164, 7766,  \n11814, 3475, 14872,  4254, 5608, 4824,  11305, 20884, 18513,  \n5296, 22908, 18612,  9344, 11274, 7689,  25292, 25157, 25566,  \n25567, 25293, 25292,  3039, 8699, 11534,  25567, 25568, 25293,  \n25569, 25010, 25291,  25151, 25288, 25290,  25433, 25296, 25570,  \n25156, 25155, 25433,  25293, 25568, 25161,  7367, 9225, 4561,  \n25013, 25569, 25291,  25151, 25290, 25154,  2197, 2196, 7088,  \n25154, 25290, 25571,  25572, 25571, 25290,  17811, 2286, 13775,  \n837, 21177, 17586,  15046, 545, 10277,  8066, 6795, 10749,  \n5063, 5057, 8438,  25154, 25571, 25295,  19445, 1665, 16844,  \n16996, 16997, 20743,  25295, 25571, 25296,  5468, 12119, 5469,  \n25160, 25297, 25020,  24858, 24862, 25152,  6442, 1364, 3252,  \n1015, 6618, 13855,  13989, 2570, 2569,  25164, 25438, 24428,  \n15782, 15977, 15976,  25573, 25436, 25165,  4879, 8184, 17963,  \n13257, 22734, 8119,  9695, 5771, 14211,  23679, 24898, 11467,  \n357, 18020, 12851,  17014, 16969, 9378,  5041, 2016, 2018,  \n3728, 14025, 9568,  5041, 2018, 17775,  17695, 17499, 1492,  \n16699, 868, 8302,  25301, 24577, 25025,  17504, 3414, 5510,  \n25024, 24719, 25440,  21563, 10142, 11443,  5576, 9526, 9402,  \n13395, 21208, 21741,  25441, 25693, 25026,  15180, 18605, 12397,  \n24579, 25442, 25440,  4322, 9321, 17398,  736, 6931, 6932,  \n25026, 24451, 25441,  24451, 25575, 25441,  21661, 9364, 16380,  \n8872, 16640, 24188,  13558, 18702, 18701,  25575, 24451, 25444,  \n25442, 24579, 24587,  12422, 2663, 1574,  17494, 23499, 17495,  \n25442, 24587, 25576,  25444, 24452, 25303,  12507, 8130, 20073,  \n17125, 3071, 5994,  8113, 13122, 10270,  15667, 15666, 8569,  \n25576, 24587, 24589,  7044, 17083, 7677,  25175, 25303, 24592,  \n11153, 8573, 18739,  25576, 24589, 25174,  1655, 6958, 13565,  \n2563, 17181, 17498,  15374, 16951, 15375,  17099, 29154, 17934,  \n19567, 21480, 11984,  18610, 18677, 22367,  14519, 10697, 19549,  \n25307, 25305, 25579,  19527, 7723, 17418,  25581, 11307, 11306,  \n25580, 25174, 25309,  18004, 21835, 5351,  16014, 22819, 12827,  \n21126, 3329, 15983,  25310, 25449, 25033,  25032, 25312, 25451,  \n3683, 19017, 4611,  20606, 6021, 11950,  25030, 25308, 25176,  \n5594, 6289, 6290,  6806, 9919, 15498,  24731, 25030, 25176,  \n14899, 10827, 5028,  4766, 4768, 9514,  20436, 20440, 19073,  \n9773, 3470, 15074,  21835, 3131, 15429,  14742, 8835, 10823,  \n9763, 4542, 8711,  25176, 25453, 25036,  25519, 7601, 14197,  \n25453, 25316, 25038,  9742, 11037, 8123,  21779, 11929, 4714,  \n13500, 12021, 22246,  16304, 20592, 9884,  14247, 9988, 5173,  \n18215, 15918, 16577,  25454, 25319, 24298,  24733, 24298, 25319,  \n8072, 6112, 4418,  1394, 20663, 8318,  18034, 15088, 21139,  \n776, 6062, 1985,  25584, 9029, 8848,  12577, 16281, 628,  \n19995, 3436, 18015,  17618, 5056, 16209,  8530, 8531, 18378,  \n6083, 9680, 9679,  9251, 9252, 16688,  2192, 8030, 9690,  \n24302, 25041, 25322,  3096, 4127, 17733,  25043, 24736, 25317,  \n16999, 16050, 11130,  12115, 10666, 12116,  8828, 9424, 2471,  \n7436, 13327, 12370,  7549, 7550, 14412,  9549, 7212, 5024,  \n5741, 9997, 8622,  20707, 16846, 9939,  7648, 15693, 13457,  \n17794, 19059, 9100,  19958, 10925, 19959,  5466, 5834, 5467,  \n16742, 8820, 12560,  25180, 25044, 25455,  4777, 18760, 10653,  \n13383, 13382, 11970,  6549, 23182, 6978,  6136, 9760, 6137,  \n11606, 8706, 20651,  1510, 17330, 23172,  9211, 6521, 13929,  \n24883, 25325, 25459,  4518, 20755, 9321,  25461, 24603, 25457,  \n2667, 13162, 2208,  24465, 25459, 25325,  25327, 25460, 24886,  \n6461, 12708, 10657,  4395, 9848, 11445,  6015, 8701, 4337,  \n25588, 24465, 25183,  25327, 24886, 24887,  16106, 15316, 1343,  \n9408, 15374, 15373,  25048, 25182, 25589,  8427, 8954, 11308,  \n7112, 7428, 16049,  10983, 3472, 9457,  9576, 9181, 11822,  \n9474, 7339, 17487,  13429, 6361, 11662,  25328, 25590, 25463,  \n25591, 25049, 25048,  16791, 4044, 9211,  14861, 11819, 8381,  \n13067, 11501, 2061,  13117, 8688, 9536,  19707, 12280, 9166,  \n25184, 24888, 25593,  25463, 24744, 24745,  24467, 25049, 25186,  \n11877, 15421, 15428,  10463, 11929, 10599,  1002, 2175, 9606,  \n9485, 20181, 11701,  16087, 14225, 21758,  13217, 2404, 2405,  \n25189, 24468, 25186,  2971, 378, 5420,  7777, 13458, 4897,  \n15532, 13333, 7153,  25187, 24888, 25330,  17186, 5684, 16096,  \n13966, 15706, 19180,  20154, 22017, 16818,  21378, 12651, 10483,  \n11568, 10670, 10737,  2191, 20866, 3237,  14090, 7567, 2620,  \n15701, 12706, 8559,  11910, 11911, 20436,  25464, 25190, 25595,  \n5561, 852, 18307,  20081, 12226, 10384,  25465, 24750, 25191,  \n25595, 24748, 24751,  13308, 18054, 4166,  12222, 23390, 9772,  \n3655, 14797, 18588,  1639, 18397, 1640,  24608, 25050, 25468,  \n6304, 11486, 10651,  4235, 5467, 12040,  2466, 10454, 15593,  \n25470, 24890, 24611,  24755, 24894, 25196,  7650, 13727, 2593,  \n4900, 3510, 3511,  15783, 14091, 12199,  16163, 6807, 10555,  \n6983, 7665, 2297,  13983, 19609, 22834,  1245, 1244, 5230,  \n1458, 13506, 3223,  14573, 8874, 14574,  25473, 25597, 25472,  \n25598, 25474, 25597,  5143, 1065, 6045,  25473, 25335, 25602,  \n24613, 24893, 25601,  8148, 20414, 8149,  25471, 24894, 25053,  \n19388, 3112, 3956,  24757, 25054, 25198,  14701, 13009, 11985,  \n25597, 25474, 25603,  25597, 25603, 25472,  23480, 5283, 15936,  \n17143, 17144, 12836,  25602, 25335, 25478,  15943, 13987, 9972,  \n17338, 4049, 5736,  25471, 25053, 25604,  13513, 12085, 13432,  \n25462, 25149, 4696,  3564, 534, 6421,  19022, 20894, 18982,  \n7438, 2430, 12325,  25603, 25474, 25340,  5918, 5917, 9681,  \n20874, 15639, 15638,  13029, 15547, 2561,  11132, 5880, 14489,  \n25340, 25472, 25603,  6928, 15301, 11586,  6214, 14883, 15360,  \n5231, 5230, 1142,  25477, 25339, 25474,  3778, 15562, 14448,  \n20479, 12054, 15156,  1155, 2416, 14102,  2673, 9780, 13026,  \n24758, 24161, 25337,  6511, 22801, 12863,  20438, 20437, 20372,  \n16155, 15517, 7501,  14933, 3564, 14934,  17350, 17848, 3959,  \n17395, 11932, 16462,  18030, 21157, 14994,  21157, 10263, 14994,  \n19124, 18010, 3633,  24475, 25203, 25338,  25062, 25483, 25478,  \n24475, 24615, 25203,  25479, 25481, 24897,  9577, 19762, 8970,  \n25480, 25606, 25203,  9985, 7678, 17083,  6127, 19812, 4149,  \n25060, 24897, 25481,  8620, 22925, 19523,  18654, 23292, 18655,  \n8584, 22367, 15964,  12367, 10248, 1044,  21421, 16568, 4756,  \n22194, 4134, 12646,  25203, 24618, 25342,  10310, 4907, 15642,  \n17159, 11180, 16750,  25607, 25608, 25056,  22676, 3253, 18893,  \n11545, 11544, 18141,  11378, 9225, 4679,  25485, 25342, 24618,  \n3296, 9289, 15122,  4143, 10033, 14444,  18280, 19701, 15886,  \n25061, 25607, 25056,  707, 9001, 14762,  1409, 12649, 15729,  \n24254, 22240, 7658,  6135, 19304, 15970,  25482, 25345, 25341,  \n8690, 8691, 3634,  15605, 9812, 10379,  24907, 25347, 25484,  \n15261, 18604, 5012,  25486, 25204, 25345,  1263, 14688, 1264,  \n11874, 21564, 21201,  3699, 3146, 10232,  24905, 25346, 25061,  \n14796, 1013, 18409,  8712, 7893, 16864,  722, 15688, 723,  \n25347, 25207, 25488,  1306, 966, 9889,  24617, 24904, 25067,  \n25348, 25610, 25613,  24909, 24625, 25611,  2954, 19631, 7275,  \n10316, 19141, 18436,  8392, 17346, 7620,  24625, 25212, 25489,  \n17872, 20659, 21969,  16764, 3532, 17012,  7984, 7558, 10344,  \n25208, 25613, 25614,  4476, 4758, 16909,  12022, 12193, 11457,  \n17324, 4748, 10761,  17200, 19103, 18558,  12816, 936, 937,  \n14174, 6322, 3698,  20570, 20384, 18966,  10083, 13359, 14319,  \n9822, 14029, 8051,  6323, 11340, 6324,  14171, 402, 9135,  \n25350, 25615, 25618,  19928, 11340, 6323,  15840, 11441, 11856,  \n13224, 10878, 18899,  1033, 3529, 3530,  13282, 12137, 17904,  \n21421, 22249, 16568,  19598, 17296, 7614,  24912, 25491, 25616,  \n3031, 20259, 3032,  1969, 19015, 2378,  10812, 3767, 13367,  \n24912, 24913, 25491,  8797, 2321, 14451,  12047, 12046, 10492,  \n7735, 5346, 10957,  13704, 19642, 19641,  982, 9385, 3579,  \n8051, 8050, 20428,  25071, 25354, 25352,  2574, 11145, 12444,  \n666, 19384, 710,  25216, 25493, 25494,  25359, 24914, 25075,  \n25619, 25077, 25356,  4411, 1159, 4412,  13639, 13638, 6930,  \n17044, 8345, 17045,  25218, 25357, 25621,  17336, 18703, 6396,  \n10155, 4437, 8973,  529, 13071, 13072,  8371, 18950, 8370,  \n9304, 1250, 6312,  25621, 25495, 25218,  25219, 24488, 25622,  \n25080, 25360, 25495,  1622, 4352, 18595,  25080, 25495, 25220,  \n7157, 5921, 3615,  12259, 14442, 6097,  25623, 25215, 25362,  \n15589, 391, 4660,  15861, 22164, 12273,  25361, 25217, 24922,  \n7209, 21893, 23194,  6925, 13866, 13865,  7338, 19633, 14816,  \n2761, 21338, 21667,  9259, 9258, 14437,  2326, 12225, 3517,  \n14012, 991, 9330,  2288, 18235, 6946,  8082, 2027, 2026,  \n9261, 483, 4730,  21574, 12912, 4930,  25624, 25362, 25625,  \n24955, 22031, 6257,  16481, 9967, 1124,  25362, 25084, 25625,  \n25083, 25366, 25626,  9435, 22293, 13498,  12736, 16969, 17014,  \n14651, 17771, 23360,  25627, 13510, 18440,  25498, 24788, 24787,  \n17857, 22022, 9361,  508, 509, 9807,  8300, 13261, 17558,  \n837, 2069, 9089,  24790, 24497, 25368,  5842, 18617, 11051,  \n24384, 8749, 2077,  4044, 4043, 5357,  24789, 24646, 25370,  \n14860, 12119, 6065,  4622, 12220, 9405,  12083, 13340, 14419,  \n3251, 18419, 18622,  24646, 24791, 25501,  18243, 15633, 2601,  \n2535, 15082, 23139,  25225, 25502, 25628,  4355, 16721, 22962,  \n9468, 20950, 5858,  8726, 5812, 4920,  24344, 24791, 24935,  \n25373, 25225, 25628,  3319, 20940, 14181,  9055, 948, 5468,  \n10005, 11058, 14470,  25226, 25229, 25629,  25629, 25631, 25630,  \n25503, 25504, 24793,  25504, 24940, 24793,  8120, 18350, 2506,  \n15844, 17078, 1145,  8249, 16055, 6828,  8594, 7809, 16590,  \n25229, 25631, 25629,  14550, 5534, 5533,  18256, 22597, 25634,  \n14180, 11317, 9704,  25632, 25630, 25631,  3495, 3494, 9894,  \n10948, 13961, 5485,  11879, 22296, 11537,  21936, 17144, 17126,  \n21229, 7332, 4100,  19539, 17934, 17635,  25636, 25631, 25229,  \n1047, 10271, 6246,  25635, 25632, 25631,  10182, 19667, 10900,  \n24940, 25506, 25230,  25228, 24941, 25637,  25636, 25229, 25377,  \n17635, 17464, 12936,  25631, 25636, 25635,  24794, 25092, 25378,  \n18625, 20146, 2711,  6577, 18583, 13151,  20217, 6003, 9863,  \n24198, 25233, 25508,  13618, 23048, 22129,  948, 11655, 5468,  \n24944, 24198, 25507,  21962, 2024, 4909,  17338, 13014, 4049,  \n24947, 25095, 25512,  25509, 25511, 25235,  1028, 5951, 20597,  \n16107, 15886, 15626,  21373, 2434, 2435,  25638, 25237, 24948,  \n25380, 24949, 25513,  14968, 14969, 22966,  12495, 9302, 17527,  \n11032, 8234, 11427,  13256, 20041, 3375,  15713, 1057, 2554,  \n16799, 10807, 7200,  25639, 25238, 25098,  1158, 20059, 11270,  \n25639, 25098, 24950,  24950, 25382, 25384,  21039, 12933, 9238,  \n24949, 25097, 25513,  25238, 25759, 25099,  6160, 17127, 9466,  \n10327, 17732, 10756,  7170, 7169, 5123,  11093, 20186, 14450,  \n19988, 1943, 1944,  9222, 9223, 14983,  18729, 16228, 5491,  \n25641, 25640, 25513,  13337, 17330, 1510,  25642, 25513, 24951,  \n7618, 2405, 12640,  25239, 25762, 25643,  25642, 24951, 25240,  \n25101, 25239, 25514,  11954, 19886, 17729,  25644, 25388, 25386,  \n25386, 25388, 24956,  15632, 13023, 11328,  25645, 25241, 24952,  \n22336, 1832, 14773,  8163, 7311, 12937,  25645, 24952, 25102,  \n2892, 6028, 3168,  16953, 6894, 8514,  16378, 3530, 5239,  \n25102, 24660, 25645,  7352, 12769, 21180,  12911, 11858, 7189,  \n244, 14242, 12692,  7710, 4591, 15452,  6602, 6601, 11309,  \n22869, 17241, 12943,  10642, 1633, 21677,  25392, 25391, 25648,  \n15721, 12130, 19145,  5111, 7080, 1716,  25244, 25516, 24959,  \n11900, 11901, 20426,  5287, 12450, 18196,  4740, 7709, 13260,  \n12502, 7457, 7456,  6965, 4332, 12833,  2804, 11029, 7793,  \n25517, 25245, 25649,  25650, 25244, 25246,  18797, 21256, 7568,  \n25246, 24963, 25104,  6236, 18444, 21601,  24963, 24663, 25104,  \n25246, 25104, 25923,  4139, 4921, 20329,  25517, 25651, 25518,  \n7922, 16869, 7234,  25518, 25520, 25248,  19131, 791, 13634,  \n25651, 25654, 25518,  25654, 25520, 25518,  13489, 15932, 17249,  \n304, 20571, 7673,  25520, 25521, 25248,  8591, 8592, 4090,  \n3270, 8173, 8662,  25394, 25655, 24964,  25521, 25656, 25393,  \n6110, 8926, 10775,  25393, 25656, 25657,  25393, 25657, 24809,  \n14635, 25658, 4888,  25523, 24809, 25657,  4604, 10983, 21204,  \n15389, 294, 295,  12835, 13465, 4725,  3598, 3600, 5248,  \n25523, 24966, 25105,  25523, 25250, 24966,  25396, 25659, 25524,  \n9793, 24917, 24931,  16997, 17335, 1828,  7170, 9679, 21058,  \n16585, 21167, 16584,  25397, 24666, 25251,  25397, 25659, 25396,  \n314, 10390, 3536,  10907, 4361, 16047,  26082, 25660, 25252,  \n17083, 16313, 9985,  10861, 4085, 15314,  11524, 21575, 584,  \n20207, 5646, 15351,  15938, 991, 1040,  6764, 11436, 16177,  \n5968, 14077, 15820,  14127, 599, 14128,  26415, 25525, 25661,  \n15045, 3535, 8927,  2665, 17894, 14578,  25255, 25662, 25256,  \n25401, 24969, 24971,  25256, 25254, 25255,  12559, 10729, 8737,  \n14491, 6582, 14834,  25256, 25776, 25526,  2253, 18248, 4392,  \n20638, 14243, 4894,  1094, 5316, 17948,  18459, 11711, 12270,  \n25111, 25526, 25527,  19161, 12421, 11173,  11405, 8028, 7295,  \n16111, 7990, 8858,  8048, 18888, 7445,  25403, 25663, 25112,  \n18082, 5208, 457,  7030, 733, 735,  25528, 25663, 25403,  \n7551, 24752, 18612,  11861, 1117, 5273,  1553, 1554, 13592,  \n5607, 8666, 14555,  25528, 25403, 25404,  14107, 13623, 8388,  \n25528, 25404, 25665,  20500, 11855, 15406,  24133, 22355, 5048,  \n5499, 19574, 17867,  23139, 15082, 13308,  4264, 20683, 3194,  \n25936, 25258, 25114,  2955, 2757, 9436,  22671, 356, 16982,  \n25665, 25404, 24977,  15063, 15981, 613,  12795, 14824, 13877,  \n19965, 18689, 20199,  13740, 5106, 5639,  16603, 1178, 13154,  \n14008, 12108, 12107,  15531, 15530, 14914,  13545, 9183, 7564,  \n25262, 25263, 25536,  25536, 25263, 25265,  25666, 25408, 25536,  \n708, 13673, 17016,  17478, 20831, 12979,  25123, 25408, 25539,  \n25666, 25667, 25539,  25668, 25538, 25409,  25669, 25670, 25667,  \n25409, 25540, 25668,  12121, 15209, 6720,  6537, 1413, 1414,  \n7484, 10983, 9457,  5964, 21970, 9109,  23267, 15109, 9755,  \n25544, 25270, 25413,  11501, 11500, 13615,  3866, 16030, 6694,  \n19625, 10985, 9069,  25411, 25412, 25541,  7394, 11818, 2579,  \n8541, 18516, 22274,  25415, 25672, 25414,  5003, 13284, 15703,  \n17068, 13918, 17069,  4462, 23629, 16026,  15490, 15491, 7401,  \n25127, 25268, 25412,  22263, 6486, 25466,  22263, 12028, 6486,  \n24074, 24075, 25129,  25129, 24075, 25133,  25674, 25675, 25412,  \n25411, 25674, 25412,  23392, 9951, 12857,  22349, 15220, 10625,  \n25416, 25141, 25547,  19030, 8615, 1155,  17371, 17983, 17372,  \n5089, 19511, 5088,  15204, 18363, 11477,  25275, 25140, 24838,  \n4875, 10839, 4876,  8035, 21885, 5872,  25550, 25142, 24998,  \n6154, 22876, 2216,  24693, 25676, 25548,  14147, 18988, 14737,  \n8879, 10146, 4782,  25142, 25275, 24838,  1341, 2558, 9349,  \n9449, 15406, 13542,  3228, 24191, 7000,  15572, 13837, 2976,  \n25552, 25279, 25553,  8585, 17094, 8586,  25679, 25418, 25675,  \n25675, 25418, 25127,  13213, 14542, 6902,  13802, 11074, 3487,  \n20532, 13221, 14624,  25554, 25419, 25274,  18932, 11150, 3786,  \n25554, 25551, 25677,  21203, 19239, 12848,  5360, 1349, 22189,  \n24241, 17983, 20295,  25137, 26114, 25417,  14333, 10194, 22833,  \n25554, 25677, 25421,  15773, 2046, 11555,  18335, 21543, 6616,  \n16452, 12785, 13233,  3273, 20594, 17292,  25680, 4157, 19974,  \n22426, 2637, 12415,  5161, 5160, 21721,  9063, 9814, 3132,  \n6838, 12052, 9974,  2697, 15882, 20209,  2899, 2702, 11241,  \n12951, 22080, 12952,  11395, 14858, 13079,  13548, 20411, 11518,  \n17713, 17714, 22062,  7395, 3416, 7393,  9195, 6046, 13990,  \n25002, 25278, 25429,  12596, 18438, 20717,  17066, 23947, 18280,  \n20016, 2021, 20612,  6714, 6922, 7448,  4646, 21160, 21593,  \n6627, 11984, 18985,  3370, 18645, 4565,  29656, 13500, 22246,  \n7572, 4428, 9261,  22339, 5542, 5543,  16699, 9116, 4423,  \n7654, 6038, 5554,  16047, 10908, 10907,  8936, 17370, 17656,  \n6216, 3351, 18155,  17430, 13884, 7891,  12382, 9700, 12383,  \n24700, 25277, 25681,  3083, 18902, 14663,  25426, 25007, 25427,  \n6148, 8810, 3014,  12490, 8614, 19184,  26114, 24701, 25144,  \n10167, 16878, 5694,  25421, 25564, 25428,  19284, 6052, 15405,  \n11430, 19324, 11429,  25281, 24844, 25682,  11944, 11943, 17893,  \n3628, 13204, 21300,  14881, 2774, 20124,  25560, 24546, 23944,  \n25560, 23944, 24705,  25144, 24544, 25430,  24709, 25563, 25150,  \n9504, 11005, 2569,  11975, 5635, 3566,  1629, 7281, 1630,  \n8409, 10254, 13003,  25683, 25430, 24848,  20929, 9657, 4372,  \n22353, 11278, 15108,  3832, 1121, 1120,  9409, 13200, 22236,  \n23847, 20917, 6422,  11402, 7480, 11403,  9877, 5232, 14545,  \n25287, 25431, 25289,  7668, 22058, 16834,  5556, 5557, 18582,  \n11695, 17917, 19391,  5069, 9566, 12422,  18773, 5652, 4613,  \n4778, 17863, 18258,  25685, 25156, 25433,  3833, 21416, 8635,  \n1565, 11674, 15856,  25567, 25566, 25684,  25567, 25292, 25566,  \n11027, 1485, 4267,  10803, 16144, 7432,  25567, 25686, 25568,  \n6088, 1239, 2761,  3181, 5825, 7487,  5791, 8565, 8564,  \n6292, 14334, 8483,  2686, 1858, 2687,  25687, 25568, 25686,  \n25013, 25688, 25569,  25571, 25572, 25570,  25571, 25570, 25296,  \n566, 13095, 13096,  25013, 25163, 25688,  9787, 17781, 9961,  \n24862, 25435, 25152,  11980, 19882, 14709,  9224, 4305, 5093,  \n13943, 3531, 9233,  6348, 12526, 3654,  7624, 8764, 7623,  \n22525, 22471, 20074,  17213, 6980, 16220,  25689, 25163, 25162,  \n23190, 21327, 13125,  25298, 25573, 25165,  2233, 14720, 7108,  \n20386, 17588, 9738,  19618, 4539, 18956,  25436, 25439, 25166,  \n25162, 24570, 25690,  10874, 8432, 22719,  25691, 25167, 25022,  \n17771, 14651, 24419,  6584, 6585, 18474,  25690, 24570, 25300,  \n17254, 4714, 11929,  2158, 12957, 15102,  8617, 1019, 2872,  \n7029, 2935, 21775,  25023, 25692, 25300,  17742, 21547, 22640,  \n25168, 25693, 25023,  18112, 13005, 13004,  8911, 8157, 21824,  \n7726, 24090, 9104,  2755, 17695, 8538,  25694, 25301, 25025,  \n5014, 6810, 14415,  6455, 6454, 17131,  12509, 16565, 15434,  \n15547, 15548, 1257,  16551, 3629, 11099,  25170, 24448, 25169,  \n16406, 22267, 14149,  11917, 15000, 19045,  10901, 12260, 2068,  \n8527, 11272, 5364,  5074, 21011, 5138,  25446, 24867, 25302,  \n9431, 4448, 13731,  11874, 20501, 4274,  25576, 25174, 25580,  \n24871, 25446, 25578,  8651, 2590, 2591,  14772, 17822, 15415,  \n25304, 25579, 25305,  5068, 17152, 20421,  2291, 15643, 7060,  \n837, 19473, 20895,  25306, 25582, 25171,  17221, 15560, 15561,  \n19443, 2622, 18869,  15249, 1330, 1331,  25035, 24871, 25578,  \n1639, 15416, 1423,  8489, 5890, 22585,  25308, 25307, 25696,  \n18472, 18742, 13407,  21106, 15133, 9220,  1147, 5893, 3140,  \n17135, 13236, 23267,  12011, 2038, 13562,  25695, 25309, 25177,  \n9114, 21666, 12676,  11665, 18091, 5225,  7023, 22549, 25698,  \n4071, 16623, 7931,  12742, 12685, 15111,  25452, 25035, 25699,  \n4591, 12441, 6122,  21989, 840, 1691,  13078, 11899, 7463,  \n10568, 12731, 1748,  8650, 24236, 19089,  2042, 12382, 12383,  \n26133, 25700, 25311,  25312, 25034, 25315,  14785, 17329, 8530,  \n25315, 25039, 25178,  7427, 17179, 20506,  3925, 2115, 3926,  \n11438, 15596, 15258,  6627, 18985, 6628,  17271, 6686, 15537,  \n5878, 16283, 7943,  25284, 3812, 20486,  21318, 1761, 20994,  \n8421, 10211, 7284,  17065, 10894, 2785,  25042, 24456, 25179,  \n11566, 10275, 6141,  10048, 4042, 7622,  16144, 1214, 15259,  \n8729, 15423, 15422,  20239, 7575, 2050,  10708, 18674, 17263,  \n20635, 25549, 5268,  7465, 5914, 6448,  11864, 21758, 24086,  \n25702, 25178, 24878,  4683, 3568, 18551,  13657, 14668, 19603,  \n20120, 16666, 13566,  9906, 3485, 16510,  25702, 24878, 25321,  \n25318, 24737, 25180,  25041, 25319, 25585,  12620, 10143, 15498,  \n3365, 18945, 3366,  19882, 4673, 14708,  15680, 20506, 11074,  \n12598, 9823, 25424,  25043, 25317, 25586,  3532, 1519, 3533,  \n4559, 15684, 19177,  4046, 21796, 17639,  25586, 24881, 25043,  \n6402, 6146, 6403,  22702, 11161, 11301,  14359, 16145, 14991,  \n24457, 24880, 25587,  25180, 25455, 25705,  10924, 10925, 19958,  \n24599, 24131, 25324,  13089, 13088, 6895,  9264, 9371, 21433,  \n16203, 4482, 4481,  531, 4216, 15120,  11926, 20283, 13196,  \n19560, 9972, 10828,  9721, 2716, 22385,  14210, 6265, 17252,  \n20470, 20469, 18018,  5927, 10971, 5926,  5180, 511, 5181,  \n2874, 6078, 2873,  7882, 16505, 21567,  9559, 8489, 22585,  \n9705, 21425, 4973,  8655, 8657, 12809,  25182, 25326, 25708,  \n17226, 18297, 15921,  14298, 14297, 12436,  15736, 17477, 15735,  \n1904, 2035, 6980,  5157, 14878, 2305,  14220, 1277, 23938,  \n8087, 11527, 8086,  4845, 14047, 14048,  3886, 9076, 9534,  \n20952, 4558, 19205,  23300, 17842, 2239,  1465, 22655, 13180,  \n24745, 25328, 25463,  25592, 25709, 25185,  11510, 2760, 2107,  \n3617, 8542, 9809,  16826, 4770, 14506,  5858, 12115, 5857,  \n4660, 21387, 21521,  3919, 3918, 20223,  8712, 1719, 1718,  \n25463, 25710, 25331,  25711, 25188, 25464,  5837, 9159, 20596,  \n5986, 20144, 22295,  7458, 23824, 1737,  19383, 14819, 23580,  \n24746, 24744, 25331,  17115, 12362, 12694,  1287, 3559, 3558,  \n9247, 17445, 17446,  4973, 3954, 19289,  24606, 25465, 25330,  \n25713, 4649, 4650,  2696, 8139, 8125,  25190, 24748, 25595,  \n800, 802, 16608,  20343, 16918, 13898,  4014, 2011, 14231,  \n5939, 8020, 2681,  825, 7534, 4788,  2834, 11737, 4858,  \n24391, 1558, 1557,  3835, 13210, 3836,  8656, 16099, 18242,  \n25192, 26301, 24889,  3005, 24596, 5326,  7201, 8558, 5544,  \n25470, 25839, 25191,  12851, 18020, 973,  25469, 25193, 25051,  \n25191, 24890, 25470,  3672, 9487, 9488,  18123, 23302, 2651,  \n14122, 3641, 12179,  14844, 8733, 16824,  25715, 25470, 25716,  \n19978, 2277, 23058,  18023, 12325, 292,  12221, 14519, 4138,  \n17190, 10465, 17189,  9051, 10088, 610,  12645, 14120, 9660,  \n3848, 3849, 10945,  4487, 7103, 6618,  25473, 25717, 25599,  \n24891, 25719, 24892,  8733, 12072, 1701,  13163, 7550, 9227,  \n25599, 25597, 25473,  25471, 25196, 24894,  10818, 7960, 331,  \n15143, 8048, 2611,  25602, 25720, 25473,  25052, 24892, 25600,  \n3506, 9091, 365,  5143, 6045, 18115,  9682, 11538, 9433,  \n25718, 25477, 25598,  2360, 6727, 18260,  16221, 11972, 8321,  \n16192, 2662, 13146,  13345, 13346, 10038,  7530, 15953, 1305,  \n8488, 20474, 17747,  3974, 12461, 9969,  25598, 25477, 25474,  \n20812, 16234, 3965,  7826, 5893, 5892,  13906, 8679, 19128,  \n20407, 21591, 2078,  19544, 6383, 6100,  11408, 20894, 19022,  \n25602, 25478, 25723,  6369, 18025, 19226,  11585, 3895, 14767,  \n4294, 21796, 14898,  20156, 22018, 14434,  25724, 25054, 25338,  \n18535, 21093, 5030,  25477, 25725, 25605,  25723, 25478, 25483,  \n24161, 24613, 25337,  4220, 12660, 5000,  25604, 25053, 25336,  \n4290, 7865, 17062,  25477, 25605, 25476,  19981, 10786, 1266,  \n9229, 9956, 3692,  3414, 17505, 14351,  14987, 7984, 10344,  \n12052, 2708, 9974,  25055, 25479, 24896,  12428, 22007, 12962,  \n25608, 25604, 25336,  18861, 18766, 7823,  25605, 25482, 25476,  \n7780, 20366, 8785,  15041, 25466, 6486,  9087, 17933, 8992,  \n21882, 15556, 18642,  24902, 25060, 25481,  14706, 3402, 12616,  \n10889, 10827, 3104,  5623, 10593, 21749,  8310, 3266, 6377,  \n1314, 18584, 17540,  584, 21575, 7545,  3629, 3630, 11099,  \n24759, 24758, 25337,  10429, 15483, 17426,  7115, 11574, 7116,  \n4715, 4714, 6696,  11167, 18954, 4668,  1415, 6356, 2986,  \n25345, 25482, 25609,  25061, 25346, 25607,  10619, 17030, 12210,  \n12084, 11771, 18343,  6829, 21728, 6830,  25609, 25486, 25345,  \n7446, 5358, 20454,  17809, 17137, 1364,  12468, 9747, 10730,  \n21849, 12448, 12983,  25612, 25346, 24905,  25206, 25486, 25610,  \n25348, 25206, 25610,  24905, 24909, 25611,  25067, 24904, 25487,  \n24905, 25611, 25612,  14727, 5353, 9028,  747, 18848, 11841,  \n25487, 25210, 25067,  9052, 9355, 1167,  24625, 25489, 25611,  \n13700, 18553, 1077,  4898, 4897, 13458,  9080, 15087, 15482,  \n11136, 4291, 7273,  12383, 9700, 1974,  2546, 8376, 3111,  \n3968, 21005, 3949,  12719, 20147, 20146,  20516, 15396, 9464,  \n25350, 25208, 25615,  4616, 10060, 10326,  16166, 7184, 3690,  \n11717, 2242, 4949,  25212, 24912, 25616,  25350, 25618, 25351,  \n25070, 25071, 25352,  19139, 15305, 15680,  9287, 5661, 12401,  \n9896, 9279, 15563,  12623, 8916, 17168,  16571, 2748, 9391,  \n8752, 4617, 10951,  24913, 25729, 25491,  25355, 25351, 25618,  \n7739, 542, 13887,  5740, 22379, 5739,  25074, 25072, 25492,  \n25353, 25617, 24913,  2014, 4004, 9923,  25353, 24913, 25214,  \n7010, 7009, 12334,  8267, 16625, 8793,  25073, 25355, 25493,  \n13859, 3278, 11353,  25215, 25620, 25354,  14849, 3528, 16741,  \n25214, 24914, 25359,  8012, 3823, 18354,  5622, 21349, 19472,  \n25357, 25731, 25621,  25731, 25730, 25621,  25357, 25077, 25358,  \n25358, 25077, 25619,  10566, 12616, 10567,  15714, 12065, 23938,  \n25621, 25732, 25495,  13552, 5448, 2784,  720, 22397, 1389,  \n18264, 14540, 14575,  25733, 25495, 25732,  5029, 18535, 5030,  \n25623, 25620, 25215,  24488, 25074, 25622,  7232, 12380, 18227,  \n25734, 25220, 25733,  16276, 5109, 5108,  25220, 25495, 25733,  \n19682, 3819, 2487,  25220, 25734, 25496,  25496, 24923, 25220,  \n25219, 25622, 24920,  5787, 3569, 4548,  1327, 7783, 7784,  \n24462, 13596, 14121,  6673, 20043, 14371,  15714, 9132, 16417,  \n24924, 25737, 25361,  3215, 3142, 18780,  13210, 11515, 18790,  \n1486, 11165, 2174,  20676, 18831, 6471,  17378, 5458, 10126,  \n3228, 3230, 24191,  11106, 21914, 12414,  2062, 21143, 16211,  \n8423, 2528, 2530,  5999, 2179, 22615,  19563, 7445, 18888,  \n25624, 25625, 25740,  962, 961, 21754,  4161, 1988, 17124,  \n16279, 6381, 1345,  19869, 5258, 17728,  25084, 25226, 25625,  \n25625, 25741, 25740,  6357, 5044, 5043,  10433, 2681, 5190,  \n9766, 13468, 9765,  6956, 7937, 4915,  11707, 11995, 10805,  \n15126, 9461, 2450,  9808, 1237, 1236,  25743, 25502, 25087,  \n9793, 21018, 9654,  3896, 2627, 3004,  7210, 9191, 15292,  \n25625, 25226, 25629,  25625, 25629, 25742,  4738, 4600, 17080,  \n25630, 25744, 25629,  3380, 15280, 8988,  12415, 2637, 535,  \n12401, 16266, 15381,  20252, 13158, 11437,  11333, 21693, 14236,  \n25373, 25628, 25745,  9332, 9331, 11135,  15559, 4628, 15052,  \n14896, 1507, 15781,  25744, 25630, 25632,  25744, 25632, 25746,  \n668, 5322, 21195,  7466, 21940, 20116,  25747, 25746, 25632,  \n14447, 10982, 20680,  15585, 17767, 16376,  20092, 8454, 9036,  \n24938, 25633, 24791,  25748, 25632, 25635,  9934, 10982, 14447,  \n4434, 6543, 5953,  18041, 17023, 18042,  14965, 15471, 14964,  \n15227, 14811, 13780,  11600, 19708, 21217,  11860, 5406, 18772,  \n15180, 19972, 18605,  3678, 9253, 449,  24941, 25378, 25637,  \n15907, 11575, 11574,  20562, 2792, 4243,  14232, 1967, 17486,  \n932, 7662, 9541,  383, 2016, 15301,  25635, 25749, 25748,  \n16231, 15045, 9394,  19849, 8195, 8196,  25093, 25752, 25094,  \n7418, 7419, 14126,  24504, 25375, 25750,  25752, 25510, 24946,  \n24946, 25094, 25752,  17265, 8791, 8792,  2946, 8249, 19216,  \n21876, 10307, 17750,  25754, 25749, 25635,  7886, 23167, 17038,  \n9835, 4283, 13192,  25234, 24796, 25507,  15000, 11917, 8421,  \n16051, 2248, 17407,  25511, 25509, 25753,  16871, 7059, 1532,  \n5292, 933, 6953,  25511, 25755, 25512,  25758, 25377, 25380,  \n25636, 25377, 25758,  19541, 29626, 21133,  24948, 25236, 25638,  \n25638, 25757, 25237,  4870, 1722, 22704,  25384, 25383, 25757,  \n16514, 690, 16214,  25757, 25383, 25237,  10928, 5836, 5838,  \n5079, 10471, 11753,  8628, 17857, 14429,  6652, 4405, 14721,  \n25384, 25382, 25383,  25380, 25513, 25758,  25640, 25758, 25513,  \n6544, 1633, 6034,  13855, 15357, 775,  19354, 11900, 20426,  \n7618, 16058, 12437,  25385, 25099, 25759,  18040, 15789, 5172,  \n23410, 13676, 18054,  25100, 25385, 25762,  2747, 9814, 18868,  \n12103, 12104, 11355,  10105, 6629, 2399,  22299, 5786, 13373,  \n25641, 25760, 25640,  1791, 17263, 17924,  25513, 25642, 25641,  \n25514, 25239, 25643,  25101, 25514, 25386,  10807, 16799, 14190,  \n20578, 13555, 13556,  9083, 9085, 9124,  9667, 19269, 7617,  \n25646, 25515, 25388,  25390, 25515, 25764,  483, 1726, 11712,  \n19242, 2569, 2568,  25391, 25390, 25647,  7662, 20583, 9541,  \n7227, 7226, 14062,  12640, 6997, 16058,  25391, 25647, 25648,  \n9021, 15333, 15334,  25243, 25392, 25648,  14669, 4801, 14132,  \n25245, 25243, 25922,  19830, 22272, 15252,  16021, 12379, 6543,  \n20294, 17372, 20295,  9465, 12359, 3063,  25517, 25649, 25765,  \n1006, 19326, 8852,  25104, 24964, 25655,  25651, 25766, 25654,  \n20219, 1908, 5252,  19638, 584, 12454,  25769, 24965, 25395,  \n25394, 24965, 25769,  11880, 11879, 11537,  12803, 21894, 343,  \n5204, 2442, 2443,  25659, 25770, 25524,  25770, 25395, 25524,  \n6286, 9979, 21717,  13175, 1051, 1052,  25250, 25771, 25251,  \n25251, 25659, 25397,  25251, 25771, 25659,  13411, 3626, 2332,  \n2095, 23491, 15722,  14478, 8136, 14611,  25252, 25399, 25772,  \n10498, 18309, 10497,  9226, 2535, 2536,  25773, 25399, 25400,  \n12530, 11852, 11423,  3652, 3311, 19464,  25400, 25525, 25773,  \n25525, 25400, 25108,  10261, 6679, 11761,  25253, 25775, 25255,  \n25398, 25774, 25253,  11056, 1007, 9484,  3892, 16480, 10268,  \n12591, 9556, 2820,  22081, 10239, 11946,  8231, 11795, 9245,  \n25662, 25255, 25775,  12678, 12722, 8071,  12571, 14461, 9726,  \n25525, 25401, 25661,  25777, 25401, 24971,  25256, 25662, 25776,  \n3268, 20028, 9668,  1778, 8698, 12376,  5678, 8213, 4520,  \n18657, 12419, 1371,  25527, 25526, 25778,  3049, 2076, 21591,  \n25779, 25527, 25778,  8639, 5237, 22267,  25405, 25527, 25779,  \n11639, 10300, 8703,  11250, 19634, 13949,  763, 14538, 3450,  \n2858, 2403, 9669,  13623, 10167, 8388,  11029, 9769, 7745,  \n25405, 25664, 25114,  8907, 5830, 10088,  11078, 22124, 8335,  \n20743, 20237, 16996,  1429, 12104, 12103,  25257, 25258, 25531,  \n22889, 12282, 2427,  24977, 25530, 25665,  2427, 8881, 2222,  \n25257, 25531, 24979,  25406, 25780, 25781,  24981, 25781, 25530,  \n25406, 25781, 24981,  3424, 7433, 3719,  9651, 7926, 7925,  \n25118, 24979, 25532,  25118, 25532, 25782,  25783, 25407, 25782,  \n25534, 25407, 25783,  11552, 6221, 17928,  25533, 25784, 25780,  \n13691, 11984, 18331,  19209, 19421, 13897,  25533, 25780, 25406,  \n25534, 25784, 25535,  25535, 25784, 25533,  5124, 11277, 14927,  \n25785, 25536, 25265,  25265, 25538, 25786,  25666, 25539, 25408,  \n11400, 12880, 4174,  11459, 21911, 11041,  18832, 18833, 3090,  \n25787, 25785, 25786,  25786, 25538, 25668,  25542, 25541, 25539,  \n25541, 25268, 25539,  25790, 25786, 25788,  5085, 6158, 9466,  \n11246, 15047, 7596,  5797, 15480, 15479,  4408, 15392, 13722,  \n25789, 25269, 25544,  21188, 19070, 14533,  8938, 8939, 4407,  \n25788, 25668, 25540,  961, 18715, 9348,  25790, 25540, 25543,  \n25790, 25788, 25540,  25544, 25413, 25792,  6217, 19505, 11175,  \n25411, 25541, 25542,  25790, 25414, 25672,  7402, 7946, 2531,  \n25792, 25413, 25271,  25271, 25671, 25792,  25412, 25268, 25541,  \n25543, 25414, 25790,  6613, 2223, 6612,  28350, 13538, 9240,  \n11895, 5426, 13276,  10241, 13865, 9153,  4067, 11114, 11986,  \n13412, 9350, 3710,  19036, 9524, 1270,  25794, 25275, 25142,  \n21475, 6936, 15981,  25550, 25794, 25142,  12425, 11635, 11605,  \n11770, 20452, 5765,  26249, 25671, 25271,  25675, 25127, 25412,  \n16353, 13506, 1458,  23146, 17493, 12080,  17547, 18359, 1046,  \n25550, 25795, 25794,  22290, 17170, 21680,  17740, 15637, 17840,  \n23901, 4531, 13713,  1735, 11105, 3334,  6019, 4969, 2851,  \n25141, 25555, 25547,  14676, 2229, 3490,  7082, 15474, 17355,  \n12262, 10001, 9741,  15670, 4273, 6199,  15690, 5873, 21202,  \n3504, 16244, 8333,  4359, 6412, 9059,  24694, 13510, 25627,  \n10841, 11547, 6643,  19636, 8739, 1666,  1701, 12297, 8733,  \n21683, 12118, 22451,  25797, 24836, 24696,  16925, 1322, 5137,  \n25551, 25548, 25798,  1317, 15935, 16907,  6260, 20966, 7935,  \n3149, 17362, 20358,  11630, 12957, 2158,  17686, 18889, 20514,  \n7913, 10709, 12417,  3640, 6660, 12179,  18545, 12626, 15289,  \n17540, 6476, 6597,  7559, 7984, 8670,  25679, 24994, 25418,  \n2003, 7209, 23194,  2552, 18461, 16375,  25145, 25006, 25801,  \n5339, 10203, 15871,  25802, 25417, 26114,  17397, 3744, 10839,  \n19374, 13296, 570,  25558, 24994, 25679,  13078, 539, 538,  \n3026, 15044, 21783,  20079, 20133, 15762,  12560, 16743, 16742,  \n2200, 18547, 2201,  292, 19191, 18023,  26113, 25559, 24708,  \n13116, 17297, 19386,  1305, 12494, 881,  25277, 24695, 24994,  \n19027, 13809, 16256,  3433, 3244, 3379,  16834, 22454, 22573,  \n15884, 363, 5275,  15652, 21549, 6840,  19633, 15931, 14816,  \n20018, 7974, 13356,  5154, 7451, 4798,  16413, 21719, 9507,  \n9969, 18673, 6382,  25421, 25803, 25564,  25681, 24705, 24700,  \n2467, 16381, 8934,  6367, 6366, 8845,  5791, 20221, 12464,  \n5890, 16654, 1939,  17667, 8183, 15542,  13447, 14619, 1983,  \n15506, 6504, 9500,  19065, 1754, 20038,  25682, 24844, 25561,  \n25561, 24547, 25282,  24546, 25560, 25282,  16926, 16925, 18480,  \n13610, 10289, 20756,  17772, 19209, 21766,  25285, 25564, 25963,  \n25805, 25150, 25563,  16498, 6534, 7528,  16116, 15222, 12744,  \n21675, 15148, 10780,  6205, 18104, 2091,  25807, 25432, 25152,  \n21826, 12996, 14040,  12174, 12175, 3772,  6181, 6180, 20667,  \n13544, 13543, 16550,  15546, 6058, 7998,  25685, 25809, 25684,  \n6242, 6232, 1638,  25012, 25011, 25808,  14996, 5344, 3412,  \n20411, 15830, 14872,  25809, 25685, 25810,  17211, 586, 2148,  \n2146, 3643, 3004,  25156, 25685, 25566,  25684, 25566, 25685,  \n20713, 18344, 21029,  25686, 25567, 25684,  25433, 25570, 25811,  \n16763, 2622, 3942,  9664, 13131, 11522,  16274, 4819, 7233,  \n15169, 1951, 3265,  25570, 25572, 25811,  6802, 4022, 9468,  \n16515, 7841, 7840,  25160, 25568, 25812,  13048, 562, 1804,  \n14142, 10960, 11082,  2431, 2851, 2430,  516, 19057, 19643,  \n25297, 25160, 25972,  21680, 17170, 17920,  15429, 6540, 10982,  \n474, 14816, 11624,  7799, 7800, 7167,  25573, 25814, 25436,  \n6976, 6977, 12303,  2591, 796, 18579,  25814, 25439, 25436,  \n15683, 9892, 6381,  6703, 6704, 16598,  25162, 25690, 25689,  \n5561, 1360, 1995,  21764, 554, 17348,  25691, 25022, 25439,  \n20456, 18825, 14503,  23539, 9080, 15482,  10771, 17811, 17810,  \n25299, 25024, 25440,  13728, 13729, 16575,  25815, 25690, 25300,  \n2495, 17685, 20514,  6584, 17881, 2518,  3575, 3574, 4849,  \n15549, 17722, 14754,  4233, 14523, 9366,  25692, 25815, 25300,  \n25167, 25816, 24717,  17558, 1097, 8300,  8734, 18257, 18767,  \n1658, 13539, 5084,  16222, 21138, 3781,  22033, 4234, 6302,  \n14541, 10184, 14542,  25693, 25692, 25023,  25025, 24863, 24717,  \n7784, 3366, 20408,  1447, 19355, 9272,  10956, 13986, 8408,  \n14953, 14954, 3868,  8059, 5427, 2402,  1982, 14733, 1983,  \n915, 5244, 14348,  11938, 18394, 18395,  14596, 11587, 9769,  \n2136, 19924, 2135,  3679, 4116, 23742,  22713, 23146, 23748,  \n23336, 16368, 1573,  7592, 3815, 10664,  24577, 25301, 25445,  \n25818, 25575, 25444,  5049, 8918, 21319,  20039, 21229, 22775,  \n14500, 14142, 10163,  21392, 8362, 20734,  23058, 15150, 21969,  \n2277, 15150, 23058,  17638, 13813, 8295,  3586, 12341, 16102,  \n24631, 9471, 940,  7310, 9471, 24631,  17047, 10300, 11639,  \n5146, 386, 19525,  9932, 13339, 2319,  1404, 8621, 18979,  \n20231, 12812, 6693,  12277, 18915, 25376,  25304, 25171, 25447,  \n25820, 25175, 25449,  7811, 7810, 17804,  9722, 5033, 22959,  \n25447, 25171, 25582,  25582, 25306, 25448,  5678, 23572, 8213,  \n25309, 25695, 25580,  25450, 25822, 25448,  16188, 14712, 6465,  \n4084, 1253, 7748,  2650, 5091, 4305,  25451, 25825, 25450,  \n25825, 25822, 25450,  25823, 25308, 25696,  24873, 25824, 25310,  \n1879, 16425, 19027,  20525, 17858, 22560,  25312, 25826, 25451,  \n25311, 24873, 24732,  25697, 24873, 25311,  25308, 25823, 25176,  \n910, 909, 12647,  8270, 668, 669,  2058, 6712, 2057,  \n24876, 24875, 25827,  23529, 17389, 19557,  14066, 16097, 14064,  \n18949, 12691, 11524,  21070, 17533, 9703,  25037, 25318, 26133,  \n21349, 12575, 6445,  10407, 10406, 18149,  10148, 10147, 3176,  \n25037, 24737, 25318,  25829, 25316, 25453,  14570, 18171, 585,  \n12237, 11679, 16015,  25315, 25178, 25583,  7295, 8028, 8029,  \n25702, 25583, 25178,  11330, 12941, 14284,  19037, 12881, 20244,  \n20283, 17190, 2769,  9227, 14851, 2207,  19140, 1943, 13294,  \n8817, 305, 19858,  12302, 23051, 17572,  12802, 12803, 343,  \n3482, 3483, 20825,  7685, 23847, 3068,  20113, 8233, 2764,  \n25322, 25041, 25585,  7757, 12006, 9650,  18089, 9629, 5606,  \n12862, 8863, 15987,  8376, 3112, 3111,  2216, 4367, 6162,  \n9989, 5811, 5810,  21814, 11451, 22836,  2516, 14437, 2517,  \n25705, 25704, 25180,  25117, 23836, 25490,  10432, 14622, 8863,  \n15501, 15500, 16229,  25833, 24880, 25322,  17890, 1648, 16715,  \n12205, 4384, 13899,  19900, 20435, 16660,  2945, 16016, 2333,  \n25834, 25324, 25835,  8461, 14832, 5983,  24882, 24457, 26137,  \n6845, 18943, 5406,  12254, 20195, 696,  25459, 25456, 24883,  \n25707, 25455, 25046,  25326, 25045, 25837,  18938, 12250, 14003,  \n21456, 7883, 11185,  25707, 25046, 25460,  21672, 15619, 7850,  \n7951, 2884, 22871,  12323, 12686, 20392,  5772, 5402, 2961,  \n21190, 4895, 5235,  25459, 24465, 25588,  14471, 6366, 12655,  \n9462, 13834, 1397,  4357, 1251, 1048,  11345, 16844, 13728,  \n17925, 4151, 1366,  15713, 1058, 1057,  16244, 3468, 3469,  \n25708, 25589, 25182,  25327, 24887, 25709,  6756, 4577, 6757,  \n25593, 25183, 25184,  9404, 5555, 17871,  8763, 20262, 18339,  \n25048, 25589, 25591,  9757, 14995, 12527,  25709, 24887, 25185,  \n1064, 6868, 2104,  21636, 15468, 4256,  3499, 5886, 20633,  \n16188, 16187, 14712,  18037, 14683, 14682,  7928, 19349, 8236,  \n4062, 10618, 19873,  18358, 14341, 11898,  9374, 10580, 10581,  \n13631, 10335, 1764,  19043, 10308, 9020,  1785, 11126, 17670,  \n12570, 2385, 19876,  20930, 6653, 16484,  17201, 14378, 4828,  \n25465, 25191, 25839,  805, 3140, 20033,  9388, 18086, 13289,  \n25840, 25595, 25193,  11616, 5602, 1848,  11268, 1381, 2504,  \n7238, 7239, 15960,  25332, 25838, 25050,  3089, 7384, 6891,  \n3293, 5789, 3752,  4182, 23334, 4183,  648, 650, 772,  \n11707, 10805, 7500,  18711, 24723, 23383,  16625, 8702, 10835,  \n15188, 4134, 15212,  15034, 4742, 5408,  17140, 4882, 3773,  \n9809, 8550, 3616,  13165, 13166, 1113,  25841, 25597, 25599,  \n25841, 25598, 25597,  4609, 16593, 4610,  25716, 25470, 25334,  \n25719, 25194, 25842,  10046, 19316, 3713,  25599, 25843, 25841,  \n25844, 25717, 25473,  3235, 798, 799,  24891, 25194, 25719,  \n25841, 25718, 25598,  3353, 12874, 1960,  21283, 18770, 6846,  \n18730, 6117, 13138,  25844, 25473, 25720,  14394, 20837, 19504,  \n25722, 25469, 25196,  7337, 19632, 7338,  11285, 7041, 8696,  \n8011, 8010, 7759,  3939, 20239, 1091,  12469, 5278, 577,  \n25720, 25602, 25721,  9180, 9181, 17622,  14766, 11386, 11385,  \n7404, 2306, 3889,  15109, 2891, 2893,  17422, 2134, 13595,  \n25477, 25718, 25725,  17354, 2780, 12739,  19663, 21047, 4702,  \n2344, 2040, 2318,  10673, 7716, 13788,  18266, 15757, 694,  \n25723, 25721, 25602,  3353, 12087, 20674,  10637, 6343, 9761,  \n18693, 18692, 11287,  5647, 6521, 20114,  2897, 14173, 18582,  \n4939, 21945, 11173,  4237, 4238, 14302,  3665, 14617, 5344,  \n1134, 14139, 9191,  8724, 5664, 5713,  11106, 4548, 21914,  \n22228, 18369, 11852,  20096, 11547, 12589,  3570, 3571, 25848,  \n3900, 21062, 22364,  3579, 9385, 351,  6715, 10976, 6716,  \n18086, 16797, 2412,  10449, 1325, 10448,  9887, 16286, 22479,  \n9288, 12892, 18416,  6549, 1683, 1682,  15796, 15965, 14921,  \n20644, 7864, 10614,  22600, 14361, 18752,  22765, 19732, 10981,  \n25482, 25605, 26010,  25727, 25849, 25484,  18752, 14361, 21292,  \n25849, 25483, 25484,  25203, 25606, 25338,  25608, 25336, 25056,  \n6209, 11748, 6210,  9024, 6310, 17608,  8769, 2962, 2768,  \n12117, 16249, 13043,  23207, 17959, 23235,  25343, 24903, 24902,  \n1734, 1735, 3334,  25727, 25347, 25851,  25727, 25484, 25347,  \n14376, 12250, 9252,  14062, 18894, 14061,  19281, 21842, 14233,  \n1938, 13501, 23170,  17572, 10049, 16708,  2087, 5958, 11263,  \n25486, 25609, 25853,  12950, 22834, 19609,  9174, 2246, 1003,  \n12206, 1043, 14145,  25610, 25486, 25853,  10627, 10628, 15137,  \n25854, 24904, 24759,  10120, 1577, 14587,  6575, 11875, 6576,  \n1313, 11542, 17879,  10770, 3897, 3898,  21220, 8944, 1656,  \n25855, 25613, 25610,  7755, 1032, 10486,  17590, 16726, 16884,  \n8190, 9932, 2318,  9272, 19355, 13087,  15784, 8901, 15785,  \n25615, 25208, 25614,  24628, 25210, 25857,  7392, 15225, 11124,  \n25070, 25352, 25858,  14887, 14886, 2132,  8054, 8055, 2805,  \n25213, 24628, 26023,  25616, 25491, 25729,  25355, 25618, 25859,  \n12285, 1954, 15232,  5687, 23537, 5686,  25729, 24913, 25617,  \n19282, 19281, 17524,  11616, 1848, 1850,  6096, 12258, 6097,  \n3405, 13935, 3484,  755, 15327, 18002,  20904, 17178, 14110,  \n10587, 19973, 10588,  6743, 6325, 16538,  25352, 25354, 25860,  \n16305, 5126, 5125,  25359, 25353, 25214,  2363, 1517, 1792,  \n25863, 25620, 25864,  25862, 25494, 25493,  14106, 5781, 19068,  \n6009, 16465, 6010,  12012, 12011, 13562,  448, 12741, 10548,  \n25865, 25730, 25731,  21996, 6724, 25867,  18685, 16114, 13863,  \n25358, 25866, 25731,  25619, 25866, 25358,  3106, 3105, 10577,  \n25356, 25079, 25494,  17083, 7044, 12667,  25731, 25357, 25358,  \n25620, 25623, 25864,  25074, 26178, 25622,  14574, 8874, 22911,  \n2680, 19837, 6372,  10062, 18822, 12929,  25868, 25733, 25732,  \n25217, 25869, 25359,  5619, 5620, 14641,  25496, 25870, 25871,  \n25735, 25217, 25361,  25622, 25872, 24920,  17910, 20038, 1754,  \n6825, 6824, 4434,  25872, 25364, 24920,  17984, 784, 783,  \n19502, 9911, 19065,  4446, 2305, 20903,  21186, 9221, 13561,  \n21283, 15514, 17313,  7452, 19942, 7764,  14256, 12090, 866,  \n16281, 15306, 5646,  25738, 25624, 25874,  17299, 5334, 18066,  \n14688, 4447, 6513,  25365, 25082, 25739,  20385, 19013, 18853,  \n25874, 25624, 25740,  18657, 359, 12419,  14847, 7170, 21058,  \n6246, 10965, 7975,  15498, 11176, 12620,  24934, 25365, 25739,  \n15292, 11049, 7210,  25368, 24788, 25498,  24934, 25739, 25500,  \n15789, 8821, 13769,  2166, 19322, 6438,  23566, 16475, 6305,  \n12520, 6109, 6108,  26036, 25741, 25876,  25367, 24789, 25370,  \n3882, 3883, 19272,  25741, 25625, 25742,  24790, 25368, 25085,  \n14140, 20073, 2171,  22160, 18785, 17251,  9820, 6258, 6759,  \n14693, 4527, 8357,  3164, 11288, 3408,  19569, 3968, 10350,  \n15139, 12071, 1223,  25370, 24646, 25877,  16740, 14400, 20585,  \n16018, 12435, 12436,  2093, 2094, 4151,  18991, 15095, 2299,  \n5195, 597, 599,  25741, 25742, 25876,  16137, 6633, 12780,  \n6804, 15956, 4694,  5205, 11200, 3858,  25087, 25371, 25743,  \n25744, 25742, 25629,  25744, 25876, 25742,  5623, 3249, 13870,  \n2237, 18031, 5385,  6900, 9550, 5163,  24498, 25085, 25224,  \n5881, 5792, 14877,  6748, 13831, 17931,  2704, 5309, 1461,  \n7107, 1443, 13607,  7290, 20753, 7291,  25878, 25744, 25746,  \n15085, 15811, 8727,  18673, 2594, 6382,  25879, 25746, 25880,  \n20511, 2402, 2403,  15973, 20342, 761,  7454, 2211, 13763,  \n3568, 2990, 8332,  14405, 21594, 13204,  9566, 9565, 12422,  \n25880, 25746, 25747,  25881, 25882, 25880,  4442, 13932, 15832,  \n9427, 5644, 2526,  25881, 25880, 25747,  8461, 5983, 1205,  \n17579, 21555, 5869,  3509, 19201, 12339,  7939, 9702, 709,  \n15067, 20915, 370,  25745, 25505, 25373,  25747, 25748, 25881,  \n25748, 25747, 25632,  25881, 25748, 25883,  11119, 22671, 16982,  \n25884, 25881, 25883,  4751, 7844, 11478,  25883, 25748, 25885,  \n24940, 25886, 25506,  25637, 24938, 25228,  12291, 21402, 811,  \n25594, 10031, 10032,  2497, 6698, 13802,  25752, 25093, 25887,  \n10040, 20192, 18236,  25897, 25885, 25748,  6304, 2883, 2328,  \n8600, 21534, 8251,  9946, 9945, 11325,  7815, 19627, 3283,  \n18214, 12001, 4896,  25375, 25374, 25888,  11383, 7432, 11382,  \n11824, 1370, 11324,  25378, 25092, 25751,  6583, 2160, 2161,  \n6565, 4790, 20315,  22415, 20707, 21331,  25890, 25233, 25750,  \n25233, 24504, 25750,  8826, 938, 10311,  25893, 25092, 25892,  \n25092, 25893, 25751,  25894, 26205, 25753,  14147, 18024, 23450,  \n25509, 25510, 25889,  25507, 24198, 25508,  16924, 8994, 15146,  \n9843, 8255, 7664,  8181, 9994, 1787,  25092, 25379, 25892,  \n25892, 25379, 25891,  1830, 10139, 20168,  25754, 25635, 25636,  \n25754, 25897, 25749,  8775, 15362, 7523,  13723, 12213, 10529,  \n25512, 25755, 25896,  25638, 24947, 25512,  25638, 25236, 24947,  \n673, 15121, 16031,  25636, 25756, 25754,  22958, 13854, 17002,  \n25758, 25756, 25636,  25756, 25898, 25754,  25384, 25757, 25899,  \n25756, 25758, 25900,  7076, 15989, 8128,  25902, 25904, 25384,  \n14423, 14732, 13147,  25384, 25899, 25902,  16556, 18365, 3371,  \n21398, 14165, 15079,  25903, 25639, 25904,  25904, 25639, 25384,  \n25384, 25639, 24950,  2925, 23361, 17771,  7173, 7174, 21297,  \n25758, 25640, 25900,  25898, 25901, 25905,  25903, 25759, 25238,  \n25903, 25238, 25639,  25900, 25760, 25761,  25900, 25640, 25760,  \n5398, 10640, 5399,  25901, 25900, 25761,  25907, 25908, 25906,  \n25906, 25898, 25905,  13763, 3273, 7454,  25906, 25909, 25907,  \n25901, 25761, 25905,  25910, 25909, 25906,  20216, 13713, 19707,  \n2475, 4222, 6012,  25905, 25910, 25906,  9685, 9661, 12662,  \n19830, 10716, 22272,  25910, 25905, 25761,  15133, 15134, 9213,  \n25913, 25911, 25910,  1083, 18199, 20066,  5900, 14812, 6411,  \n11864, 24086, 10584,  8084, 8083, 4146,  25641, 25763, 25760,  \n25760, 25763, 25910,  25761, 25760, 25910,  25912, 25910, 25763,  \n6080, 15595, 6456,  12365, 13768, 12366,  11382, 7432, 14515,  \n25915, 25763, 25641,  25642, 25915, 25641,  15395, 15396, 20516,  \n676, 675, 12909,  516, 515, 19057,  14097, 11504, 12994,  \n25514, 25644, 25386,  3823, 6752, 6753,  12095, 4891, 1157,  \n17579, 13835, 21555,  25916, 25240, 25241,  12241, 15238, 10176,  \n11338, 1027, 11337,  25646, 25388, 25644,  10758, 21726, 18531,  \n11006, 6702, 1810,  25515, 25646, 25917,  13696, 14260, 6104,  \n12186, 12187, 4241,  25515, 25917, 25764,  18773, 21402, 12291,  \n25918, 25390, 25764,  25390, 25918, 25647,  5751, 5716, 13441,  \n25706, 5525, 15740,  3591, 21204, 8921,  8342, 1944, 19140,  \n17384, 14094, 11093,  18212, 15004, 3191,  25920, 25648, 25921,  \n25922, 25648, 25920,  4670, 6326, 4289,  25649, 25245, 25922,  \n15508, 16463, 3899,  2050, 2049, 20240,  20262, 14701, 8641,  \n17072, 7312, 12305,  16322, 14122, 10607,  25650, 25246, 25923,  \n2789, 19382, 18212,  5815, 332, 333,  25517, 25765, 25651,  \n5314, 7551, 13399,  7942, 2972, 659,  1028, 15273, 5951,  \n4706, 6806, 6802,  25766, 25767, 25924,  25766, 25651, 25767,  \n25394, 25925, 25655,  16897, 2803, 7425,  23836, 25117, 22714,  \n3337, 9828, 13159,  7944, 10183, 10184,  820, 7749, 819,  \n9857, 8012, 9858,  1895, 11159, 4224,  1438, 1439, 11474,  \n14030, 15517, 16155,  25927, 25766, 25928,  25768, 25766, 25927,  \n25766, 25768, 25654,  25768, 25520, 25654,  25521, 25520, 25768,  \n25521, 25768, 25656,  22147, 21458, 21930,  2033, 2605, 4373,  \n2083, 2082, 12522,  25926, 26227, 25657,  16621, 5276, 7132,  \n25523, 25929, 25250,  3809, 10596, 21256,  25929, 25771, 25250,  \n17697, 8128, 15989,  3409, 15060, 8696,  16013, 6623, 17244,  \n25774, 25398, 25660,  18688, 7278, 4050,  13240, 7620, 13322,  \n19082, 16584, 14085,  25772, 26082, 25252,  25773, 25772, 25399,  \n25930, 25931, 25773,  3556, 10968, 14009,  8185, 14813, 14814,  \n25775, 25253, 25774,  9190, 9735, 19563,  25525, 25930, 25773,  \n21935, 7397, 7396,  15025, 15636, 3248,  718, 14972, 19158,  \n25775, 25932, 25662,  25930, 25525, 26415,  9833, 15786, 1459,  \n11151, 9046, 2308,  25933, 24971, 25402,  25935, 25933, 25402,  \n21407, 19533, 741,  10232, 694, 16981,  6270, 8997, 14294,  \n17875, 798, 3235,  25112, 25935, 25402,  2617, 11436, 11435,  \n16232, 8549, 7375,  23339, 5255, 6090,  9403, 12220, 839,  \n16008, 21762, 10267,  5537, 13219, 14749,  10777, 1797, 9871,  \n756, 7272, 7631,  1751, 1218, 12761,  17130, 12244, 5559,  \n6500, 6147, 10929,  6253, 2722, 19944,  25114, 25664, 25936,  \n12361, 13814, 481,  25528, 25665, 26091,  17015, 12580, 12659,  \n14146, 4381, 13831,  14176, 14328, 7866,  5245, 10159, 9825,  \n11271, 14322, 7611,  8008, 9060, 12158,  17597, 7981, 7034,  \n6755, 6754, 20482,  17574, 17673, 16168,  12870, 14737, 25267,  \n4291, 21042, 4292,  14411, 11247, 13626,  3817, 11659, 1773,  \n10765, 8818, 17974,  25783, 25784, 25534,  25666, 25536, 25785,  \n25938, 25785, 25787,  25785, 25939, 25667,  25785, 25667, 25666,  \n20042, 3359, 12555,  25785, 25265, 25786,  2441, 13127, 2798,  \n8553, 3597, 16295,  25787, 25786, 25790,  25667, 25542, 25539,  \n25670, 25542, 25667,  25786, 25668, 25788,  16600, 483, 4427,  \n1302, 3980, 362,  17890, 21659, 10437,  2576, 2575, 15672,  \n25789, 25544, 25792,  11368, 8658, 12154,  25673, 24825, 25940,  \n12038, 2737, 18201,  19830, 536, 10716,  3925, 17901, 7686,  \n25670, 25411, 25542,  25791, 25790, 25672,  20851, 508, 15492,  \n8545, 13897, 3408,  15389, 295, 2095,  2651, 5091, 2650,  \n25942, 25793, 25794,  5086, 8761, 6529,  5886, 22397, 20633,  \n21145, 10900, 10903,  13177, 7835, 11010,  13862, 10684, 1417,  \n20324, 22044, 13674,  25138, 8848, 4078,  25944, 25415, 25547,  \n25275, 26252, 25140,  14054, 15995, 19816,  25793, 26252, 25275,  \n8871, 23933, 712,  4946, 3224, 10676,  25943, 25945, 25949,  \n10335, 13632, 20540,  1278, 5322, 17790,  14699, 14569, 9042,  \n21214, 5050, 5051,  25795, 25550, 25552,  8705, 11706, 7957,  \n13633, 18124, 14193,  13228, 13229, 5457,  26107, 25129, 25133,  \n11187, 6380, 5112,  25674, 25411, 25949,  15390, 13093, 13094,  \n24996, 25140, 25799,  25140, 25796, 25799,  1861, 18058, 20101,  \n2026, 6697, 8082,  6618, 1015, 12483,  878, 18995, 19689,  \n15921, 1635, 16327,  25948, 25546, 25128,  8734, 18767, 10359,  \n2831, 14874, 11086,  20087, 13157, 23720,  20394, 10677, 9283,  \n2035, 19619, 16511,  25946, 25271, 25417,  24693, 25546, 25676,  \n12342, 21208, 16301,  21255, 29731, 13560,  25556, 25947, 25555,  \n25951, 25798, 25548,  15544, 10462, 8855,  25953, 25674, 25949,  \n25954, 25953, 25945,  24996, 25799, 25278,  3238, 9216, 2911,  \n25678, 25145, 25801,  16093, 12550, 9030,  1409, 1408, 2999,  \n14459, 12414, 9352,  25679, 25675, 25674,  2305, 12724, 20903,  \n14718, 2235, 7028,  20931, 9239, 6200,  25677, 25551, 25798,  \n26954, 24697, 25139,  25674, 25953, 25679,  6549, 12164, 23182,  \n18030, 10781, 5385,  14052, 13501, 17448,  25677, 25803, 25421,  \n16059, 16058, 20526,  25801, 25006, 25559,  25956, 25679, 25953,  \n25956, 25558, 25679,  9352, 12414, 21914,  10316, 10421, 11787,  \n8765, 4649, 12726,  933, 5291, 934,  1096, 1095, 6197,  \n14789, 2987, 11423,  5613, 11268, 13765,  25008, 25958, 25427,  \n5986, 15947, 20143,  25008, 25280, 25959,  8011, 4497, 8919,  \n3420, 8797, 3419,  25960, 25681, 25558,  25277, 25558, 25681,  \n25956, 25961, 25960,  25563, 24709, 25429,  2134, 4701, 10836,  \n17353, 21126, 15983,  5953, 10295, 18448,  1960, 5146, 5147,  \n8298, 7269, 4470,  21838, 5834, 8167,  10527, 8232, 2302,  \n25803, 25963, 25564,  1407, 1409, 8209,  4635, 10266, 4634,  \n8151, 13843, 1406,  14826, 17015, 12659,  13340, 12083, 13995,  \n14179, 22343, 13015,  7206, 7207, 13174,  22861, 20462, 20461,  \n10376, 23480, 15936,  1969, 6842, 9928,  17794, 9100, 5446,  \n16422, 4351, 17679,  6590, 6161, 17677,  25285, 25963, 25431,  \n25431, 25963, 25806,  10767, 6968, 15369,  25432, 25807, 25147,  \n3892, 18707, 4739,  11960, 6462, 11959,  20497, 3072, 17124,  \n15148, 23249, 14393,  25431, 25806, 25289,  5833, 14791, 9593,  \n25011, 25150, 25808,  20317, 10574, 15996,  17935, 12494, 12495,  \n4244, 10995, 13484,  15519, 7675, 15518,  4261, 14209, 4260,  \n25966, 25289, 25967,  523, 1556, 12538,  6890, 9893, 9892,  \n17699, 5959, 16887,  20305, 6671, 5814,  4261, 20004, 14209,  \n25289, 25966, 25290,  24560, 25010, 25286,  6910, 6911, 7104,  \n25966, 25811, 25572,  25969, 25968, 25809,  21004, 15064, 17070,  \n25809, 25968, 25684,  16400, 13662, 13780,  9732, 898, 7929,  \n25966, 25572, 25290,  3585, 8179, 11558,  25433, 25811, 25810,  \n25685, 25433, 25810,  5706, 5581, 18832,  25970, 25684, 25968,  \n20181, 11971, 11701,  12176, 14635, 12177,  12859, 426, 10545,  \n18721, 8136, 15527,  25970, 25687, 25686,  6088, 2761, 21667,  \n25164, 25012, 25971,  6110, 8927, 8926,  11592, 17646, 21146,  \n3932, 13540, 3211,  8367, 12564, 16934,  23201, 21306, 6145,  \n18989, 12163, 18605,  5156, 5767, 12825,  2305, 14878, 12724,  \n13330, 7190, 8648,  8258, 11598, 18415,  25972, 25573, 25298,  \n16789, 15520, 18033,  12923, 3233, 1909,  25573, 25813, 25814,  \n25690, 25975, 25689,  11588, 2807, 1812,  25439, 25814, 25976,  \n16510, 6545, 18036,  25691, 25439, 25976,  17909, 5455, 22447,  \n23070, 8015, 2453,  25974, 24718, 25438,  21351, 8750, 14454,  \n12134, 12135, 3910,  8262, 5929, 8188,  12514, 5178, 20980,  \n1109, 6601, 3160,  11238, 7279, 22862,  25979, 24717, 25816,  \n3102, 21887, 8028,  4269, 23668, 3593,  17537, 19868, 17536,  \n14688, 5407, 5408,  25692, 25693, 25978,  11151, 10214, 18538,  \n20921, 15901, 11766,  25441, 25980, 25978,  25441, 25978, 25693,  \n10841, 6643, 10371,  23302, 5092, 5091,  14524, 14536, 8539,  \n1767, 2108, 12330,  1431, 10285, 4113,  462, 12792, 11320,  \n6844, 4308, 1342,  25170, 25169, 25981,  10774, 7233, 19389,  \n4833, 3154, 23536,  1159, 9057, 4412,  11353, 21440, 4804,  \n17200, 18558, 6822,  12810, 8657, 11985,  18006, 6600, 372,  \n4562, 1596, 316,  8325, 17865, 12471,  5099, 13569, 751,  \n25442, 25576, 25819,  3968, 19569, 21005,  25303, 25818, 25444,  \n8273, 22065, 11775,  7873, 13895, 7874,  15157, 14559, 15439,  \n3894, 7880, 12554,  1829, 7512, 3705,  11003, 18086, 11002,  \n1002, 18388, 1001,  21779, 476, 11170,  25819, 25576, 25580,  \n12552, 10062, 17858,  8209, 8045, 10294,  25304, 25447, 25582,  \n21968, 11648, 21264,  25983, 25820, 25449,  25983, 25449, 25310,  \n6572, 23572, 5678,  3598, 5248, 9505,  25307, 25821, 25696,  \n6996, 22760, 15206,  8266, 7525, 13546,  11636, 715, 13244,  \n25984, 25825, 25451,  6336, 10415, 4435,  6464, 7403, 22284,  \n12773, 20179, 7667,  25451, 25826, 25984,  6095, 10598, 2707,  \n21739, 6353, 15932,  20197, 12184, 19193,  12270, 12910, 18719,  \n25695, 25177, 25313,  25827, 24875, 24872,  10784, 18178, 13851,  \n6875, 1706, 14760,  5107, 8495, 15697,  25828, 25176, 25823,  \n9433, 18742, 18472,  2140, 13516, 3153,  17926, 4631, 10871,  \n9924, 9923, 4005,  25313, 25320, 25830,  978, 10315, 420,  \n1309, 21046, 1310,  25314, 25452, 25701,  25454, 25314, 25701,  \n17716, 1197, 12092,  19069, 11727, 12618,  14225, 14224, 21806,  \n13396, 10018, 10019,  22106, 11647, 22107,  5069, 5071, 9438,  \n25986, 25316, 25829,  10580, 9370, 21998,  18145, 2513, 7117,  \n19901, 10836, 8577,  25381, 5218, 14435,  3180, 8914, 14496,  \n5624, 16723, 8021,  9172, 18367, 9171,  25454, 25987, 25319,  \n5070, 12402, 954,  11767, 14084, 6440,  25318, 25180, 25704,  \n3364, 6687, 10105,  25831, 25702, 25321,  25323, 25456, 25988,  \n16973, 11704, 15939,  1486, 2174, 18133,  3506, 18463, 3003,  \n12477, 11679, 12237,  6537, 1494, 6538,  4285, 500, 3521,  \n9997, 5741, 10381,  4964, 1814, 18931,  24881, 25586, 25836,  \n23629, 4462, 8959,  24131, 24882, 25991,  25045, 24881, 25836,  \n3725, 11487, 18941,  9274, 5230, 15600,  17689, 18019, 17690,  \n9061, 9060, 17526,  15998, 14286, 12794,  3476, 3207, 6903,  \n13591, 15918, 18215,  3970, 20937, 21522,  2439, 2438, 19213,  \n18789, 2809, 20585,  9999, 18527, 9234,  15112, 11812, 9806,  \n736, 1397, 13834,  10940, 303, 8166,  21690, 12355, 18093,  \n25708, 25326, 25994,  12981, 4108, 4828,  13633, 3198, 16748,  \n9204, 3730, 5553,  1574, 16717, 20732,  18932, 3786, 4451,  \n19541, 21133, 6068,  1550, 18329, 13488,  17676, 5194, 13702,  \n12222, 8536, 8434,  12011, 8099, 18026,  2150, 17584, 6506,  \n8089, 15360, 1682,  17102, 15223, 7571,  12819, 14439, 436,  \n25593, 24888, 25187,  25049, 25591, 25186,  19599, 3954, 21425,  \n16635, 17890, 10437,  14196, 12106, 3519,  25188, 25711, 25997,  \n12733, 22652, 19791,  3368, 13244, 20047,  22379, 13508, 21584,  \n7721, 7492, 5494,  3654, 11271, 11096,  7697, 17046, 14492,  \n20376, 16734, 14956,  25330, 25465, 25999,  4225, 8674, 3390,  \n13220, 1111, 3462,  3069, 3070, 17804,  15367, 9709, 16442,  \n13582, 16319, 13581,  20505, 4164, 26391,  25465, 25839, 25999,  \n9190, 4942, 9735,  881, 17935, 3043,  14525, 1027, 2425,  \n19316, 19315, 19665,  5891, 21865, 19705,  10375, 16301, 9728,  \n26001, 24889, 26301,  25050, 25838, 25714,  4754, 4755, 11303,  \n21532, 10251, 10010,  24889, 26001, 25195,  5955, 15175, 20667,  \n17831, 13873, 9117,  25194, 25468, 25842,  19807, 21923, 3342,  \n25197, 25195, 26001,  25718, 25841, 26004,  22491, 23617, 13826,  \n13396, 9217, 20986,  18027, 1275, 1274,  25841, 26002, 26004,  \n25718, 26004, 26006,  22406, 20156, 13026,  3668, 13533, 13197,  \n26007, 25716, 25334,  25471, 25722, 25196,  14278, 17846, 14279,  \n26007, 25334, 25845,  25600, 24892, 25719,  832, 11720, 15208,  \n14278, 23904, 17847,  25334, 25198, 25845,  9917, 19288, 10856,  \n25718, 26006, 25847,  7607, 3158, 7606,  15277, 12271, 10563,  \n2094, 18919, 4150,  12227, 8480, 8993,  25718, 25847, 25725,  \n4305, 9224, 19092,  8182, 10242, 1564,  26009, 25845, 25198,  \n23499, 18249, 9523,  7619, 20872, 8391,  25054, 26009, 25198,  \n12358, 10945, 3085,  25605, 25725, 25847,  7094, 7751, 7088,  \n26009, 25054, 25724,  8581, 4486, 14999,  25847, 26010, 25605,  \n501, 18076, 5842,  25723, 25483, 25849,  5322, 11197, 17790,  \n905, 6783, 5630,  25337, 24613, 25601,  13429, 17198, 23913,  \n9113, 2606, 10820,  2468, 3775, 9297,  7528, 21893, 16498,  \n25482, 26010, 26012,  25850, 25849, 25727,  25726, 25481, 25479,  \n7009, 12763, 13923,  7887, 13588, 18583,  29781, 17075, 12069,  \n7714, 12393, 20645,  16566, 13528, 7213,  4985, 4970, 16042,  \n7974, 18736, 10844,  25728, 24902, 25481,  25482, 26012, 26015,  \n25203, 25342, 25480,  1082, 4604, 1083,  25728, 25343, 24902,  \n11015, 12395, 11016,  8754, 18856, 8753,  25485, 25480, 25342,  \n3481, 2419, 6382,  11335, 4971, 6099,  4675, 1818, 13646,  \n25609, 25482, 26015,  5823, 14540, 2928,  25609, 26015, 25853,  \n16338, 4286, 11567,  6665, 9658, 2612,  9926, 1708, 9927,  \n17594, 17596, 596,  24759, 25344, 25854,  19465, 13357, 15006,  \n1570, 21534, 2190,  3110, 23676, 16054,  26017, 25488, 25349,  \n24910, 25349, 25488,  25855, 25610, 26019,  21460, 12093, 17031,  \n8727, 15811, 4519,  25210, 25487, 25856,  16375, 18461, 14317,  \n14754, 16919, 6725,  800, 8667, 22070,  17859, 4845, 15131,  \n18569, 1716, 7080,  26021, 25489, 25212,  11747, 17429, 20687,  \n19610, 4781, 349,  11486, 14409, 4792,  25352, 26022, 25858,  \n26023, 24628, 25857,  13697, 12067, 15196,  25352, 25860, 26022,  \n6481, 12542, 12543,  8383, 15771, 16879,  19244, 20138, 17700,  \n25072, 25213, 26023,  18541, 12770, 12771,  12357, 13813, 9962,  \n26024, 25729, 25617,  19551, 28821, 4142,  25860, 25354, 25620,  \n6645, 18388, 1002,  13571, 18680, 6647,  2195, 2194, 16619,  \n1870, 6390, 14021,  25493, 25861, 26026,  25493, 25355, 25861,  \n2831, 9183, 3245,  3059, 21725, 7822,  25493, 26026, 25862,  \n18164, 1231, 4308,  1294, 15989, 7076,  14677, 15397, 15831,  \n3367, 915, 14517,  25621, 26028, 25732,  25730, 26028, 25621,  \n25730, 25865, 26028,  20278, 13743, 14316,  14253, 19168, 519,  \n8068, 22857, 20727,  25865, 25731, 26029,  25866, 26029, 25731,  \n14983, 2246, 2247,  11092, 16077, 1819,  24462, 10282, 10281,  \n848, 5656, 369,  25619, 26030, 25866,  9304, 6312, 5372,  \n12015, 5350, 8485,  6463, 25443, 5558,  8849, 8854, 8489,  \n15093, 17353, 15983,  1983, 14619, 1982,  25864, 25623, 25736,  \n14987, 10119, 8670,  12530, 16956, 11852,  20712, 14235, 15163,  \n19496, 9903, 9904,  1768, 6272, 19689,  14272, 21564, 4274,  \n7869, 10996, 7870,  25738, 25736, 25623,  19174, 10240, 3087,  \n10780, 21156, 20837,  13678, 10392, 10391,  8536, 8535, 10987,  \n10804, 2978, 19696,  25497, 25496, 25871,  25738, 25623, 25362,  \n25737, 25735, 25361,  12794, 20911, 997,  24786, 2400, 9232,  \n6676, 1479, 1303,  6381, 21886, 15683,  25497, 25871, 26183,  \n9157, 8590, 9156,  25738, 25362, 25624,  3776, 3777, 19212,  \n13712, 21599, 22369,  11627, 2446, 11626,  26034, 8765, 13031,  \n25363, 25364, 26032,  26035, 26033, 25874,  19907, 10183, 7944,  \n17512, 2430, 13621,  25740, 26035, 25874,  25082, 25497, 25739,  \n14329, 16010, 4639,  26036, 26035, 25740,  25083, 25626, 26037,  \n25740, 25741, 26036,  15863, 12907, 18065,  6422, 10638, 15846,  \n25366, 25367, 25626,  25875, 25368, 25498,  7318, 17373, 7319,  \n3328, 9337, 10932,  19235, 16107, 16569,  18716, 9972, 8728,  \n1798, 3636, 353,  10921, 5092, 14365,  14664, 14419, 14665,  \n11345, 13728, 20164,  6527, 18224, 12677,  20295, 17372, 21166,  \n1534, 11946, 10239,  25502, 25743, 26191,  2936, 22785, 15659,  \n18524, 13738, 13737,  25878, 25876, 25744,  1337, 15076, 18858,  \n12742, 15111, 12743,  25502, 26191, 26039,  2625, 17863, 12970,  \n15276, 2186, 2185,  17151, 1242, 1243,  5049, 11415, 8918,  \n25878, 25746, 25879,  14071, 14070, 9075,  17245, 20693, 5984,  \n19825, 17455, 13612,  15196, 6877, 1660,  8716, 15291, 4733,  \n25628, 25502, 26039,  6905, 10955, 4441,  25879, 25880, 25882,  \n20642, 17119, 22453,  9231, 17987, 19030,  19238, 13959, 4404,  \n25628, 26039, 25745,  5138, 21011, 5139,  26041, 25745, 26042,  \n25881, 25884, 25882,  12608, 3940, 7522,  18642, 2767, 2766,  \n7905, 6661, 10502,  10016, 10017, 14700,  7796, 3101, 7797,  \n25886, 24940, 25504,  26044, 25231, 25505,  11966, 9730, 21995,  \n25633, 24938, 26045,  11091, 10889, 3104,  24938, 25637, 26045,  \n7346, 18937, 22038,  26046, 25883, 25885,  18722, 7288, 11603,  \n26047, 25093, 25231,  3288, 21916, 16974,  8972, 7672, 13773,  \n2372, 21737, 10717,  18360, 4155, 2048,  25750, 25375, 25888,  \n25751, 25637, 25378,  25748, 25749, 25897,  26048, 25885, 25897,  \n25885, 26048, 26046,  3084, 16939, 2654,  26049, 25888, 26050,  \n26049, 25750, 25888,  6139, 4529, 3546,  19444, 14625, 8575,  \n23595, 1182, 15873,  11192, 2156, 2155,  26205, 25755, 25511,  \n10919, 17225, 6916,  26052, 25753, 25509,  19935, 6216, 17235,  \n25750, 26051, 25890,  5311, 18429, 4343,  25508, 25233, 26053,  \n1755, 6096, 1756,  25507, 25508, 26054,  16007, 6848, 14717,  \n20940, 20858, 11825,  23938, 14246, 18064,  2397, 8687, 2398,  \n17207, 8086, 5742,  1160, 6395, 1161,  25379, 25234, 25891,  \n15325, 15267, 8354,  20686, 3455, 9498,  26055, 25897, 25754,  \n16635, 13529, 17890,  25754, 25898, 26055,  22419, 23947, 20658,  \n15584, 19459, 3263,  17263, 14340, 21109,  5191, 1389, 2445,  \n533, 534, 3564,  25756, 25901, 25898,  25898, 25906, 26055,  \n10400, 14299, 16700,  8251, 4320, 14851,  10813, 13003, 13002,  \n25756, 25900, 25901,  25908, 26055, 25906,  4775, 3631, 4776,  \n11979, 10858, 11696,  14867, 18933, 18569,  17556, 21123, 12846,  \n25907, 25909, 25911,  25907, 25911, 26058,  2460, 5624, 7300,  \n13562, 15911, 15129,  4361, 2289, 16885,  25911, 25909, 25910,  \n3917, 16930, 10817,  2351, 2350, 19096,  10125, 19572, 11795,  \n26060, 25910, 25912,  25913, 25910, 26060,  21980, 11453, 3930,  \n1255, 18663, 1254,  25762, 26061, 25643,  25912, 25763, 25914,  \n26062, 25643, 26061,  12683, 17706, 17705,  25914, 25763, 26063,  \n13076, 13077, 16192,  25514, 25643, 26062,  12687, 7874, 2334,  \n5742, 8086, 11527,  6355, 20188, 10129,  25642, 25240, 25916,  \n25642, 25916, 25915,  25916, 26066, 25915,  1922, 5476, 3175,  \n16639, 16638, 12350,  26067, 25646, 25644,  14709, 14708, 22634,  \n8705, 10540, 11706,  25646, 26068, 26069,  25916, 25241, 26217,  \n13553, 501, 13997,  25645, 24660, 25389,  640, 19314, 10993,  \n25647, 26072, 26073,  25918, 26072, 25647,  25919, 25645, 25389,  \n421, 12776, 1091,  25648, 25647, 26073,  25921, 25648, 26073,  \n679, 2608, 307,  9525, 1632, 10352,  17190, 16243, 8043,  \n4771, 4770, 4268,  25243, 25648, 25922,  13271, 8273, 11775,  \n9694, 15690, 21202,  25765, 25649, 26075,  6470, 8257, 20860,  \n10500, 12722, 12723,  12036, 2484, 3425,  14238, 4378, 4377,  \n25651, 25765, 25767,  29756, 1464, 1463,  25765, 26076, 25767,  \n12189, 8027, 20992,  26076, 25924, 25767,  14313, 15938, 8853,  \n1360, 18307, 1359,  1501, 16714, 4078,  3728, 9568, 3435,  \n25928, 25766, 26078,  25924, 26078, 25766,  4252, 10964, 19472,  \n6344, 12651, 9913,  16009, 18204, 5711,  25926, 25768, 26079,  \n7376, 6568, 4524,  25926, 25657, 25656,  25768, 25927, 26079,  \n8148, 8410, 26080,  25926, 25656, 25768,  26081, 25771, 25929,  \n25659, 25771, 25770,  25771, 26081, 25770,  11150, 18932, 23467,  \n4112, 14083, 4110,  10174, 12271, 1579,  1779, 2615, 15175,  \n26082, 25774, 25660,  10704, 6701, 6700,  21550, 13228, 14171,  \n9087, 8992, 21815,  5288, 11802, 8108,  6716, 19892, 12404,  \n17651, 8824, 11949,  25773, 26083, 25772,  26085, 25931, 25930,  \n25775, 25774, 25932,  18945, 9109, 16562,  13597, 2890, 10482,  \n16352, 249, 17786,  7537, 8124, 1580,  10724, 11755, 17064,  \n6233, 6242, 489,  11270, 20694, 3647,  16455, 4579, 4580,  \n8258, 7909, 13258,  11560, 10018, 18425,  5956, 3027, 12096,  \n25776, 25662, 26088,  24971, 25933, 25777,  25776, 26088, 25934,  \n10407, 16793, 11643,  19161, 8314, 16126,  17046, 1856, 9232,  \n25526, 25934, 26090,  25526, 25776, 25934,  7159, 20517, 10404,  \n12266, 1484, 1434,  25526, 26090, 25778,  18060, 12785, 20589,  \n6002, 15044, 14787,  12805, 14251, 768,  15995, 9894, 19816,  \n26091, 25663, 25528,  25664, 25405, 25779,  13284, 17879, 11542,  \n21391, 12712, 2824,  16409, 10570, 18452,  9420, 22197, 23479,  \n26091, 25665, 25937,  25258, 25936, 26093,  25937, 25665, 25530,  \n9533, 10166, 10165,  978, 8704, 9263,  22738, 22459, 12296,  \n24979, 25531, 25532,  25531, 26094, 25532,  26094, 26095, 25532,  \n15572, 15573, 11847,  10884, 12060, 14291,  25782, 25532, 26096,  \n26095, 26096, 25532,  12442, 14776, 14775,  25782, 26096, 25783,  \n25783, 26096, 26097,  25783, 26097, 25784,  10162, 16389, 5723,  \n25939, 25785, 25938,  1856, 17046, 17056,  25787, 26099, 25938,  \n13774, 22278, 16990,  16945, 8642, 22755,  8129, 7076, 8128,  \n1087, 15751, 14929,  26099, 25787, 25790,  26099, 25790, 25791,  \n26246, 24825, 25269,  25792, 26101, 25789,  25669, 25667, 26100,  \n13794, 21392, 20734,  340, 12585, 5853,  25791, 25672, 25941,  \n19086, 9879, 19824,  25846, 17324, 10761,  6583, 15174, 2160,  \n25671, 26101, 25792,  7480, 11215, 12921,  12370, 12535, 7436,  \n25944, 25941, 25672,  25132, 24825, 25673,  3427, 10134, 20692,  \n2488, 1975, 14092,  6167, 7641, 10526,  3250, 9119, 637,  \n25793, 25275, 25794,  25795, 26103, 25794,  3120, 3056, 3785,  \n26104, 26103, 25795,  25411, 25670, 25943,  19520, 17071, 2315,  \n5156, 4328, 2902,  7070, 10583, 21468,  25553, 25795, 25552,  \n18936, 21543, 8760,  24696, 25132, 25673,  9433, 589, 18742,  \n10174, 1678, 977,  5311, 4343, 10628,  14803, 15383, 16632,  \n7190, 9444, 2759,  25140, 26252, 25796,  17562, 9575, 9576,  \n18829, 1803, 1802,  3346, 3348, 1179,  9629, 20719, 5606,  \n26249, 25271, 25946,  8654, 14659, 14660,  25949, 25411, 25943,  \n6942, 3166, 3016,  11429, 19324, 16477,  4268, 13642, 4771,  \n26107, 25128, 25129,  5092, 10921, 7349,  5516, 872, 17872,  \n2868, 4069, 10513,  10800, 15949, 14397,  5791, 8564, 5792,  \n5410, 13725, 13204,  10321, 10937, 11861,  12469, 589, 9433,  \n11657, 18003, 16033,  9080, 15088, 15087,  22653, 25158, 11400,  \n13362, 1955, 14001,  8535, 18783, 16421,  4107, 16727, 2706,  \n6700, 15677, 19934,  3218, 24029, 26109,  1406, 15676, 8152,  \n25953, 25949, 25945,  15676, 23682, 14589,  8111, 21648, 9346,  \n25951, 25548, 25676,  25954, 25945, 26110,  20549, 22250, 2983,  \n3857, 902, 5204,  6938, 2503, 9994,  23522, 21812, 21330,  \n12160, 10361, 4041,  7177, 775, 4189,  25947, 25556, 25800,  \n25955, 25801, 25559,  5077, 17025, 2082,  4591, 7710, 4592,  \n8422, 8421, 7284,  26112, 25677, 25798,  25951, 26112, 25798,  \n21777, 6412, 4359,  22197, 2389, 11577,  25556, 25283, 25800,  \n25955, 26113, 26791,  25803, 25677, 26115,  26115, 25677, 26112,  \n3978, 18061, 492,  18954, 16525, 9398,  15436, 17963, 4560,  \n18954, 13360, 4668,  12314, 452, 4801,  13495, 4925, 17121,  \n25953, 25957, 25956,  15609, 14603, 23330,  20775, 22449, 5474,  \n6932, 7081, 12797,  9057, 19940, 14862,  26116, 25803, 26115,  \n25957, 25961, 25956,  2008, 1808, 1807,  25144, 26117, 26114,  \n13017, 1149, 1148,  768, 14251, 16716,  976, 5458, 17669,  \n25956, 25960, 25558,  8007, 7646, 8008,  11430, 21306, 23201,  \n11888, 13382, 15267,  25803, 26116, 25963,  25282, 25964, 25561,  \n25964, 25282, 25560,  16797, 17608, 2412,  24705, 25681, 25560,  \n25964, 25560, 25960,  25681, 25960, 25560,  25962, 25563, 25429,  \n26117, 25144, 25430,  5219, 5220, 20091,  2439, 3796, 15166,  \n6530, 11247, 14411,  2701, 7040, 21358,  1304, 21812, 23522,  \n25808, 25150, 25805,  2214, 16484, 19393,  5698, 11508, 17376,  \n2097, 8580, 937,  24039, 6425, 11083,  3941, 3374, 7452,  \n11330, 14890, 13124,  8358, 3873, 8040,  6329, 6330, 14389,  \n20849, 19068, 14493,  25289, 25806, 25967,  5216, 5496, 5820,  \n23139, 13308, 4166,  21195, 5321, 3740,  514, 8011, 7759,  \n15610, 17587, 15146,  6347, 8501, 9757,  20350, 22359, 22454,  \n6346, 12059, 9381,  26118, 22495, 25017,  25811, 25966, 25967,  \n26119, 25811, 25967,  26119, 25810, 25811,  25810, 25969, 25809,  \n356, 17691, 18021,  6772, 3718, 11283,  26120, 25286, 25010,  \n15709, 3565, 3566,  25686, 25684, 25970,  9371, 2492, 4743,  \n25971, 25012, 25808,  26120, 25010, 25569,  5776, 9950, 8053,  \n1944, 7852, 7853,  25812, 25568, 25687,  25807, 25152, 25435,  \n13650, 11311, 18746,  25160, 25812, 25972,  20283, 7188, 19520,  \n10594, 21457, 23236,  25972, 25812, 26122,  1540, 1107, 3583,  \n16383, 14875, 6944,  6061, 29287, 17721,  25438, 25164, 25971,  \n16215, 6950, 20937,  18243, 2601, 13766,  19900, 1177, 18468,  \n8883, 19602, 4968,  25975, 25690, 25815,  342, 341, 11459,  \n3205, 15759, 3204,  4583, 18829, 14372,  24718, 25974, 25977,  \n703, 1965, 3510,  25978, 25815, 25692,  16253, 12367, 21090,  \n20800, 7150, 5735,  9777, 2815, 14089,  24864, 24718, 25977,  \n9321, 4322, 16461,  25694, 24717, 25979,  22160, 8977, 10288,  \n25694, 25025, 24717,  11569, 11178, 4218,  20479, 534, 23046,  \n20970, 6199, 5323,  25575, 25980, 25441,  16895, 6034, 1633,  \n25445, 25301, 25817,  18915, 12277, 14695,  22863, 15146, 17587,  \n2309, 9046, 7401,  5062, 5061, 15824,  15691, 14642, 1695,  \n1512, 1652, 1651,  6852, 12893, 3631,  6407, 9133, 9819,  \n4244, 4243, 20083,  17077, 17167, 17915,  10981, 20120, 15062,  \n13697, 19063, 6909,  24726, 25170, 25981,  18338, 9400, 13908,  \n21960, 22291, 10470,  19046, 15871, 10203,  1459, 11401, 1460,  \n12279, 10658, 2595,  17383, 8393, 13250,  19368, 14544, 8989,  \n24872, 25577, 26127,  26130, 25983, 25310,  25304, 25582, 26128,  \n25579, 25304, 26129,  25307, 25579, 26129,  25821, 25307, 26129,  \n25580, 25695, 25982,  9474, 17487, 13246,  21247, 14406, 3093,  \n25582, 25448, 25822,  5319, 18748, 1066,  25697, 25824, 24873,  \n21365, 13065, 17923,  25696, 25985, 25823,  11894, 20922, 10365,  \n25697, 25311, 25700,  12833, 9532, 16834,  25985, 25828, 25823,  \n7736, 4157, 7737,  25695, 25830, 25982,  16728, 6554, 470,  \n14329, 21975, 16010,  25695, 25313, 25830,  25311, 25037, 26133,  \n25826, 25312, 25315,  13564, 13172, 4661,  19412, 20469, 14463,  \n26131, 25826, 25315,  12687, 2334, 2335,  3361, 10979, 8562,  \n18710, 4499, 3672,  7728, 19233, 7727,  25176, 25828, 25453,  \n13223, 21493, 17875,  5702, 6395, 1160,  3848, 12358, 9883,  \n24876, 25827, 26132,  6652, 3125, 2544,  25315, 25583, 26131,  \n10138, 12206, 6917,  13062, 22242, 21862,  18585, 12050, 12049,  \n2589, 15672, 2575,  5924, 9676, 9677,  19128, 8679, 19129,  \n7519, 691, 16078,  25316, 25986, 25317,  26005, 2630, 17461,  \n21307, 8304, 21306,  26134, 25042, 25179,  1506, 12273, 23770,  \n5242, 299, 23164,  5851, 6522, 9067,  25585, 25319, 25987,  \n14770, 643, 1537,  6576, 11875, 22820,  2551, 11201, 18462,  \n462, 2401, 12791,  14463, 6684, 17472,  25320, 25323, 25988,  \n25317, 25703, 25586,  7168, 17434, 7760,  19789, 14462, 1176,  \n18259, 2545, 8983,  500, 10570, 15668,  18520, 19938, 14252,  \n2192, 9690, 2193,  25832, 25321, 25324,  25832, 26136, 25831,  \n10194, 14333, 6712,  15668, 3522, 3521,  6558, 12370, 6559,  \n25833, 25322, 25989,  2800, 9285, 12196,  24457, 25587, 26137,  \n24880, 25833, 25587,  17552, 16368, 11939,  13257, 8119, 8009,  \n4008, 4653, 17969,  13223, 3234, 13222,  25042, 25990, 25457,  \n25324, 24131, 25835,  24882, 26288, 25991,  25835, 24131, 25991,  \n4950, 2175, 21318,  25836, 26138, 25045,  3471, 7230, 4484,  \n25457, 25992, 25461,  25705, 25455, 25707,  12438, 7936, 7935,  \n26139, 10032, 5899,  12340, 5311, 738,  12536, 15463, 11779,  \n25994, 25326, 25837,  18542, 1463, 18543,  26140, 25047, 25461,  \n11921, 17737, 19210,  9821, 16483, 9822,  20342, 22309, 11930,  \n16564, 1387, 12150,  8100, 7862, 19667,  5287, 17045, 20070,  \n5474, 11282, 5473,  11037, 11322, 16088,  2368, 16529, 9221,  \n26141, 25708, 25994,  13464, 6869, 13036,  14496, 5802, 12487,  \n22495, 26118, 19379,  26486, 25183, 25593,  7524, 3080, 3079,  \n13970, 8663, 9788,  25591, 25589, 25996,  25995, 25709, 25592,  \n8941, 14349, 14549,  25593, 25187, 25712,  8522, 23856, 12027,  \n1383, 15256, 5841,  25658, 25522, 4888,  25185, 25188, 25997,  \n24932, 24917, 21078,  9098, 1981, 21531,  14940, 3212, 14522,  \n1603, 15444, 6581,  25463, 26142, 25710,  10795, 9491, 13726,  \n22945, 7122, 17436,  21499, 16103, 13327,  10112, 2959, 3739,  \n25330, 25999, 25998,  2217, 2218, 2413,  25332, 25331, 25710,  \n6530, 8887, 11248,  1026, 1025, 8878,  23572, 21565, 8214,  \n21514, 17117, 15639,  5344, 9218, 11842,  10501, 8713, 4664,  \n10016, 3657, 11378,  9162, 6733, 18229,  18384, 11651, 13025,  \n25840, 25193, 25596,  1127, 7889, 1380,  16621, 8219, 5276,  \n15409, 7191, 5633,  9383, 9382, 11471,  26145, 26002, 25841,  \n25843, 26145, 25841,  11037, 16088, 5419,  13906, 19128, 2153,  \n3892, 20208, 18707,  7126, 7388, 7124,  946, 23036, 10434,  \n18351, 894, 6118,  2989, 9471, 2990,  21071, 16157, 5584,  \n26003, 25843, 25599,  25717, 26003, 25599,  4254, 4824, 553,  \n7860, 18562, 7861,  18019, 14561, 15482,  13455, 4352, 1291,  \n10534, 13512, 9038,  18764, 14007, 22306,  26006, 26146, 26147,  \n26006, 26004, 26146,  25197, 26001, 26148,  16365, 14396, 16366,  \n5910, 17622, 9575,  25721, 26149, 25720,  7348, 9180, 2771,  \n17208, 17489, 2793,  11064, 16641, 20362,  26150, 25721, 25723,  \n20538, 15576, 11420,  26006, 26151, 25847,  20615, 13984, 23229,  \n1093, 1295, 1092,  889, 17042, 10299,  9505, 4677, 12529,  \n25847, 26151, 26010,  7860, 20600, 18562,  17926, 8609, 15896,  \n25723, 25849, 26153,  19536, 11960, 13137,  13845, 5933, 366,  \n12735, 18309, 8472,  15055, 9796, 2415,  5616, 16484, 3227,  \n847, 7617, 12073,  14743, 13868, 17980,  11182, 1881, 24060,  \n26011, 25055, 25052,  8390, 4539, 19618,  6303, 15763, 9702,  \n11178, 2580, 4219,  6224, 3538, 16014,  523, 524, 10873,  \n17090, 909, 910,  18735, 20345, 2781,  16208, 11344, 11160,  \n25337, 25601, 26155,  1006, 4598, 1004,  21854, 9738, 17589,  \n25728, 25481, 25726,  7483, 7482, 9922,  11182, 10712, 16374,  \n14044, 14793, 375,  9957, 9097, 11585,  25608, 25607, 26156,  \n26014, 25850, 25727,  26012, 26157, 26015,  1898, 22155, 15702,  \n17061, 18345, 16193,  10186, 6487, 6488,  20691, 9744, 2170,  \n12113, 1945, 2599,  26014, 25727, 25851,  350, 19845, 9698,  \n24759, 25337, 25344,  12842, 12843, 8905,  16656, 3205, 14783,  \n6636, 2356, 6637,  14974, 14918, 18863,  25853, 26015, 26016,  \n1920, 10870, 2367,  25851, 25347, 25852,  3841, 10044, 23236,  \n11360, 11361, 13021,  828, 6742, 5785,  25852, 25347, 25488,  \n26159, 25852, 25488,  4544, 5512, 1466,  26159, 25488, 26017,  \n25610, 26160, 26019,  25487, 24904, 25854,  25612, 25611, 26018,  \n14635, 8572, 12177,  21092, 4289, 7834,  3038, 11534, 4163,  \n22996, 7648, 13457,  9705, 9706, 16164,  9474, 4913, 9623,  \n16750, 10056, 7296,  25614, 25613, 25855,  7264, 4546, 6884,  \n19166, 20454, 5663,  8497, 15655, 5976,  26020, 25070, 25858,  \n19085, 9451, 18498,  15841, 8212, 14350,  1516, 1517, 21770,  \n2030, 2587, 4854,  4518, 9321, 7251,  18629, 14028, 14805,  \n16740, 20585, 5530,  25859, 25618, 25615,  26161, 25858, 26022,  \n18096, 9819, 9672,  12268, 9432, 17512,  25859, 25615, 26162,  \n8940, 26084, 8941,  19678, 15837, 15836,  8617, 3763, 3762,  \n26164, 26163, 26165,  5705, 1524, 5170,  11010, 3701, 6001,  \n26025, 26166, 26165,  25620, 26163, 25860,  26163, 25620, 25863,  \n15727, 15726, 22525,  18675, 20234, 19196,  25861, 25355, 25859,  \n11623, 2597, 12860,  16723, 2460, 2462,  26025, 26165, 25863,  \n1986, 12193, 11393,  6645, 307, 18388,  25864, 26167, 26025,  \n3514, 15207, 14484,  16987, 11417, 5377,  26025, 25863, 25864,  \n4629, 2885, 3943,  10633, 6429, 22033,  26027, 25353, 25359,  \n26168, 26169, 25865,  25862, 26170, 25494,  25494, 26170, 25356,  \n26171, 26028, 25865,  26171, 25865, 26169,  16656, 14116, 17762,  \n26168, 25865, 26029,  26172, 26029, 25866,  18741, 16654, 22632,  \n26030, 25619, 26173,  26174, 25619, 25356,  26173, 25619, 26174,  \n25356, 26170, 26174,  6268, 577, 18835,  25732, 26175, 25868,  \n3024, 15078, 15077,  25866, 26030, 26172,  26167, 25864, 25736,  \n17379, 19181, 3122,  25733, 25868, 26179,  20619, 15211, 10113,  \n6110, 3717, 2796,  26029, 26172, 26176,  5233, 11947, 13331,  \n16101, 11732, 12479,  2215, 2214, 16881,  5740, 5739, 10509,  \n26172, 26180, 26176,  25733, 26179, 25734,  3831, 19644, 9627,  \n12650, 7291, 15002,  22753, 14657, 6962,  10588, 16689, 2826,  \n26179, 25870, 25734,  5891, 11981, 764,  25217, 25735, 25869,  \n16095, 4615, 13012,  13768, 12365, 3064,  25870, 25496, 25734,  \n25738, 26182, 25736,  11181, 14999, 14966,  26032, 25364, 25872,  \n15895, 8610, 17885,  14880, 14471, 15135,  11122, 6247, 2523,  \n13477, 7589, 5072,  25874, 26033, 25738,  17865, 8325, 15157,  \n13584, 12847, 19264,  22509, 16521, 12897,  20867, 17599, 21541,  \n20425, 11480, 5441,  22517, 22150, 22149,  20440, 14032, 19073,  \n25363, 26184, 24787,  13221, 20532, 17248,  19722, 21475, 8402,  \n15779, 4734, 19677,  24924, 24927, 25083,  25739, 25497, 26183,  \n15214, 10622, 12319,  16966, 1890, 11500,  7545, 21575, 4767,  \n22575, 18586, 18580,  11940, 12292, 12568,  12420, 11821, 17450,  \n26185, 26036, 26187,  733, 5731, 734,  6800, 18465, 6798,  \n26188, 26187, 26036,  7880, 6680, 12554,  8907, 5714, 2952,  \n1287, 17885, 10013,  25222, 25500, 25223,  26188, 26036, 25876,  \n17310, 22111, 10188,  25876, 26189, 26188,  10855, 10081, 11449,  \n5592, 23705, 1988,  14061, 12984, 14062,  1661, 17625, 16173,  \n26539, 25371, 26355,  25223, 26355, 25371,  25368, 26190, 25085,  \n22942, 9310, 2433,  26539, 26191, 25371,  25371, 26191, 25743,  \n21166, 17372, 18650,  26189, 25876, 25878,  7939, 709, 11941,  \n26189, 25878, 25879,  25224, 25085, 26192,  877, 11545, 19259,  \n5037, 8620, 19523,  14529, 12287, 7261,  26193, 26356, 25879,  \n4140, 2653, 14075,  19528, 4664, 11460,  25877, 24646, 25501,  \n25882, 26193, 25879,  14883, 12164, 15360,  8287, 5272, 18028,  \n10068, 6491, 21783,  4882, 4881, 3773,  15588, 15587, 1732,  \n13945, 3386, 2038,  6195, 19247, 980,  7156, 19641, 19025,  \n26192, 26196, 25224,  25884, 26195, 25882,  25224, 26196, 26040,  \n25224, 26040, 25503,  7581, 15027, 15026,  16556, 22518, 22627,  \n12990, 1849, 14799,  6364, 6365, 15382,  25504, 25503, 26043,  \n2616, 1199, 1200,  25745, 26199, 25505,  21777, 14372, 15052,  \n25886, 25504, 26043,  26044, 25505, 26199,  6860, 13940, 7148,  \n17200, 12874, 22486,  26044, 26047, 25231,  26200, 25883, 26046,  \n25884, 25883, 26200,  5066, 4559, 19177,  25374, 25230, 25506,  \n464, 463, 15926,  19986, 22092, 19166,  25093, 26047, 25887,  \n25886, 25374, 25506,  25374, 25886, 26201,  10354, 5498, 10470,  \n4325, 1828, 23025,  10875, 18622, 18419,  13798, 5883, 20627,  \n25752, 25889, 25510,  26203, 26046, 26048,  2858, 2859, 4637,  \n16069, 19367, 9587,  6941, 11012, 11827,  1570, 3497, 3498,  \n6539, 20699, 595,  26205, 25896, 25755,  26205, 25511, 25753,  \n26052, 25509, 25889,  380, 379, 9821,  4931, 4932, 20895,  \n26050, 25888, 26206,  26051, 25750, 26049,  25233, 25890, 26053,  \n10612, 3417, 12893,  19695, 6136, 16779,  12086, 9610, 9611,  \n5666, 691, 690,  12223, 6512, 2377,  21062, 3900, 6279,  \n690, 12561, 16214,  26054, 25508, 26053,  18858, 17720, 5067,  \n25234, 25507, 26054,  544, 543, 9874,  25897, 25908, 26048,  \n25908, 26209, 26048,  26209, 26203, 26048,  15644, 10558, 4330,  \n26054, 26053, 26210,  11288, 3164, 6278,  25908, 25897, 26055,  \n25757, 26056, 25899,  25638, 26056, 25757,  25908, 26211, 26209,  \n4476, 8325, 12471,  13214, 13033, 8065,  25907, 26211, 25908,  \n26057, 25904, 25902,  15965, 17375, 14921,  8863, 8928, 10432,  \n26059, 25759, 26212,  25759, 25903, 26212,  25907, 26058, 26211,  \n5973, 6411, 1018,  5763, 11572, 10817,  14842, 14843, 21660,  \n25911, 26213, 26058,  25759, 26059, 25385,  25385, 26059, 26214,  \n12315, 17888, 10866,  26213, 25911, 25913,  20923, 24007, 4149,  \n19890, 2618, 8525,  9987, 19238, 2805,  19677, 1100, 11582,  \n26215, 25913, 26060,  1536, 740, 10788,  21916, 3404, 3484,  \n26060, 25912, 25914,  515, 15380, 2459,  26063, 25763, 25915,  \n3925, 7965, 17901,  26062, 26064, 25514,  26064, 25644, 25514,  \n26067, 25644, 26064,  10600, 2032, 10601,  17347, 8175, 12940,  \n25915, 26066, 26065,  26216, 26065, 26066,  11258, 7181, 6609,  \n12688, 11376, 5762,  17365, 3482, 20825,  954, 12402, 19419,  \n10432, 8928, 5307,  26068, 25646, 26067,  5977, 14117, 6408,  \n795, 794, 9223,  26217, 26066, 25916,  1600, 7055, 12932,  \n1085, 21539, 8805,  25241, 25645, 26217,  15417, 1616, 1615,  \n25645, 26071, 26217,  3602, 3604, 4646,  720, 13657, 15134,  \n6583, 15640, 17202,  5566, 829, 6468,  25918, 25764, 26218,  \n1930, 1210, 2853,  4514, 4515, 16657,  25918, 26218, 26072,  \n4916, 7546, 2109,  3619, 21834, 15270,  18954, 11167, 19666,  \n22702, 17447, 11161,  10431, 10027, 10429,  9946, 3376, 23164,  \n1075, 21845, 7921,  3472, 15747, 9457,  25389, 25516, 25919,  \n26219, 25920, 25921,  19688, 9890, 6866,  26221, 25920, 26220,  \n2173, 2172, 10419,  25920, 26221, 25922,  25649, 25922, 26221,  \n25649, 26221, 26075,  25516, 25650, 26222,  6850, 4019, 350,  \n14824, 12795, 8199,  18632, 11316, 2263,  25923, 25104, 26077,  \n10452, 11458, 16436,  17274, 18156, 21572,  26223, 26076, 25765,  \n12013, 20415, 2128,  26077, 25104, 25655,  26224, 25923, 26077,  \n7842, 17020, 8684,  26225, 26077, 25655,  26226, 25655, 25925,  \n6364, 7179, 19666,  506, 3602, 21593,  12790, 8220, 4057,  \n25929, 25523, 25657,  25395, 25770, 26228,  7561, 885, 886,  \n15068, 2324, 13353,  26230, 26079, 25927,  25926, 26079, 26231,  \n25769, 25395, 26228,  19583, 22865, 14753,  26233, 26234, 25774,  \n26233, 25774, 26082,  19461, 17175, 5489,  2252, 12637, 17877,  \n9821, 12737, 12736,  1215, 10169, 16689,  26233, 26082, 26235,  \n26233, 26235, 26594,  26082, 25772, 26235,  16938, 14586, 10752,  \n6310, 9024, 18012,  25773, 25931, 26083,  3023, 1932, 2635,  \n25931, 26236, 26083,  25932, 26232, 26237,  26232, 25932, 25774,  \n18174, 2483, 10399,  13234, 17311, 22606,  14164, 5214, 9196,  \n17660, 17659, 8153,  26086, 26085, 25930,  25662, 25932, 26237,  \n12572, 7627, 15837,  7696, 7697, 23284,  14864, 20078, 8545,  \n11129, 11741, 16602,  8527, 491, 5711,  8297, 21020, 12034,  \n26238, 26088, 25662,  1607, 16137, 13896,  4545, 4522, 12931,  \n16022, 9624, 3001,  17148, 14616, 24188,  20694, 12032, 7429,  \n25661, 25401, 26089,  25401, 25777, 26089,  11881, 2690, 3477,  \n10648, 7684, 4690,  18289, 4500, 7065,  19391, 17917, 25475,  \n9281, 10677, 20194,  365, 366, 13453,  25112, 26239, 25935,  \n4154, 5360, 19134,  10991, 23046, 18964,  5757, 3052, 1854,  \n17677, 6161, 20072,  18697, 2839, 17953,  26090, 26240, 25778,  \n25112, 25663, 26239,  6441, 2732, 3551,  15989, 15451, 17697,  \n26239, 25663, 26091,  18444, 19698, 12190,  6100, 6383, 1715,  \n26241, 25664, 26240,  14256, 12804, 1569,  25664, 25779, 26240,  \n5328, 10767, 4665,  26091, 25937, 26604,  25936, 25664, 26092,  \n1926, 4278, 6689,  2043, 1974, 1292,  26094, 25531, 26244,  \n5970, 21336, 8606,  3170, 14347, 18174,  1721, 6235, 1722,  \n15961, 5769, 7665,  2026, 2028, 6697,  25781, 25780, 26420,  \n539, 15026, 522,  20004, 1094, 20005,  14057, 14048, 19535,  \n10084, 5443, 20367,  26420, 25784, 26097,  9758, 1279, 4486,  \n25784, 26420, 25780,  16257, 2293, 8318,  3759, 15179, 16390,  \n5574, 6539, 595,  25939, 25938, 26098,  2417, 2416, 8615,  \n1596, 14088, 315,  26246, 25269, 25789,  26101, 26247, 25789,  \n22635, 474, 5461,  26100, 25667, 25939,  14521, 19964, 2283,  \n26098, 26100, 25939,  10979, 17161, 8562,  6488, 8856, 8673,  \n3951, 3952, 14680,  2368, 21186, 2369,  25940, 24825, 26246,  \n1763, 4664, 19528,  12609, 6323, 9986,  22634, 18435, 16376,  \n7408, 10693, 11847,  22096, 21726, 9363,  19312, 1351, 15901,  \n26250, 25673, 25090,  26101, 25671, 26249,  26102, 26251, 25943,  \n8150, 15198, 7501,  9161, 12450, 4700,  25672, 25415, 25944,  \n5859, 6474, 15124,  1845, 12572, 15837,  25942, 25794, 26103,  \n1308, 19394, 9418,  26102, 25943, 25670,  1701, 1700, 15113,  \n12749, 14005, 3065,  16197, 4736, 14252,  25943, 26253, 26255,  \n17654, 18629, 14805,  13720, 14140, 11871,  9284, 10276, 15656,  \n4502, 16952, 14709,  17552, 4371, 4370,  26106, 25795, 25553,  \n17105, 14698, 10500,  15086, 4087, 20106,  26106, 25553, 25678,  \n12778, 11750, 21364,  26106, 25678, 25801,  17003, 10958, 10957,  \n11632, 12465, 2438,  3635, 20903, 6968,  14749, 17807, 19970,  \n13694, 8405, 8955,  25951, 25676, 25546,  25133, 24697, 25950,  \n4572, 12468, 16754,  7102, 6618, 7103,  11694, 11695, 3611,  \n10872, 20542, 13312,  2262, 2263, 8751,  5233, 11521, 11948,  \n10339, 10333, 16292,  26257, 25951, 26256,  12217, 16786, 16261,  \n20989, 3159, 9106,  21031, 18156, 9955,  8262, 5928, 5929,  \n15519, 12097, 7675,  10543, 713, 2269,  18043, 3684, 2793,  \n26257, 26112, 25951,  16376, 11802, 19441,  4720, 4924, 20597,  \n12591, 11721, 9898,  16465, 15240, 14922,  25278, 26111, 25429,  \n24708, 25426, 26113,  25280, 24836, 25797,  26112, 26259, 26115,  \n26260, 19758, 22841,  16517, 17417, 13358,  26258, 25953, 25954,  \n12118, 9178, 22451,  26261, 26113, 25426,  20324, 20325, 3082,  \n26259, 26116, 26115,  15942, 18292, 15011,  5660, 4995, 5368,  \n26796, 26261, 25426,  20674, 12874, 3353,  5291, 15030, 934,  \n25961, 25957, 26262,  22004, 7585, 20026,  3198, 3197, 4536,  \n11320, 16786, 12217,  17032, 14205, 7241,  26264, 25281, 25682,  \n25283, 25005, 25965,  16002, 16855, 18893,  7377, 18804, 2398,  \n25147, 25965, 25005,  20400, 20100, 19581,  2583, 5748, 6693,  \n12272, 13842, 8987,  16315, 6269, 14157,  26266, 25964, 25960,  \n26266, 25960, 25961,  4884, 16402, 20138,  18399, 21565, 22133,  \n1733, 3638, 3639,  25563, 25962, 25805,  26116, 26267, 25963,  \n25147, 25807, 25965,  3397, 4572, 3398,  8653, 15029, 9073,  \n11200, 6077, 21856,  11260, 13953, 6171,  15768, 15135, 19451,  \n16328, 7872, 12452,  16579, 19935, 5672,  26268, 25806, 25963,  \n26267, 26268, 25963,  3581, 3580, 17654,  26269, 25967, 26268,  \n6785, 1923, 526,  4968, 12689, 14292,  27180, 25807, 26270,  \n4048, 888, 7832,  2030, 2029, 15521,  25286, 26120, 26271,  \n17133, 9208, 7497,  25967, 26269, 26119,  13262, 17518, 20116,  \n2031, 1927, 3665,  3982, 3981, 6732,  2392, 2686, 9475,  \n26272, 25810, 26119,  26272, 25969, 25810,  21394, 2530, 21393,  \n20445, 8982, 4515,  12597, 12596, 5267,  9879, 19774, 19824,  \n14918, 18864, 18863,  25812, 25687, 26274,  8883, 22362, 2702,  \n5201, 7426, 5202,  25688, 25163, 26121,  26121, 25163, 26123,  \n17190, 11926, 11925,  7733, 821, 19810,  11946, 1535, 21914,  \n337, 6683, 11940,  10422, 1997, 8167,  596, 7318, 9709,  \n25972, 25298, 25297,  13510, 10522, 18440,  25299, 26628, 25435,  \n26123, 25163, 25689,  26122, 25573, 25972,  26122, 25813, 25573,  \n10633, 22033, 10415,  25689, 25975, 26123,  4621, 5533, 839,  \n20119, 6098, 1335,  25438, 25971, 25974,  21856, 16279, 10837,  \n9769, 7744, 7745,  25691, 25976, 26124,  16021, 6543, 23533,  \n25816, 25167, 26275,  26275, 25167, 25691,  808, 15321, 15087,  \n9728, 16301, 22167,  13878, 1817, 10857,  14247, 19947, 9988,  \n19427, 13219, 7507,  15635, 19357, 3249,  25169, 24864, 25977,  \n7599, 15725, 1558,  16612, 3486, 2596,  6486, 12028, 12215,  \n26277, 25694, 25979,  4457, 435, 20162,  25440, 25442, 26464,  \n5053, 10623, 3370,  6854, 10612, 12893,  3212, 22059, 15116,  \n14851, 9227, 8600,  26278, 26464, 25442,  10115, 8532, 13268,  \n26277, 25817, 25301,  26278, 25442, 26125,  11832, 11831, 10667,  \n1218, 1751, 3488,  12909, 22950, 19223,  7682, 5615, 13153,  \n2650, 11453, 14494,  12611, 12613, 8612,  15432, 13513, 22346,  \n6712, 6711, 10194,  26279, 25446, 25302,  13649, 16057, 17627,  \n25577, 24726, 25981,  25577, 25981, 26127,  12942, 14263, 13415,  \n8843, 11666, 11284,  3054, 11816, 7703,  19963, 4689, 15476,  \n6575, 6576, 16078,  26471, 25175, 25820,  2521, 17251, 4204,  \n25824, 26130, 25310,  9943, 9942, 6848,  26129, 25304, 26128,  \n15584, 3263, 4247,  6958, 1697, 1696,  12318, 18513, 21454,  \n7971, 20492, 13735,  19732, 18295, 12882,  20453, 16715, 1648,  \n5529, 2091, 18104,  19156, 7142, 16838,  13724, 16651, 5071,  \n13902, 10742, 10760,  4333, 15693, 12833,  2480, 5483, 1592,  \n26280, 25984, 25826,  20888, 21442, 5007,  26131, 26280, 25826,  \n1392, 9959, 15631,  21375, 22680, 21851,  12403, 14739, 1991,  \n6264, 15499, 6265,  15575, 1070, 12029,  19893, 2429, 5520,  \n26131, 26281, 26280,  5678, 4520, 20224,  20392, 23182, 15808,  \n10108, 4848, 15622,  1570, 12804, 3497,  26281, 26131, 25583,  \n1000, 911, 12726,  25179, 24876, 26132,  13686, 1701, 12072,  \n26133, 25318, 25704,  3445, 8683, 12071,  10593, 20022, 20049,  \n25583, 25702, 26281,  1308, 12275, 7956,  23685, 20005, 4699,  \n22608, 23972, 21758,  25986, 26135, 25317,  3545, 13664, 1221,  \n16585, 16584, 19499,  25988, 26282, 25320,  6892, 13141, 8146,  \n7878, 11352, 6175,  13715, 10600, 10601,  6731, 4502, 23471,  \n13005, 16808, 15058,  16972, 12881, 14649,  20469, 6684, 14463,  \n13093, 14627, 21258,  13701, 3590, 13702,  25585, 26283, 25322,  \n15095, 18991, 8329,  9153, 13040, 13376,  14222, 20853, 20241,  \n25042, 26134, 25990,  25831, 25321, 25832,  12147, 14739, 12759,  \n16645, 833, 19029,  25324, 25834, 25832,  12614, 15638, 5293,  \n19559, 16950, 15266,  4096, 17192, 11144,  13085, 10232, 11593,  \n26288, 24882, 26137,  25457, 25990, 25992,  7829, 7830, 20589,  \n4118, 2604, 9521,  3910, 23334, 4182,  23046, 534, 18964,  \n11854, 11094, 6823,  15622, 4848, 22070,  9249, 1478, 1571,  \n5833, 15477, 3814,  25459, 25588, 26289,  15256, 6320, 6563,  \n18697, 2838, 2839,  16941, 9722, 6201,  7112, 16049, 17861,  \n1579, 14548, 7537,  2211, 2210, 1823,  20133, 20079, 425,  \n20553, 4763, 23348,  25995, 25592, 25997,  11817, 10495, 11403,  \n25185, 25997, 25592,  25591, 25996, 26292,  1229, 9220, 18502,  \n17446, 17325, 9247,  19781, 19356, 2081,  6862, 6863, 5966,  \n6860, 2748, 13940,  1914, 6667, 9209,  5692, 5693, 17500,  \n25187, 25330, 25998,  15522, 172, 12692,  26294, 25711, 25464,  \n1557, 6532, 6531,  9007, 10117, 18352,  15255, 14491, 14834,  \n26294, 25464, 26295,  25333, 25189, 25186,  13047, 16456, 19742,  \n25999, 25839, 26296,  25464, 25595, 25840,  3763, 16912, 12191,  \n25192, 26297, 26301,  4834, 15812, 4835,  26296, 25839, 26298,  \n10049, 9304, 14380,  26299, 11306, 18988,  9961, 17781, 1702,  \n11277, 6599, 11976,  26492, 26004, 26489,  26144, 26489, 26002,  \n23730, 13653, 3513,  347, 8006, 348,  26145, 26144, 26002,  \n26002, 26489, 26004,  12001, 22833, 10194,  22232, 15637, 17740,  \n26300, 25843, 26003,  10094, 8683, 3149,  844, 3769, 12362,  \n3667, 5918, 7270,  7018, 10479, 11031,  20018, 16066, 7974,  \n14326, 14327, 1998,  26300, 26003, 26303,  26003, 25717, 26303,  \n25468, 25050, 25714,  19119, 11776, 17590,  26001, 26301, 26305,  \n1362, 8183, 14370,  26004, 26306, 26146,  8115, 12680, 12454,  \n25470, 26304, 25839,  15591, 21145, 21276,  26303, 25717, 25844,  \n9862, 13389, 20304,  3334, 10408, 15139,  5998, 9112, 5577,  \n25469, 25722, 25193,  6059, 11136, 7023,  8231, 8425, 19578,  \n26006, 26147, 26151,  22860, 9612, 13001,  11395, 13079, 1252,  \n16530, 9221, 16529,  15011, 15012, 6503,  13147, 9609, 14423,  \n15411, 3896, 19888,  26308, 26309, 26310,  11064, 12566, 16641,  \n17791, 8939, 10464,  1665, 16751, 20247,  14361, 9673, 21292,  \n9027, 9028, 11153,  21729, 21297, 17218,  21632, 12554, 12555,  \n20423, 3754, 9557,  1601, 12932, 7120,  18748, 2928, 1066,  \n9666, 1560, 6084,  25601, 24893, 25197,  19035, 1692, 18997,  \n6291, 14274, 18182,  5618, 8585, 7353,  4933, 14418, 17456,  \n25849, 25850, 26153,  26010, 26151, 26152,  4582, 15764, 21592,  \n8534, 15508, 5103,  10485, 10467, 9849,  13421, 1729, 1728,  \n16303, 15243, 9091,  17447, 17936, 11161,  12561, 13171, 16214,  \n14845, 8026, 7836,  23323, 11707, 14072,  5287, 18196, 5497,  \n26010, 26152, 26012,  13092, 3828, 7973,  1366, 22906, 17925,  \n4096, 11144, 6832,  15537, 6686, 4286,  2470, 15732, 13497,  \n881, 12494, 17935,  25724, 25338, 25606,  17341, 16885, 2290,  \n5101, 6741, 10687,  3935, 3480, 14959,  26312, 26157, 26012,  \n20748, 9799, 21687,  16545, 11031, 4033,  25343, 25728, 26314,  \n17611, 23676, 22117,  26315, 25480, 25485,  3277, 13667, 3278,  \n7982, 20574, 23001,  21190, 9708, 13054,  26016, 26015, 26157,  \n21081, 18839, 19272,  456, 20727, 455,  13502, 7090, 4209,  \n6918, 10515, 4365,  21865, 765, 18539,  4710, 4866, 2363,  \n4346, 4345, 14034,  26158, 25607, 25612,  25607, 25346, 25612,  \n21203, 19110, 8976,  1680, 4448, 9431,  17474, 5375, 509,  \n1430, 5535, 15287,  18136, 4341, 15288,  25610, 25853, 26160,  \n9249, 9347, 1478,  1949, 17732, 10617,  4215, 16360, 23317,  \n13489, 12764, 16284,  2863, 3920, 2862,  14235, 1706, 10794,  \n15693, 11022, 13457,  14369, 21086, 8346,  5822, 5392, 4482,  \n25349, 25070, 26020,  7185, 7184, 20386,  13713, 4531, 7146,  \n4619, 18690, 4620,  4753, 21961, 5823,  26318, 26020, 25858,  \n25857, 25210, 25856,  7902, 20267, 6030,  26021, 25212, 25616,  \n6415, 18846, 15745,  13862, 1417, 13571,  13955, 4130, 4132,  \n25615, 25855, 26162,  12577, 13705, 11689,  9733, 5841, 9775,  \n26022, 26163, 26320,  14445, 5471, 11217,  17652, 20005, 23685,  \n11851, 11080, 21751,  26319, 25616, 25729,  26163, 25863, 26165,  \n26165, 26166, 26164,  1112, 13950, 6350,  11906, 13299, 13300,  \n21178, 1960, 5147,  26321, 26166, 26025,  19675, 6249, 20403,  \n11155, 5244, 23940,  26163, 26022, 25860,  23706, 20819, 16108,  \n19945, 18742, 19545,  26321, 26025, 26167,  26167, 26322, 26321,  \n8638, 13448, 7362,  15601, 12474, 11698,  26167, 26324, 26322,  \n25861, 25859, 26162,  3307, 17500, 13101,  25861, 26162, 26323,  \n16466, 5380, 7024,  25492, 25072, 26325,  15439, 10810, 20236,  \n26327, 26328, 26326,  26329, 26330, 26327,  26331, 26330, 26329,  \n988, 990, 10716,  26332, 25861, 26323,  26334, 26324, 26333,  \n25617, 25353, 26027,  26326, 26335, 26336,  21449, 4665, 15252,  \n4849, 4851, 1100,  26332, 26026, 25861,  2778, 1847, 2120,  \n18362, 20101, 18058,  10019, 11560, 9424,  16832, 16833, 5375,  \n8809, 4082, 8399,  26329, 26327, 26326,  26338, 25492, 26325,  \n26337, 26335, 26326,  26326, 26336, 26329,  9116, 16699, 18235,  \n5651, 22352, 16348,  10469, 10470, 22291,  26329, 26175, 26331,  \n26171, 26339, 26175,  26175, 26339, 26331,  13064, 450, 449,  \n2467, 11346, 2258,  15406, 11855, 1089,  26178, 25074, 25492,  \n26178, 25492, 26338,  18210, 11909, 18209,  26336, 26335, 26341,  \n26329, 26336, 26175,  22658, 19824, 19774,  26175, 25732, 26028,  \n26175, 26028, 26171,  26339, 26171, 26169,  26340, 26343, 26168,  \n26340, 26029, 26176,  26340, 26168, 26029,  26167, 25736, 26333,  \n506, 14287, 10302,  12495, 17527, 18481,  3156, 21408, 13961,  \n26175, 26336, 25868,  16170, 619, 10097,  9327, 17369, 20679,  \n13030, 2937, 20912,  18137, 24752, 12713,  5838, 5951, 5950,  \n4159, 13248, 4160,  13103, 517, 2458,  26181, 26172, 26030,  \n14447, 21021, 19382,  16183, 16689, 10588,  18917, 9750, 1746,  \n26027, 25359, 25869,  5681, 722, 18558,  4702, 3435, 3437,  \n26341, 26179, 26336,  26336, 26179, 25868,  26344, 26343, 26340,  \n26176, 26344, 26340,  6489, 6857, 8099,  25736, 26182, 26333,  \n22376, 16004, 23292,  12687, 3991, 22155,  3873, 8358, 13639,  \n14304, 14305, 625,  17806, 20819, 23706,  26180, 26344, 26176,  \n26182, 26345, 26333,  26346, 25622, 26178,  19444, 15040, 14625,  \n10574, 10573, 4323,  19866, 12082, 7595,  14345, 6236, 21601,  \n26172, 26181, 26180,  14927, 13995, 1992,  3131, 21835, 15470,  \n6360, 6359, 10351,  26031, 25869, 25735,  6521, 9211, 20114,  \n3079, 4074, 1925,  7093, 11223, 17887,  10137, 14541, 13213,  \n25738, 26033, 26182,  902, 10816, 5204,  15481, 9762, 13412,  \n6318, 1010, 7976,  5881, 14877, 17082,  4016, 2387, 20904,  \n18197, 7105, 7166,  12872, 3270, 8662,  18383, 20793, 15806,  \n26035, 26349, 26033,  9831, 4106, 17237,  7424, 1510, 20437,  \n7377, 5880, 17259,  24924, 26350, 25737,  4425, 9948, 13629,  \n26351, 26349, 26352,  14597, 11204, 15689,  12893, 3417, 2579,  \n25363, 26032, 26184,  25498, 24787, 26184,  24924, 25083, 26037,  \n2230, 14689, 13191,  26035, 26185, 26349,  17865, 7772, 17312,  \n4373, 15426, 19078,  2824, 7399, 2825,  26185, 26035, 26036,  \n1951, 15169, 13390,  15517, 14030, 21788,  4806, 2519, 19605,  \n12227, 16471, 16472,  20680, 5308, 18212,  25500, 25739, 26354,  \n12087, 17381, 19258,  25875, 25498, 26353,  10817, 11572, 1471,  \n4467, 1027, 16318,  4761, 14745, 8626,  3824, 12418, 16274,  \n6000, 2550, 13177,  13942, 3531, 13943,  2294, 22577, 22115,  \n14602, 15721, 15708,  18418, 13068, 13067,  6190, 14607, 20068,  \n12705, 14034, 15777,  6563, 6322, 14174,  26187, 26188, 26189,  \n26189, 26356, 26187,  25368, 25875, 26190,  26189, 25879, 26356,  \n19389, 16298, 11730,  19915, 10356, 9937,  15992, 13046, 13394,  \n20402, 3327, 3328,  26194, 26039, 26191,  26193, 25882, 26195,  \n14454, 14422, 14421,  881, 3043, 3526,  8064, 13685, 17800,  \n26039, 26194, 26357,  14275, 8769, 16643,  15370, 11837, 11838,  \n11645, 295, 20527,  26039, 26042, 25745,  11484, 4405, 4404,  \n19692, 8565, 5791,  21193, 3246, 3269,  13927, 5529, 18104,  \n26043, 25503, 26040,  5010, 20136, 19244,  1453, 3482, 17365,  \n25633, 26197, 24791,  3357, 4617, 8752,  26200, 26358, 25884,  \n7929, 898, 21271,  25886, 26043, 26361,  8479, 13325, 10365,  \n853, 12602, 10782,  17550, 20959, 9187,  26363, 26358, 26200,  \n9121, 2401, 12895,  26045, 26362, 25633,  26364, 25886, 26361,  \n15201, 7420, 17919,  25886, 26364, 26201,  3989, 3474, 10423,  \n26046, 26203, 26200,  26203, 26365, 26200,  16710, 7916, 7915,  \n11011, 11246, 7596,  15736, 10331, 16713,  16840, 16961, 16133,  \n13639, 8358, 8357,  8304, 9255, 6145,  25374, 26201, 25888,  \n12623, 25499, 19804,  7329, 19477, 19566,  21449, 14876, 14861,  \n26365, 26363, 26200,  5446, 21953, 5445,  17846, 23904, 14279,  \n13164, 18555, 4012,  25512, 25896, 26204,  25896, 26367, 26204,  \n26368, 26205, 25894,  1867, 3106, 13423,  13538, 13433, 21961,  \n12901, 20057, 13535,  6083, 7916, 16710,  2860, 19160, 14675,  \n26049, 26050, 26370,  26370, 26051, 26049,  26051, 26370, 26371,  \n26372, 26051, 26371,  25890, 26372, 26053,  14308, 7218, 14836,  \n26207, 25892, 25891,  3919, 15136, 3917,  26208, 26373, 25893,  \n19487, 20166, 20126,  26374, 26203, 26209,  26374, 26365, 26203,  \n14445, 900, 15511,  18678, 17051, 22140,  2543, 7146, 4531,  \n26210, 26053, 26375,  26376, 26054, 26210,  26054, 26376, 25234,  \n25891, 25234, 26376,  10470, 5498, 1921,  26208, 25893, 25892,  \n13514, 13431, 11778,  5127, 18636, 12555,  13242, 2409, 3779,  \n26377, 26056, 25638,  26378, 26210, 26375,  9745, 4482, 5392,  \n26379, 26376, 26380,  26381, 26376, 26379,  5959, 3877, 16089,  \n26382, 26374, 26209,  3408, 9017, 14864,  26210, 26380, 26376,  \n5698, 7154, 11508,  10072, 1168, 12125,  26209, 26211, 26382,  \n19501, 7979, 14185,  18761, 12600, 3245,  12998, 14397, 10055,  \n26211, 26383, 26382,  4120, 16309, 12224,  25904, 26384, 25903,  \n9191, 7210, 9192,  5217, 5218, 25381,  26058, 26383, 26211,  \n26058, 26385, 26383,  1610, 5139, 17481,  19607, 18631, 10236,  \n12936, 18998, 17635,  26385, 26058, 26213,  4212, 4213, 9891,  \n26386, 26385, 26213,  12637, 2252, 2251,  23706, 18152, 17806,  \n26387, 26386, 26213,  18048, 19020, 3674,  25913, 26387, 26213,  \n25762, 25385, 26214,  26214, 26388, 25762,  14764, 1393, 13781,  \n21230, 6415, 20168,  26215, 26387, 25913,  15426, 17160, 19078,  \n20306, 17401, 2659,  19777, 3876, 14300,  7939, 6303, 9702,  \n12389, 7949, 5185,  15755, 7014, 12926,  5610, 10862, 5611,  \n1415, 6357, 6356,  7862, 7861, 6475,  26063, 26060, 25914,  \n26389, 26060, 26063,  26215, 26060, 26389,  7976, 1010, 9640,  \n22036, 15650, 14903,  26390, 26064, 26062,  11012, 21460, 11013,  \n14960, 10010, 10009,  25915, 26065, 26063,  4734, 15779, 3575,  \n26065, 26392, 26063,  4190, 6718, 18627,  26392, 26065, 26216,  \n26392, 26216, 26393,  9560, 12213, 13723,  4408, 13722, 5271,  \n26394, 26393, 26216,  26573, 26068, 26067,  8954, 8428, 18859,  \n9382, 10052, 11471,  1837, 16330, 15494,  17466, 17086, 17087,  \n26395, 26394, 26216,  1319, 16101, 8468,  1580, 20726, 1581,  \n26216, 26066, 26397,  303, 10941, 18942,  21592, 6303, 4582,  \n25917, 25646, 26069,  3172, 3171, 2339,  13952, 13091, 13092,  \n26066, 26217, 26397,  13309, 10651, 3811,  8169, 12295, 8170,  \n26218, 26399, 26072,  26399, 26400, 26072,  994, 3655, 18588,  \n26072, 26400, 26073,  3786, 6024, 4451,  12017, 9984, 7548,  \n25919, 26071, 25645,  26073, 26401, 26402,  26073, 26402, 25921,  \n25921, 26402, 26219,  5944, 14044, 375,  19191, 3914, 835,  \n7336, 15194, 6321,  25920, 26219, 26220,  13126, 13693, 13692,  \n12457, 11488, 11487,  7924, 8445, 8446,  26404, 25765, 26075,  \n16338, 7369, 16339,  19555, 22181, 23167,  26404, 26223, 25765,  \n13027, 1193, 11848,  12439, 12440, 1306,  2702, 2899, 2703,  \n14394, 10781, 15148,  11066, 6881, 6880,  12715, 2180, 11372,  \n5272, 15489, 17407,  872, 7746, 20659,  12715, 11372, 6371,  \n26078, 26076, 26223,  26076, 26078, 25924,  15192, 22591, 6515,  \n26225, 25655, 26226,  26408, 26225, 26226,  25928, 26407, 26229,  \n2914, 6895, 12247,  25929, 25657, 26227,  25394, 25769, 25925,  \n7368, 15192, 6515,  26229, 25927, 25928,  508, 20851, 3098,  \n13594, 9249, 1571,  16236, 1119, 4509,  26234, 26233, 26409,  \n10673, 13788, 18224,  16234, 20812, 16783,  16345, 17067, 1913,  \n5456, 7140, 5417,  442, 9386, 6327,  10704, 15168, 6701,  \n26234, 26410, 26232,  25774, 26234, 26232,  17227, 16606, 19098,  \n11050, 6927, 1832,  10946, 10945, 3849,  25772, 26083, 26411,  \n26235, 25772, 26411,  3596, 14183, 13911,  10025, 15200, 2870,  \n4328, 6546, 13579,  26412, 26083, 26236,  3619, 7032, 11046,  \n25931, 26085, 26236,  26085, 26413, 26236,  12934, 16792, 12601,  \n22132, 3102, 8028,  18395, 4483, 11938,  6639, 13648, 14869,  \n775, 15357, 15358,  6423, 14825, 1664,  6669, 13739, 16479,  \n9073, 10557, 11765,  26237, 26414, 26238,  26086, 25930, 26415,  \n19650, 21007, 760,  25662, 26237, 26238,  18681, 10259, 18679,  \n15230, 11789, 9322,  1634, 5855, 15813,  13628, 14220, 867,  \n17877, 9523, 18248,  10800, 14397, 13324,  26089, 25777, 25933,  \n26088, 26238, 26601,  7357, 5875, 11295,  26088, 26601, 26416,  \n25934, 26088, 26416,  11881, 3477, 3478,  13146, 9304, 9289,  \n26416, 26090, 25934,  3219, 8134, 17911,  15953, 9302, 1305,  \n3776, 18698, 3777,  6626, 6628, 16205,  12460, 17129, 22153,  \n11482, 8021, 8035,  7250, 7759, 7249,  15825, 10206, 5295,  \n19544, 6100, 6101,  25779, 25778, 26240,  12601, 7602, 11275,  \n17835, 16433, 8346,  8065, 9989, 8064,  25664, 26241, 26092,  \n6625, 17595, 21084,  10679, 14926, 3258,  2886, 21393, 2885,  \n25937, 25530, 26418,  1824, 8957, 7776,  722, 723, 11477,  \n13237, 15377, 8018,  14549, 4688, 15648,  26418, 25530, 25781,  \n22098, 2912, 10397,  22101, 7243, 20087,  25069, 8917, 11796,  \n26095, 26421, 26096,  11326, 3314, 29382,  26419, 26097, 26096,  \n26419, 26096, 26421,  7956, 19653, 9866,  26420, 26097, 26419,  \n21693, 5583, 14236,  26422, 25938, 26423,  10490, 21214, 20858,  \n8192, 9719, 16035,  4648, 5532, 14820,  26423, 25938, 26099,  \n9113, 5379, 12956,  9153, 26424, 20574,  10109, 4787, 7326,  \n25941, 26245, 25791,  22101, 13960, 18410,  2425, 3130, 4563,  \n16862, 12151, 16863,  23790, 9389, 9856,  16623, 9900, 13864,  \n26607, 25941, 25944,  26426, 25942, 26103,  11991, 13175, 15531,  \n4940, 10315, 978,  7378, 7379, 3495,  1701, 15113, 12297,  \n11973, 11373, 2180,  26428, 26104, 26429,  26430, 26101, 26249,  \n25547, 25555, 25944,  14188, 12387, 2695,  937, 12579, 2097,  \n15386, 13515, 2169,  16373, 8277, 12638,  8285, 887, 16428,  \n12430, 6731, 10217,  13922, 22813, 24110,  2030, 14629, 8414,  \n26105, 25944, 25555,  26254, 25796, 26252,  26104, 25795, 26106,  \n12492, 11914, 11044,  5805, 4088, 20029,  3958, 20904, 13751,  \n6914, 6913, 592,  19959, 10441, 19958,  1651, 6832, 15894,  \n22490, 11290, 11221,  6664, 6665, 2612,  25945, 25943, 26255,  \n26250, 24696, 25673,  2702, 22362, 15446,  18111, 12195, 13160,  \n26108, 25945, 26255,  26105, 25555, 25947,  3257, 3256, 20142,  \n17106, 16141, 1821,  13535, 16029, 14100,  26106, 25801, 25955,  \n12858, 951, 953,  9931, 3780, 18022,  21127, 15166, 3774,  \n18540, 15303, 12948,  4028, 12699, 19215,  6771, 20565, 17254,  \n1248, 1249, 7279,  14607, 2837, 2836,  1176, 10263, 23828,  \n17596, 7322, 17373,  4464, 7301, 4465,  26110, 25945, 26108,  \n6470, 20860, 10315,  14820, 10578, 8161,  14924, 17946, 7390,  \n25954, 26110, 26432,  13310, 4159, 15229,  3324, 21016, 3139,  \n26433, 25278, 25799,  25802, 25946, 25417,  26256, 25546, 25948,  \n5958, 2123, 5584,  1029, 5146, 15273,  26435, 26257, 26256,  \n11247, 11248, 10318,  26256, 25951, 25546,  25954, 26432, 26437,  \n10599, 12234, 2481,  25955, 25559, 26113,  5146, 7237, 15273,  \n3782, 3784, 16979,  26111, 25278, 26433,  6791, 8366, 1931,  \n16890, 12511, 7012,  9754, 8916, 9753,  18199, 21204, 13493,  \n4991, 11016, 11347,  5072, 7588, 20668,  5219, 21663, 5220,  \n11258, 6609, 5121,  8922, 12607, 8923,  19237, 6820, 11921,  \n26438, 26112, 26257,  7556, 7557, 12338,  9911, 14277, 9912,  \n5665, 18027, 1274,  26259, 26438, 26439,  26112, 26438, 26259,  \n2991, 3507, 2656,  16915, 15646, 4302,  25957, 26258, 26262,  \n25953, 26258, 25957,  13547, 17346, 8392,  2633, 2632, 392,  \n17600, 14785, 11550,  9916, 6881, 11066,  26264, 25000, 25281,  \n3540, 3539, 3015,  2314, 10809, 7557,  852, 16613, 6273,  \n22676, 11937, 3253,  26259, 26441, 26116,  17848, 17789, 16138,  \n2066, 7393, 3418,  8806, 4559, 17641,  3514, 17615, 18506,  \n18029, 21851, 22680,  9635, 704, 3573,  19314, 11050, 11815,  \n26441, 26267, 26116,  26262, 26266, 25961,  26447, 25561, 25964,  \n11698, 12474, 12473,  26447, 25964, 26266,  8853, 1040, 9468,  \n10105, 3289, 3364,  13455, 17831, 9117,  26445, 26448, 26267,  \n9536, 8688, 16818,  26268, 26267, 26450,  18769, 3102, 22132,  \n6816, 9330, 3180,  26268, 25967, 25806,  526, 2920, 2919,  \n822, 22722, 16275,  18329, 1549, 3804,  450, 9372, 7656,  \n12666, 8721, 689,  26119, 26269, 26451,  17579, 20154, 16818,  \n26272, 26119, 26451,  26272, 26452, 25969,  26273, 25969, 26452,  \n25969, 26273, 25968,  7536, 1705, 20712,  13547, 20088, 18627,  \n25968, 26453, 25970,  17767, 23471, 4502,  19412, 5075, 20469,  \n14222, 19095, 15720,  1480, 18028, 1481,  12315, 10866, 2533,  \n10847, 10718, 10636,  10506, 14157, 6269,  25970, 26454, 25687,  \n26270, 25807, 25435,  26120, 25569, 25688,  14999, 4486, 14966,  \n19926, 11514, 13129,  13093, 15390, 14627,  13569, 5099, 6315,  \n26456, 26274, 25687,  8736, 8735, 9135,  5782, 8681, 8682,  \n21539, 12412, 8805,  8146, 23005, 1068,  9962, 3716, 12357,  \n6129, 11359, 6130,  17771, 23361, 23360,  5962, 6942, 5963,  \n8023, 15841, 14350,  4381, 14146, 10774,  8065, 5811, 9989,  \n25813, 26458, 25814,  12874, 17200, 6821,  26459, 26460, 25975,  \n15461, 2575, 2576,  25976, 25814, 26458,  25815, 26459, 25975,  \n25976, 26461, 26124,  1328, 18945, 22894,  20973, 15688, 12683,  \n25299, 25440, 25973,  26459, 25815, 25978,  6941, 21460, 11012,  \n14740, 18214, 4642,  2699, 22074, 11622,  26459, 25978, 26462,  \n19819, 5785, 6742,  10023, 23667, 11981,  8764, 14111, 20140,  \n1114, 7787, 10935,  26464, 26463, 25440,  3073, 14564, 21730,  \n26462, 26465, 26466,  10288, 10290, 18785,  14725, 14724, 14620,  \n14526, 1260, 16000,  16792, 12934, 26468,  16133, 16961, 8491,  \n25301, 25694, 26277,  3773, 11805, 11804,  19664, 5591, 18826,  \n14012, 19516, 992,  26277, 26469, 25817,  26125, 25442, 25819,  \n3953, 20100, 20400,  8834, 14962, 13479,  15588, 419, 418,  \n14415, 6810, 13289,  5152, 1048, 4354,  9766, 19212, 13468,  \n26470, 25818, 26471,  20346, 7150, 10748,  17360, 771, 1524,  \n25819, 25580, 26472,  25303, 25175, 26471,  25446, 26279, 26126,  \n2307, 1350, 1874,  19777, 19687, 17245,  11849, 13669, 11393,  \n18448, 18809, 10911,  12472, 15406, 15654,  5686, 10008, 19062,  \n8954, 12863, 11310,  20726, 3318, 3317,  2433, 16738, 10046,  \n4839, 12150, 1386,  12164, 6549, 15360,  6918, 14831, 10515,  \n25582, 26475, 26128,  25824, 25697, 26474,  1156, 4891, 12095,  \n25582, 25822, 26476,  22011, 10840, 10371,  25035, 26984, 25699,  \n25985, 25696, 26477,  19643, 16408, 23148,  9221, 10848, 13561,  \n3959, 2739, 8526,  750, 3163, 5097,  17601, 13043, 12293,  \n19306, 5789, 6072,  5617, 1305, 882,  26478, 25828, 25985,  \n25452, 25699, 26988,  5691, 13230, 9590,  11298, 8866, 9889,  \n25701, 25452, 26988,  25829, 25453, 25828,  4294, 12410, 21796,  \n2252, 17877, 2253,  16683, 7671, 12391,  12332, 458, 15642,  \n26480, 26280, 26281,  11879, 5035, 4566,  21776, 13204, 3628,  \n13447, 8836, 14619,  25830, 25320, 26282,  17552, 11939, 4371,  \n14040, 19035, 18997,  15812, 2938, 4835,  10835, 15555, 12230,  \n13179, 20623, 23157,  26481, 25987, 25454,  5182, 16785, 3467,  \n26281, 25702, 26482,  26135, 25703, 25317,  23190, 803, 16454,  \n4210, 22236, 8453,  3602, 6079, 9805,  25831, 26482, 25702,  \n18864, 14918, 3386,  1591, 1590, 9032,  13665, 19124, 19338,  \n13129, 21693, 19926,  25549, 20635, 10283,  14915, 850, 3979,  \n2711, 20146, 20147,  26482, 25831, 26136,  6065, 12571, 12570,  \n25989, 25322, 26283,  15418, 21004, 17070,  26286, 25988, 25456,  \n3203, 2448, 3804,  17887, 7273, 21400,  15113, 14790, 12297,  \n25458, 22288, 24884,  22653, 11400, 13311,  3007, 17835, 21660,  \n11530, 3071, 1055,  305, 9881, 19858,  9626, 11793, 21581,  \n21571, 20538, 8274,  5460, 11757, 23441,  17082, 9439, 5881,  \n9858, 8012, 12290,  2839, 16175, 12636,  15801, 19274, 8445,  \n26138, 26484, 25837,  9441, 14936, 14937,  3932, 3211, 3931,  \n26485, 25993, 25707,  10368, 759, 13942,  17278, 2617, 11435,  \n5325, 3231, 13451,  25707, 25460, 25327,  2794, 13947, 18566,  \n25992, 26140, 25461,  3130, 2425, 3129,  15090, 11026, 14452,  \n8704, 1091, 20239,  25588, 25183, 26486,  7540, 17714, 17713,  \n10004, 4602, 5032,  13067, 21513, 11501,  2401, 9121, 8447,  \n13047, 5539, 23473,  25328, 25047, 25590,  15541, 20902, 8766,  \n16164, 16111, 16072,  12461, 4126, 9968,  25463, 25590, 26291,  \n3666, 1290, 2631,  7145, 5615, 7682,  3883, 8563, 16949,  \n17344, 4145, 15034,  4239, 13013, 8276,  1785, 17670, 11379,  \n25591, 26292, 25186,  2005, 9119, 3250,  9029, 25081, 10842,  \n16113, 13068, 6596,  26488, 23210, 14307,  25838, 25332, 25710,  \n7798, 15701, 2278,  8555, 21137, 6859,  13021, 998, 2027,  \n11148, 11147, 9090,  26491, 26489, 26144,  9679, 5122, 15669,  \n2694, 7286, 14035,  26656, 26491, 26144,  26493, 26656, 26144,  \n18074, 6739, 6480,  26300, 26493, 26145,  16546, 16545, 11843,  \n13342, 6275, 6561,  26493, 26144, 26145,  15340, 6055, 20900,  \n17373, 5356, 7319,  2299, 15095, 2300,  19064, 14626, 9280,  \n1631, 17997, 16362,  18575, 7165, 16323,  1422, 12017, 7719,  \n2147, 5332, 4958,  26300, 26145, 25843,  18915, 26494, 25376,  \n12995, 13776, 14041,  13981, 5900, 16016,  21555, 15601, 6586,  \n9916, 6210, 6881,  22514, 8860, 8859,  13472, 3975, 8263,  \n26306, 26004, 26492,  2372, 904, 903,  26304, 26298, 25839,  \n8497, 16435, 16437,  13583, 559, 1479,  2110, 2109, 7546,  \n11313, 24390, 3812,  18919, 10122, 4150,  18933, 18932, 623,  \n345, 19915, 21236,  10427, 16814, 429,  10027, 17997, 9525,  \n8262, 2473, 17627,  26146, 26496, 26495,  26146, 26495, 26147,  \n9966, 17299, 814,  26303, 25844, 26497,  10989, 6060, 1493,  \n864, 863, 8571,  22879, 4745, 4744,  18689, 18807, 18808,  \n7369, 16338, 11567,  19228, 21629, 6937,  8013, 15496, 7678,  \n26497, 25844, 26149,  5367, 11716, 5269,  26499, 25715, 25716,  \n2467, 19510, 11346,  26148, 26001, 26305,  11267, 14701, 11985,  \n19990, 22218, 1895,  293, 292, 12325,  8236, 15667, 10811,  \n26499, 25716, 26007,  7868, 11433, 4008,  26147, 26500, 26151,  \n25721, 26150, 26307,  17178, 23972, 10436,  12971, 11263, 16157,  \n25723, 26153, 26150,  20904, 2387, 17178,  26501, 25052, 25600,  \n26502, 20995, 22813,  26151, 26500, 26152,  14388, 7420, 8173,  \n25471, 26503, 25722,  18644, 18864, 18400,  10403, 18516, 11764,  \n18688, 14836, 7218,  21193, 3269, 16425,  2699, 17033, 6309,  \n19043, 9020, 3696,  26154, 26009, 26311,  26152, 26312, 26012,  \n9149, 6426, 9685,  7123, 6551, 22408,  19195, 5912, 5911,  \n26009, 25724, 26311,  19096, 4846, 14939,  16526, 21150, 15587,  \n25604, 26505, 25471,  4950, 10626, 4951,  1034, 19166, 5663,  \n25479, 26013, 25726,  5093, 15972, 9224,  25604, 25608, 26505,  \n26666, 25850, 26014,  26506, 25606, 25480,  25726, 26013, 25728,  \n6494, 6506, 8452,  2041, 17420, 14058,  25343, 26314, 25485,  \n14622, 10432, 3992,  26014, 25851, 26507,  9494, 15686, 19951,  \n5303, 18475, 12682,  5957, 21995, 15344,  1246, 13118, 9802,  \n25634, 8629, 22782,  26156, 25607, 26158,  19177, 15684, 14536,  \n12502, 7456, 23377,  1201, 1233, 1232,  5623, 3247, 3249,  \n26160, 26016, 26509,  25853, 26016, 26160,  5023, 14236, 5583,  \n13110, 13109, 22906,  21814, 4334, 11851,  6380, 11187, 2461,  \n6508, 5481, 1924,  10872, 13743, 20542,  26316, 25612, 26018,  \n17033, 2698, 4501,  26017, 25349, 26020,  12925, 4090, 4089,  \n18017, 9625, 12129,  3035, 1978, 1977,  16675, 8116, 8115,  \n7407, 17640, 7406,  1340, 22278, 4943,  25611, 25489, 26511,  \n476, 19496, 9779,  2816, 13720, 12107,  11903, 14806, 12929,  \n413, 8361, 15325,  10786, 10333, 16011,  10607, 14122, 12179,  \n26513, 26318, 26161,  26318, 25858, 26161,  26512, 26513, 26161,  \n26514, 26161, 26022,  26514, 26512, 26161,  25855, 26019, 26317,  \n17197, 18342, 11759,  25855, 25615, 25614,  9849, 1655, 13565,  \n11410, 7573, 7574,  19208, 18723, 19030,  2296, 16583, 2541,  \n26514, 26022, 26320,  16383, 7017, 20370,  13020, 19314, 11815,  \n18686, 2184, 17687,  19503, 15611, 15613,  12605, 4204, 17251,  \n20713, 6934, 20705,  14878, 12826, 15710,  13940, 2510, 12606,  \n26321, 26322, 26680,  20793, 14373, 23325,  26024, 26319, 25729,  \n13467, 18899, 10877,  22187, 19541, 6068,  13937, 8203, 12504,  \n26334, 26518, 26324,  26330, 26519, 26328,  2390, 11577, 2389,  \n26324, 26167, 26333,  8968, 12305, 10280,  26520, 26326, 26328,  \n14125, 18360, 5570,  26330, 26328, 26327,  2245, 3028, 11734,  \n11857, 4126, 21278,  16609, 8543, 11663,  15776, 22709, 11833,  \n11646, 11647, 22106,  26520, 26337, 26326,  7120, 12932, 3574,  \n26521, 26331, 26342,  21770, 1517, 2363,  26342, 26331, 26339,  \n16095, 19803, 18943,  26523, 26521, 26342,  26335, 26337, 26524,  \n10687, 12368, 1365,  18929, 20596, 9159,  10635, 3606, 3605,  \n3486, 16612, 16611,  26026, 26170, 25862,  10459, 18257, 3400,  \n8937, 844, 12362,  26337, 26522, 26524,  26342, 26339, 26687,  \n21174, 18656, 9840,  26687, 26339, 26169,  26525, 26169, 26168,  \n10382, 10384, 12226,  15260, 15259, 8410,  10439, 3369, 5701,  \n3010, 3566, 3565,  9797, 5065, 10613,  12454, 12455, 8115,  \n17703, 10082, 15816,  26524, 26526, 26335,  26341, 26335, 26526,  \n21395, 12434, 11147,  26525, 26168, 26343,  6356, 16601, 2986,  \n26181, 26173, 26527,  26181, 26030, 26173,  9330, 6816, 5952,  \n8378, 1611, 13285,  26341, 26526, 26179,  7770, 13714, 7146,  \n12439, 12845, 12440,  18369, 20432, 18370,  26345, 26334, 26333,  \n18049, 18357, 8055,  5127, 19717, 5125,  26179, 26526, 26528,  \n9215, 4496, 4497,  19907, 2081, 2080,  6860, 9739, 2748,  \n26181, 26529, 26180,  6434, 6433, 3555,  26179, 26528, 25870,  \n2700, 15841, 8023,  25872, 25622, 26346,  3994, 8633, 19032,  \n20085, 3559, 1353,  4243, 2792, 21486,  6360, 10351, 10353,  \n26347, 25869, 26031,  10302, 14457, 17792,  26345, 26182, 26033,  \n26033, 26348, 26345,  26032, 25872, 26697,  12260, 23370, 11489,  \n7163, 8212, 10064,  8739, 19636, 4984,  26348, 26349, 26530,  \n21096, 19634, 21962,  26031, 25735, 25737,  13765, 11268, 21237,  \n26349, 26348, 26033,  26351, 26530, 26349,  16735, 17748, 11807,  \n7940, 16563, 16633,  293, 19517, 292,  19896, 18912, 7797,  \n2710, 5625, 18511,  26699, 26184, 26032,  3259, 4125, 3260,  \n2726, 11974, 5235,  23058, 8335, 8334,  16153, 16154, 16961,  \n8054, 4414, 9309,  26037, 26350, 24924,  4163, 17723, 374,  \n26183, 26354, 25739,  26352, 26349, 26185,  14500, 10163, 18557,  \n6157, 6156, 14103,  18951, 489, 732,  26531, 26352, 26185,  \n6705, 13554, 20033,  26531, 26185, 26187,  2115, 3925, 7686,  \n23572, 8214, 8213,  26535, 26531, 26187,  26534, 25875, 26353,  \n11642, 8424, 15356,  25500, 26354, 26533,  10453, 4432, 18634,  \n3335, 17583, 2753,  17662, 11419, 14573,  14394, 5780, 10781,  \n4917, 2219, 7407,  5793, 12779, 15556,  26534, 26536, 25875,  \n25626, 25367, 26038,  26537, 25626, 26038,  2662, 1250, 13146,  \n8234, 10815, 12032,  26538, 26355, 25223,  6018, 1433, 21613,  \n18140, 18141, 24303,  4551, 19050, 13978,  339, 12476, 11352,  \n26536, 26190, 25875,  26540, 26187, 26356,  26540, 26535, 26187,  \n9193, 2004, 7356,  11622, 2700, 2699,  26542, 26194, 26191,  \n26539, 26542, 26191,  9978, 636, 13253,  26356, 26193, 26540,  \n26192, 25085, 26190,  11179, 9014, 22455,  26712, 26193, 26195,  \n15468, 1218, 1217,  7685, 12008, 15660,  7500, 10805, 20487,  \n18534, 14820, 21239,  18772, 20180, 17226,  13781, 13191, 14764,  \n25877, 25501, 26544,  8922, 12212, 12211,  23711, 6016, 6015,  \n12231, 12232, 5875,  6937, 6634, 6633,  8114, 4213, 13122,  \n950, 952, 6398,  26545, 26192, 26543,  14910, 14909, 20657,  \n26192, 26545, 26196,  26195, 26358, 26712,  1036, 2464, 6194,  \n25501, 24791, 26197,  26195, 25884, 26358,  6140, 8544, 885,  \n5621, 18413, 18786,  4300, 4301, 303,  1696, 16287, 6958,  \n6740, 21191, 13485,  17205, 16166, 3690,  19269, 7777, 7617,  \n26199, 25745, 26041,  22979, 13995, 12083,  22955, 20823, 17645,  \n4307, 10976, 4306,  10510, 21343, 20888,  16490, 11189, 18294,  \n9512, 18159, 4354,  26197, 25633, 26362,  26547, 26358, 26363,  \n18087, 21624, 9693,  10898, 16950, 10897,  20871, 16528, 17655,  \n2196, 11833, 7088,  9030, 12550, 9031,  16950, 19559, 10897,  \n26045, 26548, 26362,  26549, 26362, 26548,  1375, 1374, 412,  \n11905, 29738, 11904,  16604, 9020, 17175,  19087, 7340, 9452,  \n18791, 2693, 14080,  16068, 20571, 304,  11036, 6523, 16829,  \n11336, 9094, 15097,  25887, 26550, 25889,  25752, 25887, 25889,  \n9154, 18038, 9155,  26201, 26366, 25888,  25637, 25751, 26369,  \n5856, 10713, 7220,  2493, 464, 12100,  10172, 9033, 9034,  \n12805, 768, 769,  26205, 26367, 25896,  17108, 6308, 6309,  \n18123, 2651, 15119,  25753, 25895, 25894,  26052, 25895, 25753,  \n26052, 25889, 26550,  7559, 8670, 12111,  26206, 25888, 26366,  \n25751, 25893, 26369,  25638, 25512, 26377,  25512, 26204, 26377,  \n9734, 13814, 3623,  25890, 26051, 26372,  25893, 26373, 26369,  \n26552, 26365, 26374,  7788, 9729, 18578,  14388, 17919, 7420,  \n26553, 26371, 26370,  26553, 26372, 26371,  26372, 26554, 26375,  \n26375, 26053, 26372,  25892, 26207, 26555,  26373, 26208, 26556,  \n15712, 21016, 416,  1226, 1158, 1227,  26558, 26552, 26374,  \n8577, 18809, 10237,  26553, 26370, 26559,  8982, 5131, 14298,  \n1000, 4649, 11220,  7367, 4561, 19095,  25891, 26376, 26381,  \n305, 8817, 9394,  25891, 26381, 26207,  26208, 25892, 26555,  \n18517, 11040, 18012,  3759, 3760, 5362,  26560, 26057, 26056,  \n26377, 26560, 26056,  26558, 26374, 26382,  26370, 26050, 26561,  \n1089, 11441, 11454,  2643, 11222, 11289,  25904, 26057, 26562,  \n26056, 26057, 25899,  26383, 26558, 26382,  26563, 26050, 26206,  \n26559, 26370, 26561,  5844, 5843, 9285,  5223, 3454, 18082,  \n26562, 26384, 25904,  1082, 10070, 4604,  6252, 9143, 12493,  \n1778, 19846, 21094,  8730, 15287, 15288,  26563, 26561, 26050,  \n6244, 3836, 18790,  3800, 20056, 17432,  14495, 23676, 21819,  \n1266, 11671, 20884,  16824, 15514, 20566,  12954, 2458, 517,  \n26383, 26385, 26566,  26566, 26385, 26567,  26386, 26567, 26385,  \n25762, 26388, 26569,  4726, 2250, 16984,  26569, 26062, 26061,  \n3294, 7459, 8280,  25762, 26569, 26061,  26571, 26387, 26215,  \n7255, 21146, 14661,  17593, 15224, 6896,  11112, 19978, 11077,  \n14361, 22600, 14360,  14024, 17713, 15003,  26062, 26569, 26390,  \n14702, 9312, 7609,  26389, 26571, 26215,  15361, 11426, 1590,  \n26572, 26389, 26063,  26573, 26067, 26390,  26067, 26064, 26390,  \n17118, 19617, 16729,  26572, 26063, 26392,  3630, 3629, 20705,  \n7807, 10120, 9301,  369, 847, 848,  26574, 26572, 26392,  \n15353, 15354, 17293,  26574, 26393, 26575,  26393, 26574, 26392,  \n26575, 26576, 26574,  26575, 26394, 26396,  26575, 26393, 26394,  \n14407, 5752, 2753,  17824, 14404, 10827,  26575, 26396, 26577,  \n26575, 26577, 26576,  11724, 6090, 19969,  11866, 3998, 14191,  \n15042, 15043, 4981,  26216, 26397, 26395,  4411, 4412, 950,  \n20478, 18731, 13137,  26394, 26395, 26396,  26577, 26396, 26578,  \n26579, 26069, 26068,  1342, 22852, 7611,  8445, 15571, 10560,  \n19282, 17956, 19281,  26396, 26395, 26578,  23682, 1406, 21069,  \n26579, 25917, 26069,  816, 13828, 7447,  9602, 9603, 16349,  \n14119, 17888, 12315,  15131, 19913, 15130,  5898, 26139, 5899,  \n15134, 13657, 19603,  26218, 25764, 26398,  7034, 7981, 14821,  \n26581, 26217, 26582,  13201, 6940, 13199,  4463, 9257, 9259,  \n26217, 26071, 26582,  7127, 19809, 4769,  17547, 13602, 4100,  \n26073, 26400, 26401,  2315, 13406, 13405,  7822, 7683, 7820,  \n10852, 15279, 18398,  26219, 26402, 26583,  26219, 26583, 26403,  \n4958, 1543, 4959,  15015, 22955, 5829,  26757, 26403, 26583,  \n8397, 9528, 9529,  26220, 26219, 26403,  26584, 26220, 26403,  \n4389, 22860, 13001,  25516, 25244, 25650,  5988, 18999, 1698,  \n882, 14786, 8585,  10898, 10897, 23011,  25650, 26917, 26222,  \n17127, 17126, 17143,  25650, 26585, 26917,  14878, 15710, 12724,  \n25923, 26586, 25650,  26586, 26585, 25650,  26586, 25923, 26224,  \n26587, 26223, 26404,  10457, 9865, 14353,  26224, 26588, 26586,  \n26587, 26589, 26223,  26224, 26225, 26588,  26224, 26077, 26225,  \n15588, 418, 14889,  26225, 26405, 26588,  4553, 4552, 21026,  \n26407, 26078, 26590,  26590, 26078, 26223,  26408, 26405, 26225,  \n14924, 11124, 11123,  26588, 26405, 26591,  26588, 26591, 26593,  \n22352, 22453, 17119,  25928, 26078, 26407,  25925, 26592, 26226,  \n11453, 3929, 3930,  16357, 3922, 11564,  8182, 1564, 4579,  \n6606, 20097, 14753,  17421, 14351, 14811,  26593, 26591, 26410,  \n13640, 19497, 14757,  4784, 22543, 6082,  17845, 9197, 6876,  \n26410, 26409, 26593,  10424, 10883, 13338,  18426, 7321, 12855,  \n9327, 9638, 8566,  26229, 26407, 26595,  19438, 13135, 18851,  \n12178, 7918, 17749,  26230, 25927, 26229,  26227, 25926, 26596,  \n11101, 11100, 21719,  26408, 26226, 26592,  17424, 4449, 12714,  \n26597, 26405, 26414,  26405, 26408, 26414,  26597, 26591, 26405,  \n26410, 26591, 26232,  26409, 26410, 26234,  6276, 6277, 20540,  \n26079, 26230, 26231,  1517, 1516, 10437,  26228, 25770, 26081,  \n1531, 1532, 1252,  4872, 4873, 12881,  26591, 26597, 26232,  \n12906, 3680, 3681,  26594, 26235, 26411,  26237, 26232, 26597,  \n24041, 11279, 11278,  10737, 17871, 896,  26412, 26411, 26083,  \n26237, 26597, 26414,  12854, 11063, 11064,  12013, 2128, 6969,  \n478, 5559, 12511,  13142, 11669, 2195,  8454, 7130, 17675,  \n3195, 3194, 12969,  6438, 16818, 22017,  26598, 26413, 26085,  \n8220, 13606, 4057,  12503, 7848, 7457,  26086, 26598, 26085,  \n20830, 15210, 11304,  3980, 3982, 7850,  5064, 11952, 4923,  \n26086, 26415, 26598,  7150, 11891, 12716,  2423, 12161, 1151,  \n6637, 2356, 2355,  26414, 26599, 26238,  15569, 294, 13762,  \n7190, 9443, 9444,  681, 7746, 872,  13593, 17395, 16462,  \n25933, 26600, 26089,  4486, 1279, 2498,  26599, 26601, 26238,  \n25935, 26600, 25933,  9484, 9483, 14531,  1080, 5505, 919,  \n350, 1503, 19845,  26239, 26600, 25935,  14897, 5045, 19219,  \n5421, 15562, 11904,  21188, 13430, 3847,  26416, 26602, 26603,  \n26090, 26416, 26603,  22841, 8954, 7136,  1862, 23132, 4852,  \n19907, 2080, 10183,  4761, 8626, 4760,  26417, 26240, 26090,  \n1922, 3089, 5476,  1406, 3567, 21069,  8016, 5431, 5433,  \n26239, 26091, 26923,  26091, 26604, 26923,  26240, 26417, 26605,  \n8346, 20792, 22116,  18080, 8604, 14700,  16429, 5754, 6430,  \n5298, 10124, 11351,  6962, 1749, 9971,  2861, 7235, 1242,  \n10748, 7150, 12716,  25258, 26243, 26244,  25258, 26093, 26243,  \n25531, 25258, 26244,  26778, 26094, 26244,  18625, 5217, 25381,  \n26606, 26420, 26419,  11926, 17190, 20283,  25781, 26420, 26606,  \n25781, 26606, 26418,  4438, 14452, 18969,  19957, 17493, 17495,  \n10731, 16526, 20790,  11949, 11520, 17651,  17630, 20298, 4443,  \n838, 839, 20932,  21506, 18907, 10920,  26422, 26781, 25938,  \n1588, 1589, 9371,  26245, 25941, 26607,  22652, 14190, 4079,  \n13094, 9413, 13762,  26246, 25789, 26425,  6160, 6159, 17127,  \n4491, 4492, 20803,  26100, 26248, 26609,  1484, 22170, 3455,  \n26098, 26248, 26100,  10931, 14186, 8955,  5417, 11209, 5418,  \n26428, 26103, 26104,  25940, 26246, 26610,  3893, 14392, 2615,  \n6558, 6559, 21678,  26608, 26247, 26101,  26608, 26101, 26430,  \n25670, 25669, 26609,  26102, 25670, 26609,  18178, 18177, 13851,  \n1028, 4924, 5147,  15557, 5944, 15085,  15546, 14630, 6058,  \n17730, 5703, 11934,  11803, 16275, 13661,  25793, 25942, 26252,  \n7365, 21540, 1357,  9931, 646, 12857,  1447, 9272, 18973,  \n12465, 16417, 9132,  26251, 26253, 25943,  10627, 15137, 20175,  \n11020, 20093, 21015,  7377, 5803, 7391,  22776, 14467, 19131,  \n10675, 10413, 20843,  4654, 4008, 11433,  10643, 4064, 5269,  \n21493, 20855, 17875,  26106, 26612, 26104,  12281, 15033, 22253,  \n26106, 25955, 26612,  26249, 25946, 26611,  10143, 3560, 3562,  \n6168, 9602, 16348,  10894, 17065, 20161,  6819, 979, 12691,  \n11558, 9581, 3586,  9481, 17016, 13673,  10263, 1176, 10264,  \n14123, 14124, 13229,  369, 21118, 15067,  16604, 22770, 13550,  \n3592, 13493, 3591,  344, 15500, 14607,  25128, 26107, 25948,  \n21645, 1573, 20671,  13591, 17639, 17638,  13974, 16678, 12882,  \n13386, 12072, 16533,  26434, 25955, 26791,  20415, 9474, 13246,  \n3182, 15355, 18849,  10167, 5694, 8388,  5042, 20017, 21491,  \n20753, 12158, 18267,  9014, 9016, 22455,  14645, 4757, 4476,  \n1823, 4953, 1822,  17127, 17143, 8709,  12802, 15203, 12803,  \n25954, 26437, 26258,  559, 4824, 1479,  4962, 2789, 4963,  \n8830, 5306, 8831,  6961, 10913, 1057,  5715, 5716, 17560,  \n26435, 26616, 26438,  26438, 26257, 26435,  22596, 3020, 20839,  \n26258, 26437, 26615,  10385, 18052, 12275,  6404, 2194, 11669,  \n6568, 4214, 19802,  15521, 17852, 18512,  26438, 26616, 26439,  \n16055, 4249, 6828,  25427, 26796, 25426,  6369, 2337, 2329,  \n21724, 16116, 2025,  11470, 21762, 13303,  26258, 26615, 26262,  \n9524, 19036, 1857,  25008, 25959, 25958,  720, 721, 13657,  \n26441, 26259, 26439,  18425, 16440, 11560,  23522, 13196, 7837,  \n11108, 8789, 3015,  10800, 9970, 16113,  13682, 20576, 16539,  \n1813, 1812, 1450,  15317, 6202, 15878,  8297, 16306, 6232,  \n26446, 26264, 25682,  16184, 17277, 3568,  14926, 20075, 3259,  \n3232, 10200, 11913,  11232, 4759, 2045,  14526, 2834, 4858,  \n8121, 5302, 6435,  26446, 25682, 25561,  26447, 26446, 25561,  \n26266, 26262, 26443,  14188, 22016, 14787,  371, 5420, 378,  \n25430, 26617, 26117,  20207, 19935, 5646,  25807, 26618, 25965,  \n25683, 26617, 25430,  6477, 8673, 20010,  1764, 11596, 12459,  \n15456, 8283, 9106,  18572, 19362, 5251,  26448, 26450, 26267,  \n26617, 25683, 26619,  26620, 25808, 25805,  9278, 6725, 10681,  \n1259, 10666, 3562,  3296, 19171, 16192,  25286, 26619, 25683,  \n26268, 26450, 26269,  26450, 26622, 26621,  3395, 15829, 19611,  \n9009, 9011, 18778,  2783, 11289, 13710,  26451, 26621, 26623,  \n26451, 26269, 26621,  13032, 5345, 14088,  5072, 5073, 15343,  \n4079, 14190, 9633,  26623, 26624, 26451,  4117, 1786, 1785,  \n25808, 26625, 25971,  26272, 26451, 26624,  26272, 26624, 26452,  \n9208, 5061, 13929,  5474, 9495, 20775,  22031, 24955, 11347,  \n7536, 20712, 21158,  2902, 13578, 14414,  6624, 8365, 13088,  \n19787, 3525, 10190,  11291, 7589, 23149,  19288, 11061, 5328,  \n17040, 13136, 13135,  11876, 17473, 10127,  11600, 21106, 9220,  \n19222, 15340, 20900,  24955, 16310, 11347,  2502, 13751, 13750,  \n13787, 6740, 20015,  26455, 25435, 26628,  21627, 6699, 11052,  \n16993, 5414, 1629,  14697, 14698, 21627,  25812, 26629, 26122,  \n26457, 26630, 25971,  26630, 25974, 25971,  13893, 4081, 18826,  \n526, 2919, 4471,  26632, 26123, 25975,  26122, 26631, 25813,  \n25813, 26631, 26458,  26628, 25299, 25973,  16602, 20223, 3918,  \n26458, 26633, 25976,  21048, 7281, 7280,  26460, 26632, 25975,  \n3999, 8327, 10926,  10036, 15425, 15566,  26275, 26124, 26634,  \n8934, 16381, 3178,  8429, 7428, 21993,  26275, 25691, 26124,  \n3241, 17262, 8808,  6165, 9101, 3938,  26634, 25979, 26275,  \n7639, 18770, 21283,  15442, 19535, 12914,  25816, 26275, 25979,  \n25978, 25980, 26462,  15958, 7244, 5211,  13997, 9204, 24039,  \n3807, 13050, 12488,  6427, 1125, 1127,  15073, 18252, 9773,  \n14317, 17565, 14481,  1876, 12735, 8472,  25979, 26467, 26277,  \n17946, 327, 2397,  8431, 8475, 4278,  25205, 13018, 19439,  \n26465, 25980, 25575,  21883, 16056, 21645,  25302, 25817, 26279,  \n25302, 25445, 25817,  25818, 25303, 26471,  10119, 9881, 4505,  \n22022, 8302, 17850,  17675, 18395, 4795,  17794, 13217, 19059,  \n26636, 26472, 25580,  26473, 26471, 25820,  25983, 26473, 25820,  \n15785, 22317, 15784,  21298, 5502, 12980,  619, 1769, 19952,  \n4498, 19912, 3976,  26982, 26130, 25824,  8132, 5842, 18076,  \n26474, 26982, 25824,  4341, 19876, 11258,  3702, 2360, 17798,  \n25035, 25578, 26984,  26475, 25582, 26476,  17821, 19685, 659,  \n17896, 13220, 11539,  26474, 25697, 26638,  26477, 25696, 25821,  \n3246, 21193, 14388,  21492, 10516, 8339,  20224, 5679, 5678,  \n14887, 2131, 7211,  2764, 8233, 14825,  26639, 25985, 26477,  \n9343, 3374, 9635,  10897, 6889, 22150,  12752, 2417, 19640,  \n8461, 2958, 18489,  27203, 25982, 25830,  1950, 13550, 12783,  \n25984, 26280, 26479,  5509, 16220, 2034,  14218, 10078, 9806,  \n17885, 15183, 15895,  2482, 10994, 2483,  14325, 4763, 20553,  \n1642, 14414, 6970,  26281, 26640, 26480,  25701, 26642, 25454,  \n25829, 26641, 25986,  18867, 14748, 14747,  6317, 18844, 11719,  \n25179, 26132, 26134,  21208, 12342, 15432,  7550, 22038, 9227,  \n26642, 26481, 25454,  18816, 6656, 10412,  918, 11165, 11027,  \n17417, 10223, 21373,  26482, 26640, 26281,  10290, 10289, 13611,  \n2202, 19297, 2203,  5863, 8993, 8480,  560, 22828, 20161,  \n4425, 6446, 9948,  7505, 7504, 6300,  14649, 2436, 20104,  \n9196, 15960, 13405,  21693, 11333, 19926,  20687, 17429, 1163,  \n21558, 10624, 2658,  9375, 2646, 2648,  11460, 3256, 18401,  \n10189, 10053, 15939,  25585, 25987, 26283,  26482, 26136, 26643,  \n26643, 26644, 26482,  18217, 22818, 1568,  8756, 8757, 15840,  \n1584, 9626, 21581,  1340, 12304, 10374,  9808, 1236, 21410,  \n18616, 4180, 3418,  2336, 430, 12033,  25832, 26643, 26136,  \n9310, 22942, 9309,  7421, 6556, 1970,  8663, 15646, 15645,  \n25832, 25834, 26645,  4015, 5241, 20600,  25832, 26645, 26643,  \n7255, 19222, 17405,  7371, 12679, 1262,  14732, 14733, 7566,  \n5684, 11323, 5685,  23073, 11996, 23323,  898, 9401, 21271,  \n25835, 26645, 25834,  25587, 26288, 26137,  13469, 7847, 13470,  \n26287, 26646, 26288,  5681, 1906, 1905,  26646, 25835, 25991,  \n4217, 14172, 16361,  7631, 19162, 9048,  15811, 2187, 7350,  \n11517, 12723, 19778,  8597, 2205, 16355,  4278, 1926, 17400,  \n25705, 25707, 25993,  25837, 25045, 26138,  26286, 25459, 26289,  \n3458, 3459, 12669,  11282, 21408, 7306,  21236, 9937, 2137,  \n26290, 25708, 26141,  16985, 16042, 16041,  25708, 26290, 25589,  \n17083, 7678, 7677,  16579, 18426, 6216,  2441, 2961, 2440,  \n25590, 25047, 26140,  23901, 20216, 20217,  1758, 16884, 4019,  \n12146, 16247, 610,  16380, 7548, 10387,  4464, 4466, 7597,  \n3535, 9511, 3534,  2267, 11740, 9729,  10792, 7504, 13034,  \n5134, 12284, 15232,  26291, 25590, 26487,  19780, 15142, 19781,  \n5106, 13740, 23866,  3721, 3722, 17496,  20529, 9199, 9198,  \n10923, 9508, 10922,  15987, 14622, 3738,  9032, 8941, 26084,  \n3744, 9588, 14645,  26142, 25463, 26291,  1042, 529, 16062,  \n2300, 15095, 11306,  7854, 2239, 8515,  25997, 25711, 26294,  \n25117, 25490, 26070,  18289, 11014, 21462,  11944, 10579, 5016,  \n26490, 26650, 26651,  380, 9821, 22046,  8822, 16088, 11322,  \n20042, 6680, 3359,  18985, 2515, 6628,  14743, 17980, 13914,  \n3820, 16121, 20860,  21346, 14612, 7751,  12889, 4420, 16920,  \n26654, 26655, 26651,  25998, 25999, 26296,  3399, 15297, 3397,  \n18923, 15992, 3995,  25333, 25186, 26000,  17734, 17733, 4127,  \n25464, 25840, 26295,  13144, 26657, 4106,  2587, 8415, 5336,  \n7960, 7048, 331,  26490, 26489, 26491,  2862, 10978, 19838,  \n10196, 10872, 13586,  18942, 16445, 303,  26490, 26651, 26489,  \n10027, 10026, 10352,  2081, 19356, 4507,  8563, 9566, 14877,  \n7698, 5713, 14490,  18546, 4281, 895,  25192, 26000, 26297,  \n9099, 20040, 20481,  2817, 6070, 15213,  25192, 25333, 26000,  \n8657, 8656, 11985,  26651, 26655, 26496,  9328, 13112, 18825,  \n3031, 8134, 20259,  8114, 1383, 9733,  26492, 26489, 26651,  \n26492, 26651, 26496,  3444, 7815, 778,  17207, 5742, 2079,  \n21433, 20880, 9139,  26306, 26492, 26496,  26300, 26303, 26659,  \n26303, 26660, 26659,  12679, 8290, 1262,  4969, 293, 2851,  \n5749, 7183, 10912,  26146, 26306, 26496,  12987, 13270, 11889,  \n12241, 19106, 20965,  6344, 6345, 10483,  8780, 11081, 969,  \n8555, 14771, 12437,  13399, 7434, 5314,  5314, 7434, 7435,  \n10056, 10055, 15949,  26495, 26496, 26835,  11877, 13610, 6617,  \n3658, 4645, 2297,  1848, 5602, 17739,  20014, 12817, 7156,  \n11937, 11936, 20935,  25470, 25715, 26304,  25714, 26662, 25468,  \n26147, 26495, 26664,  25844, 25720, 26149,  10056, 16750, 11180,  \n12844, 5872, 3,  26500, 26147, 26664,  26500, 26664, 26665,  \n22218, 5038, 1894,  11491, 3975, 13472,  561, 8095, 2815,  \n19451, 14471, 2821,  22858, 22337, 19884,  3746, 1267, 3747,  \n8989, 14544, 17164,  23499, 9523, 17495,  11124, 7390, 7392,  \n4379, 5248, 4377,  14836, 18688, 4051,  1276, 4415, 12249,  \n3396, 19611, 13198,  25601, 25197, 26008,  26667, 25845, 26009,  \n14836, 8419, 14308,  13528, 7214, 7213,  10801, 13788, 16006,  \n26153, 25850, 26666,  3177, 14268, 16845,  19051, 12285, 10977,  \n26668, 26312, 26152,  26011, 25479, 25055,  10335, 22854, 16673,  \n1152, 1218, 3488,  7394, 3079, 11818,  1793, 16715, 20452,  \n5693, 4287, 1559,  22495, 19379, 14737,  14676, 18771, 14689,  \n8479, 10365, 2451,  13379, 12374, 12375,  8006, 19642, 13704,  \n10135, 3260, 11432,  26313, 26506, 25480,  6747, 14695, 6209,  \n20670, 11489, 23370,  26013, 26670, 25728,  17825, 15057, 8312,  \n25337, 26155, 26671,  15625, 2873, 453,  15742, 6709, 8202,  \n26315, 26313, 25480,  25337, 26671, 25344,  10518, 16484, 2214,  \n2478, 1592, 1593,  19465, 1120, 1121,  22680, 7346, 22038,  \n10707, 678, 4773,  26016, 26157, 26509,  10396, 11782, 11781,  \n5416, 6447, 16073,  26673, 25854, 25344,  25852, 26508, 25851,  \n26509, 26157, 26672,  12174, 15966, 17567,  1289, 2669, 2668,  \n5083, 1658, 5084,  26316, 26158, 25612,  26508, 25852, 26159,  \n6737, 18209, 6738,  20647, 15804, 20648,  15475, 5518, 15476,  \n12079, 9500, 6504,  17438, 21502, 17940,  14590, 14589, 23682,  \n26017, 26674, 26159,  26017, 26675, 26674,  10813, 19079, 13003,  \n16933, 7268, 9244,  13478, 4465, 19440,  25856, 25487, 26510,  \n26020, 26675, 26017,  26676, 26019, 26160,  26677, 26675, 26020,  \n14922, 12699, 7232,  17714, 8543, 21999,  26317, 26019, 26676,  \n4431, 18634, 4432,  10896, 22760, 22270,  15929, 12118, 3000,  \n4950, 21318, 10626,  25611, 26511, 26018,  22599, 22874, 4027,  \n26515, 25856, 26678,  13495, 17121, 17447,  16369, 14607, 2836,  \n22776, 19131, 5836,  10761, 21895, 26070,  26511, 25489, 26021,  \n15321, 17324, 15322,  25857, 25856, 26515,  12283, 8000, 2975,  \n16280, 10888, 18828,  22272, 10716, 6945,  19684, 22127, 3501,  \n26164, 26849, 26320,  14070, 20673, 7055,  4088, 18518, 2861,  \n6475, 11828, 10903,  26164, 26320, 26163,  26166, 26517, 26164,  \n8567, 18394, 4313,  3186, 10649, 374,  5258, 19869, 18494,  \n7745, 8537, 7793,  26166, 26321, 26680,  4327, 1915, 15330,  \n14125, 1711, 18360,  14550, 5533, 4437,  16305, 21048, 5126,  \n26680, 26322, 26681,  26324, 26682, 26681,  14938, 20648, 6453,  \n7298, 5430, 7299,  26681, 26322, 26324,  26023, 25857, 26516,  \n22455, 9016, 22789,  2701, 16129, 13329,  26023, 26516, 26683,  \n21880, 22419, 19702,  12118, 12801, 9178,  18440, 10522, 27385,  \n8050, 2000, 21257,  15409, 5633, 19795,  22965, 21184, 13482,  \n15566, 19119, 19118,  19900, 21382, 1177,  26683, 26325, 26023,  \n22353, 15108, 17440,  19349, 7928, 12955,  4162, 5993, 19430,  \n7653, 17640, 2219,  26330, 26684, 26519,  26330, 26685, 26684,  \n8479, 2451, 2452,  29732, 15194, 24410,  26023, 26325, 25072,  \n17433, 3243, 17012,  23326, 10230, 3036,  26685, 26330, 26331,  \n26521, 26685, 26331,  11335, 15097, 3620,  10549, 12809, 17113,  \n15993, 15994, 7889,  26337, 26520, 26686,  4976, 4180, 8540,  \n4233, 14827, 2852,  26687, 26523, 26342,  10188, 22837, 11451,  \n26522, 26688, 26524,  26169, 26689, 26687,  23360, 14652, 15495,  \n6208, 16076, 20932,  26525, 26689, 26169,  26690, 26173, 26174,  \n26690, 26174, 26170,  26027, 25869, 26691,  6961, 14537, 3805,  \n9122, 10630, 6516,  12108, 11444, 12506,  10330, 19955, 18442,  \n26692, 26334, 26345,  26346, 26178, 26338,  26693, 26525, 26343,  \n7954, 17181, 3735,  3957, 5775, 19825,  5590, 15682, 4397,  \n5013, 9601, 3948,  10704, 17412, 13748,  9561, 17148, 24188,  \n17977, 9946, 15999,  12428, 12962, 12429,  26693, 26343, 26344,  \n25869, 26347, 26691,  5593, 3851, 3850,  8874, 12100, 464,  \n18011, 12382, 2042,  26260, 7136, 26695,  25872, 26696, 26697,  \n9638, 2571, 17498,  26348, 26698, 26345,  26530, 26698, 26348,  \n6875, 14760, 17915,  12167, 15434, 19493,  26699, 26032, 26697,  \n26697, 26701, 26699,  3156, 7307, 21408,  14901, 11877, 11878,  \n359, 18178, 16176,  26700, 26351, 26703,  12138, 18543, 3284,  \n26703, 26351, 26352,  2571, 14685, 4594,  1823, 2537, 16221,  \n16060, 1845, 20338,  7457, 18331, 7456,  6764, 16177, 14026,  \n11936, 11937, 573,  1323, 4061, 8411,  10510, 15302, 21343,  \n26531, 26703, 26352,  7695, 1027, 4467,  460, 9458, 3852,  \n26704, 26533, 26354,  11321, 10191, 7950,  12413, 20664, 11434,  \n14685, 7922, 4594,  6137, 20962, 863,  14659, 8654, 18323,  \n7311, 8163, 13990,  26707, 26037, 25626,  26707, 26532, 26037,  \n26706, 26531, 26535,  26708, 26534, 26353,  4379, 10079, 12129,  \n14739, 5095, 12759,  24586, 4852, 16614,  10611, 8707, 7159,  \n25500, 26538, 25223,  20645, 6132, 9082,  4532, 4233, 1788,  \n26355, 26538, 26710,  9356, 23339, 9355,  25367, 25370, 26038,  \n9945, 9770, 21579,  26355, 26710, 26539,  7110, 10132, 10131,  \n15135, 14471, 19451,  18220, 18221, 5767,  26540, 26706, 26535,  \n8653, 8198, 15029,  26711, 26540, 26193,  26193, 26712, 26711,  \n26711, 26712, 26713,  8258, 18415, 7909,  18702, 13558, 13557,  \n6946, 11882, 2288,  26544, 26714, 25877,  21169, 15382, 6365,  \n26039, 26357, 26042,  5920, 10660, 5040,  16975, 16819, 18925,  \n10674, 10675, 20843,  20573, 7985, 2323,  26545, 26715, 26546,  \n26715, 26545, 26543,  3464, 17923, 13065,  22362, 15445, 15446,  \n25501, 26197, 26544,  12300, 9569, 12301,  26712, 26358, 26547,  \n26717, 26545, 26546,  26716, 26196, 26717,  26717, 26196, 26545,  \n26716, 26040, 26196,  21366, 20925, 21486,  26359, 26544, 26197,  \n5280, 12578, 5281,  26362, 26359, 26197,  26719, 26044, 26718,  \n26719, 26047, 26044,  26720, 26361, 26043,  14863, 20078, 14864,  \n26722, 26362, 26549,  23334, 3910, 15890,  1748, 1747, 10222,  \n5871, 5872, 9581,  12647, 4864, 910,  26552, 26363, 26365,  \n26364, 26361, 26721,  26364, 26721, 26551,  19472, 4569, 8240,  \n26201, 26364, 26551,  13338, 10883, 14391,  5439, 15667, 19349,  \n1622, 18595, 1621,  12165, 1419, 12385,  3226, 10518, 2519,  \n2247, 9222, 14983,  5200, 8823, 2232,  26201, 26551, 26724,  \n26201, 26724, 26726,  26366, 26201, 26726,  22531, 16448, 16029,  \n3425, 2484, 10246,  10722, 12934, 10723,  26369, 26045, 25637,  \n8606, 21336, 4887,  17028, 2410, 2411,  13202, 6591, 19075,  \n16086, 5656, 21668,  7780, 12094, 16199,  18266, 694, 17150,  \n8504, 8861, 943,  17959, 15254, 14850,  26724, 26551, 26727,  \n21346, 7751, 7094,  26206, 26366, 26728,  1246, 9802, 16716,  \n12134, 3910, 3911,  11950, 11530, 11529,  22551, 21560, 10443,  \n23287, 20664, 611,  26057, 25902, 25899,  17626, 4691, 20429,  \n20196, 404, 1972,  8019, 5939, 6374,  2189, 11717, 16132,  \n15345, 12779, 12780,  26206, 26728, 26563,  11376, 3217, 5762,  \n22398, 13237, 8018,  22417, 8817, 19858,  26373, 26556, 26557,  \n6038, 773, 3470,  26556, 26732, 26557,  21092, 7834, 7833,  \n21576, 11171, 13276,  26731, 26553, 26559,  18586, 17847, 24612,  \n26730, 26558, 26566,  26383, 26566, 26558,  18999, 20433, 22228,  \n26210, 26378, 26565,  26733, 26208, 26555,  1977, 12943, 10296,  \n18181, 6655, 600,  10112, 3739, 15422,  15698, 13462, 18499,  \n26380, 26210, 26735,  26379, 26380, 26736,  26379, 26736, 26734,  \n26737, 26212, 25903,  817, 15475, 14663,  3769, 843, 3770,  \n26559, 26561, 26738,  26210, 26565, 26735,  26214, 26059, 26568,  \n12920, 15147, 20379,  26561, 26563, 26739,  13764, 686, 23112,  \n23222, 3505, 1456,  26736, 26380, 26735,  15366, 12767, 871,  \n758, 11840, 11398,  6288, 6348, 3653,  21442, 1895, 1894,  \n26740, 26738, 26561,  18529, 16459, 16460,  13307, 566, 565,  \n18728, 17150, 695,  2615, 6735, 3893,  26570, 26567, 26386,  \n19207, 9267, 9266,  4888, 4887, 17802,  26570, 26386, 26387,  \n16070, 586, 17211,  26571, 26570, 26387,  9312, 9313, 14348,  \n14456, 14458, 19923,  21970, 1686, 1685,  23026, 9897, 11934,  \n16382, 2607, 3758,  26389, 26741, 26571,  6547, 933, 934,  \n26741, 26389, 26743,  26743, 26389, 26572,  26573, 26390, 26742,  \n26744, 26743, 26572,  7573, 9496, 22579,  9348, 15829, 2829,  \n19479, 18926, 12139,  26745, 26744, 26572,  26574, 26745, 26572,  \n26746, 26068, 26573,  26745, 26574, 26747,  20477, 9423, 3379,  \n26747, 26574, 26576,  15111, 8437, 18339,  12387, 10152, 16198,  \n26576, 26748, 26747,  26577, 26748, 26576,  7391, 5803, 7392,  \n26749, 26748, 26577,  1915, 7147, 2505,  22211, 1265, 1266,  \n17296, 19598, 17297,  26749, 26577, 26578,  14153, 13143, 14154,  \n26750, 26395, 26397,  4501, 1674, 12946,  26395, 26750, 26578,  \n26749, 26578, 26750,  26398, 25764, 25917,  26397, 26580, 26750,  \n11975, 5579, 5635,  26580, 26397, 26217,  7670, 12334, 7009,  \n26400, 26399, 26751,  26751, 26399, 26752,  22024, 6204, 6206,  \n14719, 7843, 7108,  26582, 26071, 26753,  26400, 26754, 26401,  \n15688, 20973, 15204,  26755, 26401, 26754,  26755, 26402, 26401,  \n26753, 26071, 25919,  17505, 10443, 14351,  26756, 26583, 26402,  \n25516, 26222, 25919,  15804, 20647, 22543,  26403, 26757, 26758,  \n22078, 12246, 627,  11359, 6129, 2020,  2716, 24391, 22385,  \n16278, 16911, 16279,  26220, 26916, 26221,  26759, 26221, 26916,  \n26221, 26759, 26075,  10579, 14777, 3335,  7709, 22524, 13260,  \n633, 16812, 634,  11195, 13199, 8393,  14176, 1352, 17844,  \n2280, 23347, 17263,  26588, 26760, 26586,  9740, 17677, 4485,  \n26761, 26760, 26588,  26762, 26761, 26593,  14093, 16104, 19377,  \n18276, 14790, 17100,  8136, 8135, 14611,  26761, 26588, 26593,  \n18952, 6233, 489,  5416, 16073, 5415,  26762, 26593, 26409,  \n19802, 16626, 4525,  26594, 26763, 26762,  15957, 11014, 10039,  \n13214, 13215, 2710,  7409, 14143, 1917,  26409, 26233, 26594,  \n26594, 26762, 26409,  1003, 916, 503,  13873, 1291, 13176,  \n20058, 4601, 1571,  5853, 17933, 9087,  26081, 25929, 26227,  \n2357, 12565, 11063,  1013, 4779, 1014,  26592, 25925, 25769,  \n10158, 19807, 10944,  11545, 18140, 13044,  3323, 3324, 3960,  \n16193, 29506, 13875,  3092, 3167, 5436,  2207, 2208, 13163,  \n14318, 19221, 14731,  18570, 624, 16739,  10197, 887, 14056,  \n26230, 26229, 26765,  25769, 26228, 26768,  16036, 19019, 14157,  \n11732, 16101, 7533,  3682, 3683, 12035,  16108, 20819, 19870,  \n26764, 26414, 26408,  20973, 12683, 17705,  16452, 20819, 7005,  \n3856, 2514, 6420,  6761, 15646, 15093,  8060, 20312, 22612,  \n14516, 16149, 1295,  8562, 13442, 3361,  2541, 16307, 2284,  \n19379, 16753, 13499,  9965, 9964, 12358,  17798, 17801, 8437,  \n10605, 10075, 10074,  26770, 26598, 26415,  26770, 26415, 26771,  \n22443, 15584, 10895,  2860, 13671, 19160,  26772, 26771, 26415,  \n2593, 19975, 7650,  25661, 26772, 26415,  344, 21894, 15500,  \n26772, 25661, 26089,  1188, 1187, 7460,  26769, 26599, 26414,  \n9687, 18079, 14249,  18256, 22782, 19680,  12322, 12417, 9135,  \n7985, 7461, 2835,  12949, 10680, 9865,  2677, 12243, 12244,  \n26601, 26774, 26775,  26416, 26601, 26775,  26602, 26416, 26775,  \n13439, 5083, 13440,  410, 18602, 19893,  7596, 7595, 11011,  \n26605, 26417, 26776,  26240, 26605, 26241,  18112, 19726, 4348,  \n20990, 10727, 14765,  18796, 14067, 21940,  15440, 13210, 3835,  \n26418, 26777, 25937,  1959, 2392, 2393,  8147, 13352, 6203,  \n25936, 26092, 26093,  8027, 8026, 6074,  16093, 20002, 12550,  \n26778, 26244, 26243,  5955, 6180, 4358,  4999, 23146, 12080,  \n3721, 19639, 3722,  26779, 26094, 26778,  16794, 2620, 1338,  \n26421, 26095, 26780,  14323, 8761, 11820,  26928, 26419, 26421,  \n26419, 26928, 26606,  26094, 26779, 26095,  26095, 26779, 26780,  \n17217, 3231, 5325,  4918, 8971, 14503,  1332, 11088, 11087,  \n25791, 26423, 26099,  26782, 26248, 26098,  26423, 25791, 26245,  \n20116, 21940, 14068,  26781, 26782, 26098,  26781, 26098, 25938,  \n12502, 23377, 9248,  26426, 26103, 26427,  26427, 26103, 26428,  \n16553, 19584, 11918,  26425, 25789, 26247,  12412, 12411, 8652,  \n25944, 26783, 26607,  12732, 12416, 12415,  388, 11999, 17816,  \n13882, 17340, 16841,  20528, 6299, 4668,  25942, 26426, 26252,  \n11480, 20011, 11481,  5546, 5545, 20570,  20658, 22745, 19702,  \n14630, 6972, 6839,  3954, 4973, 21425,  15253, 15031, 8529,  \n17450, 9159, 18327,  7027, 17884, 21898,  25090, 25940, 26610,  \n26430, 26611, 26784,  7032, 2720, 4813,  902, 5184, 10816,  \n26611, 26430, 26249,  2656, 5643, 7879,  7880, 1257, 6680,  \n23022, 10819, 22624,  16414, 15430, 15410,  17647, 21327, 23190,  \n25799, 25796, 26613,  17274, 19002, 18156,  25955, 26434, 26612,  \n26250, 26431, 24696,  26787, 25947, 25800,  20001, 10179, 19602,  \n2811, 18894, 17631,  25946, 25802, 26945,  1771, 15621, 16610,  \n22080, 4327, 12952,  14356, 10652, 18061,  26788, 26434, 26791,  \n9260, 10828, 10793,  26614, 26432, 26110,  26614, 26110, 26108,  \n21745, 8281, 21744,  16943, 16944, 22277,  26789, 26790, 26436,  \n15855, 13319, 1566,  19689, 19690, 878,  26436, 25950, 25952,  \n12612, 2390, 2389,  22514, 8859, 13957,  7238, 1987, 7239,  \n12503, 13470, 7847,  7393, 9448, 7394,  15724, 13055, 1300,  \n21641, 22357, 13868,  25952, 24697, 26954,  12394, 12395, 15039,  \n20522, 3092, 5436,  14407, 3263, 19459,  14632, 10049, 23051,  \n26793, 26111, 26433,  26113, 26261, 26791,  10347, 22926, 17441,  \n12041, 5862, 6982,  9254, 5021, 11350,  3954, 3953, 24533,  \n26792, 26616, 26435,  13385, 7045, 20576,  13625, 11705, 13360,  \n797, 11755, 10724,  21726, 12588, 8757,  8766, 18898, 15541,  \n14207, 18158, 11869,  827, 11021, 10658,  10707, 4773, 10708,  \n15899, 12262, 3573,  13296, 13297, 3937,  10583, 13647, 18366,  \n3617, 3616, 9787,  25962, 26111, 26793,  25962, 25429, 26111,  \n25958, 26796, 25427,  13633, 16748, 16173,  13071, 529, 1042,  \n26615, 26795, 26262,  6476, 17540, 1550,  1644, 1362, 14370,  \n22560, 17858, 11090,  26439, 26797, 26441,  8607, 4902, 17449,  \n26263, 25283, 25965,  6389, 6390, 10216,  26440, 26114, 26117,  \n26795, 26443, 26262,  7215, 14170, 8091,  7541, 15916, 6288,  \n26798, 26442, 26264,  26799, 26798, 26446,  10025, 11966, 14725,  \n26798, 26264, 26446,  8985, 7288, 8986,  9210, 16859, 9873,  \n15723, 14626, 14627,  26444, 26445, 26797,  26267, 26441, 26445,  \n679, 307, 7265,  26799, 26446, 26800,  11479, 14487, 552,  \n26447, 26800, 26446,  11113, 5139, 21011,  26266, 26802, 26447,  \n26802, 26266, 26443,  7410, 1276, 12249,  2038, 18026, 5720,  \n13524, 9763, 9764,  1908, 9144, 14723,  26448, 26445, 26444,  \n12084, 22289, 12085,  26448, 26444, 26804,  18325, 6521, 7978,  \n13124, 14890, 15683,  20812, 3965, 3964,  1499, 1752, 657,  \n7234, 5657, 10867,  12270, 12269, 18459,  21142, 10783, 484,  \n17191, 1495, 408,  26618, 25807, 27180,  13604, 9923, 9924,  \n12585, 340, 517,  21366, 1080, 918,  17388, 1409, 2999,  \n26621, 26269, 26450,  26622, 26623, 26621,  11262, 3543, 5620,  \n15124, 6474, 19074,  9138, 4953, 8322,  8120, 2506, 19318,  \n26452, 26624, 26626,  12622, 813, 15674,  14736, 4436, 11375,  \n18417, 13620, 7439,  10058, 5948, 5947,  6298, 17327, 4668,  \n26454, 25970, 26453,  15458, 7492, 7721,  7849, 7333, 3872,  \n25687, 26454, 26456,  18501, 2479, 18500,  12949, 15309, 16461,  \n26121, 26123, 26627,  11552, 17928, 3350,  6347, 9757, 6348,  \n26632, 26627, 26123,  26629, 25812, 26274,  6619, 9556, 9898,  \n8224, 7852, 20064,  26631, 26122, 26629,  13395, 22167, 21208,  \n13166, 14997, 11261,  6249, 6250, 1504,  9864, 9865, 13901,  \n17363, 17790, 11197,  24870, 12883, 3255,  26633, 26461, 25976,  \n13635, 9858, 20256,  6741, 5101, 18909,  26461, 26633, 26806,  \n2980, 8388, 5694,  26461, 26806, 26634,  26124, 26461, 26634,  \n6248, 14939, 22737,  26463, 25973, 25440,  26634, 26806, 26807,  \n26634, 26807, 25979,  1009, 6318, 19477,  9727, 8955, 8405,  \n26467, 26807, 26809,  26467, 25979, 26807,  18934, 10301, 17147,  \n5885, 1360, 18281,  1591, 23849, 15860,  2442, 16290, 4385,  \n12708, 393, 11071,  20209, 15882, 6277,  2037, 9978, 20197,  \n25981, 25169, 26276,  4528, 7950, 1168,  18095, 13108, 16477,  \n26810, 12058, 25467,  20056, 6237, 17432,  12012, 992, 19516,  \n11093, 14094, 20186,  4966, 12746, 12745,  8317, 8097, 8098,  \n337, 21584, 6683,  5217, 2711, 2712,  17370, 21008, 9951,  \n4826, 4825, 19022,  12830, 18996, 6836,  19622, 4295, 22828,  \n20871, 17370, 20872,  17729, 19886, 19211,  14590, 1184, 1183,  \n15159, 18189, 18188,  25578, 25446, 26126,  14325, 4226, 9309,  \n7779, 4401, 2428,  15411, 2627, 3896,  2485, 3894, 21632,  \n20410, 6631, 22284,  7044, 11346, 9421,  7530, 5617, 4267,  \n961, 2829, 21754,  9036, 8454, 4795,  10646, 10647, 7308,  \n20428, 9822, 8051,  3155, 3157, 15280,  21591, 22775, 3049,  \n4400, 3013, 14298,  3958, 4016, 20904,  10183, 3238, 1784,  \n25227, 26812, 12856,  26129, 26128, 26637,  17439, 21088, 9643,  \n25821, 26129, 26637,  25697, 25700, 26814,  9059, 17608, 6310,  \n23118, 19085, 18498,  13764, 23112, 20189,  2653, 2654, 14074,  \n19762, 16610, 21843,  624, 12498, 1853,  16128, 9129, 9130,  \n26478, 25985, 26639,  7784, 16242, 3366,  26814, 25700, 26133,  \n14595, 2746, 2747,  2328, 11486, 6304,  22230, 10735, 12037,  \n10211, 11917, 19045,  9444, 9443, 6777,  25828, 26478, 25829,  \n11464, 16489, 5464,  12109, 10574, 4323,  8905, 8904, 11674,  \n8510, 22054, 1052,  22399, 9061, 17526,  13514, 11778, 21354,  \n26483, 26133, 25704,  1093, 15657, 745,  11299, 6274, 11591,  \n18136, 6065, 12570,  18773, 13598, 16385,  3188, 6211, 7640,  \n21245, 766, 767,  1950, 19042, 13550,  9147, 789, 8474,  \n3692, 6893, 14951,  3912, 12977, 17289,  22785, 7702, 15022,  \n22366, 1104, 798,  26481, 26283, 25987,  26482, 26817, 26640,  \n9628, 13859, 11353,  1715, 6490, 6100,  8806, 18032, 4559,  \n400, 976, 977,  26644, 26817, 26482,  10355, 17695, 2755,  \n11743, 19805, 1213,  5406, 18943, 20180,  26283, 26818, 25989,  \n26644, 26643, 26819,  26644, 26819, 26820,  3904, 3905, 4735,  \n25989, 26818, 25833,  9365, 13919, 4615,  26645, 26821, 26643,  \n26819, 26643, 26821,  25586, 25703, 25836,  2775, 23205, 2774,  \n15687, 6509, 1576,  26818, 26822, 25833,  3646, 14024, 22445,  \n26822, 25587, 25833,  2100, 1799, 18165,  15149, 11774, 11775,  \n26823, 26821, 26645,  5592, 1988, 1989,  4473, 17685, 14080,  \n8257, 6470, 2914,  26138, 25836, 26824,  7176, 11438, 7175,  \n26825, 26287, 26822,  26287, 26288, 26822,  11155, 20714, 7610,  \n10840, 22011, 4426,  25835, 26823, 26645,  11669, 6611, 6404,  \n26288, 25587, 26822,  19413, 19414, 20224,  26646, 25991, 26288,  \n23539, 17426, 15951,  26823, 25835, 26646,  26286, 25456, 25459,  \n21138, 11309, 13334,  26826, 26646, 26287,  6511, 22841, 6510,  \n22098, 13325, 1784,  17125, 5994, 5993,  7861, 11828, 6475,  \n9724, 10266, 8439,  3906, 3908, 5991,  3195, 4205, 4901,  \n17945, 14736, 11375,  26485, 25327, 25995,  11867, 10433, 5190,  \n13963, 17431, 8878,  15572, 11847, 10692,  25589, 26290, 25996,  \n19141, 16543, 12982,  6929, 12172, 3709,  20388, 2305, 4446,  \n9407, 1433, 1918,  20030, 3460, 9161,  1837, 1836, 16816,  \n1765, 12725, 1764,  14497, 13826, 6044,  15595, 17577, 8867,  \n3177, 8692, 14268,  25712, 25187, 25998,  15638, 15639, 10766,  \n16000, 4995, 14526,  4567, 5035, 19257,  26829, 25998, 26652,  \n26830, 26650, 26490,  13267, 14532, 13268,  18667, 14672, 20193,  \n5282, 16726, 14374,  25997, 26294, 26649,  14710, 18469, 16781,  \n831, 6635, 3685,  17567, 14205, 14204,  1557, 1558, 15725,  \n26491, 26653, 26830,  26831, 26830, 26653,  21373, 11552, 2434,  \n3995, 21741, 21354,  21416, 12967, 16125,  6140, 4397, 8544,  \n26491, 26830, 26490,  13984, 11992, 13985,  5445, 22270, 22760,  \n26832, 26654, 26651,  26832, 26651, 26650,  10079, 2723, 10080,  \n26833, 26653, 26491,  1235, 1237, 18868,  7872, 2890, 8269,  \n17108, 6309, 17107,  2367, 21960, 1921,  3253, 9845, 3254,  \n26300, 26658, 26493,  13880, 14715, 15611,  2533, 15167, 8141,  \n4095, 4069, 3306,  21354, 11778, 18923,  4452, 7297, 16166,  \n5009, 9474, 9623,  1422, 1423, 9983,  26496, 26655, 26835,  \n4841, 3438, 20855,  19229, 4832, 19614,  20938, 7232, 18227,  \n2036, 1034, 1033,  15062, 16287, 15819,  26495, 26835, 26663,  \n2746, 18887, 3382,  11989, 4868, 6392,  14797, 5001, 7796,  \n26660, 26303, 26661,  26661, 26303, 26497,  17859, 22737, 4845,  \n4104, 10139, 9350,  20732, 9716, 20886,  17372, 20520, 20457,  \n19619, 19945, 16511,  26495, 26663, 26664,  26307, 26497, 26149,  \n13483, 12233, 6796,  12270, 18719, 22765,  26149, 25721, 26307,  \n7988, 10772, 12498,  10048, 4041, 4042,  16265, 11595, 12839,  \n7469, 9528, 18671,  2432, 22942, 2433,  2328, 7292, 9129,  \n21146, 12747, 11591,  5922, 5924, 23193,  4603, 3752, 3751,  \n26150, 26153, 26840,  17507, 9472, 4055,  3746, 16460, 19297,  \n5738, 11643, 14282,  26500, 26665, 26152,  26842, 26008, 25197,  \n3734, 3735, 17181,  9424, 11560, 18374,  19906, 1603, 6581,  \n26667, 26839, 25845,  26667, 26009, 26154,  4039, 4040, 29562,  \n3609, 22115, 11421,  26503, 25471, 26504,  1786, 16141, 11126,  \n26080, 15259, 1214,  16295, 3597, 10649,  18305, 10900, 21145,  \n8342, 7193, 1944,  8197, 13745, 8198,  16330, 16329, 16845,  \n26155, 25601, 26008,  12102, 11308, 21489,  11908, 856, 7417,  \n26011, 26843, 25479,  6464, 14256, 16880,  7525, 5775, 5776,  \n26668, 26669, 26312,  20560, 20159, 11957,  15797, 17903, 19801,  \n15722, 15723, 15389,  25479, 26843, 26013,  26504, 25471, 26505,  \n13637, 16661, 4474,  17295, 7134, 3388,  7046, 7172, 6240,  \n10890, 18905, 5901,  10654, 22733, 10645,  21841, 2315, 12004,  \n2564, 14814, 7801,  15124, 19074, 19983,  12291, 9185, 1957,  \n26670, 26314, 25728,  18538, 2714, 6354,  15443, 12671, 8506,  \n12261, 13901, 10457,  26315, 25485, 26314,  2110, 4432, 18063,  \n25608, 26156, 26505,  7343, 8808, 7344,  14555, 8666, 3748,  \n7744, 13337, 21974,  26672, 26157, 26669,  16929, 21483, 11811,  \n19505, 6156, 6157,  604, 13970, 13628,  11458, 17632, 16437,  \n17599, 20867, 17600,  2393, 19453, 10702,  26673, 25344, 27247,  \n3694, 12208, 17973,  20618, 23668, 20617,  2846, 7877, 6028,  \n5071, 954, 13724,  26158, 26316, 26846,  10202, 2396, 4874,  \n17218, 11018, 18512,  8254, 5300, 5301,  15899, 3573, 705,  \n26509, 26847, 26676,  3630, 6934, 6935,  26160, 26509, 26676,  \n12139, 16056, 21883,  25487, 25854, 26510,  26676, 26847, 26848,  \n9040, 7856, 8206,  7190, 2759, 7191,  5159, 17833, 5158,  \n16742, 16743, 5032,  22384, 8624, 1553,  6745, 19938, 23384,  \n26677, 26020, 26318,  9166, 9167, 13642,  21824, 21641, 15416,  \n2420, 18093, 2779,  8613, 8612, 12613,  11300, 2683, 6189,  \n4879, 8622, 6459,  12694, 8592, 8591,  15864, 10345, 18088,  \n9408, 9407, 15374,  23948, 13125, 17688,  344, 14607, 16369,  \n783, 785, 14839,  8927, 3534, 8926,  6391, 20886, 19949,  \n23370, 16958, 17397,  26679, 26514, 26320,  5392, 19790, 19791,  \n5065, 7828, 18616,  4003, 21244, 23549,  16223, 2653, 4140,  \n1414, 484, 1494,  1962, 5404, 18041,  26516, 25857, 26515,  \n9558, 20931, 4272,  1414, 1413, 484,  18594, 16335, 18547,  \n5048, 22355, 18717,  10862, 326, 5611,  15447, 15449, 19852,  \n26681, 26849, 26680,  18342, 2522, 13733,  26849, 26164, 26517,  \n1580, 1579, 7537,  26517, 26166, 26680,  2654, 16939, 14074,  \n14894, 10713, 10712,  12253, 16188, 12252,  20075, 11906, 13300,  \n26162, 25855, 26850,  3358, 7229, 15998,  3072, 3071, 17125,  \n4910, 12248, 4911,  26323, 26162, 26850,  13766, 2601, 21213,  \n6806, 4022, 6802,  26851, 26683, 26516,  16180, 3588, 2394,  \n6700, 3750, 15677,  26519, 26684, 26852,  9991, 7560, 10458,  \n3685, 5504, 5503,  15315, 5001, 3655,  26519, 26686, 26328,  \n26685, 26853, 26684,  17343, 17342, 4534,  26686, 26520, 26328,  \n1060, 870, 1069,  11660, 7003, 9682,  26521, 26854, 26685,  \n978, 9263, 7817,  18542, 18543, 19352,  18490, 15291, 2209,  \n16322, 17392, 14122,  18650, 17983, 21166,  26337, 26686, 26522,  \n1503, 4208, 19845,  20188, 4797, 11531,  26026, 26332, 26856,  \n17619, 1544, 17003,  1866, 3106, 1867,  26857, 26521, 26523,  \n13130, 2156, 20142,  25617, 26027, 27253,  1980, 8857, 1981,  \n26857, 26687, 26858,  26857, 26523, 26687,  26689, 26858, 26687,  \n7756, 12864, 20513,  26170, 26026, 26856,  26334, 26692, 26518,  \n26690, 26170, 26856,  14348, 11154, 9312,  13457, 11022, 11021,  \n11615, 17925, 22906,  2616, 667, 594,  26690, 26860, 26527,  \n26690, 26527, 26173,  985, 1115, 6204,  3675, 15188, 17529,  \n9218, 12787, 11842,  13102, 6201, 13696,  26526, 26524, 26528,  \n4637, 13648, 10337,  26861, 26689, 26862,  16295, 17393, 15674,  \n2730, 6442, 12289,  11410, 11409, 13848,  8671, 1975, 2488,  \n19565, 16664, 4631,  17761, 22313, 22312,  26181, 26694, 26529,  \n15724, 21930, 21458,  5991, 6933, 7276,  26698, 26692, 26345,  \n27060, 26698, 26530,  8639, 19679, 5237,  26530, 26865, 27060,  \n12093, 17030, 17031,  26530, 26351, 26865,  8699, 3039, 16789,  \n26701, 26697, 26863,  26864, 26031, 25737,  15810, 11120, 17706,  \n26865, 26351, 26700,  9797, 9798, 10700,  6271, 8997, 6270,  \n24870, 9975, 16351,  20088, 12871, 18627,  11518, 20411, 472,  \n18373, 5313, 13349,  26699, 26701, 26867,  16928, 14274, 6291,  \n26702, 26699, 26867,  5554, 9774, 17871,  11179, 22455, 11934,  \n2421, 18229, 18190,  15168, 5607, 6701,  17643, 15491, 4996,  \n22094, 13113, 20912,  9954, 19456, 19866,  17420, 9499, 13836,  \n26532, 26350, 26037,  23437, 4707, 16448,  26703, 26531, 26705,  \n3677, 5688, 14418,  25498, 26184, 26353,  26184, 26868, 26353,  \n8144, 16846, 7747,  21462, 2480, 2479,  26869, 26533, 26704,  \n26706, 26705, 26531,  12120, 7263, 10367,  7704, 22043, 13672,  \n2327, 13625, 9398,  25500, 26533, 26538,  7826, 1304, 5291,  \n8458, 19110, 21203,  26871, 26534, 26708,  14685, 9639, 7922,  \n26872, 20813, 14394,  11230, 11229, 9747,  796, 2039, 1593,  \n1216, 23357, 19582,  13187, 13150, 10664,  11002, 14138, 9724,  \n26707, 25626, 26537,  7863, 2933, 1213,  26534, 26871, 26873,  \n26534, 26873, 26536,  13959, 3798, 9750,  17070, 15064, 4855,  \n26710, 26538, 26874,  26710, 26875, 26539,  5151, 20732, 6391,  \n23170, 13501, 14052,  26542, 26539, 26875,  26540, 26711, 26706,  \n26876, 26190, 26536,  16336, 13092, 7973,  11906, 13823, 13299,  \n21567, 9319, 7882,  3416, 3418, 7393,  5309, 5310, 1461,  \n10590, 9820, 9382,  3889, 3890, 6692,  25877, 26714, 26877,  \n7416, 857, 11772,  4400, 12436, 12435,  21572, 18143, 18144,  \n26712, 27080, 26713,  1440, 6380, 2461,  6599, 21238, 2600,  \n9631, 5090, 15101,  13025, 8369, 6636,  6929, 21806, 12173,  \n13707, 8751, 17726,  18741, 10277, 1939,  5323, 1093, 745,  \n26712, 26547, 26879,  17434, 7907, 7761,  17421, 3415, 14351,  \n20046, 7107, 3373,  20680, 10982, 6540,  16482, 5687, 11961,  \n16389, 11922, 11384,  6148, 6149, 14230,  13955, 10699, 20390,  \n22612, 17395, 18818,  11974, 11975, 3566,  26716, 26717, 26880,  \n10884, 14291, 14290,  26716, 26720, 26040,  26880, 26720, 26716,  \n1210, 17622, 5910,  26040, 26720, 26043,  26718, 26044, 26199,  \n5757, 1854, 10750,  1330, 17556, 17134,  6121, 6120, 13703,  \n26882, 26717, 26881,  26546, 26881, 26717,  20912, 13113, 13030,  \n21514, 8307, 4298,  8665, 18881, 10469,  14880, 19716, 11845,  \n2751, 17703, 1781,  19015, 1886, 2378,  12606, 2510, 2511,  \n2135, 18384, 6478,  26362, 26722, 26359,  3728, 22445, 14025,  \n5472, 15510, 20129,  26720, 26721, 26361,  10235, 9995, 9026,  \n17512, 9432, 2431,  4955, 17225, 18907,  26885, 26721, 26720,  \n8219, 20916, 5276,  16012, 14982, 13968,  7501, 17839, 16155,  \n1710, 10855, 1709,  16051, 22324, 13178,  26367, 27089, 26204,  \n18468, 8825, 17651,  10146, 3295, 19943,  12725, 29507, 13631,  \n12221, 15791, 13318,  6864, 21024, 4823,  19082, 6147, 19499,  \n11744, 4123, 16565,  26722, 26549, 26888,  8581, 8580, 2573,  \n23071, 9022, 20804,  8035, 5871, 11482,  26548, 26045, 26369,  \n13356, 9333, 4516,  18586, 9298, 18580,  26551, 26721, 26725,  \n13558, 876, 13885,  26551, 26725, 26727,  26726, 26724, 26889,  \n4739, 15845, 11863,  26372, 26553, 26554,  26562, 26057, 26560,  \n26730, 26552, 26558,  26724, 26727, 26889,  24133, 5048, 1408,  \n18037, 12365, 14683,  26553, 26731, 26891,  26554, 26553, 26891,  \n18378, 18759, 4065,  12528, 21109, 14477,  26890, 26557, 26732,  \n9298, 18586, 24612,  13694, 8955, 14186,  10931, 14185, 14186,  \n14484, 15207, 13447,  7002, 3304, 9533,  12009, 2689, 7820,  \n14281, 16757, 21407,  2121, 21694, 15519,  4469, 2574, 12573,  \n2121, 14102, 21694,  10454, 10455, 17503,  26892, 26207, 26381,  \n26555, 26207, 26729,  18465, 15289, 6798,  8097, 3199, 15014,  \n16015, 3635, 21651,  14048, 19913, 15131,  26893, 26894, 26732,  \n14968, 13255, 8588,  26895, 26889, 26727,  26896, 26381, 26379,  \n12058, 4650, 4649,  3891, 1584, 15753,  8060, 1741, 20312,  \n9832, 17086, 16024,  26731, 26559, 26738,  3423, 11836, 18751,  \n19677, 11410, 13848,  26208, 26733, 26556,  4743, 3240, 13936,  \n13770, 17543, 11510,  3818, 10655, 12283,  26565, 26378, 26564,  \n22871, 12894, 21163,  2107, 13770, 11510,  7149, 1647, 9527,  \n7632, 21177, 22572,  15494, 13825, 18172,  26728, 26739, 26563,  \n26561, 26739, 26740,  26731, 26738, 26897,  19948, 7905, 4245,  \n26898, 9823, 17525,  9657, 17240, 4472,  9654, 21895, 10761,  \n11223, 8223, 17886,  4566, 13225, 11879,  26738, 26740, 26897,  \n21251, 7092, 21400,  6507, 16874, 4614,  13365, 13511, 13366,  \n17949, 2317, 21332,  26740, 26739, 26900,  26897, 26740, 26900,  \n684, 6725, 9165,  2402, 20511, 8057,  26202, 17969, 17970,  \n21582, 1096, 4076,  3140, 5893, 20033,  1429, 18509, 883,  \n26569, 26388, 26901,  6240, 6239, 18075,  1979, 2933, 7863,  \n26570, 26571, 26902,  16547, 5179, 12060,  18955, 9847, 18152,  \n4505, 4506, 17223,  26741, 26902, 26571,  26742, 26390, 26569,  \n17731, 378, 2971,  18630, 21254, 7934,  5453, 3066, 9077,  \n2241, 4947, 2242,  16830, 7304, 3824,  26746, 26573, 26904,  \n26573, 26742, 26904,  26905, 26744, 26745,  26905, 26745, 26747,  \n16762, 8721, 20563,  6901, 13213, 6902,  12940, 16023, 17347,  \n26748, 26905, 26747,  26906, 26905, 26748,  26906, 26748, 26749,  \n9311, 13792, 21210,  26068, 26907, 26579,  26909, 26910, 26906,  \n26750, 26911, 26749,  26911, 26909, 26749,  15505, 1675, 7140,  \n757, 21285, 16316,  21877, 5525, 5818,  13004, 17632, 11458,  \n21624, 13811, 17035,  14561, 23539, 15482,  18172, 8044, 8045,  \n13492, 8981, 18114,  26912, 26750, 26580,  16328, 12452, 16329,  \n26754, 26400, 26751,  12397, 14737, 19379,  12690, 11475, 16277,  \n2510, 14893, 18121,  9129, 7293, 9130,  22575, 9298, 9299,  \n12201, 10166, 9533,  13558, 1587, 876,  21929, 10802, 9540,  \n2145, 2144, 20887,  6171, 2128, 11260,  26756, 26402, 26755,  \n26913, 26756, 26755,  26753, 25919, 27122,  25919, 26222, 27122,  \n8859, 8860, 4512,  26583, 26756, 26757,  18873, 16887, 5959,  \n26914, 26757, 26915,  26915, 26757, 26756,  26916, 26220, 26584,  \n8388, 2980, 5810,  6048, 1946, 16011,  17357, 9683, 4633,  \n26075, 26759, 26404,  26759, 26587, 26404,  10773, 10772, 2883,  \n716, 19045, 15000,  4860, 4859, 7628,  26760, 26585, 26586,  \n8275, 14465, 1454,  20165, 9887, 22479,  26590, 26223, 26589,  \n13576, 12053, 14840,  1960, 6821, 2118,  12495, 18481, 19620,  \n26918, 26763, 26411,  26763, 26594, 26411,  6134, 20413, 6135,  \n3745, 3744, 1411,  20234, 14519, 11731,  26918, 26411, 26412,  \n12229, 6251, 3513,  25926, 26231, 26596,  26227, 26766, 26081,  \n5912, 4722, 5911,  5330, 2332, 5331,  26592, 25769, 26768,  \n26767, 26768, 26228,  17470, 16527, 3564,  12611, 20606, 20698,  \n26920, 26764, 26768,  26592, 26764, 26408,  26764, 26592, 26768,  \n5196, 19281, 17956,  14358, 13297, 14058,  3048, 1433, 24760,  \n26769, 26764, 26920,  1109, 1110, 11377,  17273, 13314, 17803,  \n15050, 2967, 2968,  2933, 11743, 1213,  7011, 1763, 19528,  \n1075, 16184, 3568,  12576, 13136, 17728,  15300, 2231, 4063,  \n26414, 26764, 26769,  7810, 15405, 20344,  17130, 5559, 478,  \n6287, 2098, 6285,  14027, 8885, 6555,  16640, 8872, 8873,  \n9290, 5461, 6737,  22489, 2185, 13909,  11725, 7703, 19645,  \n14111, 8763, 8546,  21911, 4783, 17128,  1727, 6215, 8090,  \n26921, 26089, 26922,  26600, 26922, 26089,  18774, 5055, 8819,  \n10049, 14380, 16708,  10711, 20717, 10933,  4921, 4139, 4922,  \n26239, 26923, 26600,  9743, 18190, 21520,  22895, 19168, 16626,  \n26773, 26601, 26599,  6888, 9905, 12849,  26923, 26604, 26924,  \n14134, 4767, 16277,  1115, 13927, 18104,  26775, 26925, 26926,  \n26775, 26926, 26602,  26601, 26773, 26774,  26417, 26090, 26603,  \n19368, 455, 22857,  26774, 26773, 26927,  16501, 9754, 19800,  \n16070, 20477, 15245,  26603, 26602, 26926,  4783, 13039, 14486,  \n8883, 2702, 2703,  4879, 17731, 9902,  3552, 5966, 9795,  \n19278, 20184, 19449,  26777, 26604, 25937,  26241, 26242, 26092,  \n2614, 659, 3614,  13411, 13149, 3626,  15826, 2600, 5118,  \n26093, 26092, 26242,  24100, 1176, 1175,  26928, 26418, 26606,  \n29730, 21558, 22899,  1802, 15559, 15052,  1376, 21071, 5584,  \n25181, 5386, 5780,  3835, 3836, 591,  5133, 2017, 4315,  \n12732, 8632, 9546,  6655, 2587, 2997,  24932, 24931, 24917,  \n26928, 26421, 26780,  5373, 1197, 17716,  17133, 7497, 17243,  \n4391, 22288, 2253,  13692, 26929, 25846,  11416, 20688, 20879,  \n19387, 7659, 21818,  27141, 27150, 26930,  26931, 27141, 26930,  \n16122, 4185, 13356,  27149, 26931, 26933,  26930, 26932, 26934,  \n26934, 26935, 26930,  26935, 26931, 26930,  26933, 26931, 26936,  \n12271, 12675, 10563,  4189, 3279, 4188,  15947, 5986, 5987,  \n26936, 26931, 26935,  4584, 4338, 19295,  26937, 26935, 26934,  \n19078, 17160, 10480,  15574, 21082, 8529,  20394, 18411, 10630,  \n20429, 563, 17626,  7713, 3109, 2317,  26610, 26425, 26943,  \n7002, 4759, 3304,  3814, 3331, 3333,  27366, 26939, 26248,  \n27366, 26248, 26782,  9127, 12861, 5997,  5151, 6391, 7947,  \n26940, 26252, 26426,  19078, 10480, 7152,  26610, 26246, 26425,  \n7682, 10370, 12009,  26608, 26430, 26784,  18894, 11454, 14061,  \n4566, 4568, 13225,  26609, 25669, 26100,  13753, 10535, 16727,  \n6493, 5054, 5055,  26254, 26252, 26940,  7323, 17034, 6638,  \n21721, 10441, 10440,  7588, 5072, 7589,  9334, 21880, 17603,  \n4928, 5271, 734,  9498, 11785, 5605,  26784, 26611, 26942,  \n26785, 26253, 26251,  4442, 8968, 10280,  7504, 17671, 6300,  \n11914, 11045, 11044,  20927, 2024, 14302,  26105, 26786, 27369,  \n26105, 25947, 26786,  5868, 2911, 9216,  13321, 15704, 18704,  \n19184, 2262, 8024,  19960, 8943, 11135,  25796, 26254, 26613,  \n13378, 4177, 4178,  15152, 9002, 6085,  12137, 763, 3450,  \n9852, 7534, 6555,  7021, 14767, 7022,  12044, 12043, 20332,  \n18744, 8272, 15350,  19207, 9266, 15041,  25946, 26945, 26611,  \n19216, 8250, 13302,  26787, 25800, 26950,  7224, 1187, 5977,  \n26946, 26612, 26434,  488, 6182, 6183,  18401, 16674, 21745,  \n19653, 11593, 9866,  4051, 17209, 568,  26946, 26434, 26788,  \n13037, 10698, 4893,  18401, 21745, 21744,  25802, 26948, 26945,  \n26949, 26432, 26614,  16880, 14256, 865,  11469, 14613, 2224,  \n26177, 24274, 19379,  20823, 17085, 17645,  26949, 26437, 26432,  \n18873, 2878, 22406,  7200, 10807, 7199,  5012, 9616, 5013,  \n8195, 14563, 14565,  26107, 25133, 25950,  26790, 26107, 25950,  \n25800, 26263, 26950,  24915, 17646, 16017,  25802, 26114, 26948,  \n21005, 3926, 15261,  26435, 26951, 26792,  26435, 26256, 26951,  \n17021, 17022, 13854,  26263, 25800, 25283,  16111, 16164, 7990,  \n21096, 18816, 10412,  7217, 18797, 5566,  15008, 5575, 7681,  \n2224, 2082, 11469,  26794, 25280, 25797,  26440, 26955, 26114,  \n26792, 26953, 26616,  26616, 26953, 26957,  12890, 19597, 19596,  \n15158, 17219, 5132,  13014, 17042, 889,  2258, 1834, 9364,  \n25804, 3426, 26958,  17069, 12134, 3911,  21935, 3544, 7397,  \n5729, 23479, 11577,  25522, 10922, 9508,  25280, 26794, 25959,  \n26616, 26957, 26959,  26439, 26616, 26959,  7200, 18532, 16799,  \n6237, 5563, 9107,  10206, 16752, 5295,  3410, 16246, 20413,  \n10661, 13435, 19990,  10078, 15961, 9096,  13409, 12322, 10882,  \n5464, 7408, 5465,  26797, 26439, 26961,  26443, 26795, 26960,  \n9140, 3122, 11224,  5860, 4240, 5859,  26802, 26443, 26960,  \n18593, 5025, 5027,  9389, 23790, 5758,  4224, 5079, 11753,  \n2697, 20209, 18352,  26797, 26961, 26444,  26445, 26441, 26797,  \n4157, 26845, 8427,  26801, 26962, 26800,  3913, 5596, 10740,  \n11110, 6600, 8271,  20241, 12372, 15950,  26447, 26801, 26800,  \n26801, 26447, 26802,  4970, 4971, 12730,  14338, 17321, 14337,  \n25805, 25962, 26964,  26963, 26804, 26444,  14459, 9352, 14460,  \n6358, 12820, 6833,  25286, 26271, 26619,  11888, 11970, 13382,  \n21571, 17041, 9952,  12008, 7684, 8902,  7831, 10420, 10316,  \n26623, 26966, 26624,  26624, 26966, 26626,  12805, 769, 956,  \n26452, 26626, 26273,  26453, 25968, 26273,  11162, 11164, 15795,  \n26120, 25688, 26967,  3733, 17109, 3732,  25971, 26625, 26457,  \n26456, 26968, 26805,  26456, 26805, 26274,  17899, 17900, 4293,  \n19122, 21582, 19123,  4965, 20947, 14700,  25434, 19616, 20202,  \n26969, 26455, 26628,  17051, 18678, 18042,  22876, 15126, 589,  \n7065, 7064, 7768,  1462, 5304, 14823,  5596, 3913, 8241,  \n22471, 16595, 16594,  2304, 7712, 10094,  5756, 3051, 5757,  \n1803, 15559, 1802,  26971, 26458, 26631,  15930, 9454, 9455,  \n11486, 2328, 14409,  26458, 26971, 26633,  16814, 787, 786,  \n25974, 26630, 26972,  26459, 26973, 26460,  18738, 15022, 7702,  \n17227, 5884, 17993,  26462, 26973, 26459,  9376, 6501, 9323,  \n26806, 26808, 26807,  25977, 25974, 26972,  18992, 25420, 7697,  \n26464, 26278, 26463,  8737, 8457, 8458,  5523, 13982, 5317,  \n5952, 19516, 14012,  1414, 1494, 6537,  12585, 8992, 17933,  \n26467, 26809, 26974,  12379, 12070, 15454,  4827, 4826, 12258,  \n25169, 25977, 26276,  26277, 26467, 26469,  26467, 26974, 26469,  \n1522, 25423, 12738,  25575, 25818, 26635,  492, 18061, 9493,  \n16526, 15587, 14888,  26811, 26469, 26975,  15878, 6202, 5940,  \n6377, 7063, 23693,  10112, 15422, 15423,  26635, 25818, 26976,  \n3504, 8333, 8645,  26470, 26976, 25818,  8531, 7569, 18759,  \n989, 3679, 19052,  10602, 6791, 16911,  25817, 26977, 26279,  \n26127, 25981, 26978,  11974, 15059, 5235,  19913, 14048, 14057,  \n16577, 22833, 18214,  18016, 11699, 16428,  6199, 3118, 1093,  \n1946, 8157, 8911,  3030, 16505, 21789,  9280, 11369, 17023,  \n26636, 25580, 25982,  14623, 21982, 14624,  26980, 26984, 26126,  \n25578, 26126, 26984,  12966, 20414, 26080,  2622, 16763, 18869,  \n4352, 19586, 10647,  25827, 24872, 26983,  21397, 26985, 3387,  \n702, 1637, 703,  11904, 6926, 11905,  26637, 26128, 26986,  \n15204, 20973, 17839,  14641, 12996, 21826,  8440, 9499, 8441,  \n21475, 16655, 6936,  2822, 6801, 2287,  25822, 25825, 26813,  \n26477, 25821, 26987,  17985, 13487, 4316,  21448, 21226, 14007,  \n1896, 19611, 4338,  13359, 13358, 13422,  20949, 2316, 1141,  \n4119, 613, 15981,  26813, 25984, 26479,  15773, 14126, 2046,  \n26989, 27203, 25830,  18388, 2607, 16382,  14553, 18289, 7065,  \n8049, 4922, 6161,  1594, 12319, 10622,  21521, 16610, 15023,  \n5155, 16922, 5156,  11963, 8725, 17782,  17672, 8091, 8466,  \n12208, 13213, 19968,  11735, 18096, 16746,  26134, 26132, 26815,  \n3224, 5270, 2755,  26990, 26480, 26640,  9238, 1623, 21038,  \n6665, 20599, 12595,  26641, 26991, 25986,  2810, 13542, 19993,  \n1125, 22881, 1126,  1538, 18216, 406,  16623, 6105, 7931,  \n25986, 26991, 26135,  18393, 1932, 3024,  7025, 7026, 13579,  \n418, 15738, 14889,  5771, 5770, 17914,  26817, 26816, 26640,  \n26135, 26991, 25703,  8109, 22430, 4817,  13136, 15495, 17728,  \n8103, 20624, 20688,  22399, 17484, 22220,  1571, 12828, 1572,  \n7929, 11391, 16013,  26283, 26481, 26992,  4662, 20069, 8678,  \n14044, 13387, 14793,  26070, 25490, 10761,  649, 648, 13695,  \n11852, 18370, 14789,  5245, 10057, 20476,  27402, 25704, 25705,  \n26818, 26283, 26992,  15335, 10103, 9379,  13479, 21215, 10822,  \n23962, 8329, 26498,  21228, 14687, 11015,  19037, 14649, 12881,  \n22572, 18251, 7632,  13262, 20116, 14068,  11651, 8833, 13025,  \n4286, 9792, 13727,  6469, 19531, 13606,  12095, 22575, 9299,  \n13664, 19385, 18727,  17541, 15525, 17391,  7307, 7306, 21408,  \n10875, 10876, 11945,  26994, 25705, 25993,  470, 16870, 959,  \n26646, 26995, 26823,  14627, 14626, 21258,  15926, 8436, 6051,  \n26995, 26646, 26826,  2842, 2843, 14486,  801, 17158, 17157,  \n26997, 26826, 26825,  26998, 26826, 26997,  26995, 26826, 26998,  \n7644, 1834, 2258,  9411, 13554, 16015,  18692, 606, 13243,  \n9592, 7983, 13672,  10315, 4940, 13089,  21395, 11147, 14981,  \n26995, 26998, 26999,  13435, 7249, 19990,  20487, 6767, 7500,  \n25475, 4370, 23919,  27001, 26999, 26998,  2235, 14720, 2233,  \n25837, 26484, 27002,  13519, 1618, 23630,  21632, 18636, 18637,  \n27001, 26998, 27000,  26485, 25707, 25327,  17588, 7184, 1020,  \n25588, 26486, 26289,  17135, 15377, 13236,  2063, 12109, 3903,  \n8748, 10911, 3885,  6809, 5616, 4203,  13444, 891, 11564,  \n17860, 22789, 9016,  25327, 25709, 25995,  26290, 26141, 27002,  \n21056, 11646, 4931,  13573, 13248, 5868,  20915, 15067, 20916,  \n7661, 10360, 15818,  1181, 5037, 5036,  19097, 5229, 5228,  \n5787, 6174, 3569,  23541, 10828, 9260,  12315, 2533, 8141,  \n11916, 8235, 11915,  3432, 17216, 23742,  14908, 17706, 12683,  \n343, 21361, 12802,  8134, 3219, 17281,  11292, 6682, 6684,  \n26292, 25996, 26647,  8117, 15049, 6033,  16331, 423, 5196,  \n27010, 27011, 27228,  17458, 19438, 1787,  11989, 18875, 15005,  \n3889, 2306, 3890,  27011, 27010, 27009,  11791, 2093, 19917,  \n21150, 10732, 22872,  27009, 27014, 27013,  5746, 4535, 17342,  \n27011, 27009, 27013,  5143, 18115, 20130,  26650, 27228, 26832,  \n3757, 6148, 6133,  26654, 27013, 27015,  27013, 26654, 27011,  \n27011, 26654, 26832,  21849, 12983, 15900,  27012, 26830, 26831,  \n7123, 18589, 7121,  1253, 10630, 10631,  16139, 12590, 19274,  \n8673, 10186, 6488,  19940, 22083, 14862,  15576, 11421, 11420,  \n12903, 11620, 18776,  27017, 27015, 27013,  14248, 10554, 8981,  \n14224, 11864, 18618,  15617, 10555, 6807,  26831, 26653, 26833,  \n26833, 26491, 26656,  26834, 26833, 26656,  19908, 1182, 23595,  \n8204, 7879, 3220,  26834, 26656, 26493,  6677, 4537, 14255,  \n26654, 27015, 26835,  2506, 2534, 19318,  4654, 4653, 4008,  \n25186, 26292, 27016,  8601, 9442, 1103,  1569, 1570, 2190,  \n3459, 20866, 6957,  26654, 26835, 26655,  2314, 12904, 10809,  \n7845, 18259, 860,  27232, 26658, 26659,  27016, 26297, 26000,  \n6731, 16952, 4502,  26659, 26658, 26300,  16240, 11132, 14489,  \n15177, 8459, 7708,  11289, 11222, 11290,  15506, 9555, 1542,  \n19007, 6343, 6342,  7843, 14719, 7902,  26663, 26835, 27018,  \n15858, 17669, 15857,  6727, 6729, 3552,  26295, 25840, 25596,  \n14191, 3998, 11678,  11774, 13271, 11775,  8120, 4222, 2475,  \n7291, 12457, 17114,  6677, 9548, 9547,  4236, 3692, 14951,  \n27019, 26295, 25596,  26663, 27018, 26837,  20006, 19248, 20859,  \n1277, 13628, 16801,  20607, 2623, 5657,  22755, 14655, 486,  \n20256, 19055, 13635,  11249, 18755, 15726,  2347, 20819, 17806,  \n26837, 27430, 27020,  17594, 12066, 21084,  19340, 19388, 17565,  \n13598, 13599, 20129,  12863, 11312, 11310,  27023, 26307, 26150,  \n26664, 27020, 27024,  8286, 8530, 21249,  3078, 10418, 23451,  \n4229, 9273, 15632,  26665, 26664, 27024,  26840, 26153, 26666,  \n3030, 19608, 16676,  25143, 17320, 27026,  6261, 4633, 9684,  \n25197, 26148, 26842,  26152, 26665, 27024,  14985, 12333, 22362,  \n1504, 6250, 21138,  9249, 11884, 9347,  6577, 6195, 980,  \n26152, 27024, 26668,  27028, 26011, 26501,  26011, 25052, 26501,  \n7223, 18518, 13800,  1268, 11699, 20662,  12909, 5262, 5263,  \n26666, 26014, 27029,  6963, 1619, 11483,  18897, 20069, 4662,  \n9186, 17975, 9187,  27030, 26311, 25724,  26670, 26013, 26843,  \n27031, 26669, 26668,  2171, 20073, 13812,  6939, 11370, 9929,  \n4120, 12224, 4121,  26312, 26669, 26157,  1796, 3201, 1970,  \n13146, 9289, 3296,  3799, 10222, 1747,  12459, 4558, 19672,  \n9990, 9618, 8512,  9456, 4030, 8069,  16628, 9487, 3672,  \n19103, 1906, 5681,  6591, 13552, 21073,  26507, 25851, 26508,  \n26846, 26156, 26158,  13562, 2038, 15911,  26509, 26672, 26847,  \n22789, 17860, 6578,  17144, 17143, 17126,  13044, 2130, 20125,  \n14530, 14919, 16558,  26675, 27035, 26674,  9660, 14120, 13033,  \n20732, 20886, 6391,  26675, 27036, 27035,  3960, 7700, 18262,  \n16565, 12509, 13772,  26677, 27036, 26675,  20520, 10591, 5392,  \n27037, 25854, 26673,  26510, 25854, 27037,  15132, 5946, 16615,  \n26512, 27038, 26513,  16689, 10169, 2826,  9145, 18074, 5964,  \n26514, 27039, 26512,  25856, 26510, 26678,  19587, 7903, 9477,  \n17825, 20971, 7091,  18105, 13619, 9980,  23348, 15930, 7325,  \n4890, 4249, 16055,  11239, 10904, 18757,  27039, 26514, 26679,  \n6592, 8156, 6892,  26849, 27040, 26320,  3784, 5905, 16764,  \n15151, 9991, 1999,  10578, 19523, 22925,  2935, 7029, 13732,  \n26849, 26517, 26680,  26681, 27252, 26849,  26681, 27041, 27252,  \n27042, 26516, 26515,  25616, 26511, 26021,  6060, 1675, 15505,  \n26681, 27043, 27041,  6918, 14832, 14831,  21271, 18338, 18337,  \n26851, 26516, 27042,  19783, 21660, 17835,  640, 10993, 638,  \n27043, 26681, 26682,  12562, 11344, 16208,  13036, 6869, 17299,  \n7172, 10784, 13850,  12419, 11821, 12420,  579, 12407, 12406,  \n27044, 26323, 26850,  18420, 17545, 15214,  27458, 26319, 26024,  \n19509, 12137, 3450,  1653, 12411, 12412,  27045, 26683, 26851,  \n16139, 11700, 12590,  26682, 26518, 27046,  26682, 26324, 26518,  \n11405, 22132, 8028,  11142, 5444, 9842,  19414, 19413, 13332,  \n6172, 4914, 5174,  15358, 681, 872,  6735, 12039, 8794,  \n3060, 19414, 12453,  26852, 26686, 26519,  14103, 5532, 21889,  \n18986, 2394, 3588,  18755, 22525, 15726,  7343, 7104, 14131,  \n22370, 16547, 8080,  13658, 14669, 13657,  19386, 17297, 18119,  \n26522, 26686, 26855,  2437, 6402, 6403,  14781, 2896, 2897,  \n5844, 9285, 7033,  718, 719, 11584,  26518, 27047, 27046,  \n23730, 3513, 12493,  6980, 14001, 1955,  17817, 15453, 8105,  \n4439, 21308, 4440,  27048, 27049, 26857,  27050, 26332, 27051,  \n7700, 3960, 13430,  3596, 13845, 3117,  27052, 26338, 26325,  \n14373, 22715, 3007,  9428, 4388, 1144,  27048, 26857, 27053,  \n11161, 7774, 11301,  20040, 20407, 20481,  27054, 27253, 26027,  \n27055, 26857, 27056,  13175, 1052, 9397,  1382, 1381, 4056,  \n27056, 26857, 26858,  6717, 6435, 8589,  17769, 18545, 18465,  \n9995, 1625, 3815,  22635, 7337, 7338,  16114, 18355, 13444,  \n20018, 13356, 4516,  26692, 27047, 26518,  11250, 18756, 18755,  \n2715, 2716, 22404,  5758, 1478, 10994,  27056, 26858, 26861,  \n3370, 9885, 9884,  19848, 13659, 17761,  27057, 26528, 26524,  \n11656, 7873, 1898,  26181, 26527, 27058,  26527, 26860, 27058,  \n12139, 18926, 780,  20578, 19215, 13767,  12619, 2807, 2995,  \n9759, 10604, 2742,  26694, 26181, 27058,  27059, 27060, 27061,  \n25872, 26346, 27052,  24060, 20064, 7852,  3983, 13888, 433,  \n16373, 9681, 5917,  17362, 3688, 12644,  26344, 27062, 26693,  \n15823, 12204, 7751,  14187, 9035, 1270,  13986, 4122, 8407,  \n9699, 14580, 5650,  27060, 26692, 26698,  26347, 26031, 26859,  \n524, 17912, 21863,  19336, 19785, 9068,  2161, 4617, 15640,  \n5886, 1390, 1389,  26528, 27063, 25870,  25871, 25870, 27063,  \n11155, 7610, 7609,  6413, 14261, 12983,  6148, 14230, 8809,  \n8954, 22841, 6511,  4799, 15598, 6400,  26700, 27065, 26865,  \n5195, 22520, 597,  25737, 26866, 26864,  27066, 26864, 26866,  \n12010, 8345, 8344,  26697, 27069, 26863,  3494, 3496, 11115,  \n20696, 13020, 22336,  15258, 17538, 17539,  11287, 11286, 18693,  \n11298, 18382, 16315,  14581, 1449, 13742,  3234, 22276, 13222,  \n6687, 18575, 6629,  26863, 27067, 26701,  26867, 26701, 27067,  \n10452, 16436, 18872,  27068, 26863, 27069,  27067, 26863, 27068,  \n27070, 26699, 26702,  27070, 26184, 26699,  26183, 25871, 27064,  \n14521, 3249, 19357,  26700, 26703, 27065,  23480, 10376, 20569,  \n27070, 26868, 26184,  26183, 27064, 26354,  26704, 26354, 27064,  \n15418, 2841, 2840,  19195, 386, 387,  26705, 27071, 26703,  \n11613, 3312, 21776,  3056, 13267, 3055,  26708, 26353, 26868,  \n9626, 3891, 14200,  26868, 26870, 26708,  7708, 1934, 22524,  \n947, 11454, 11441,  26709, 26705, 26706,  16266, 1447, 7612,  \n1961, 5980, 9890,  19988, 8224, 5797,  23997, 10755, 19409,  \n19326, 1006, 1005,  27072, 26532, 26707,  8197, 17568, 19592,  \n6701, 14555, 6700,  14337, 17322, 2937,  9558, 6385, 20931,  \n13113, 1640, 3761,  27073, 26709, 26706,  26708, 27074, 26871,  \n27073, 26706, 26711,  13819, 13820, 10095,  23626, 19649, 15835,  \n26871, 27075, 26873,  6538, 1494, 1496,  26536, 26873, 26876,  \n26873, 27075, 27076,  5900, 13981, 14812,  27077, 26190, 26876,  \n5619, 13019, 12862,  12099, 2493, 12100,  26542, 27278, 26194,  \n27073, 26711, 26713,  17232, 13953, 11260,  26194, 27278, 26357,  \n6814, 6697, 6815,  15368, 14520, 2283,  26871, 27074, 27079,  \n5888, 18753, 7611,  6426, 19227, 2858,  5255, 20653, 390,  \n11931, 17060, 4994,  26190, 27077, 26192,  6144, 11430, 23201,  \n26192, 27077, 26543,  25877, 26877, 25370,  19244, 9903, 19496,  \n26878, 26714, 26544,  27080, 26712, 26879,  10187, 16467, 21594,  \n27081, 26715, 26543,  26041, 26042, 27488,  1432, 4297, 8413,  \n16335, 14050, 15286,  5782, 17345, 5783,  4725, 21375, 12835,  \n8103, 20688, 15226,  4667, 2987, 10010,  26878, 27083, 27082,  \n10964, 4569, 19472,  27083, 26878, 26544,  21789, 16505, 7882,  \n26041, 27084, 26199,  3113, 23216, 20890,  27083, 26544, 26359,  \n26718, 26199, 27084,  19774, 20924, 11279,  14207, 1011, 1955,  \n17435, 7907, 17434,  6121, 12817, 15396,  26717, 26882, 26880,  \n16264, 6293, 809,  12938, 6943, 6775,  26719, 27086, 26047,  \n17409, 19853, 15449,  26881, 26546, 26715,  7069, 7070, 21468,  \n26880, 26882, 27087,  6606, 22865, 2354,  17613, 18918, 17614,  \n26359, 26722, 27085,  25887, 26047, 27086,  12748, 11388, 20626,  \n6793, 3908, 7352,  27088, 26882, 26881,  6337, 8786, 2960,  \n16037, 5881, 21154,  26722, 26884, 27085,  8972, 12516, 304,  \n27086, 26550, 25887,  12819, 5944, 14439,  9690, 18500, 2478,  \n11281, 24586, 6690,  18478, 9446, 5492,  16199, 12093, 21460,  \n26204, 27089, 27090,  26205, 26368, 26723,  11869, 14098, 11660,  \n26368, 25894, 27091,  27092, 27088, 26881,  8106, 18826, 4081,  \n26884, 26722, 27093,  27295, 26884, 27093,  14757, 14759, 13640,  \n27090, 26377, 26204,  13647, 10583, 2848,  26888, 27093, 26722,  \n27506, 26560, 26377,  19499, 16584, 19082,  26548, 26369, 26887,  \n18590, 14578, 17894,  16601, 20025, 16600,  413, 16760, 8361,  \n26725, 26721, 26886,  26373, 26890, 26369,  26887, 26369, 26890,  \n26888, 26549, 27094,  13379, 1889, 12374,  27093, 26888, 27094,  \n1937, 15535, 4925,  5301, 9954, 19866,  12377, 967, 19494,  \n26373, 26557, 26890,  26887, 26890, 26894,  10401, 13617, 18122,  \n2933, 10759, 11743,  27095, 26562, 26560,  4370, 4371, 23919,  \n20261, 20260, 12426,  3031, 18601, 17911,  20340, 9075, 8582,  \n20851, 20852, 21798,  26366, 26726, 27096,  26728, 26366, 27096,  \n10989, 4508, 5390,  13145, 11087, 15577,  26894, 26890, 26732,  \n21739, 15933, 18758,  26737, 25903, 26384,  27098, 26891, 26731,  \n26375, 26554, 26564,  4841, 4012, 3438,  26896, 26892, 26381,  \n4535, 6099, 4534,  15297, 15352, 3397,  8261, 15251, 15776,  \n12575, 21349, 7263,  14613, 11469, 13531,  8339, 29091, 20090,  \n15010, 20596, 18929,  7728, 4156, 19233,  19703, 8776, 19982,  \n26896, 26379, 26734,  26555, 26729, 26733,  20335, 21483, 16929,  \n26893, 27099, 26894,  27100, 26727, 26725,  8644, 17251, 2520,  \n7380, 17067, 7381,  11773, 14984, 5170,  26564, 26378, 26375,  \n16328, 16330, 20887,  9327, 2623, 20607,  7864, 20644, 16724,  \n26893, 26732, 26556,  27101, 27099, 26893,  26212, 27102, 26059,  \n26730, 26566, 27097,  8992, 12585, 8897,  1512, 11304, 1652,  \n26889, 26895, 27103,  9465, 3063, 10220,  7039, 15739, 7040,  \n26556, 26733, 27101,  26893, 26556, 27101,  3582, 9281, 1796,  \n27104, 27097, 26566,  8689, 4987, 23325,  27100, 26895, 26727,  \n5416, 14067, 18796,  20886, 6011, 19949,  2977, 2086, 8340,  \n7020, 7019, 12328,  26897, 27098, 26731,  27105, 26565, 26564,  \n27106, 27101, 26733,  12649, 1409, 17388,  26214, 26568, 27107,  \n26567, 27104, 26566,  2590, 797, 796,  9965, 12358, 3085,  \n1212, 7863, 1213,  4238, 6013, 4910,  4910, 6013, 12248,  \n26736, 27108, 26734,  18751, 4809, 4225,  27104, 26567, 26570,  \n26739, 26728, 26899,  13115, 9662, 13114,  9708, 15059, 3009,  \n18704, 21522, 20979,  16444, 16355, 17468,  27522, 26388, 26214,  \n7449, 5103, 3684,  26899, 27111, 26739,  26739, 27111, 26900,  \n26900, 27110, 26897,  4146, 8083, 27112,  3009, 15059, 3010,  \n26735, 26565, 27114,  26736, 26735, 27114,  8646, 13142, 13086,  \n12348, 22074, 6309,  20161, 14896, 560,  16617, 20434, 27347,  \n2759, 16355, 3282,  27115, 26901, 26388,  12903, 18776, 12129,  \n733, 14756, 5731,  5111, 1716, 16739,  23693, 4573, 7628,  \n9742, 13486, 21588,  12978, 8999, 13335,  12236, 12927, 11531,  \n26903, 26902, 26741,  26903, 26743, 27117,  26903, 26741, 26743,  \n27117, 26743, 26744,  27118, 27117, 26744,  14436, 15385, 2517,  \n27118, 26744, 26905,  27119, 27118, 26905,  5155, 5157, 2305,  \n15392, 12343, 11820,  16204, 17062, 15186,  26906, 27119, 26905,  \n26908, 27119, 26906,  9282, 17421, 15227,  3505, 23222, 16599,  \n7349, 8078, 5093,  8397, 6974, 6975,  26910, 26908, 26906,  \n26749, 26909, 26906,  5340, 14477, 21968,  26910, 26909, 27120,  \n17129, 10798, 5545,  7058, 6159, 11394,  7927, 3697, 7925,  \n26399, 26218, 26752,  22975, 22294, 18451,  7317, 9467, 901,  \n1244, 2099, 23685,  26750, 26912, 26911,  10546, 2124, 10547,  \n26581, 26912, 26580,  15868, 8539, 14536,  5939, 10433, 5938,  \n19447, 689, 8722,  26580, 26217, 26581,  2280, 17263, 18674,  \n6508, 9013, 5481,  26751, 27121, 26754,  20698, 17817, 17816,  \n8148, 20009, 8410,  6250, 5192, 21138,  16678, 4630, 12882,  \n3384, 5441, 3385,  19041, 8504, 943,  12651, 11366, 9913,  \n26756, 26913, 26915,  7832, 888, 7831,  11884, 515, 3169,  \n26757, 26914, 26758,  17834, 13671, 5056,  17266, 8750, 21351,  \n5819, 5360, 4154,  1160, 4411, 6604,  27122, 26222, 26917,  \n13591, 17638, 16074,  15283, 5602, 11616,  12343, 14323, 11820,  \n27123, 26587, 26759,  26587, 27123, 26589,  26761, 27124, 26760,  \n26761, 26762, 27124,  26763, 27125, 26762,  26762, 27125, 27124,  \n27327, 26590, 26589,  26590, 27327, 26407,  27126, 27125, 26763,  \n1412, 7224, 20724,  1702, 15879, 10449,  26918, 27126, 26763,  \n5830, 611, 10088,  14636, 1117, 9415,  4407, 8939, 17791,  \n21214, 14808, 5050,  581, 9268, 2788,  26919, 26918, 26412,  \n26229, 26595, 27547,  6461, 393, 12708,  4747, 18532, 18761,  \n10487, 3844, 13917,  5175, 22655, 1465,  15686, 3288, 19951,  \n1254, 14442, 23538,  4267, 3287, 11027,  3044, 7642, 19660,  \n15334, 10769, 10768,  3595, 1372, 6164,  2182, 18359, 17547,  \n12169, 12837, 3294,  4420, 12889, 1288,  13213, 12400, 19968,  \n10135, 10136, 2325,  5329, 16716, 14251,  12809, 14299, 17113,  \n10526, 13784, 16136,  5600, 4518, 7251,  26770, 26771, 27128,  \n27130, 26771, 26772,  9820, 24955, 6257,  17879, 13284, 5003,  \n26089, 27130, 26772,  26921, 27130, 26089,  21157, 18030, 18031,  \n27131, 26599, 26769,  17432, 9107, 813,  14675, 16203, 2692,  \n3491, 8100, 17724,  10835, 8793, 16625,  23325, 14373, 8689,  \n16197, 11786, 11785,  14200, 3891, 5730,  12017, 1422, 9984,  \n21210, 2776, 1241,  27132, 26599, 27131,  26599, 27132, 26773,  \n12998, 11838, 11837,  19152, 1478, 1477,  12180, 13796, 18390,  \n13691, 7457, 7848,  3827, 13708, 8331,  16431, 18782, 8737,  \n26774, 26925, 26775,  12423, 8944, 9331,  8473, 20495, 3928,  \n19142, 3339, 4822,  26773, 27132, 27133,  17448, 13495, 17447,  \n1367, 9288, 1368,  19120, 14843, 14842,  26928, 27135, 26418,  \n12365, 12366, 11550,  26927, 26773, 27136,  26773, 27133, 27136,  \n26093, 26242, 26243,  26242, 27138, 26243,  24870, 3255, 2844,  \n2634, 2635, 10544,  17645, 17085, 5043,  27140, 26779, 26778,  \n27136, 27137, 26927,  5270, 5269, 11716,  21072, 14666, 14665,  \n447, 2104, 2106,  27142, 27143, 27137,  27143, 27141, 27137,  \n6181, 13804, 6180,  14876, 11819, 14861,  4785, 7787, 13804,  \n5296, 3466, 22908,  20457, 5392, 5822,  10713, 14894, 12484,  \n13408, 13407, 1904,  27144, 27141, 27145,  5398, 19192, 6406,  \n5975, 14802, 18958,  27146, 27143, 27142,  8206, 19554, 9040,  \n11728, 1214, 10803,  8614, 12490, 18060,  22325, 4496, 13903,  \n27145, 27148, 27149,  9235, 17879, 5003,  19684, 1852, 6170,  \n27148, 27145, 27141,  27150, 27143, 27146,  27141, 27143, 27150,  \n13274, 14984, 11447,  2623, 20679, 16544,  3469, 5976, 16440,  \n8041, 11043, 13253,  27148, 27141, 26931,  27148, 26931, 27149,  \n2968, 3509, 16163,  13498, 22293, 597,  11082, 9354, 10163,  \n27150, 27146, 26932,  6155, 19709, 21424,  8437, 12685, 17798,  \n11504, 16608, 11505,  27149, 26933, 27151,  27150, 26932, 26930,  \n22344, 18683, 11102,  9185, 9184, 10962,  18348, 8382, 10014,  \n1158, 1226, 5930,  19338, 11544, 13665,  26937, 26936, 26935,  \n27152, 26936, 26937,  27153, 26934, 26932,  27154, 26934, 27153,  \n26937, 26934, 27154,  3737, 12862, 15987,  20560, 17098, 20159,  \n27155, 26781, 27156,  9835, 13192, 21147,  27157, 26422, 26423,  \n2177, 20873, 2178,  12876, 10798, 10802,  23979, 20390, 22247,  \n861, 3429, 551,  13100, 13986, 18251,  26423, 26245, 26607,  \n26812, 26607, 25064,  18209, 19589, 13867,  17790, 10380, 13278,  \n7301, 3760, 4934,  14737, 18988, 11306,  9227, 22038, 18937,  \n898, 19579, 2512,  12862, 13019, 8862,  16311, 24955, 9820,  \n22398, 3108, 8948,  26883, 26247, 26608,  26883, 26425, 26247,  \n24612, 19066, 9298,  27368, 27158, 26609,  26939, 26609, 26248,  \n25944, 27369, 26783,  15259, 26080, 8410,  21863, 17912, 14920,  \n12471, 14645, 4476,  8649, 2641, 24236,  6363, 18999, 22228,  \n26965, 2163, 2162,  6886, 6115, 15966,  13275, 20094, 13274,  \n27158, 26102, 26609,  22570, 20365, 13750,  26255, 26253, 26785,  \n25673, 25940, 25090,  4072, 15079, 11865,  14113, 27160, 16268,  \n17141, 3982, 6732,  7281, 1629, 10057,  13655, 4080, 8219,  \n15322, 25846, 26929,  26429, 26104, 26612,  13737, 11387, 18524,  \n26947, 26108, 26255,  4286, 6686, 11567,  18045, 8030, 2192,  \n14554, 13898, 5664,  26947, 26614, 26108,  7087, 18058, 11281,  \n6051, 6050, 15203,  8429, 16112, 10417,  26433, 25799, 26613,  \n22544, 8744, 16272,  14331, 19544, 14332,  11618, 14400, 4006,  \n7702, 2936, 18738,  26788, 27162, 26946,  15608, 13196, 21330,  \n2611, 8048, 1446,  16183, 5241, 16688,  12470, 17036, 9065,  \n18603, 9483, 10952,  12205, 3319, 14181,  970, 2996, 14648,  \n26437, 26949, 27163,  20672, 16250, 21645,  18242, 19489, 4479,  \n27566, 26791, 26261,  25797, 24696, 26431,  26256, 27165, 26951,  \n10545, 18686, 11233,  25948, 27165, 26256,  25950, 24697, 25952,  \n20217, 2866, 20157,  9409, 20529, 9198,  12970, 12583, 4877,  \n6710, 24917, 9793,  9174, 4103, 9182,  16983, 753, 752,  \n7040, 15739, 21358,  26792, 26951, 27166,  20237, 27167, 16996,  \n19464, 3311, 2836,  26796, 27566, 26261,  26956, 26114, 26955,  \n26953, 27166, 27168,  26953, 26792, 27166,  8291, 5383, 12306,  \n23630, 6035, 16894,  1283, 14290, 19144,  1058, 3450, 14537,  \n1836, 1185, 16816,  407, 1281, 21760,  26952, 27171, 25959,  \n26952, 25959, 26794,  19515, 5865, 16371,  25148, 21912, 4696,  \n27172, 27168, 27169,  3066, 12748, 3065,  27172, 26957, 27168,  \n26957, 26953, 27168,  19026, 1488, 20014,  8853, 15938, 1040,  \n3513, 6252, 12493,  27171, 25958, 25959,  10996, 10458, 10997,  \n16250, 16252, 21883,  10997, 10458, 14241,  13437, 3548, 16373,  \n26263, 25965, 26618,  20329, 4555, 16223,  6613, 4262, 2223,  \n27172, 27174, 26959,  25139, 25000, 26264,  27173, 25139, 26264,  \n15078, 17195, 15076,  26961, 26959, 27174,  26961, 26439, 26959,  \n26960, 27175, 26962,  27177, 27175, 26960,  27178, 26961, 27174,  \n16176, 10784, 13956,  15242, 20552, 21519,  20494, 20470, 21524,  \n26960, 26801, 26802,  26960, 26962, 26801,  19295, 18715, 17838,  \n13464, 417, 21016,  16041, 14643, 12190,  11112, 11077, 11316,  \n22854, 8966, 8965,  4912, 22099, 22100,  18981, 19022, 18982,  \n26962, 27179, 26799,  12578, 5200, 14725,  19040, 20306, 13301,  \n14719, 16522, 7902,  26799, 26800, 26962,  27178, 26444, 26961,  \n26440, 26117, 26617,  27180, 26803, 27575,  3067, 7685, 3068,  \n25805, 26964, 26449,  787, 9452, 7340,  8346, 2908, 14369,  \n19717, 3732, 5125,  13704, 19641, 13703,  25805, 26449, 26620,  \n17312, 11171, 1411,  26804, 27181, 26448,  7020, 18318, 7019,  \n26625, 25808, 26620,  5249, 9085, 7991,  26622, 27182, 26623,  \n2798, 13127, 13001,  13007, 15655, 18189,  1616, 21213, 12443,  \n26623, 27182, 26966,  8389, 1207, 6362,  1666, 16235, 4791,  \n14908, 7049, 17706,  16434, 10102, 16734,  6199, 1093, 5323,  \n1248, 4672, 715,  8872, 672, 673,  26455, 26270, 25435,  \n1983, 5648, 13447,  27183, 20361, 3463,  12333, 7670, 22362,  \n2057, 17953, 2058,  741, 8532, 10115,  25688, 26121, 27184,  \n26121, 26627, 27184,  15568, 6607, 7235,  18001, 1129, 13857,  \n12194, 14273, 5492,  26628, 27186, 26969,  16219, 2645, 5522,  \n26805, 27185, 26629,  26274, 26805, 26629,  5709, 5710, 4096,  \n10219, 7968, 5747,  18716, 10793, 10828,  4023, 20950, 9468,  \n5327, 11868, 15484,  26631, 26629, 26970,  26971, 27187, 27188,  \n26971, 26631, 27187,  26970, 27187, 26631,  27186, 26628, 25973,  \n6554, 4206, 14019,  6656, 6657, 10412,  11163, 6648, 1594,  \n19744, 10846, 6569,  15943, 8002, 8001,  8689, 633, 5627,  \n552, 11178, 11569,  26806, 27188, 26808,  27188, 26806, 26633,  \n27188, 26633, 26971,  11302, 11304, 15210,  11248, 11057, 2887,  \n6440, 10763, 15189,  6104, 6012, 13696,  7746, 12594, 8335,  \n16232, 17137, 8549,  26276, 25977, 26972,  10940, 21817, 10941,  \n13510, 14147, 10522,  18073, 2905, 18257,  19114, 21508, 12834,  \n26808, 26809, 26807,  27189, 26809, 26808,  4486, 2498, 13737,  \n13692, 13693, 26929,  26462, 25980, 26465,  8631, 5822, 4482,  \n9947, 11109, 2115,  26809, 27189, 26974,  12366, 11551, 11550,  \n1671, 1221, 18727,  27189, 27190, 27191,  27191, 26974, 27189,  \n6469, 11104, 17223,  6052, 19284, 21130,  20478, 9338, 13570,  \n15164, 6481, 869,  6793, 5990, 3908,  6155, 23583, 20980,  \n13328, 4798, 4797,  21139, 26929, 13693,  22635, 7338, 14816,  \n20047, 4672, 4598,  7400, 14569, 14699,  11082, 10163, 14142,  \n26469, 26974, 27191,  2051, 19867, 19868,  27192, 27193, 26975,  \n10088, 9051, 12076,  27191, 26975, 26469,  7780, 21851, 18029,  \n9383, 11060, 8868,  1081, 4344, 4335,  7681, 667, 17081,  \n4626, 4627, 11891,  26125, 25819, 27194,  8363, 8909, 19353,  \n4624, 1362, 11999,  900, 17279, 20641,  4784, 18764, 22543,  \n25817, 26469, 26811,  25817, 26811, 26977,  5199, 9859, 1676,  \n16332, 11115, 1995,  7819, 9432, 15536,  19748, 2893, 3168,  \n26979, 26470, 26471,  26279, 26977, 26981,  20940, 17955, 20858,  \n12276, 9177, 12801,  6136, 6137, 16779,  10641, 19867, 2051,  \n7749, 12208, 3694,  18455, 8687, 19150,  26126, 26279, 26980,  \n26279, 26981, 26980,  23035, 13699, 13700,  6976, 17375, 15965,  \n9316, 22526, 22082,  551, 3429, 8264,  20900, 6055, 13754,  \n4204, 4203, 3226,  8081, 1352, 4509,  9818, 11108, 8695,  \n20879, 20688, 15391,  13189, 2381, 2380,  27197, 26980, 26981,  \n3212, 15116, 12942,  26982, 27198, 26130,  26980, 27197, 26984,  \n24872, 26127, 26983,  15229, 4159, 4160,  12307, 11476, 17288,  \n7558, 7984, 7559,  1120, 21745, 16674,  26986, 26128, 26475,  \n26637, 26986, 26987,  26984, 27200, 25699,  17768, 17769, 7008,  \n13540, 10825, 3211,  13515, 21056, 19473,  25821, 26637, 26987,  \n15421, 6808, 10762,  25984, 26813, 25825,  26476, 25822, 26813,  \n26477, 26987, 27201,  20186, 14884, 10850,  25699, 27200, 26988,  \n12133, 12132, 20985,  1954, 1951, 14573,  9166, 13642, 11448,  \n10774, 13831, 13830,  19136, 16142, 21468,  4157, 8427, 7737,  \n1330, 17134, 17133,  1156, 24612, 1157,  26282, 26989, 25830,  \n19760, 17761, 22312,  11553, 4397, 6140,  27206, 26280, 26480,  \n1199, 17830, 1200,  8937, 12362, 17115,  13615, 2061, 11501,  \n9131, 8978, 20351,  25701, 26988, 27208,  27204, 27208, 26988,  \n1586, 18072, 1224,  12816, 937, 8580,  14238, 14237, 10195,  \n16168, 11215, 11216,  5950, 5951, 10338,  18634, 2285, 1527,  \n22861, 5739, 22379,  9271, 19705, 18244,  9270, 19705, 9271,  \n12403, 3377, 2429,  17776, 21072, 7599,  27208, 26481, 26642,  \n5283, 18343, 11771,  26481, 27208, 27209,  21569, 413, 15325,  \n10372, 11494, 13254,  27209, 26992, 26481,  4073, 11865, 16507,  \n3700, 327, 328,  576, 15041, 9266,  27210, 26992, 27209,  \n9432, 7819, 6019,  27404, 26644, 27211,  12279, 2595, 11614,  \n26644, 26820, 27211,  27784, 26824, 25836,  3473, 3474, 5599,  \n10649, 3597, 374,  26818, 26992, 27212,  26822, 26818, 27212,  \n12486, 7027, 21898,  27213, 26822, 27212,  26825, 26822, 27213,  \n21320, 4893, 6630,  5707, 21418, 7315,  12541, 10223, 8442,  \n26825, 27213, 27214,  26821, 26823, 26819,  8389, 7987, 8064,  \n26819, 27215, 26820,  4101, 4549, 2671,  21982, 9950, 3957,  \n26826, 26287, 26825,  26819, 26823, 26995,  8921, 3650, 5089,  \n9910, 9909, 16027,  27211, 26820, 27216,  19299, 18111, 3822,  \n26484, 26138, 26824,  13200, 14151, 13201,  6133, 16725, 3757,  \n26825, 27214, 26997,  5775, 3957, 9950,  4330, 4329, 16537,  \n4353, 8926, 10885,  9428, 1144, 1143,  19915, 9937, 21236,  \n27211, 27216, 27222,  6045, 2448, 4490,  18774, 6493, 5055,  \n6405, 19500, 6334,  18165, 18290, 2101,  2092, 20585, 2809,  \n27218, 26998, 26997,  665, 7051, 5362,  27000, 26998, 27218,  \n16403, 21185, 15966,  3427, 2005, 19629,  15428, 10762, 18784,  \n6348, 12527, 12526,  27214, 27217, 27218,  27218, 26997, 27214,  \n12221, 13318, 13319,  12554, 20042, 12555,  687, 10349, 23112,  \n27410, 27001, 27219,  25994, 25837, 27002,  14398, 8487, 7242,  \n27005, 27219, 27001,  27410, 27219, 27220,  11799, 8210, 11800,  \n13981, 1017, 14812,  2923, 16831, 6786,  8025, 10719, 20711,  \n27000, 27005, 27001,  15355, 3182, 12987,  8973, 11881, 14534,  \n27000, 27218, 27003,  27000, 27004, 27005,  27220, 27219, 27005,  \n27004, 27000, 27003,  9640, 9641, 13527,  1300, 14978, 1301,  \n659, 19685, 19719,  27221, 27220, 27005,  19075, 7507, 17224,  \n5538, 6967, 18647,  14383, 20622, 8931,  27218, 27217, 27003,  \n1256, 3741, 5365,  493, 20839, 11265,  5867, 5476, 1712,  \n27002, 26141, 25994,  27224, 27221, 27005,  27003, 27225, 27223,  \n5745, 15049, 8117,  27003, 27223, 27004,  26486, 25593, 27006,  \n7738, 7737, 26406,  27224, 27005, 27004,  24086, 23972, 19617,  \n23103, 14852, 13539,  27414, 27221, 27224,  17117, 8819, 10765,  \n27223, 27225, 27009,  27224, 27004, 27223,  9000, 8990, 21769,  \n15078, 3024, 6383,  25590, 27226, 26487,  27224, 27223, 27008,  \n8478, 4796, 3109,  26290, 26828, 25996,  5848, 12396, 14512,  \n704, 3374, 3940,  15828, 315, 10034,  27010, 27224, 27008,  \n27229, 27227, 27007,  27229, 27007, 26830,  13743, 20278, 20542,  \n25593, 25712, 26648,  27008, 27223, 27009,  27230, 27224, 27010,  \n8481, 19063, 1660,  6957, 18782, 12669,  3462, 1111, 6350,  \n7448, 4306, 6715,  13147, 9608, 9609,  27229, 26830, 27012,  \n15727, 22525, 554,  14533, 17293, 15354,  27010, 27008, 27009,  \n22391, 15242, 21519,  27228, 26650, 27007,  2668, 2669, 16756,  \n18655, 15515, 3840,  16107, 19235, 15886,  13187, 10664, 14223,  \n27007, 26650, 26830,  12240, 12239, 2856,  27231, 27012, 26831,  \n25712, 25998, 26829,  27228, 27011, 26832,  18094, 2003, 8710,  \n9679, 15669, 6083,  11582, 17381, 9497,  13145, 6891, 11087,  \n20904, 14110, 13751,  9313, 859, 5575,  27231, 26833, 26834,  \n26658, 26834, 26493,  26292, 26647, 27016,  27013, 27014, 27017,  \n17241, 930, 929,  1161, 6394, 6283,  10095, 10094, 13819,  \n9062, 17548, 18718,  1162, 10966, 15391,  4376, 4296, 4295,  \n27015, 27017, 27233,  17848, 17350, 17789,  26000, 25186, 27016,  \n10595, 1770, 2734,  9767, 16655, 21475,  1135, 19564, 1136,  \n26652, 25998, 26296,  609, 608, 13289,  1436, 1435, 330,  \n20611, 1668, 1667,  7998, 6217, 11175,  27018, 27015, 27233,  \n26835, 27015, 27018,  9805, 6079, 6456,  2958, 16535, 2957,  \n7756, 10486, 6991,  27235, 27232, 26659,  9059, 11742, 2412,  \n26660, 27235, 26659,  8793, 10835, 12230,  1343, 4926, 16105,  \n6350, 20003, 7062,  16306, 15400, 2641,  26837, 27233, 27236,  \n3791, 16267, 10888,  18015, 18014, 19996,  17030, 16847, 9619,  \n9761, 4332, 6965,  3896, 23443, 16447,  18274, 7340, 19824,  \n11706, 5816, 11705,  1439, 1438, 3637,  9761, 11269, 4332,  \n11448, 13642, 1136,  27236, 27428, 26837,  2431, 2430, 17512,  \n8364, 15791, 4138,  8889, 9922, 7482,  4913, 9474, 20415,  \n6704, 6025, 16598,  27018, 27233, 26837,  18632, 8614, 1609,  \n16521, 13477, 5072,  4236, 14951, 6789,  7417, 21829, 11908,  \n9979, 1245, 17778,  17514, 18036, 18035,  23112, 10349, 18504,  \n6957, 20866, 17979,  4054, 3887, 13264,  5068, 20421, 9470,  \n26661, 26497, 26307,  26661, 26307, 27023,  2205, 18161, 16355,  \n26663, 26837, 27020,  25596, 25193, 27021,  25842, 25468, 26662,  \n26664, 26663, 27020,  18911, 6753, 18181,  26840, 27023, 26150,  \n26841, 25722, 26503,  18936, 8760, 8759,  8725, 2807, 12619,  \n27027, 26840, 26666,  26007, 25845, 26839,  18611, 5296, 18612,  \n19398, 22722, 822,  26668, 27024, 27239,  18954, 19666, 16525,  \n5941, 3143, 9141,  14015, 14016, 4491,  4216, 531, 4217,  \n7219, 1617, 7278,  2836, 3310, 16369,  10026, 10431, 24304,  \n5776, 5775, 9950,  10084, 21811, 13358,  14570, 6504, 18171,  \n15043, 2854, 4981,  26843, 26011, 27028,  8744, 22544, 6752,  \n4049, 4048, 8521,  9471, 2989, 938,  439, 440, 9349,  \n25606, 26506, 25724,  27031, 27240, 26669,  8290, 21220, 18133,  \n19849, 8196, 3906,  16170, 467, 22305,  18856, 8754, 998,  \n2408, 16663, 17523,  6298, 19919, 12156,  5942, 7916, 15859,  \n6298, 6299, 19919,  17688, 21327, 17689,  3355, 12461, 2976,  \n1034, 3529, 1033,  17020, 4042, 8684,  14215, 18877, 12957,  \n10883, 22284, 7403,  27034, 26508, 26159,  15769, 4632, 19716,  \n14084, 14086, 16034,  10741, 14229, 19786,  27034, 26159, 26674,  \n27243, 27244, 27035,  6808, 6809, 10762,  7256, 6131, 15186,  \n15488, 5046, 637,  27245, 27035, 27036,  14363, 16543, 4423,  \n27244, 26674, 27035,  9717, 9718, 6533,  8995, 22959, 11242,  \n26250, 25090, 25089,  14278, 14279, 23904,  12353, 19144, 12354,  \n27625, 27245, 27246,  9336, 16452, 7005,  14191, 21619, 11866,  \n27245, 27036, 27246,  27248, 26846, 26316,  22752, 10229, 14980,  \n27036, 26318, 27246,  316, 315, 10301,  765, 17005, 20159,  \n5915, 6371, 12960,  2147, 18085, 2148,  14715, 13880, 6892,  \n27248, 26316, 26018,  26318, 27036, 26677,  27038, 26512, 27039,  \n5503, 5504, 4259,  26848, 27250, 26676,  27249, 27039, 26679,  \n18516, 8541, 12240,  18969, 14452, 18995,  17647, 16454, 2808,  \n15226, 11415, 5049,  27249, 26679, 27040,  13053, 7818, 11417,  \n26317, 26676, 27250,  27251, 26678, 26510,  7736, 11801, 12664,  \n27040, 26679, 26320,  9940, 20707, 9939,  11314, 642, 8397,  \n7341, 17167, 17166,  16627, 20222, 9487,  12464, 15956, 6804,  \n26849, 27252, 27040,  26515, 26678, 27042,  7566, 4705, 13147,  \n9631, 4040, 4039,  4601, 6103, 2800,  7794, 1803, 14778,  \n4875, 3839, 1258,  1736, 16456, 13047,  14292, 12689, 5762,  \n12727, 16620, 16619,  14490, 5664, 23236,  17488, 15666, 15667,  \n25616, 26319, 27454,  26682, 27046, 27043,  4018, 6915, 4017,  \n6264, 4317, 4316,  9296, 16119, 9295,  7959, 1030, 5598,  \n26024, 27253, 27458,  12088, 23467, 14867,  20192, 9571, 10369,  \n2111, 12359, 2112,  18356, 18281, 11025,  27255, 26852, 26684,  \n10632, 11070, 3795,  2353, 12584, 2354,  12617, 6033, 6035,  \n7026, 6970, 14414,  26686, 26852, 27257,  26853, 26685, 26854,  \n27256, 26332, 26323,  17660, 16853, 18617,  8873, 3101, 3100,  \n1973, 3372, 13040,  12946, 1673, 12265,  27254, 27046, 27047,  \n26686, 27257, 26855,  27049, 26854, 26521,  27049, 26521, 26857,  \n11898, 3799, 16438,  21193, 16425, 13263,  26855, 27258, 26522,  \n14226, 18222, 15394,  6676, 1303, 361,  15532, 7153, 15071,  \n26325, 26683, 27052,  1121, 10342, 13357,  26024, 25617, 27253,  \n7544, 11456, 7703,  26688, 26522, 27259,  11063, 12854, 12853,  \n27055, 27053, 26857,  23112, 18504, 20844,  16215, 5245, 20476,  \n3595, 6164, 12838,  27050, 26856, 26332,  15640, 4617, 3357,  \n14996, 3412, 18119,  14545, 15795, 5078,  27047, 26692, 27059,  \n27059, 27254, 27047,  27052, 26346, 26338,  26858, 26689, 26861,  \n26856, 27260, 26690,  16207, 12562, 16208,  4937, 9698, 9697,  \n532, 22232, 23521,  8766, 20902, 10007,  8440, 4749, 9499,  \n26524, 26688, 27057,  13650, 6499, 11311,  15612, 7503, 5908,  \n2416, 1155, 8615,  27058, 27262, 26694,  27059, 26692, 27060,  \n26347, 26859, 26691,  26691, 26859, 27263,  2962, 1149, 11440,  \n27264, 26525, 26693,  26696, 25872, 27052,  27261, 26691, 27263,  \n20634, 7372, 5549,  26344, 27266, 27062,  27266, 26344, 26180,  \n14828, 4233, 9366,  4313, 12569, 17642,  2604, 550, 20227,  \n6982, 15522, 19402,  13311, 4173, 14988,  16646, 18024, 13510,  \n26697, 26696, 27267,  1113, 9028, 5353,  26031, 26864, 26859,  \n6197, 14777, 1096,  27065, 27061, 26865,  4296, 16235, 5240,  \n7718, 2937, 13030,  12896, 14690, 16383,  12706, 4138, 8559,  \n27063, 27064, 25871,  3284, 18543, 21683,  11277, 8371, 8370,  \n303, 16445, 5396,  27066, 26866, 27270,  11315, 5652, 16349,  \n3825, 3824, 16274,  3013, 4400, 4401,  4926, 15878, 14717,  \n13719, 23292, 18654,  26867, 27067, 27272,  26867, 27272, 26702,  \n26350, 27273, 26866,  26866, 25737, 26350,  22249, 15642, 4908,  \n27274, 27272, 27067,  26702, 27272, 27070,  7191, 9928, 6842,  \n11720, 18904, 15208,  2737, 11392, 2736,  27274, 27067, 27068,  \n15808, 14884, 20186,  16727, 14523, 13753,  4132, 17633, 9797,  \n27275, 26532, 27072,  9437, 12585, 517,  16316, 15370, 11838,  \n13973, 1641, 13972,  8022, 14046, 18478,  23193, 8651, 5922,  \n9283, 7516, 6479,  3279, 775, 15358,  17741, 10150, 9618,  \n12186, 2629, 2628,  742, 18996, 12830,  1987, 934, 13521,  \n10837, 3857, 3858,  6923, 18455, 11196,  27278, 26542, 26875,  \n9298, 20419, 2238,  10332, 15473, 19485,  20057, 12901, 7709,  \n26876, 26873, 27076,  27076, 27077, 26876,  13619, 23048, 13618,  \n14461, 10367, 21349,  13078, 13079, 14858,  26877, 26038, 25370,  \n11386, 10314, 11385,  27279, 27076, 27075,  19040, 17401, 20306,  \n5665, 15469, 2311,  27080, 27078, 26713,  27074, 27280, 27281,  \n17914, 4317, 6265,  5909, 5908, 8046,  14096, 8368, 10565,  \n27281, 27079, 27074,  26871, 27079, 27282,  27284, 26714, 27283,  \n22306, 14007, 14006,  13251, 9823, 11313,  12238, 17949, 17317,  \n8677, 9813, 14358,  27075, 26871, 27282,  27283, 26714, 26878,  \n17257, 8960, 18587,  27282, 27285, 27075,  5805, 14528, 6384,  \n10185, 9061, 22399,  27283, 26878, 27082,  4722, 4721, 5911,  \n13277, 13450, 9768,  6124, 21550, 8735,  5596, 8241, 463,  \n6906, 9707, 11830,  8972, 13773, 6754,  27286, 27282, 27079,  \n8296, 18697, 2057,  1971, 21547, 17742,  5989, 19517, 4609,  \n985, 12574, 8586,  11418, 9657, 20929,  27083, 26359, 27085,  \n27287, 26547, 26363,  9089, 9090, 13863,  20935, 9845, 3253,  \n14406, 9846, 5519,  26885, 26720, 26880,  2217, 13768, 3064,  \n26367, 26205, 26723,  15754, 20525, 22560,  9569, 12443, 22994,  \n8592, 12694, 12362,  18061, 10652, 10653,  26882, 27088, 27087,  \n26885, 26880, 27087,  23441, 19589, 6737,  27290, 27085, 26884,  \n7410, 9835, 1276,  27090, 27089, 27291,  17571, 4577, 6756,  \n2555, 16378, 4951,  26363, 26552, 27287,  27290, 26884, 27295,  \n19589, 23441, 11757,  6005, 707, 14762,  9905, 14149, 3971,  \n20566, 9918, 9917,  3192, 12758, 17747,  27884, 26052, 26550,  \n12976, 11740, 2267,  27092, 27294, 27088,  16755, 18819, 15176,  \n14322, 21107, 3383,  26886, 26721, 26885,  5738, 7521, 11643,  \n25894, 25895, 27091,  3818, 8289, 15737,  27092, 26881, 27289,  \n12672, 7258, 8781,  9169, 19287, 11142,  7906, 11645, 4245,  \n14307, 23210, 4191,  12237, 16015, 21651,  21567, 11862, 9319,  \n26548, 26887, 27296,  26549, 26548, 27296,  27295, 27093, 27094,  \n27506, 27095, 26560,  9934, 15429, 10982,  27094, 27298, 27295,  \n26384, 26562, 27095,  766, 9696, 2367,  1874, 5087, 5935,  \n26887, 26894, 27299,  5741, 8621, 1404,  13673, 7833, 13674,  \n26549, 27296, 27300,  13621, 17936, 17121,  26725, 26886, 27301,  \n4719, 4720, 20597,  9734, 3623, 7552,  26726, 26889, 27096,  \n5723, 16389, 16388,  27099, 27302, 26894,  12662, 4636, 6041,  \n27096, 26889, 27303,  26729, 26207, 26892,  1844, 29618, 1843,  \n1074, 14243, 20638,  15571, 1082, 1083,  8618, 10695, 3410,  \n13241, 16103, 21499,  26891, 27098, 27304,  26891, 27304, 26554,  \n26554, 27304, 26564,  5755, 2540, 13242,  8384, 2967, 10270,  \n16316, 10442, 13811,  5004, 3021, 11117,  16324, 22077, 12172,  \n13398, 22433, 5753,  4296, 17674, 16235,  27301, 27100, 26725,  \n7223, 7235, 2861,  27306, 26728, 27096,  15230, 9322, 8300,  \n16328, 2144, 10482,  11386, 1531, 12603,  26059, 27102, 26568,  \n4378, 10079, 4379,  26899, 26728, 27306,  19420, 320, 5854,  \n6780, 8625, 8624,  18040, 15788, 15789,  27307, 27105, 26564,  \n13907, 6959, 6971,  20724, 7224, 8415,  13978, 19050, 21079,  \n16632, 4522, 11407,  16241, 17077, 22277,  27309, 26895, 27100,  \n11243, 19396, 3318,  7634, 19169, 14249,  27103, 27303, 26889,  \n18965, 17221, 5546,  27098, 26897, 27110,  27310, 27105, 27307,  \n18105, 11962, 17584,  1107, 6801, 3583,  13512, 23694, 9039,  \n27308, 27106, 26733,  7460, 12351, 13518,  6489, 15696, 510,  \n16331, 7847, 13469,  27311, 26895, 27309,  27103, 27311, 27312,  \n27103, 26895, 27311,  25424, 9823, 13251,  19943, 12837, 13730,  \n8234, 20694, 20059,  26214, 27107, 27522,  21750, 21602, 19446,  \n26570, 27116, 27104,  9518, 21184, 1864,  8231, 19578, 14182,  \n6705, 16922, 5155,  4178, 12328, 13378,  1047, 15846, 10271,  \n27105, 27113, 26565,  7803, 2879, 17988,  27109, 27111, 26899,  \n14703, 7089, 14704,  18420, 15214, 12319,  27313, 27110, 26900,  \n27113, 27314, 26565,  15176, 9390, 2483,  4493, 2066, 4179,  \n26565, 27314, 27114,  27114, 27314, 26736,  13410, 5334, 20328,  \n27315, 26736, 27314,  27108, 26736, 27315,  12953, 15004, 11125,  \n13929, 13928, 9208,  20083, 16384, 16679,  8417, 23346, 511,  \n9259, 2516, 16410,  7569, 7744, 9769,  1119, 9335, 20200,  \n27116, 26570, 26902,  14670, 8772, 8093,  26742, 26569, 26901,  \n8281, 4444, 21744,  12066, 596, 9709,  26901, 27115, 26742,  \n26742, 27115, 26904,  27316, 26903, 27117,  6624, 6625, 8365,  \n27316, 27117, 27118,  16921, 16918, 17534,  19748, 14425, 14424,  \n8574, 7833, 13673,  27317, 27119, 26908,  17261, 19461, 5488,  \n13826, 14471, 14880,  20879, 17855, 6231,  10913, 18707, 20208,  \n7057, 2991, 4420,  4817, 18718, 9919,  26909, 27318, 27120,  \n26909, 26911, 27318,  969, 2996, 970,  27319, 27318, 26912,  \n26911, 26912, 27318,  9187, 17938, 18989,  9074, 5164, 21320,  \n8438, 8507, 8508,  26581, 27319, 26912,  27121, 26751, 27320,  \n6757, 15812, 12467,  18224, 16023, 12677,  26755, 26754, 27121,  \n27321, 26581, 26582,  13092, 5100, 13952,  27121, 27322, 26755,  \n12415, 12416, 2210,  26913, 26755, 27322,  21085, 9767, 19722,  \n7707, 9930, 13095,  27321, 26582, 26753,  7819, 2557, 6019,  \n26913, 27323, 26915,  11983, 1628, 1410,  9152, 9173, 2531,  \n26913, 27324, 27323,  22551, 4574, 4575,  26403, 26758, 26584,  \n20119, 2302, 11488,  20952, 19205, 15978,  19422, 15235, 6975,  \n2581, 6942, 4219,  21841, 17194, 2315,  26758, 26914, 27325,  \n13550, 22770, 12783,  27326, 26584, 26758,  11664, 21867, 18091,  \n27326, 26916, 26584,  21916, 3484, 16974,  5275, 18775, 18776,  \n5700, 8852, 24271,  22819, 4455, 1195,  12238, 17317, 18820,  \n19458, 7623, 8764,  13231, 10211, 11626,  5737, 14283, 18503,  \n26229, 27547, 26765,  11773, 1525, 2592,  26081, 26766, 27329,  \n26228, 26081, 26767,  10437, 22067, 16635,  24462, 9531, 13596,  \n22518, 7995, 23136,  14261, 4712, 12983,  26767, 27330, 26768,  \n5329, 12362, 3769,  27331, 26768, 27330,  26920, 26768, 27331,  \n17474, 16160, 4148,  16187, 21004, 15418,  16187, 21946, 21004,  \n18142, 13436, 6188,  27129, 26920, 27331,  27129, 26769, 26920,  \n18189, 15159, 13007,  5878, 819, 16283,  19638, 11524, 584,  \n14547, 5165, 3137,  21953, 5446, 9100,  10120, 6416, 1577,  \n26236, 26413, 27328,  12663, 22828, 560,  9035, 14187, 9036,  \n7245, 4765, 897,  15649, 8633, 5644,  5145, 21889, 8218,  \n7844, 18259, 7845,  2086, 2977, 11568,  26769, 27129, 27337,  \n27131, 26769, 27337,  7940, 16633, 13121,  2248, 16051, 13178,  \n14133, 10691, 3609,  2994, 22975, 12618,  289, 14265, 2565,  \n26600, 26923, 26922,  633, 14373, 9648,  16938, 4353, 17461,  \n4768, 4654, 9514,  432, 18809, 18448,  26926, 26925, 27340,  \n26926, 27340, 26603,  26603, 27341, 26417,  27340, 27341, 26603,  \n11188, 16634, 22067,  27341, 26776, 26417,  6301, 6300, 17671,  \n26774, 26927, 27134,  13576, 14840, 10992,  11605, 8706, 11606,  \n26925, 26774, 27134,  22100, 22099, 8576,  25423, 21489, 12738,  \n26241, 27343, 26242,  20385, 14782, 19013,  414, 22229, 5042,  \n27134, 26927, 27344,  1393, 15092, 14833,  8976, 26965, 21203,  \n14433, 21159, 14434,  26927, 27137, 27344,  27347, 20434, 24439,  \n2739, 16138, 15091,  8203, 11447, 11773,  26928, 27139, 27135,  \n22336, 7093, 21252,  27727, 26778, 27138,  10147, 7268, 8692,  \n26779, 27348, 26780,  26928, 26780, 27139,  9348, 4338, 15829,  \n6374, 10684, 6375,  12290, 8013, 9985,  18161, 7626, 16355,  \n27137, 27349, 27344,  4700, 20030, 9161,  27132, 27346, 27133,  \n17634, 1271, 11073,  6570, 7173, 21729,  27136, 27133, 27142,  \n8288, 544, 9874,  27137, 27136, 27142,  27141, 27144, 27137,  \n27349, 27137, 27144,  27349, 27144, 27351,  27346, 27142, 27133,  \n1762, 16626, 19802,  9585, 11732, 3768,  5299, 1064, 2104,  \n16926, 9527, 16925,  15506, 9500, 5448,  27144, 27352, 27351,  \n17271, 1059, 6686,  22001, 17996, 23913,  27352, 27144, 27147,  \n1272, 5888, 5614,  14306, 17138, 7192,  27147, 27144, 27145,  \n2338, 857, 11498,  27146, 27142, 27346,  21013, 20169, 12867,  \n15130, 382, 15131,  18923, 10326, 15992,  27149, 27147, 27145,  \n2659, 9908, 16342,  27149, 27353, 27147,  27355, 27356, 27353,  \n20979, 20937, 6950,  17034, 12998, 10055,  27149, 27151, 27353,  \n8500, 13587, 18033,  18788, 7329, 19406,  3519, 15962, 3520,  \n572, 6372, 10696,  26932, 27146, 27360,  27360, 27146, 27357,  \n27359, 27151, 26933,  22107, 21577, 15615,  12569, 11938, 16368,  \n27359, 26933, 27361,  27361, 26933, 26936,  27362, 26932, 27360,  \n26936, 27363, 27361,  26936, 27152, 27363,  23699, 13799, 10830,  \n15245, 20477, 3379,  17986, 16572, 14473,  26932, 27362, 27153,  \n5146, 2118, 386,  9596, 2618, 1133,  27153, 27364, 27154,  \n27365, 26937, 27364,  27364, 26937, 27154,  26937, 27365, 27152,  \n19012, 7470, 14948,  21960, 2367, 9696,  13166, 8573, 12592,  \n19614, 4832, 2424,  13072, 16642, 20111,  27155, 27366, 26782,  \n11065, 10134, 6807,  14085, 16584, 14086,  15177, 4340, 9495,  \n2730, 2768, 9895,  26812, 26423, 26607,  18284, 9581, 11558,  \n8610, 6742, 17885,  24274, 16753, 19379,  6423, 9206, 14825,  \n27155, 26782, 26781,  25064, 26607, 27367,  26940, 26426, 26427,  \n12267, 4052, 16598,  15684, 18032, 5763,  26360, 26425, 26883,  \n26102, 27158, 26941,  10675, 7421, 10413,  16569, 16107, 5891,  \n17888, 14119, 16538,  9577, 8970, 20668,  26607, 26783, 27367,  \n13972, 14451, 2322,  26938, 26428, 26429,  26784, 26883, 26608,  \n26785, 26251, 27370,  26251, 26102, 26941,  18787, 15228, 17010,  \n25944, 26105, 27369,  22084, 394, 11367,  9199, 20529, 1063,  \n22682, 15635, 11839,  29171, 7161, 4254,  15643, 2291, 9262,  \n13598, 20129, 18000,  1993, 20599, 6665,  14710, 1750, 18469,  \n16133, 8491, 23307,  19938, 18520, 23384,  7807, 1416, 2560,  \n26787, 26786, 25947,  27373, 26946, 27162,  26942, 26611, 26945,  \n6031, 20267, 10063,  13652, 13651, 21668,  18430, 7230, 12745,  \n5220, 20615, 23229,  11303, 4755, 1650,  12358, 3848, 10945,  \n3313, 22748, 17073,  26431, 26250, 27374,  21712, 6778, 3682,  \n20677, 16231, 15887,  26787, 26950, 27375,  26433, 26613, 27161,  \n4895, 5236, 5235,  20917, 23847, 10639,  22004, 4847, 7585,  \n22285, 12176, 12178,  17655, 17974, 17656,  6355, 17986, 14473,  \n14650, 1793, 11770,  27376, 26788, 26791,  6118, 10695, 3967,  \n27377, 26433, 27161,  26794, 25797, 26431,  19804, 9039, 10533,  \n3740, 10161, 20420,  21491, 15580, 16624,  16141, 1786, 1821,  \n25948, 26107, 26790,  26950, 26263, 27164,  26793, 26433, 27377,  \n10348, 8956, 1020,  20790, 14888, 14889,  26951, 27165, 27378,  \n24231, 21731, 15054,  12137, 762, 763,  9351, 342, 13285,  \n26437, 27163, 26615,  8374, 4106, 26657,  27379, 27380, 27168,  \n19387, 19388, 19392,  1049, 16798, 5324,  27166, 26951, 27381,  \n27381, 26951, 27378,  11244, 5032, 19396,  11794, 29758, 7694,  \n13977, 22628, 9838,  27380, 27169, 27168,  27379, 27168, 27166,  \n27379, 27166, 27381,  26795, 27382, 27383,  27382, 26795, 26615,  \n27170, 27566, 26796,  803, 7382, 8182,  6081, 2706, 13661,  \n27172, 27169, 27384,  10237, 432, 10238,  2736, 19848, 2254,  \n12734, 14874, 7199,  2581, 12912, 21574,  3473, 10423, 3474,  \n8748, 13864, 4433,  20486, 3812, 24390,  4707, 5971, 4811,  \n27172, 26959, 26957,  20662, 1269, 1268,  5050, 14808, 14807,  \n5277, 13845, 3596,  9843, 7664, 1122,  8057, 8059, 2402,  \n27177, 26960, 27383,  27383, 26960, 26795,  2648, 20240, 2049,  \n6126, 800, 6125,  27172, 27384, 27174,  27174, 27384, 27573,  \n21788, 22224, 8150,  20903, 20332, 6968,  4740, 13260, 13259,  \n9380, 9381, 9430,  25064, 1521, 1523,  19471, 19284, 7809,  \n15548, 14465, 8275,  27178, 27174, 27573,  26962, 27175, 27179,  \n5212, 14236, 5023,  3943, 2885, 12505,  17689, 17647, 13619,  \n12339, 21376, 2667,  19142, 4822, 20629,  27574, 26799, 27179,  \n3449, 19509, 3450,  7248, 19695, 10967,  26440, 26617, 27756,  \n26444, 27178, 26963,  919, 5505, 11565,  2719, 22773, 14423,  \n21379, 9136, 11964,  27387, 26617, 26619,  26963, 27386, 27388,  \n26963, 27388, 26804,  20583, 23905, 18125,  21102, 7625, 4336,  \n13836, 11672, 8677,  21918, 1922, 3175,  27180, 26270, 26803,  \n1216, 19582, 22447,  22339, 11251, 18075,  19583, 14753, 17913,  \n5327, 4365, 4364,  8424, 15937, 14049,  18571, 13440, 6264,  \n26448, 27181, 26450,  17913, 14753, 1288,  8424, 1602, 15937,  \n26450, 27390, 26622,  27758, 26271, 26967,  8112, 2377, 3928,  \n16550, 9884, 9885,  3078, 10522, 14737,  7279, 4718, 1248,  \n18653, 7621, 18148,  12744, 4829, 1602,  26967, 26271, 26120,  \n26966, 27391, 26626,  3443, 672, 8872,  23167, 9015, 19555,  \n27184, 26967, 25688,  6647, 13862, 13571,  16843, 19886, 11954,  \n27393, 26453, 26273,  20663, 16257, 8318,  13729, 19647, 16575,  \n12830, 12832, 2096,  18158, 19965, 11869,  12052, 6839, 6973,  \n10284, 964, 963,  19145, 12781, 16171,  5285, 4944, 9274,  \n11566, 6141, 6142,  27185, 26970, 26629,  823, 4098, 4052,  \n26630, 26457, 27761,  15484, 7465, 6448,  6753, 12349, 18181,  \n3044, 15504, 3045,  2503, 17458, 1787,  17640, 7652, 18866,  \n18846, 7807, 7808,  1226, 18207, 5931,  17293, 14533, 11751,  \n2831, 7199, 14874,  26463, 27186, 25973,  8982, 14298, 4546,  \n17739, 15224, 1848,  15061, 7376, 6088,  22572, 21177, 4932,  \n21641, 13868, 15416,  22288, 24884, 23499,  15695, 8738, 15739,  \n20947, 10016, 14700,  21180, 15978, 7352,  15397, 21849, 15831,  \n7884, 7715, 10672,  5184, 9467, 5185,  7781, 2512, 19579,  \n3348, 3347, 5551,  10745, 12799, 15281,  11269, 14301, 10782,  \n21865, 5891, 764,  26465, 25575, 26635,  27190, 26975, 27191,  \n17885, 1287, 15183,  15193, 17749, 5874,  25981, 26276, 27195,  \n2958, 2957, 18489,  27397, 26975, 27190,  2033, 4373, 4374,  \n27193, 26811, 26975,  19350, 12283, 2975,  4643, 2209, 15290,  \n16107, 15626, 10023,  27193, 27398, 26811,  27398, 26977, 26811,  \n17804, 3070, 7811,  11401, 25158, 23626,  14355, 12977, 3912,  \n10838, 9646, 20670,  26977, 27398, 26981,  10218, 6211, 3979,  \n8822, 11322, 6733,  27399, 26979, 26471,  27400, 27399, 26473,  \n26471, 26473, 27399,  7440, 13620, 13621,  9824, 5692, 17500,  \n20480, 8632, 5996,  2138, 7526, 7525,  2053, 17868, 2052,  \n22606, 19469, 12397,  13772, 11062, 8164,  3292, 1767, 12330,  \n25983, 26130, 26473,  11701, 11971, 11889,  6986, 11496, 22247,  \n7147, 7148, 2505,  1535, 9351, 9352,  3507, 10377, 2656,  \n13199, 11195, 22699,  4038, 16977, 4036,  27203, 26636, 25982,  \n18095, 8237, 13108,  27199, 27775, 27973,  3502, 19788, 18242,  \n7118, 9379, 10103,  27197, 27199, 26984,  9032, 26084, 23848,  \n27202, 25827, 26983,  27199, 27200, 26984,  8286, 14683, 12365,  \n4931, 19493, 1899,  17280, 17396, 14530,  21730, 10656, 6271,  \n26986, 26475, 26476,  2453, 13900, 23070,  1203, 9759, 8289,  \n10906, 10905, 14919,  5118, 7740, 15826,  13448, 5997, 5096,  \n2283, 14520, 14521,  15874, 6127, 4363,  26813, 26479, 27780,  \n18140, 24303, 23011,  1775, 12846, 5228,  5486, 17687, 9086,  \n11969, 11971, 20181,  4481, 9745, 11017,  22115, 22577, 11420,  \n27204, 26988, 27200,  7175, 11438, 15258,  4429, 8556, 19413,  \n19195, 387, 17087,  15705, 15706, 19580,  15563, 21714, 9896,  \n27205, 26814, 26133,  26478, 27207, 25829,  7162, 8499, 8500,  \n23856, 7832, 14681,  8913, 10162, 10161,  4326, 10008, 5686,  \n27206, 26480, 26990,  21520, 11037, 9743,  27207, 26641, 25829,  \n3793, 5495, 5216,  11471, 8869, 11060,  27401, 27208, 27204,  \n26642, 25701, 27208,  26990, 26640, 26816,  8186, 22724, 8731,  \n10808, 2849, 20798,  3267, 1032, 3879,  17664, 4082, 17378,  \n27205, 26483, 27402,  20230, 9613, 1071,  26993, 26282, 25988,  \n17700, 4781, 17699,  22911, 5134, 15232,  10305, 8555, 16059,  \n3657, 7459, 3295,  26816, 26817, 27404,  14988, 13900, 13311,  \n19847, 6869, 3324,  26817, 26644, 27404,  9637, 14879, 4708,  \n16915, 15645, 15646,  10362, 3737, 4196,  14531, 9473, 9472,  \n26134, 27405, 25990,  17198, 11211, 22001,  27212, 26992, 27210,  \n2314, 367, 12904,  26993, 25988, 26286,  27402, 25705, 26994,  \n9753, 27358, 9203,  21478, 20050, 4060,  14173, 532, 23521,  \n15214, 17545, 15213,  18710, 18709, 9924,  27408, 27211, 27222,  \n5126, 21048, 18636,  6598, 20510, 8912,  11611, 11612, 11911,  \n26820, 27215, 27216,  15947, 7271, 4873,  27215, 26819, 26995,  \n2885, 21393, 2529,  27214, 27213, 27409,  26995, 26999, 27215,  \n27216, 27215, 27410,  19091, 7662, 1329,  27001, 27410, 27215,  \n26999, 27001, 27215,  16535, 12615, 12763,  6400, 1545, 4799,  \n10238, 17952, 3332,  16844, 1665, 20247,  27410, 27220, 27216,  \n4569, 10964, 29591,  13909, 6708, 15650,  27214, 27409, 27217,  \n9016, 7887, 18583,  3902, 4403, 2183,  4718, 7862, 8100,  \n13250, 8393, 6940,  27216, 27220, 27222,  5800, 8442, 13105,  \n17818, 3784, 16764,  22572, 1900, 13100,  27220, 27221, 27222,  \n7622, 3886, 10048,  27217, 27409, 27413,  27411, 27408, 27222,  \n8477, 15256, 15257,  10163, 18371, 18557,  8418, 19827, 14308,  \n21369, 10746, 4403,  27411, 27222, 27221,  27414, 27411, 27221,  \n6864, 5036, 21024,  3118, 1295, 1093,  22284, 10424, 20410,  \n27003, 27415, 27225,  2693, 11017, 15046,  5689, 20532, 14624,  \n12881, 4873, 20244,  10408, 12194, 9446,  27412, 27414, 27227,  \n15544, 7538, 5400,  2227, 13757, 8843,  27415, 27003, 27217,  \n5440, 20425, 5441,  16091, 4394, 6906,  27412, 27227, 27229,  \n11019, 9240, 4752,  10707, 10708, 1791,  1115, 6205, 6204,  \n3208, 1224, 1223,  1323, 465, 14295,  5515, 3603, 17386,  \n17761, 22402, 22313,  17585, 2069, 837,  27230, 27414, 27224,  \n27228, 27414, 27230,  27414, 27228, 27227,  27228, 27007, 27227,  \n7452, 7764, 1370,  27418, 27229, 27012,  9280, 17023, 18041,  \n2844, 3255, 9368,  6262, 10772, 7988,  15428, 21900, 13610,  \n27014, 27009, 27225,  10360, 14777, 6197,  4226, 4228, 19020,  \n5948, 5236, 16050,  27231, 27418, 27012,  7439, 17710, 18417,  \n11703, 10189, 11704,  27420, 26647, 25996,  413, 21569, 6626,  \n24980, 27421, 19379,  16332, 22881, 11115,  27230, 27010, 27228,  \n27225, 27419, 27014,  371, 14448, 15562,  13284, 18576, 2625,  \n27231, 26831, 26833,  16676, 5717, 3838,  2055, 6490, 1714,  \n1273, 625, 21217,  9050, 2621, 16391,  15364, 6790, 6789,  \n27424, 26834, 26658,  15069, 7284, 13231,  27014, 27419, 27423,  \n25710, 26142, 26293,  11495, 2606, 9251,  27426, 27016, 26647,  \n3712, 10046, 3713,  27423, 27017, 27014,  26034, 27427, 8765,  \n15696, 16211, 21143,  20496, 19951, 3288,  6662, 18695, 16630,  \n25710, 26293, 25838,  20415, 19712, 7380,  14205, 13709, 7241,  \n17877, 1407, 2141,  27234, 26296, 26836,  19212, 18016, 15604,  \n27017, 27236, 27233,  5567, 12025, 14680,  27017, 27428, 27236,  \n20515, 3574, 5910,  1115, 18104, 6205,  2355, 2356, 5946,  \n419, 15588, 16705,  19211, 2303, 17729,  26837, 27428, 27430,  \n1446, 20121, 17453,  27237, 26661, 27023,  14446, 2369, 21186,  \n9310, 6907, 2433,  25838, 27431, 27432,  18119, 17297, 19598,  \n2918, 13452, 16892,  14529, 10480, 7174,  26297, 27433, 26301,  \n25838, 27432, 25714,  10658, 12279, 10012,  22893, 20215, 10270,  \n2944, 15422, 3739,  18958, 7529, 5975,  17217, 6037, 3231,  \n7695, 2425, 1027,  10925, 12296, 19959,  2612, 3394, 2611,  \n13249, 1425, 5868,  2975, 5462, 19350,  12860, 11624, 11623,  \n26301, 27434, 26305,  25842, 26662, 27025,  27021, 25193, 25722,  \n351, 9385, 12875,  8533, 8532, 741,  7713, 8478, 3109,  \n975, 8189, 13048,  25719, 25842, 27436,  21349, 4252, 19472,  \n8048, 14335, 18888,  6753, 18911, 18354,  27024, 27020, 27435,  \n15601, 21555, 2491,  1748, 19605, 10568,  26148, 26305, 27618,  \n25842, 27025, 27436,  5565, 16793, 4921,  25600, 25719, 27436,  \n7773, 17865, 17864,  2923, 12061, 16831,  27024, 27435, 27239,  \n27437, 26667, 27438,  27437, 26839, 26667,  5362, 4399, 665,  \n16920, 908, 12889,  26668, 27239, 27031,  27027, 26666, 27029,  \n5189, 20571, 16068,  19396, 17210, 8485,  26155, 26008, 26671,  \n14871, 10924, 12869,  5013, 9616, 9601,  7625, 6559, 12370,  \n3462, 6350, 19635,  27030, 25724, 26506,  13651, 7078, 15852,  \n1642, 18220, 2902,  21552, 6507, 22231,  27439, 26315, 26314,  \n5016, 11943, 11944,  771, 13695, 772,  27622, 26156, 27033,  \n27441, 27622, 27033,  26507, 26508, 27440,  5482, 7018, 7143,  \n1796, 9281, 20194,  26156, 26846, 27033,  2708, 23595, 9974,  \n20166, 4793, 3141,  379, 19199, 16483,  27247, 25344, 26844,  \n16573, 2779, 18093,  16958, 4757, 17397,  26669, 27442, 26672,  \n8905, 29640, 8904,  26847, 26672, 27442,  27244, 27443, 26674,  \n27035, 27245, 27243,  20336, 18450, 11006,  11055, 14531, 12115,  \n5603, 5602, 9396,  10840, 10556, 10377,  17381, 17380, 19258,  \n2003, 23194, 8493,  27625, 27246, 27444,  9725, 1678, 10174,  \n11373, 11973, 12189,  13531, 7134, 14613,  27446, 27038, 27447,  \n22024, 18930, 7353,  27448, 27037, 27247,  27247, 27037, 26673,  \n26318, 27446, 27246,  26513, 27038, 27446,  16177, 467, 16170,  \n27249, 27449, 27447,  27249, 27450, 27449,  12713, 23485, 18373,  \n27446, 26318, 26513,  7759, 8010, 5493,  21199, 14845, 7836,  \n27038, 27039, 27447,  27447, 27039, 27249,  7251, 5537, 5600,  \n10412, 6657, 13949,  3326, 3325, 8396,  13092, 3826, 3828,  \n27451, 27450, 27249,  22155, 1898, 12687,  12116, 10666, 1259,  \n27448, 27452, 27037,  22293, 20053, 17543,  1869, 13381, 1868,  \n12784, 1951, 1950,  27037, 27453, 26510,  27251, 26510, 27453,  \n26018, 26511, 27248,  15049, 2647, 6544,  1297, 1437, 16509,  \n7182, 3854, 7181,  27451, 27040, 27252,  21751, 11080, 18422,  \n21178, 9497, 17381,  10224, 6221, 10223,  27251, 27042, 26678,  \n26850, 26317, 27455,  26850, 25855, 26317,  8907, 12076, 18686,  \n18901, 13752, 17169,  27252, 27041, 27456,  27457, 27041, 27043,  \n3774, 24396, 18744,  6366, 8844, 8845,  15510, 18000, 20129,  \n26511, 25616, 27454,  3221, 4472, 10005,  26319, 27458, 27454,  \n27455, 27044, 26850,  20669, 11828, 17306,  18206, 12134, 13918,  \n8417, 7031, 23346,  27043, 27046, 27636,  17278, 14105, 1732,  \n27636, 27046, 27461,  11792, 7176, 7175,  10497, 12735, 20834,  \n22793, 3493, 18979,  8745, 9058, 10336,  8452, 8451, 10803,  \n26323, 27044, 27256,  27254, 27461, 27046,  27462, 27458, 27253,  \n2729, 13650, 12377,  27464, 27255, 26684,  19226, 1330, 17243,  \n27464, 26684, 27465,  9981, 10733, 6728,  10860, 6069, 5956,  \n2737, 5338, 11392,  27465, 26684, 26853,  18487, 6327, 6328,  \n26851, 27459, 27463,  14581, 13742, 6911,  27465, 26853, 27467,  \n27045, 26851, 27463,  11651, 18384, 2135,  14633, 21747, 21501,  \n12814, 13924, 22152,  14669, 13658, 4801,  27258, 27259, 26522,  \n3015, 8695, 11108,  21478, 4060, 18506,  27051, 26332, 27256,  \n838, 14195, 8627,  17994, 9774, 21596,  27470, 27045, 27463,  \n27053, 27471, 27048,  1896, 4359, 19611,  17927, 10407, 11643,  \n2062, 10463, 10599,  27470, 26683, 27045,  10292, 5183, 16398,  \n4735, 470, 958,  6805, 22632, 16453,  11368, 12154, 8908,  \n1058, 15713, 15411,  12285, 1950, 1954,  27050, 27260, 26856,  \n15576, 14133, 11421,  26027, 26691, 27054,  27473, 27054, 26691,  \n27254, 27059, 27472,  997, 18856, 998,  7842, 19381, 19911,  \n27473, 26691, 27261,  4703, 5462, 4257,  27059, 27061, 27265,  \n958, 470, 959,  26688, 27259, 27474,  16059, 19332, 10305,  \n15048, 12154, 12396,  12638, 9681, 16373,  3026, 15539, 3025,  \n11984, 18332, 18331,  27264, 26693, 27062,  27266, 26180, 26529,  \n27475, 26529, 26694,  6421, 19180, 16115,  19368, 22858, 10198,  \n10566, 11651, 19924,  16391, 15543, 4351,  7216, 7175, 15258,  \n11984, 6627, 18332,  3105, 1212, 11057,  6772, 11283, 11282,  \n26859, 26864, 27476,  27061, 27060, 26865,  5725, 12237, 21651,  \n15423, 8729, 8403,  6007, 6006, 20935,  21178, 5147, 9496,  \n3706, 7801, 3710,  13852, 4583, 19295,  27066, 27269, 26864,  \n26864, 27269, 27476,  10288, 8977, 20756,  27069, 26697, 27268,  \n17781, 9787, 3616,  27066, 27271, 27269,  4751, 18347, 4750,  \n27271, 27066, 27270,  26866, 27273, 27270,  27071, 27065, 26703,  \n27477, 27065, 27071,  11618, 4006, 2060,  18133, 2174, 8290,  \n27478, 27070, 27272,  17061, 16193, 13875,  27274, 27478, 27272,  \n19801, 17903, 16765,  27479, 27070, 27478,  27070, 26870, 26868,  \n27479, 26870, 27070,  13781, 737, 13191,  4498, 12083, 14419,  \n27480, 26538, 26533,  4485, 3367, 21182,  7386, 6045, 1065,  \n27481, 27275, 27072,  26874, 26538, 27480,  11504, 14097, 15410,  \n10182, 18305, 6579,  17652, 23685, 12824,  27268, 27276, 27069,  \n3798, 3799, 1747,  8130, 13812, 20073,  8908, 15048, 4974,  \n12594, 9117, 12593,  18761, 18532, 7200,  27068, 27069, 27276,  \n27274, 27482, 27478,  2564, 6166, 8185,  11475, 979, 6674,  \n27277, 26710, 26874,  17930, 10637, 9761,  27274, 27068, 27482,  \n5608, 11697, 1303,  20073, 2816, 12507,  27483, 27072, 26707,  \n12615, 4468, 4469,  27072, 27483, 27481,  27074, 26870, 27479,  \n10363, 21058, 9680,  10500, 1795, 1794,  13610, 11877, 15428,  \n26710, 27277, 26875,  27068, 27276, 27482,  22773, 5648, 14732,  \n27074, 26708, 26870,  1686, 6130, 1452,  26707, 27484, 27483,  \n26038, 27485, 26537,  3667, 7270, 3652,  27486, 26537, 27485,  \n8082, 6697, 8130,  26713, 27078, 27073,  27487, 26357, 27278,  \n6270, 14564, 3073,  16727, 10535, 13497,  23711, 6015, 4337,  \n27488, 26357, 27489,  21591, 20039, 22775,  22177, 27490, 22178,  \n6279, 13656, 14848,  27280, 27491, 27281,  26543, 27077, 27081,  \n26877, 26714, 27284,  21010, 20569, 10376,  13816, 15485, 3969,  \n27080, 27492, 27078,  26879, 27492, 27080,  8221, 3735, 5350,  \n14342, 2682, 8020,  5870, 5936, 688,  27075, 27285, 27279,  \n23330, 14603, 13170,  11566, 13133, 11590,  18934, 2355, 15132,  \n17331, 18556, 9910,  20016, 6226, 4709,  14943, 17498, 17181,  \n7403, 6464, 16880,  27283, 27082, 27496,  9811, 5081, 7443,  \n27493, 27283, 27496,  12981, 8394, 18422,  9064, 19679, 8639,  \n26547, 27288, 26879,  27286, 27079, 27281,  27285, 27282, 27286,  \n27083, 27290, 27497,  2814, 8825, 2813,  15262, 9922, 10164,  \n27498, 27285, 27286,  14648, 15583, 20465,  8430, 14792, 10525,  \n21079, 11066, 14368,  26881, 26715, 27495,  27083, 27085, 27290,  \n27089, 26367, 26723,  17514, 17513, 16510,  27086, 27500, 26550,  \n27289, 26881, 27495,  13443, 5297, 15720,  1207, 18999, 6363,  \n26377, 27090, 27501,  4123, 11744, 4122,  14046, 8022, 15566,  \n2593, 21308, 19626,  4050, 17209, 4051,  11401, 15835, 1460,  \n27090, 27291, 27501,  3874, 3709, 19405,  27506, 26377, 27501,  \n22024, 16679, 16384,  17751, 14945, 14859,  14945, 17751, 14946,  \n6603, 16117, 11019,  7137, 7138, 7139,  27502, 27092, 27289,  \n27087, 27088, 27294,  27503, 26885, 27087,  27297, 27293, 26730,  \n19048, 19250, 22053,  27092, 27504, 27294,  27087, 27294, 27503,  \n27505, 26886, 26885,  18144, 7423, 5982,  6595, 10160, 408,  \n644, 16266, 7612,  563, 562, 17626,  27293, 26552, 26730,  \n20104, 2436, 8968,  18552, 22930, 18553,  12713, 13281, 13948,  \n27296, 26887, 27299,  27300, 27094, 26549,  27507, 27298, 27094,  \n13731, 4448, 10634,  17291, 14828, 9366,  27094, 27300, 27508,  \n27508, 27507, 27094,  18163, 10972, 4422,  27299, 26894, 27302,  \n26730, 27097, 27297,  12966, 26080, 1214,  18157, 20873, 2177,  \n9704, 4085, 10998,  23377, 8085, 8084,  2062, 6771, 8915,  \n26734, 27510, 26896,  27305, 26729, 26892,  2815, 9777, 9776,  \n2367, 10870, 18539,  26729, 27305, 26733,  6830, 7056, 6829,  \n27511, 26568, 27102,  1007, 1008, 9484,  13857, 13587, 8500,  \n5215, 9819, 17861,  27308, 26733, 27305,  27302, 27099, 27512,  \n27511, 27107, 26568,  15973, 22309, 20342,  3822, 3821, 19299,  \n5863, 6877, 564,  27301, 27309, 27100,  2640, 2998, 9501,  \n27312, 27303, 27103,  27513, 27303, 27312,  7978, 11688, 15464,  \n27513, 27096, 27303,  5799, 16022, 3002,  5375, 17474, 4148,  \n26564, 27515, 27307,  26564, 27304, 27515,  23537, 3297, 3298,  \n12234, 11170, 5637,  27510, 26734, 27108,  20583, 18125, 9541,  \n19119, 1758, 19118,  3642, 3512, 490,  27512, 27101, 27106,  \n27512, 27099, 27101,  4609, 4969, 16593,  27116, 27517, 27104,  \n27517, 27097, 27104,  19091, 20313, 19785,  604, 13628, 867,  \n27109, 26899, 27306,  27304, 27098, 27110,  14214, 14210, 12057,  \n9897, 23026, 12680,  11171, 21576, 1411,  16687, 11547, 10841,  \n14662, 14661, 12157,  19923, 10255, 8868,  19825, 2137, 13355,  \n7546, 4916, 2296,  27309, 27520, 27311,  27311, 27520, 27312,  \n10245, 15199, 10246,  27515, 27110, 27313,  27515, 27304, 27110,  \n8005, 5727, 19086,  6873, 15006, 14134,  8374, 26657, 18846,  \n4177, 23036, 946,  8744, 10800, 16272,  8591, 12925, 12926,  \n10768, 9021, 15334,  27109, 27521, 27111,  373, 8681, 5782,  \n27115, 26388, 27523,  12367, 1044, 1382,  27111, 27521, 27525,  \n27111, 27525, 26900,  26900, 27525, 27313,  22391, 7637, 15242,  \n15278, 9837, 18398,  27113, 27526, 27314,  27314, 27526, 27315,  \n1854, 3052, 19018,  27315, 27526, 27527,  8292, 8291, 19033,  \n3747, 15468, 16667,  7103, 14116, 22780,  17811, 13775, 2329,  \n18605, 10418, 14737,  25846, 15322, 17324,  27316, 27529, 26903,  \n3184, 11900, 19354,  9804, 6376, 5318,  27316, 27118, 27530,  \n7683, 7145, 7682,  27530, 27118, 27119,  5793, 6494, 8452,  \n17238, 12150, 4839,  6652, 6653, 3125,  27317, 27530, 27119,  \n26068, 26746, 26907,  2699, 6309, 22074,  7513, 14082, 2509,  \n2701, 13329, 7040,  8966, 22854, 15882,  27532, 26908, 26910,  \n10233, 12924, 9826,  7322, 7321, 5671,  26910, 27120, 27533,  \n1005, 1004, 11664,  740, 2975, 10788,  9951, 23392, 17370,  \n14439, 18063, 437,  7288, 18722, 8986,  27318, 27319, 27534,  \n23676, 9292, 22117,  27319, 26581, 27534,  9657, 11418, 17240,  \n15087, 22205, 17426,  7214, 1567, 8253,  27321, 27534, 26581,  \n4621, 8973, 4437,  26913, 27322, 27324,  2401, 8447, 12791,  \n6368, 6332, 12655,  27535, 27534, 27321,  13602, 13601, 4100,  \n9876, 16128, 1405,  27321, 26753, 27536,  6141, 8906, 5304,  \n27122, 27536, 26753,  10776, 14525, 2425,  14160, 7083, 15662,  \n27537, 26914, 26915,  27537, 27325, 26914,  4137, 9498, 22170,  \n20999, 1063, 20529,  22841, 7136, 26260,  7220, 10713, 12484,  \n2876, 2877, 9906,  10377, 1220, 2656,  27326, 26758, 27538,  \n4834, 12467, 15812,  27539, 26916, 27326,  27540, 26759, 26916,  \n27541, 26917, 27542,  4617, 12668, 10951,  8400, 10126, 399,  \n27540, 27123, 26759,  27541, 27122, 26917,  19227, 6426, 9149,  \n27542, 26917, 27543,  26917, 26585, 27543,  26585, 26760, 27543,  \n7342, 10756, 23005,  1074, 12517, 20378,  26760, 27124, 27543,  \n27543, 27124, 27544,  27123, 27545, 26589,  14801, 14802, 5975,  \n27124, 27125, 27544,  12402, 5070, 14691,  27545, 27327, 26589,  \n15043, 15042, 9031,  27125, 27126, 27546,  11228, 6230, 15714,  \n1344, 15614, 15529,  27332, 27333, 27128,  27336, 26919, 27127,  \n1694, 6205, 2091,  16708, 2628, 2629,  15452, 4591, 6122,  \n26231, 26230, 26596,  26230, 28116, 26596,  10614, 4290, 6132,  \n12534, 7436, 12535,  19638, 11523, 11524,  27330, 26767, 26081,  \n4445, 21745, 1120,  13376, 10241, 9153,  15767, 16321, 20810,  \n12545, 4696, 7602,  22518, 23136, 22627,  20561, 17712, 20961,  \n15604, 18016, 16428,  3902, 7990, 3901,  12022, 13939, 13938,  \n10236, 9995, 10235,  13782, 6918, 4365,  11187, 12062, 2461,  \n23851, 21844, 7445,  20053, 22293, 9435,  10642, 20941, 16894,  \n3194, 1123, 4264,  20772, 2931, 10511,  8331, 10324, 3827,  \n22671, 7388, 17814,  12575, 2924, 2926,  27130, 27128, 26771,  \n1895, 10661, 19990,  14398, 10395, 1982,  6194, 10110, 1036,  \n26921, 27338, 27130,  18209, 6737, 19589,  12875, 4540, 7415,  \n26921, 26922, 27720,  15982, 3329, 3517,  27337, 27339, 27131,  \n5816, 20528, 11705,  26924, 27548, 26923,  26923, 27548, 26922,  \n8168, 8938, 4407,  10285, 14860, 4113,  27132, 27131, 27339,  \n729, 14356, 7196,  18350, 6324, 11340,  808, 807, 16362,  \n13340, 13995, 13994,  7893, 8712, 7891,  16754, 11402, 10495,  \n14093, 19545, 15126,  5938, 1418, 1417,  1007, 18749, 2845,  \n13037, 4893, 5164,  5565, 4921, 8049,  26925, 27550, 27340,  \n27343, 26241, 26605,  14992, 2140, 10452,  5973, 13145, 5971,  \n27134, 27551, 26925,  27551, 27550, 26925,  9551, 1711, 14125,  \n3614, 19719, 6735,  9097, 7418, 14846,  11971, 11888, 11889,  \n22509, 18755, 16521,  4439, 4440, 8958,  19435, 583, 17613,  \n27134, 27344, 27551,  13507, 18711, 23383,  27138, 27345, 27552,  \n3599, 10195, 14237,  27138, 26242, 27345,  18870, 17424, 2733,  \n11737, 587, 4858,  7034, 11046, 7032,  27553, 27551, 27344,  \n26778, 26243, 27138,  26780, 27348, 27139,  20520, 17372, 20294,  \n20165, 4291, 5315,  26778, 27727, 27140,  27140, 27348, 26779,  \n19143, 3697, 14706,  26143, 19460, 19466,  3132, 9814, 14600,  \n27553, 27349, 27350,  27553, 27344, 27349,  4535, 22493, 6099,  \n27351, 27350, 27349,  21181, 16318, 16081,  1998, 20252, 1997,  \n15405, 3069, 20344,  5777, 5779, 2113,  27351, 27352, 27554,  \n14134, 4768, 4767,  10008, 7846, 1533,  1605, 16088, 8822,  \n27147, 27557, 27352,  800, 3199, 8667,  9746, 8882, 1636,  \n27146, 27346, 27354,  27356, 27557, 27147,  6134, 15969, 18275,  \n12128, 10080, 12329,  27353, 27356, 27147,  27357, 27146, 27354,  \n21285, 11398, 12700,  11406, 18005, 23696,  27559, 27353, 27151,  \n27559, 27355, 27353,  14166, 8618, 3410,  4030, 1691, 4031,  \n7517, 9282, 15227,  27359, 27559, 27151,  21751, 18422, 8394,  \n14375, 7790, 3966,  9967, 16481, 16482,  15649, 6443, 6852,  \n27360, 27560, 27362,  13873, 10847, 10636,  13571, 3006, 18680,  \n21783, 15044, 10068,  27563, 27363, 27152,  9596, 1133, 5786,  \n27563, 27152, 27365,  27362, 27564, 27153,  27564, 27364, 27153,  \n10880, 16291, 17562,  27364, 27565, 27365,  1427, 17639, 13591,  \n19132, 493, 19133,  26422, 27156, 26781,  3320, 12205, 13899,  \n18771, 18665, 20990,  11123, 15596, 11438,  9658, 6665, 12595,  \n17198, 22001, 23913,  26422, 27157, 27156,  19767, 3990, 13338,  \n9570, 10561, 19798,  17428, 1132, 1131,  22092, 4606, 20454,  \n4392, 4391, 2253,  5675, 5674, 14910,  15567, 9915, 15568,  \n12951, 20044, 11068,  7365, 9706, 15560,  26938, 26429, 27159,  \n611, 20664, 9373,  11406, 23696, 25211,  26943, 26425, 26360,  \n3142, 3144, 17607,  430, 10076, 1192,  10600, 13715, 19252,  \n11367, 12651, 19534,  16828, 20150, 17652,  26265, 26883, 26942,  \n26883, 26784, 26942,  5827, 5488, 4306,  15911, 9422, 15129,  \n9559, 8488, 8489,  27371, 26429, 26612,  5399, 11730, 17570,  \n19051, 14956, 19043,  1773, 22413, 19744,  847, 10309, 848,  \n2501, 20735, 2368,  26613, 26254, 26944,  7424, 16897, 7425,  \n11667, 13757, 13758,  14366, 17972, 25158,  4577, 4576, 6757,  \n933, 5292, 5291,  11581, 11040, 18517,  26614, 26947, 27372,  \n17134, 17556, 4059,  9873, 22752, 1476,  3870, 14940, 14522,  \n20079, 20717, 18438,  9494, 25652, 25653,  9309, 19020, 18048,  \n7361, 17459, 15614,  27376, 26791, 27566,  3095, 7856, 13992,  \n25948, 27567, 27165,  1935, 6037, 13259,  18125, 932, 9541,  \n7920, 4859, 20547,  14217, 8142, 24315,  26114, 26956, 26948,  \n27379, 27381, 27568,  2887, 478, 11248,  11881, 8973, 2690,  \n16244, 3469, 18425,  14014, 20643, 14013,  13018, 6676, 7578,  \n10147, 3538, 7268,  27380, 27379, 27569,  20365, 2501, 2502,  \n1495, 18812, 1496,  11760, 15127, 1940,  14019, 16870, 469,  \n1734, 16412, 10910,  10774, 16274, 7233,  4197, 4784, 4198,  \n3011, 11209, 5417,  6491, 11299, 11591,  14188, 12388, 12387,  \n26796, 25958, 27171,  27380, 27384, 27169,  26954, 25139, 27173,  \n24191, 5063, 686,  6734, 7045, 13956,  4040, 9631, 15101,  \n27175, 27571, 27572,  26263, 26618, 27176,  18937, 5527, 8600,  \n19926, 21599, 7106,  26964, 25962, 26793,  2466, 22822, 4035,  \n12971, 6453, 7970,  16005, 19584, 11294,  18262, 7621, 20310,  \n11831, 16852, 18103,  16039, 2940, 17132,  11402, 16754, 10730,  \n26799, 27574, 26798,  8875, 13701, 15908,  17647, 2808, 3046,  \n6232, 12192, 8297,  4101, 9000, 4549,  9076, 9075, 20340,  \n865, 866, 4724,  27178, 27573, 27386,  14120, 15455, 13033,  \n13944, 1141, 21761,  5965, 13372, 5966,  27576, 26449, 26964,  \n27386, 26963, 27178,  13597, 13594, 4001,  27575, 26618, 27180,  \n27577, 27578, 27576,  14827, 4233, 14828,  3501, 4297, 19683,  \n12150, 16863, 12151,  2064, 15060, 9785,  11572, 1300, 1471,  \n12708, 11071, 415,  7304, 12418, 3824,  27181, 26804, 27388,  \n2914, 12247, 2915,  5637, 5636, 2481,  14648, 15581, 15583,  \n20643, 15528, 13304,  20641, 20642, 15512,  20190, 12676, 21666,  \n2150, 20474, 20767,  19718, 3732, 19717,  2552, 14752, 13177,  \n27181, 27390, 26450,  19078, 7152, 7153,  27390, 27182, 26622,  \n13542, 15406, 1089,  18586, 22575, 24612,  5266, 1426, 1425,  \n9114, 18353, 21666,  27389, 26457, 26625,  27393, 26273, 26626,  \n19164, 15766, 9925,  26270, 26455, 26969,  26270, 26969, 27394,  \n14841, 16803, 16804,  15704, 21522, 18704,  10131, 11639, 7110,  \n9623, 4914, 6172,  26627, 26632, 27581,  14389, 4102, 6329,  \n27185, 26805, 26968,  2045, 4759, 5110,  18721, 8135, 8136,  \n11515, 11516, 12917,  26460, 27581, 26632,  27187, 27582, 27188,  \n27583, 27188, 27582,  14402, 9137, 8322,  6826, 12608, 818,  \n12096, 6982, 19402,  27583, 26808, 27188,  20403, 6249, 10340,  \n18463, 12622, 3003,  10125, 24833, 14572,  27395, 27189, 26808,  \n9075, 3886, 7622,  27584, 26973, 26462,  6281, 546, 10324,  \n12190, 21601, 18444,  11114, 1016, 2826,  22340, 19875, 22540,  \n21425, 9705, 16072,  27395, 27190, 27189,  27586, 26465, 27587,  \n6759, 7413, 10662,  27586, 26466, 26465,  27395, 27397, 27190,  \n27587, 26465, 26635,  5290, 5680, 21241,  9232, 14491, 17046,  \n1775, 10035, 1354,  26975, 27397, 27192,  26278, 26125, 27396,  \n3903, 16789, 14575,  26125, 27194, 27396,  6502, 20517, 7158,  \n2466, 22989, 10455,  27588, 26635, 26976,  23172, 17329, 20867,  \n2574, 4469, 4468,  14330, 15815, 19996,  27194, 25819, 26472,  \n7833, 7834, 13674,  11570, 19169, 6899,  17628, 20297, 20978,  \n14641, 21826, 18908,  27398, 27590, 26981,  18664, 19096, 14939,  \n3496, 3495, 851,  16001, 16003, 9756,  19288, 1563, 10856,  \n804, 7382, 803,  19934, 14807, 14808,  27197, 26981, 27590,  \n26472, 26636, 27196,  8425, 1241, 2776,  9196, 13406, 14164,  \n5253, 21480, 19567,  27197, 27590, 27591,  2764, 14991, 28419,  \n1985, 5110, 4759,  4504, 22820, 4503,  23267, 9755, 20269,  \n6336, 4435, 6335,  8717, 3753, 15291,  27203, 27592, 26636,  \n7846, 17623, 5353,  3531, 22064, 9233,  4163, 374, 3038,  \n4238, 4237, 18795,  1734, 3334, 16412,  9667, 847, 370,  \n5133, 17775, 2018,  1186, 18552, 13699,  8874, 23646, 22911,  \n13785, 17021, 22958,  14080, 14364, 18791,  23470, 21675, 17084,  \n15228, 18787, 5264,  18349, 13570, 6315,  27595, 26639, 26477,  \n14597, 21624, 11204,  689, 17678, 12666,  18256, 3020, 22596,  \n14742, 10823, 4939,  27593, 26814, 27205,  6809, 6808, 8456,  \n26639, 27595, 26478,  10406, 7959, 18149,  9616, 2862, 18130,  \n10482, 2890, 7872,  17756, 14314, 781,  27204, 27975, 27596,  \n26479, 26280, 27206,  6739, 6129, 6480,  1639, 2019, 15416,  \n1936, 1938, 22852,  10546, 13436, 2124,  9866, 21731, 7956,  \n15638, 17974, 16528,  5240, 2784, 2785,  22714, 21018, 21017,  \n26282, 26993, 26989,  12126, 11317, 20101,  4762, 13212, 4763,  \n1961, 9890, 3799,  27205, 26133, 26483,  11323, 17559, 18653,  \n18088, 10150, 15864,  22022, 17850, 11788,  13545, 11205, 13543,  \n27402, 26483, 25704,  26641, 27207, 27403,  26641, 27403, 26991,  \n19459, 15184, 15185,  12415, 535, 12732,  27404, 27597, 26816,  \n14687, 21228, 15039,  27401, 27210, 27209,  27208, 27401, 27209,  \n16047, 15945, 19698,  15134, 19603, 6330,  17481, 11112, 11316,  \n27784, 25836, 25703,  21185, 9562, 6887,  22004, 20026, 16508,  \n12577, 11689, 11688,  27404, 27211, 27406,  6298, 12156, 14899,  \n4960, 7220, 2487,  27212, 27210, 27407,  28744, 16145, 4009,  \n14989, 9544, 14988,  27407, 27213, 27212,  3908, 3907, 7352,  \n27598, 26286, 26289,  11745, 9068, 9069,  3354, 12462, 3355,  \n27213, 27407, 27409,  4837, 17492, 23728,  27406, 27211, 27408,  \n5148, 14011, 22458,  16870, 21502, 959,  1691, 8179, 7518,  \n14531, 12648, 12115,  26484, 27600, 27002,  8697, 15554, 22787,  \n15729, 15728, 8045,  3519, 14906, 14196,  11979, 3981, 3980,  \n9746, 18114, 540,  1168, 10072, 3173,  5200, 8694, 14818,  \n2599, 9874, 9745,  3129, 14354, 20983,  9284, 3746, 21636,  \n27791, 27411, 27412,  588, 15856, 11674,  8703, 10300, 3276,  \n8626, 5542, 6239,  15835, 11401, 23626,  17169, 8916, 16501,  \n1422, 3761, 18397,  6834, 14474, 9558,  10511, 2931, 14343,  \n13041, 13730, 11067,  27412, 27411, 27414,  27605, 27217, 27413,  \n5028, 16464, 14899,  7263, 12576, 12575,  27415, 27217, 27605,  \n7799, 13922, 5386,  18775, 364, 19568,  20114, 9211, 5357,  \n27006, 25593, 26648,  17203, 9993, 4288,  7304, 10388, 11385,  \n10687, 6741, 12368,  27417, 27412, 27418,  10145, 609, 6810,  \n27226, 25590, 26140,  24039, 11083, 18213,  11068, 16002, 12951,  \n27229, 27418, 27412,  5490, 16228, 8739,  6133, 3015, 3539,  \n15308, 14108, 15307,  20549, 18771, 14676,  2579, 1952, 3631,  \n27225, 27415, 27419,  21648, 9656, 21007,  13547, 23622, 17346,  \n26648, 25712, 26829,  6643, 11547, 6294,  8516, 16001, 10689,  \n15302, 8215, 5232,  27605, 27606, 27419,  18289, 555, 11014,  \n27607, 27608, 26829,  8396, 16512, 15838,  8656, 18242, 4480,  \n9594, 11704, 1649,  2733, 16469, 2900,  25995, 25997, 26649,  \n27231, 26834, 27422,  16081, 3579, 351,  2988, 22161, 505,  \n27424, 26658, 27425,  10601, 2032, 11468,  6418, 7604, 15075,  \n27609, 25995, 26649,  27419, 27606, 27423,  3538, 10148, 16014,  \n16548, 9057, 11072,  10053, 3419, 18482,  26658, 27232, 27425,  \n6280, 8928, 8862,  18746, 1292, 15304,  12686, 14806, 6978,  \n26294, 27609, 26649,  10685, 13156, 19268,  11860, 18772, 8882,  \n2177, 15872, 18875,  2612, 2611, 6664,  26652, 26296, 27234,  \n12314, 4801, 20098,  15334, 15333, 19542,  6743, 21316, 11362,  \n11809, 7144, 11808,  3572, 9741, 21182,  27612, 27235, 27613,  \n6638, 11840, 907,  17496, 5886, 3499,  26660, 27613, 27235,  \n5554, 6038, 3470,  13506, 16318, 21181,  26660, 26661, 27613,  \n12955, 8552, 13976,  27430, 27993, 27238,  494, 3153, 3152,  \n3245, 19654, 18761,  2949, 579, 20041,  22254, 22699, 11195,  \n12988, 3716, 16125,  21078, 17493, 24932,  16463, 18138, 3124,  \n26298, 26304, 27614,  498, 497, 3834,  8935, 5055, 5054,  \n2119, 16342, 2778,  18888, 14335, 9190,  27020, 27430, 27238,  \n11383, 5793, 5794,  26304, 25715, 27616,  1887, 3426, 18525,  \n7072, 17010, 7520,  9809, 11138, 22863,  11464, 5464, 5465,  \n2351, 19096, 2983,  11464, 9318, 16489,  25722, 26841, 27021,  \n8936, 9070, 18097,  26499, 26007, 26839,  13682, 16539, 17396,  \n1274, 16904, 7510,  8749, 18255, 2077,  21526, 3620, 6999,  \n26842, 26148, 27618,  15694, 4562, 6990,  25600, 27619, 26501,  \n461, 12753, 5519,  17484, 11408, 4825,  18796, 6447, 5416,  \n9829, 14829, 16256,  744, 743, 11915,  3063, 5483, 10220,  \n12588, 21726, 10758,  11449, 3634, 1429,  5250, 17336, 6396,  \n1166, 9570, 22994,  6802, 9468, 9469,  27239, 27620, 27031,  \n17068, 18103, 15736,  27240, 27031, 27620,  27028, 27621, 26843,  \n14356, 729, 728,  8815, 17940, 16364,  20013, 1391, 9720,  \n10088, 611, 610,  21864, 10505, 11843,  10526, 22276, 9603,  \n11138, 15668, 10570,  10129, 17987, 17986,  9755, 15109, 17390,  \n26506, 27241, 27032,  26506, 26313, 27241,  27622, 26504, 26505,  \n5122, 18589, 22408,  12699, 8891, 19215,  14897, 19219, 19220,  \n26505, 26156, 27622,  15444, 7139, 12885,  4011, 12638, 13164,  \n4985, 16042, 16985,  26844, 25344, 26671,  20070, 5691, 1647,  \n8381, 8506, 14861,  18293, 27623, 3762,  5356, 11327, 5645,  \n27440, 26508, 27034,  27243, 27245, 27624,  10509, 14463, 5740,  \n2068, 12260, 21015,  20543, 11882, 6946,  18031, 24100, 8194,  \n10386, 10387, 7548,  20921, 19312, 15901,  3600, 23553, 5248,  \n15035, 13564, 4661,  27243, 27626, 27244,  13241, 22255, 7620,  \n17428, 1131, 19562,  27247, 26844, 28013,  14803, 14804, 10891,  \n11218, 1241, 8425,  3507, 2991, 12589,  26848, 26847, 27442,  \n17032, 1398, 367,  4507, 12628, 3768,  21073, 10659, 19427,  \n571, 8554, 9636,  24654, 23655, 18605,  19299, 12195, 18111,  \n27827, 27447, 27629,  23553, 14237, 14238,  12010, 13230, 8345,  \n13528, 18217, 1567,  27629, 27447, 27449,  23667, 10022, 14582,  \n11286, 771, 18693,  11044, 14104, 1277,  12131, 10345, 6335,  \n27445, 26846, 27248,  4416, 21962, 4909,  15174, 20779, 16194,  \n14134, 10342, 4768,  2544, 3125, 7121,  27451, 27249, 27040,  \n2320, 1360, 5885,  27037, 27452, 27453,  4323, 12947, 11214,  \n1629, 1489, 16993,  11856, 11855, 8756,  26511, 27454, 27248,  \n19149, 1542, 10986,  27455, 26317, 27250,  6775, 14416, 17766,  \n19593, 5698, 17376,  27632, 27451, 27456,  19602, 8883, 2703,  \n27453, 27633, 27251,  16187, 7577, 21946,  27252, 27456, 27451,  \n13294, 13978, 13979,  4280, 20298, 4281,  13265, 17262, 18213,  \n16422, 17679, 2015,  1048, 4355, 4354,  3738, 16738, 3736,  \n4493, 4179, 3394,  27457, 27456, 27041,  27042, 27251, 27634,  \n4570, 7252, 18760,  27459, 27042, 27634,  8755, 13877, 10261,  \n14817, 584, 7545,  27455, 27635, 27044,  21326, 14948, 15973,  \n27457, 27043, 27636,  27458, 27637, 27454,  27458, 27460, 27637,  \n21076, 21754, 2829,  5579, 2158, 2157,  26851, 27042, 27459,  \n27256, 27044, 27466,  4600, 4738, 4737,  19200, 5079, 4224,  \n27638, 27636, 27461,  27460, 27458, 27462,  2772, 12267, 16598,  \n6293, 1410, 19985,  10743, 6029, 7790,  27639, 27462, 27253,  \n7369, 8207, 16339,  15828, 6478, 18384,  27464, 27640, 27255,  \n11891, 7150, 4626,  16442, 902, 3857,  27640, 27257, 26852,  \n27640, 26852, 27255,  16079, 11145, 2574,  8523, 12988, 17039,  \n27467, 27469, 27465,  27472, 27642, 27461,  4726, 16695, 1870,  \n27465, 27469, 27643,  17686, 22632, 6805,  20336, 9162, 2422,  \n662, 16097, 14066,  27472, 27461, 27254,  719, 17282, 11584,  \n12073, 12074, 10309,  1988, 20946, 21488,  9491, 10795, 9492,  \n27644, 27469, 27467,  27467, 27645, 27644,  27646, 26854, 27049,  \n27051, 27256, 27466,  11160, 11343, 13964,  27471, 27053, 27644,  \n27645, 27471, 27644,  27646, 27049, 27048,  27471, 27646, 27048,  \n23317, 18404, 4215,  11940, 4892, 4891,  27459, 27468, 27463,  \n13436, 13437, 16373,  27469, 27647, 27643,  27644, 27053, 27055,  \n6656, 16521, 6657,  7113, 23828, 12292,  27649, 27646, 27471,  \n27646, 27649, 27650,  13717, 21524, 13718,  9721, 5033, 13102,  \n27647, 27469, 27648,  27648, 27469, 27644,  7706, 13307, 9659,  \n27052, 26683, 27470,  10474, 13811, 10442,  18658, 1758, 21692,  \n21867, 19353, 12005,  15297, 15717, 6550,  27463, 27468, 27652,  \n3614, 659, 19719,  13548, 17553, 20411,  13228, 16233, 14123,  \n27651, 27472, 27059,  27052, 27470, 26696,  24586, 1927, 6690,  \n26861, 27055, 27056,  27260, 26860, 26690,  27651, 27059, 27265,  \n9371, 1589, 2492,  1567, 18217, 1568,  3468, 17300, 3469,  \n16072, 392, 19599,  26860, 27262, 27058,  22095, 7282, 12018,  \n10304, 2735, 21137,  26689, 26525, 26862,  27654, 27651, 27265,  \n2375, 17514, 18035,  26862, 26525, 27264,  21811, 19018, 13105,  \n1276, 4363, 4415,  4484, 12239, 3471,  12192, 18952, 11683,  \n21244, 21013, 23549,  26528, 27057, 27063,  13599, 10962, 19248,  \n6909, 6340, 16961,  1850, 21813, 11616,  26529, 27475, 27266,  \n27475, 26694, 27655,  15500, 21894, 16229,  27655, 26694, 27262,  \n26859, 27476, 27263,  6236, 19698, 18444,  6427, 14054, 21500,  \n15017, 5968, 5967,  20124, 19542, 15333,  16386, 16385, 18000,  \n21382, 17899, 1175,  19357, 14507, 7822,  27265, 27061, 27065,  \n27268, 26697, 27267,  17249, 12764, 13489,  21394, 20260, 2530,  \n7039, 7038, 20790,  19714, 15555, 8958,  8283, 9710, 9106,  \n8017, 13546, 7488,  11388, 2406, 20626,  10904, 10944, 19596,  \n14416, 6943, 10298,  22295, 22294, 11588,  10952, 2852, 9138,  \n17854, 7575, 17855,  26350, 27275, 27273,  7117, 2512, 7781,  \n15119, 1138, 7489,  3510, 1965, 3511,  14565, 3281, 5913,  \n21813, 15283, 11616,  7489, 1138, 6870,  9753, 12623, 27358,  \n1661, 1663, 17625,  27481, 27483, 27659,  21483, 10958, 11811,  \n7168, 7760, 24110,  1141, 21098, 17309,  27478, 27482, 27660,  \n3275, 10687, 1365,  9676, 11754, 9677,  5957, 1318, 14620,  \n6326, 4670, 17187,  8146, 7342, 23005,  27479, 27663, 27280,  \n5054, 16562, 8936,  27661, 27278, 26875,  25017, 22495, 22496,  \n23383, 3387, 13507,  3806, 23307, 23974,  15010, 5064, 20596,  \n5176, 8230, 8229,  10887, 14036, 20838,  27664, 27482, 27276,  \n27482, 27664, 27665,  27665, 27660, 27482,  27074, 27479, 27280,  \n27486, 26707, 26537,  5410, 3313, 13725,  14027, 7421, 10675,  \n8802, 9316, 22082,  27073, 27078, 27662,  1133, 2619, 17419,  \n26038, 26877, 27485,  6638, 10337, 6639,  26042, 26357, 27488,  \n21537, 20026, 7587,  9092, 20771, 18794,  27279, 27671, 27666,  \n1600, 8583, 7055,  22276, 16136, 13222,  27076, 27279, 27666,  \n13624, 17271, 11287,  880, 13790, 6207,  27494, 27281, 27491,  \n21814, 22836, 4334,  13548, 4417, 17553,  27081, 27077, 27666,  \n27077, 27076, 27666,  9264, 21433, 9139,  2553, 15127, 11760,  \n8742, 4090, 8592,  27668, 27284, 27283,  14904, 407, 21760,  \n27492, 26879, 27288,  5136, 3775, 9694,  1986, 13669, 6546,  \n26715, 27081, 27495,  387, 3363, 17466,  27668, 27283, 27493,  \n14903, 407, 14904,  16956, 6362, 6363,  27670, 26718, 27084,  \n27671, 27279, 27285,  12157, 6094, 20356,  17437, 14867, 6931,  \n16537, 1448, 1449,  3348, 15242, 1179,  27286, 27281, 27494,  \n17438, 8815, 7813,  27288, 26547, 27287,  27494, 27673, 27286,  \n26719, 27672, 27086,  12410, 13813, 17639,  27498, 27286, 27673,  \n19025, 16993, 19026,  15809, 8955, 9727,  7635, 7691, 7690,  \n27675, 27677, 27676,  13799, 23699, 20124,  26723, 26368, 27499,  \n14457, 18402, 14458,  7210, 385, 21893,  27672, 27500, 27086,  \n7722, 19586, 17502,  6511, 12863, 8954,  11022, 2595, 11021,  \n14968, 22966, 6182,  2521, 2520, 17251,  27674, 27083, 27497,  \n27674, 27082, 27083,  9794, 3552, 9795,  16921, 9780, 2673,  \n5843, 12196, 9285,  27501, 27291, 27677,  26368, 27292, 27499,  \n1162, 20687, 1163,  15335, 19258, 10140,  27500, 27884, 26550,  \n1658, 7287, 13539,  19496, 476, 5011,  5289, 20205, 6300,  \n12851, 10988, 22418,  4692, 19695, 7248,  5827, 19660, 5488,  \n858, 8999, 11331,  27678, 27290, 27295,  21683, 16719, 12118,  \n3442, 8214, 3441,  27298, 27678, 27295,  3362, 10245, 10247,  \n15719, 6718, 19555,  10267, 4395, 4396,  17587, 9809, 22863,  \n27679, 27678, 27298,  27095, 26737, 26384,  5733, 29709, 5586,  \n27502, 27504, 27092,  27680, 26885, 27503,  27680, 27505, 26885,  \n3173, 10072, 3174,  9758, 5322, 1278,  2721, 11892, 3627,  \n10783, 20300, 6595,  27681, 27294, 27504,  27503, 27294, 27681,  \n27505, 27682, 26886,  10123, 10176, 4523,  4907, 15755, 12056,  \n5265, 5264, 18787,  27683, 27300, 27296,  27683, 27508, 27300,  \n1649, 16973, 19041,  22095, 21612, 13944,  4793, 19722, 8402,  \n27684, 27298, 27507,  27298, 27684, 27679,  13422, 2434, 13421,  \n4256, 9476, 19507,  7084, 14644, 18600,  1664, 14826, 1665,  \n713, 10543, 13232,  27301, 26886, 27682,  27302, 27296, 27299,  \n7177, 4189, 1395,  13474, 14663, 18902,  7725, 2941, 8163,  \n12477, 12237, 5725,  17543, 20053, 11511,  27512, 27687, 27302,  \n27511, 27688, 27107,  9856, 3986, 23790,  10936, 10120, 10121,  \n17115, 12694, 7014,  4739, 15846, 15845,  27301, 27685, 27309,  \n27513, 27690, 27096,  27513, 27689, 27690,  27096, 27690, 27306,  \n27690, 27514, 27306,  18387, 10912, 1565,  26892, 26896, 27510,  \n27516, 27308, 27305,  20112, 1816, 4675,  3580, 10515, 18629,  \n4981, 4980, 20919,  14194, 18430, 8603,  761, 15264, 15973,  \n15928, 11766, 22109,  27312, 27692, 27513,  27306, 27514, 27109,  \n27695, 27515, 27694,  27307, 27515, 27695,  27307, 27695, 27310,  \n27310, 27695, 27518,  10124, 759, 6843,  27516, 27519, 27308,  \n27106, 27308, 27519,  4677, 22977, 4678,  27106, 27696, 27512,  \n27106, 27519, 27696,  3012, 3011, 9859,  27697, 27522, 27107,  \n9610, 18255, 8749,  10792, 10791, 7504,  27685, 27698, 27309,  \n27309, 27698, 27520,  27692, 27699, 27689,  27313, 27694, 27515,  \n7963, 4974, 7941,  11657, 11192, 18003,  21582, 6790, 1095,  \n27113, 27105, 27310,  11543, 6877, 18069,  27510, 27108, 27899,  \n6251, 9144, 6252,  14313, 9472, 15938,  27520, 27698, 27700,  \n27312, 27520, 27692,  27520, 27700, 27692,  11629, 17766, 21750,  \n27109, 27514, 27521,  27701, 27694, 27313,  27113, 27310, 27518,  \n12759, 13756, 4478,  27315, 27527, 27108,  27527, 27899, 27108,  \n13541, 19374, 3338,  27523, 26388, 27522,  20141, 9815, 17090,  \n25086, 15322, 26929,  27517, 27116, 26902,  6594, 7534, 6078,  \n27521, 27524, 27525,  27525, 27701, 27313,  6734, 7046, 7045,  \n27113, 27702, 27526,  8107, 1928, 389,  21056, 13515, 9853,  \n19527, 11374, 20992,  27524, 27704, 27525,  27525, 27704, 27701,  \n2593, 3057, 21308,  18251, 10956, 9622,  1676, 3011, 5417,  \n26902, 26903, 27517,  26904, 27115, 27528,  27517, 26903, 27529,  \n578, 4689, 19963,  4652, 9319, 4651,  27530, 27529, 27316,  \n5307, 13708, 13190,  21714, 3648, 9896,  20162, 435, 16853,  \n26908, 27532, 27705,  11191, 11241, 15887,  27532, 26910, 27533,  \n16304, 24005, 11205,  10345, 12131, 18088,  355, 4705, 13350,  \n10741, 20964, 2954,  8904, 588, 11674,  12318, 22211, 18513,  \n27320, 26751, 26752,  27120, 27318, 27706,  4381, 10774, 19389,  \n27318, 27534, 27706,  27534, 27707, 27706,  8778, 15050, 2968,  \n11392, 19848, 2736,  2130, 22517, 22149,  27324, 27322, 27708,  \n12431, 15999, 14592,  12260, 16958, 23370,  22557, 15462, 13369,  \n27536, 27535, 27321,  8726, 14608, 3384,  27709, 27707, 27710,  \n15329, 20028, 3268,  27712, 27323, 27324,  27323, 27712, 27537,  \n27323, 27537, 26915,  8739, 4984, 8311,  10385, 3641, 18053,  \n12131, 15609, 18088,  16177, 12040, 23378,  11084, 11085, 3421,  \n19465, 15006, 329,  4138, 15791, 12221,  5078, 5079, 19200,  \n16177, 9228, 12040,  27541, 27536, 27122,  21574, 3166, 2581,  \n2069, 11148, 9090,  26916, 27539, 27540,  9483, 1788, 10952,  \n8744, 15949, 10800,  27540, 27545, 27123,  24723, 23382, 23383,  \n27125, 27546, 27544,  19548, 23282, 7602,  27126, 26918, 27925,  \n16985, 15946, 17343,  27713, 26407, 27327,  26413, 26770, 27333,  \n26407, 27713, 26595,  26766, 26227, 27715,  11188, 11050, 19314,  \n15946, 16048, 17343,  8211, 2465, 15593,  16952, 11980, 14709,  \n2965, 12606, 2511,  26412, 26236, 27328,  23471, 15585, 10217,  \n27333, 27328, 26413,  10592, 14873, 19790,  27717, 27336, 27334,  \n11872, 8961, 6515,  11119, 11118, 11226,  27330, 27716, 27331,  \n6222, 7483, 9922,  7911, 2749, 15380,  5928, 8262, 17627,  \n26919, 26412, 27328,  2043, 1292, 11311,  27718, 27331, 27716,  \n9032, 23849, 1591,  27130, 27332, 27128,  22321, 504, 21089,  \n27129, 27331, 27719,  27719, 27331, 27718,  11462, 3544, 21935,  \n27928, 28313, 27720,  19382, 21021, 18212,  27339, 27337, 27719,  \n10603, 10338, 19771,  5545, 22153, 17129,  1498, 3610, 18055,  \n27548, 27720, 26922,  682, 15358, 16976,  7754, 15827, 17701,  \n8914, 1552, 14496,  27132, 27339, 27549,  26777, 26924, 26604,  \n8643, 2164, 2163,  2185, 2186, 13909,  7581, 15362, 16809,  \n13326, 14669, 14132,  5568, 13883, 19420,  26605, 26776, 27722,  \n11082, 4349, 9353,  27340, 27723, 27341,  27343, 27345, 26242,  \n5754, 7513, 9207,  27725, 27726, 27550,  27550, 27723, 27340,  \n27550, 27726, 27723,  18755, 22509, 22525,  27551, 27725, 27550,  \n12341, 19253, 12340,  20479, 15156, 19180,  18808, 1312, 17443,  \n10393, 12021, 27728,  17976, 14646, 2743,  27551, 27553, 27725,  \n20269, 3254, 23267,  5418, 5456, 5417,  5416, 8718, 14067,  \n27346, 27132, 27342,  27729, 27553, 27350,  27729, 27350, 27351,  \n18201, 2737, 2736,  6641, 12044, 15710,  27556, 27346, 27342,  \n6801, 2665, 3583,  10459, 18073, 18257,  16162, 19327, 16379,  \n18987, 23596, 14737,  6718, 15719, 9010,  27555, 27554, 27352,  \n10532, 10534, 3607,  8210, 20075, 14926,  27556, 27354, 27346,  \n21114, 17525, 9823,  7710, 10082, 7711,  21325, 5406, 11860,  \n27558, 27357, 27354,  27559, 27730, 27355,  27558, 27731, 27357,  \n14219, 14218, 11812,  27732, 27559, 27359,  14435, 5218, 16935,  \n27357, 27731, 27360,  27732, 27359, 27361,  27731, 27560, 27360,  \n1215, 1739, 11986,  27732, 27361, 27733,  7986, 18768, 2950,  \n10618, 10620, 10274,  10253, 3947, 18342,  12465, 9132, 19214,  \n27561, 27362, 27560,  27361, 27363, 27733,  27733, 27363, 27563,  \n27561, 27560, 27734,  27561, 27562, 27735,  12447, 18145, 19381,  \n27561, 27735, 27564,  27561, 27564, 27362,  27563, 27365, 27736,  \n18318, 6620, 19029,  27735, 27737, 27564,  27564, 27737, 27364,  \n27364, 27737, 27565,  27736, 27365, 27565,  6841, 3831, 9627,  \n14747, 9713, 1072,  13541, 13378, 8607,  3482, 7324, 3483,  \n19408, 7895, 18402,  12499, 5497, 2824,  5356, 7322, 11327,  \n18284, 8804, 9581,  26938, 26427, 26428,  21620, 16174, 24134,  \n9570, 9569, 22994,  1007, 11056, 18749,  4023, 10666, 20950,  \n11934, 9897, 17730,  26251, 26941, 27370,  7860, 7283, 20600,  \n10004, 8625, 4602,  13699, 12357, 1186,  7669, 20350, 22454,  \n26947, 26255, 27740,  18916, 15051, 18623,  27740, 26255, 26785,  \n19760, 19848, 17761,  13715, 18379, 19252,  27739, 26942, 26945,  \n7905, 19948, 19711,  11543, 943, 944,  4429, 4519, 7350,  \n7834, 20324, 13674,  908, 18446, 19343,  7767, 11446, 11445,  \n22064, 9999, 9233,  25873, 12564, 8367,  14595, 14189, 15086,  \n6096, 1755, 12258,  27742, 27743, 26614,  5248, 11371, 9505,  \n27741, 26787, 27375,  2323, 7985, 2835,  27743, 26949, 26614,  \n2459, 3391, 3718,  19034, 7492, 14280,  9226, 21981, 1193,  \n10504, 10505, 20060,  5985, 9730, 2687,  17628, 12773, 7667,  \n27162, 26788, 27376,  1032, 1031, 3879,  3123, 3124, 15524,  \n4389, 13001, 13127,  27163, 27744, 27382,  26615, 27163, 27382,  \n9489, 20057, 9490,  27745, 27376, 27566,  22096, 18531, 21726,  \n1709, 10855, 11449,  11972, 5996, 7389,  4961, 11496, 4962,  \n26790, 25950, 26436,  15786, 11633, 1459,  14480, 11802, 18435,  \n4082, 17664, 8400,  21500, 1125, 6427,  4836, 4945, 5211,  \n19812, 20923, 4149,  4797, 4798, 14401,  27748, 27569, 27379,  \n27748, 27379, 27568,  27568, 27381, 27749,  2149, 2766, 3192,  \n27749, 27381, 27378,  16152, 9256, 9255,  27165, 27750, 27378,  \n27165, 27567, 27750,  26436, 25952, 27570,  27747, 27177, 27383,  \n27747, 27383, 27382,  4210, 18801, 20999,  27164, 26263, 27176,  \n21079, 15568, 11066,  10311, 4646, 5515,  13017, 5499, 8368,  \n13784, 19365, 10356,  1342, 1936, 22852,  18365, 22117, 3371,  \n19814, 9141, 20145,  15984, 10087, 17927,  27751, 27380, 27569,  \n14056, 15423, 10197,  27571, 27175, 27177,  13385, 13956, 7045,  \n11305, 22211, 1266,  2169, 19473, 2170,  11439, 11123, 11438,  \n27751, 27384, 27380,  27574, 27175, 27572,  8395, 2633, 8858,  \n13917, 13038, 12720,  22117, 9292, 3371,  20310, 7621, 18986,  \n27179, 27175, 27574,  14370, 17667, 14371,  27573, 27384, 27751,  \n27753, 27754, 27574,  26798, 27574, 27754,  27176, 26618, 27755,  \n21811, 16517, 13358,  27755, 26618, 27575,  7214, 13528, 1567,  \n19446, 21602, 13150,  3976, 5790, 3977,  19976, 17783, 18590,  \n1995, 1360, 2320,  13946, 13346, 13345,  18266, 17150, 14122,  \n19440, 4934, 17455,  9438, 9566, 5069,  3013, 6884, 4546,  \n12305, 12307, 17288,  17427, 1631, 11212,  10465, 10464, 8939,  \n27757, 27388, 27386,  6917, 4374, 4373,  2272, 13165, 2271,  \n14737, 10418, 3078,  27387, 27756, 26617,  653, 21858, 10519,  \n6791, 10837, 16911,  12353, 17920, 19144,  26620, 26449, 27578,  \n4713, 4712, 8637,  21798, 17164, 20851,  8866, 2100, 12439,  \n2794, 21216, 13947,  8912, 11119, 16982,  6697, 23203, 6815,  \n12324, 12859, 10545,  21236, 7888, 21361,  19089, 13393, 5494,  \n27758, 27387, 26619,  27579, 27390, 27181,  26270, 27580, 26803,  \n26620, 27759, 26625,  4855, 5929, 5928,  4260, 13529, 16286,  \n26271, 27758, 26619,  16891, 9219, 10562,  7125, 19047, 16662,  \n4956, 19554, 15341,  4842, 3652, 19904,  7337, 9291, 19632,  \n21143, 6857, 510,  27760, 27391, 26966,  5270, 10355, 2755,  \n5432, 19072, 21992,  27392, 26626, 27391,  26626, 27392, 27393,  \n15290, 19772, 4643,  26454, 26453, 27393,  10809, 7361, 7557,  \n26456, 26454, 27762,  4330, 11184, 4331,  12713, 18373, 13281,  \n10240, 27763, 6925,  22004, 16508, 16288,  10486, 1032, 3267,  \n21390, 27764, 3218,  27765, 26968, 26456,  18501, 4500, 2479,  \n16951, 10795, 10796,  27185, 26968, 27766,  15555, 10835, 8702,  \n17609, 3099, 12770,  26972, 26630, 27767,  26970, 27185, 27766,  \n15794, 10253, 13733,  2298, 4644, 6444,  27187, 26970, 27768,  \n27187, 27768, 27582,  5666, 690, 3794,  17561, 15658, 15659,  \n19098, 3964, 17227,  13883, 13218, 19420,  3929, 19092, 14193,  \n3215, 13344, 3142,  27583, 27395, 26808,  26276, 26972, 27769,  \n27584, 26462, 26466,  20389, 8526, 2739,  4551, 2500, 19050,  \n27584, 26466, 27586,  2470, 13098, 13097,  18664, 10727, 20990,  \n16918, 10594, 13898,  16618, 12548, 2195,  17174, 522, 15027,  \n23334, 5306, 13190,  19032, 11245, 3994,  7418, 9957, 7419,  \n27588, 27587, 26635,  14937, 2758, 22102,  7126, 17814, 7388,  \n6122, 12442, 6123,  7664, 8254, 17236,  27192, 27589, 27193,  \n5657, 16544, 6747,  29037, 20521, 3427,  27771, 26976, 27772,  \n27398, 27193, 27770,  26978, 25981, 27195,  27194, 26472, 27773,  \n10730, 9747, 9748,  20867, 21542, 20372,  14816, 474, 22635,  \n21278, 19363, 18067,  7906, 5318, 11645,  1127, 1126, 15993,  \n20157, 23901, 20217,  17038, 8755, 10261,  25475, 13933, 4135,  \n16319, 6771, 2062,  12016, 4602, 6780,  8970, 8969, 15343,  \n11278, 22353, 24041,  27198, 27774, 26130,  10995, 14566, 9459,  \n1198, 7691, 14357,  26127, 26978, 26983,  11991, 12661, 13175,  \n26982, 26474, 27198,  17467, 21641, 21640,  8512, 5105, 16284,  \n17463, 19746, 6988,  8183, 4624, 15542,  3399, 15296, 15297,  \n3724, 3726, 17270,  18541, 18540, 16181,  20126, 9411, 11679,  \n6826, 6827, 11672,  13450, 4066, 14596,  12923, 19501, 3233,  \n11899, 14858, 14857,  15490, 7401, 10132,  9537, 9536, 6438,  \n19055, 16094, 14920,  27778, 26476, 26813,  14482, 12026, 21637,  \n26132, 25827, 27202,  27779, 26814, 27593,  27594, 26813, 27780,  \n2163, 8977, 22159,  7361, 10809, 17459,  3332, 10237, 10238,  \n11697, 5784, 5783,  16615, 5946, 18672,  18719, 12910, 13975,  \n9961, 1702, 10449,  1608, 15544, 5400,  8494, 2457, 14598,  \n5077, 9930, 17025,  27206, 27780, 26479,  4029, 12681, 6793,  \n13464, 21016, 3324,  3890, 5277, 3596,  16786, 10287, 16261,  \n938, 2989, 21160,  4239, 2060, 8731,  10428, 1168, 3173,  \n13417, 14841, 1003,  15674, 3003, 12622,  5747, 1670, 10219,  \n10219, 1670, 1669,  601, 2997, 5279,  7449, 18043, 10906,  \n13736, 2978, 10804,  3201, 20194, 10414,  18783, 16422, 16421,  \n9143, 10735, 22230,  6983, 17834, 7665,  6720, 15209, 6721,  \n27403, 25703, 26991,  11478, 7845, 11479,  4267, 1485, 7530,  \n11128, 9168, 18813,  27404, 27783, 27597,  15622, 2293, 2292,  \n27598, 26993, 26286,  21160, 2989, 505,  28802, 26993, 27598,  \n27402, 26994, 27785,  19704, 6474, 23974,  1512, 1651, 15894,  \n13725, 3313, 14405,  8174, 21456, 12940,  3549, 3548, 8276,  \n18119, 4152, 19386,  14199, 770, 9626,  7551, 18612, 22908,  \n27786, 27404, 27406,  27787, 26994, 27788,  25992, 25990, 26996,  \n27600, 26484, 26824,  16197, 11785, 4736,  27409, 27407, 27789,  \n25993, 26485, 27603,  3850, 11557, 5593,  5843, 15347, 12196,  \n421, 420, 13817,  27790, 27408, 27411,  4336, 7625, 8404,  \n12876, 10799, 10798,  27791, 27790, 27411,  6749, 16364, 6750,  \n25992, 27601, 26140,  4867, 22359, 20350,  17767, 22634, 16376,  \n20104, 16972, 14649,  27792, 27599, 26289,  26198, 27794, 1051,  \n16292, 14499, 6530,  27604, 26140, 27601,  11306, 15095, 8329,  \n19021, 18960, 10418,  2511, 18121, 12967,  19634, 10412, 13949,  \n27796, 26486, 27006,  4561, 10444, 13443,  20930, 16484, 17436,  \n5283, 11771, 5284,  2374, 3119, 2375,  12855, 3351, 18426,  \n27417, 27418, 27797,  13773, 4943, 13774,  4954, 4955, 13317,  \n20206, 7287, 7286,  1436, 6872, 6873,  7569, 9769, 7570,  \n518, 15680, 15305,  27798, 27797, 27418,  7874, 13895, 16358,  \n27422, 27798, 27418,  18164, 1273, 21217,  2435, 17417, 21373,  \n3360, 13442, 10664,  9648, 13238, 16812,  27422, 27418, 27231,  \n7281, 2474, 6584,  27419, 27415, 27605,  26142, 26291, 26487,  \n4733, 18490, 9885,  11724, 14772, 11723,  11065, 2667, 2208,  \n27609, 27416, 25995,  16254, 10291, 16398,  27985, 26834, 27424,  \n26829, 26652, 27607,  1253, 6516, 10630,  591, 4769, 1672,  \n1662, 17517, 9782,  12700, 2567, 4045,  7396, 620, 5668,  \n27800, 27607, 26652,  4429, 2187, 8556,  20989, 9710, 10930,  \n18578, 4594, 13800,  20438, 21542, 17537,  27606, 27801, 27423,  \n27802, 27425, 27232,  21542, 20438, 20372,  7349, 16132, 8078,  \n12034, 3682, 12035,  27800, 26652, 27234,  27802, 27232, 27235,  \n22299, 18284, 840,  12533, 15872, 2177,  7575, 20239, 3939,  \n27017, 27423, 27801,  7319, 9467, 7317,  27016, 27426, 27429,  \n27428, 27017, 27801,  16869, 20607, 7234,  26297, 27016, 27429,  \n2881, 17419, 7222,  12417, 10709, 18278,  26293, 27803, 25838,  \n10831, 9786, 10830,  11814, 15830, 11813,  2528, 16109, 18200,  \n25838, 27803, 27431,  8043, 2770, 2769,  1547, 1548, 20752,  \n27237, 27613, 26661,  15235, 19422, 15233,  13351, 12839, 21559,  \n26297, 27429, 27804,  6261, 5459, 2111,  26296, 26298, 26836,  \n5582, 2456, 318,  27430, 27428, 27993,  10620, 10619, 12210,  \n27805, 27238, 27993,  16300, 29644, 3664,  27615, 27806, 27237,  \n5493, 18478, 5492,  16383, 14690, 7017,  15881, 11606, 10427,  \n16231, 3535, 15045,  5557, 2897, 18582,  6021, 9176, 11950,  \n24013, 10939, 17826,  27994, 26298, 27614,  14587, 1577, 17874,  \n27019, 25596, 27022,  27615, 27237, 27023,  8485, 17210, 12015,  \n27433, 27434, 26301,  27022, 25596, 27021,  5589, 20894, 11408,  \n27432, 26662, 25714,  27617, 27615, 27023,  27614, 26304, 27616,  \n1193, 18841, 9358,  1370, 11824, 8775,  26840, 27617, 27023,  \n13447, 15207, 8836,  8031, 20965, 8032,  9843, 9170, 9842,  \n19408, 14457, 14287,  27020, 27238, 27809,  27618, 26305, 27434,  \n3522, 11138, 8542,  27810, 27811, 27812,  18887, 2746, 14595,  \n16045, 13841, 12272,  27812, 26839, 27813,  745, 15657, 7912,  \n24100, 1175, 8194,  12425, 4051, 11635,  10817, 16930, 5763,  \n17542, 9841, 21832,  25600, 27436, 27619,  18917, 1746, 12731,  \n17404, 11709, 17405,  9776, 561, 2815,  22914, 16871, 4133,  \n23046, 12054, 20479,  27817, 26501, 27619,  9471, 8332, 2990,  \n5192, 3210, 10466,  10906, 14919, 16856,  15184, 22270, 5445,  \n20962, 6137, 6744,  26008, 26842, 27816,  27818, 26667, 27819,  \n27027, 27029, 27820,  21065, 8244, 8245,  16228, 1666, 8739,  \n26014, 27820, 27029,  27822, 26008, 27816,  3621, 21643, 21642,  \n832, 15208, 833,  26014, 26507, 27820,  9155, 19817, 9154,  \n26154, 26311, 27030,  15284, 6759, 10662,  27240, 27620, 27821,  \n27822, 26671, 26008,  11987, 6158, 5085,  26506, 27032, 27030,  \n15910, 3878, 19947,  7062, 18963, 7061,  26314, 26670, 27242,  \n27241, 26313, 26315,  26314, 27242, 27439,  7935, 6956, 14944,  \n3387, 8954, 13251,  26669, 27240, 27442,  27823, 27440, 27034,  \n3323, 19847, 3324,  8535, 9772, 18783,  9704, 11317, 12126,  \n13494, 1081, 4335,  12217, 14250, 8056,  27626, 27243, 27624,  \n13709, 4488, 13609,  27624, 27245, 27825,  12135, 12134, 6927,  \n27825, 27245, 27625,  2141, 7382, 11853,  9786, 18356, 21286,  \n463, 8241, 748,  27443, 27034, 26674,  28215, 27443, 27244,  \n27626, 28215, 27244,  13685, 15012, 14810,  4231, 14493, 4230,  \n11384, 5094, 2399,  7321, 12853, 12855,  26846, 27826, 27033,  \n21225, 19800, 9754,  27247, 28013, 27448,  26846, 27445, 27826,  \n15268, 6174, 10942,  10993, 19314, 13020,  27444, 27246, 27827,  \n27446, 27827, 27246,  2870, 15200, 2392,  19315, 4710, 11736,  \n5596, 463, 2493,  3179, 10386, 18943,  12583, 9878, 5727,  \n15493, 1473, 3460,  27448, 27828, 27630,  16864, 8430, 6228,  \n27827, 27446, 27447,  10247, 17466, 3363,  23537, 3298, 12203,  \n15693, 11614, 11022,  27248, 27829, 27445,  3817, 3816, 11659,  \n10254, 5340, 21968,  27830, 27449, 27450,  27250, 26848, 27628,  \n19228, 6937, 16655,  27452, 27448, 27630,  27451, 27830, 27450,  \n14298, 3013, 4546,  27831, 27452, 27630,  27248, 27454, 27829,  \n17360, 15281, 13695,  12700, 6047, 21285,  27451, 27632, 27830,  \n27831, 27832, 27452,  2138, 11284, 7888,  27833, 27829, 27454,  \n19018, 19287, 1854,  27453, 27452, 27832,  7539, 12848, 14198,  \n5138, 14073, 3327,  1021, 2014, 13604,  27633, 27453, 27832,  \n27632, 27456, 27457,  5476, 5867, 3175,  10046, 16738, 19316,  \n6789, 14951, 15364,  27834, 27835, 27457,  12094, 7780, 8785,  \n12917, 6245, 18790,  13498, 22520, 5026,  7383, 16637, 23748,  \n12846, 19097, 5228,  1554, 1553, 1054,  11695, 7130, 3611,  \n10554, 540, 8981,  27454, 27637, 27833,  7355, 13117, 9536,  \n2858, 19227, 2403,  27457, 27636, 27834,  12341, 5872, 12844,  \n13616, 14758, 13617,  20493, 13717, 19412,  16599, 23222, 14992,  \n10340, 6249, 19686,  17059, 18071, 1442,  17522, 632, 9792,  \n4283, 6787, 6786,  14755, 512, 3306,  12514, 21211, 12288,  \n9588, 17397, 4757,  27257, 27640, 27838,  3183, 23549, 1503,  \n5251, 5252, 3233,  20800, 5735, 5736,  27642, 27638, 27461,  \n17146, 1608, 5401,  23511, 7163, 15648,  7655, 19621, 8258,  \n27643, 27839, 27465,  19524, 7515, 2895,  17468, 12813, 5222,  \n10604, 1202, 1232,  26853, 27645, 27467,  27645, 26853, 26854,  \n3328, 3327, 14073,  12568, 20418, 20419,  27645, 26854, 27646,  \n15334, 19542, 8932,  27840, 27841, 27253,  27471, 27645, 27649,  \n4637, 10337, 4638,  11757, 12860, 7299,  5771, 17914, 14210,  \n1245, 9979, 2099,  12397, 13499, 22606,  2100, 2101, 12439,  \n17643, 2308, 2309,  27054, 27840, 27253,  6462, 6463, 6439,  \n27259, 27258, 27474,  27647, 27839, 27643,  27642, 27472, 27651,  \n22225, 5276, 16820,  16144, 15260, 7432,  2333, 13411, 2332,  \n11885, 11839, 11886,  15296, 10205, 10206,  12930, 4522, 4523,  \n17983, 3881, 20295,  27050, 27051, 27843,  15567, 12020, 22437,  \n13125, 804, 803,  7108, 1153, 1152,  20453, 1648, 20150,  \n14918, 15911, 3386,  8125, 18510, 8126,  7926, 3909, 5019,  \n27055, 26861, 27845,  465, 22054, 19250,  23720, 22101, 20087,  \n16365, 20627, 706,  26696, 27470, 27847,  5685, 15354, 16096,  \n11998, 14417, 11767,  27260, 27848, 26860,  12048, 13139, 4467,  \n6826, 818, 6827,  27846, 27652, 27468,  27653, 27470, 27652,  \n27470, 27463, 27652,  20007, 2083, 894,  22714, 26070, 21895,  \n6271, 10656, 12959,  22591, 18691, 14654,  17558, 16903, 17559,  \n10912, 11673, 1565,  5619, 14641, 18908,  2723, 6619, 10080,  \n19013, 9018, 13744,  2250, 4725, 13465,  14433, 14435, 16935,  \n22790, 19594, 7203,  7381, 11590, 9440,  19184, 18632, 2263,  \n314, 3537, 19040,  27655, 27262, 27849,  27262, 26860, 27849,  \n18001, 13070, 8579,  3221, 10005, 15253,  2724, 12957, 2725,  \n22735, 17490, 16053,  10788, 10789, 3088,  5232, 15795, 14545,  \n27057, 27856, 27063,  13506, 21181, 6995,  27062, 27851, 27264,  \n27851, 27062, 27266,  3264, 3045, 3265,  2756, 14543, 10259,  \n8989, 17164, 22728,  15568, 16321, 16320,  11901, 1374, 2055,  \n27475, 27852, 27266,  27477, 27265, 27065,  27269, 27854, 27476,  \n27854, 27269, 27855,  6802, 9469, 1041,  27268, 27267, 27850,  \n3197, 11717, 4949,  15433, 16475, 22924,  27271, 27855, 27269,  \n3327, 20402, 1457,  1788, 2852, 10952,  13955, 4132, 10699,  \n3632, 1962, 18041,  27273, 27656, 27270,  27480, 26869, 27858,  \n3375, 14305, 670,  7104, 17545, 14377,  20001, 753, 16357,  \n26533, 26869, 27480,  11736, 21232, 20389,  26350, 26532, 27275,  \n5990, 6793, 12681,  26874, 27480, 27860,  13731, 10634, 23387,  \n12808, 5837, 4719,  965, 10720, 23357,  4172, 849, 22317,  \n26874, 27860, 27277,  27861, 27277, 27860,  27268, 27657, 27658,  \n2892, 13237, 22398,  27658, 27276, 27268,  27277, 27861, 26875,  \n3696, 16604, 13550,  27862, 26705, 26709,  17888, 7630, 16083,  \n27479, 27478, 27663,  7810, 19284, 15405,  18215, 18214, 17250,  \n27662, 27862, 26709,  4614, 9949, 16378,  13819, 10094, 12431,  \n384, 12308, 9717,  27278, 27661, 27487,  17306, 10736, 14459,  \n27662, 26709, 27073,  8968, 2436, 17072,  27658, 27664, 27276,  \n27478, 27660, 27663,  13029, 16747, 3613,  3664, 20112, 4675,  \n27658, 27863, 27664,  10811, 19265, 21381,  14466, 12145, 16297,  \n27484, 26707, 27486,  770, 14199, 14923,  27863, 27864, 27664,  \n27664, 27864, 27665,  11191, 615, 616,  13349, 13348, 14124,  \n9099, 20481, 13803,  27865, 27665, 27864,  27865, 27660, 27665,  \n27866, 27660, 27865,  27866, 27663, 27660,  27866, 27280, 27663,  \n27485, 26877, 27667,  27486, 27485, 27867,  27489, 26357, 27487,  \n17129, 8767, 9540,  27492, 27662, 27078,  27491, 27280, 27866,  \n3137, 3139, 21016,  27491, 27866, 27868,  17852, 15521, 6949,  \n15262, 590, 591,  6291, 3598, 16928,  981, 11621, 982,  \n8889, 10164, 9922,  21151, 2996, 969,  26877, 27284, 27667,  \n27667, 27284, 27668,  27084, 27488, 27869,  27084, 26041, 27488,  \n27491, 27868, 27494,  9454, 15930, 23348,  27494, 27868, 27669,  \n2660, 15379, 11122,  10024, 3813, 5094,  5631, 11570, 7105,  \n27666, 27671, 27870,  27668, 27493, 27871,  12481, 1684, 12480,  \n10895, 22270, 22443,  11422, 15717, 15825,  27495, 27081, 27872,  \n27871, 27493, 27496,  14223, 14850, 15254,  3788, 1345, 3789,  \n7360, 12475, 12476,  27285, 27870, 27671,  27872, 27289, 27495,  \n27499, 27676, 26723,  7192, 7193, 8342,  27885, 27288, 27287,  \n27885, 27875, 27288,  3221, 17398, 21832,  27494, 27669, 27673,  \n27669, 27876, 27673,  10001, 5981, 9740,  27877, 27285, 27498,  \n27870, 27285, 27877,  27496, 27082, 27674,  27677, 27291, 27676,  \n23100, 22496, 23101,  9236, 10664, 9237,  13048, 17626, 562,  \n12115, 14313, 5857,  27880, 27673, 27876,  12742, 10114, 12685,  \n27673, 27877, 27498,  27673, 27880, 27877,  27289, 27872, 27881,  \n27674, 27878, 27496,  27501, 27677, 27882,  12949, 12950, 10680,  \n975, 2473, 8262,  8108, 14480, 14708,  10020, 18932, 4451,  \n14220, 13628, 1277,  27497, 27883, 27674,  13754, 18187, 13755,  \n27293, 27287, 26552,  20634, 17478, 3326,  12570, 9726, 2385,  \n27884, 27091, 25895,  27290, 27678, 27497,  10901, 16958, 12260,  \n1480, 1481, 8598,  27886, 27289, 27881,  27289, 27886, 27502,  \n23083, 4310, 5435,  1524, 4262, 17360,  14844, 16824, 20566,  \n18466, 1384, 21735,  2048, 5570, 18360,  5833, 17952, 14791,  \n7106, 11513, 11514,  7653, 2219, 2220,  27509, 26737, 27095,  \n14078, 2456, 6190,  1678, 17756, 5294,  27887, 27888, 27886,  \n27888, 27504, 27502,  27888, 27502, 27886,  4490, 18115, 6045,  \n27681, 27680, 27503,  27889, 27505, 27680,  13582, 9817, 6771,  \n27889, 27890, 27505,  27505, 27890, 27682,  8145, 15350, 1738,  \n12634, 17333, 9058,  19385, 12338, 7557,  27888, 27891, 27504,  \n27504, 27891, 27681,  6440, 15189, 6564,  12725, 13631, 1764,  \n27893, 27684, 27507,  14035, 2414, 2934,  7054, 10159, 5245,  \n10105, 6687, 6629,  27302, 27894, 27296,  27296, 27894, 27683,  \n6391, 19949, 6392,  27507, 27508, 27893,  8603, 9687, 7105,  \n27894, 27302, 27687,  15217, 12477, 5724,  21690, 18093, 7231,  \n27682, 27890, 27685,  17961, 14674, 12536,  7811, 7783, 22466,  \n14513, 2488, 17064,  7883, 23379, 7884,  17169, 11627, 19045,  \n4460, 10563, 10564,  27301, 27682, 27685,  7747, 5642, 8144,  \n27689, 27897, 27690,  27689, 27693, 27897,  27690, 27897, 27898,  \n19479, 19478, 18926,  27899, 26892, 27510,  27899, 27686, 26892,  \n26892, 27686, 27305,  27516, 27305, 27686,  27691, 27687, 27512,  \n13688, 10407, 17927,  1548, 1547, 20644,  15457, 18286, 9178,  \n27896, 27097, 27517,  304, 7672, 8972,  27693, 27689, 27699,  \n592, 15768, 19451,  27898, 27514, 27690,  16526, 10732, 21150,  \n27902, 27695, 27694,  27695, 27902, 27518,  10729, 20652, 18994,  \n4856, 5928, 16057,  27512, 27696, 27691,  2039, 797, 10724,  \n3419, 967, 8698,  17239, 18681, 11909,  7014, 2226, 17115,  \n15953, 17527, 9302,  27692, 27689, 27513,  27514, 27898, 27906,  \n27421, 26177, 19379,  27902, 27694, 27907,  11543, 9594, 19041,  \n1017, 1712, 1018,  16367, 2951, 18768,  12158, 9060, 9061,  \n27908, 27696, 27519,  719, 17066, 19235,  6594, 5510, 3414,  \n8743, 358, 16291,  19418, 20579, 4618,  27701, 27907, 27694,  \n27909, 27907, 27701,  27702, 27113, 27518,  27904, 27899, 27527,  \n27521, 27514, 27524,  3892, 11863, 16480,  27528, 27115, 27523,  \n27704, 27909, 27701,  27703, 27526, 27702,  27526, 27910, 27527,  \n6756, 6757, 18449,  14389, 5746, 8800,  27528, 27911, 26904,  \n27913, 26904, 27911,  1190, 9778, 13323,  26904, 27913, 26746,  \n27912, 27529, 27530,  27914, 26746, 27913,  26746, 27914, 26907,  \n2001, 14029, 8315,  16037, 21154, 8595,  26907, 27914, 27915,  \n913, 23997, 19409,  25015, 7446, 5274,  27915, 27531, 26907,  \n26908, 27705, 27317,  26907, 27531, 26579,  12216, 14866, 20356,  \n14782, 14781, 2897,  4544, 1106, 12625,  27916, 27120, 27706,  \n6281, 8331, 8928,  27320, 27917, 27121,  14650, 2363, 1792,  \n27322, 27121, 27708,  27121, 27917, 27708,  13626, 21289, 14411,  \n928, 930, 21201,  27711, 27324, 27918,  13845, 5934, 5933,  \n4913, 4914, 9623,  10197, 8403, 3776,  21312, 11918, 21790,  \n27324, 27711, 27712,  27536, 27541, 27535,  26299, 25581, 11306,  \n27919, 27537, 27712,  27920, 27325, 27537,  5500, 11098, 3325,  \n13639, 8357, 4527,  3948, 13015, 3968,  15866, 6774, 2087,  \n1947, 1946, 6048,  27538, 26758, 27325,  16473, 12721, 20693,  \n7220, 12484, 2487,  1320, 11790, 8217,  11462, 9128, 9127,  \n13730, 12837, 13731,  27922, 27326, 27538,  27539, 27326, 27922,  \n12750, 5802, 1551,  8602, 1127, 10015,  12429, 6495, 6496,  \n2392, 5062, 2393,  27923, 27540, 27539,  27540, 27923, 27545,  \n27543, 27921, 27542,  27921, 27543, 27544,  9664, 13130, 13131,  \n18868, 14595, 2747,  11463, 11462, 21264,  27925, 27546, 27126,  \n22572, 4932, 1900,  26918, 26919, 27925,  1638, 8649, 8143,  \n27714, 27547, 26595,  16473, 19687, 14300,  22600, 22599, 4027,  \n11562, 16966, 11500,  4231, 4230, 17954,  26596, 28116, 27715,  \n27715, 26227, 26596,  5082, 23408, 21547,  13575, 17063, 7865,  \n27333, 27127, 26919,  12733, 19790, 14873,  11693, 11692, 11781,  \n3347, 3346, 2889,  18157, 18839, 21081,  27330, 26081, 27329,  \n27335, 27334, 27332,  5582, 318, 317,  2366, 9344, 14604,  \n1133, 2882, 8804,  5040, 17775, 5920,  3884, 1069, 871,  \n9269, 14179, 13015,  5696, 6479, 6484,  14327, 14326, 15437,  \n15302, 9877, 21343,  27337, 27129, 27719,  4091, 391, 15589,  \n10256, 12927, 10257,  19820, 13596, 9531,  27338, 26921, 27720,  \n1933, 19266, 4885,  27339, 27719, 27721,  16572, 4091, 14473,  \n2631, 3852, 3853,  26924, 27928, 27548,  8906, 9284, 7379,  \n4657, 8612, 8611,  27928, 26924, 26777,  14374, 16726, 17590,  \n2736, 2059, 18877,  27549, 27339, 27721,  7766, 2164, 8643,  \n27930, 26777, 26418,  18813, 19312, 11128,  12235, 1284, 11291,  \n27342, 27132, 27549,  27135, 27931, 26418,  2270, 6375, 21696,  \n26776, 27341, 27722,  6824, 21365, 4434,  20595, 5249, 7991,  \n3494, 22881, 1125,  27723, 27726, 27933,  16945, 5369, 8642,  \n16761, 2555, 21317,  19356, 12905, 12627,  2062, 13581, 16319,  \n14238, 10195, 10785,  27140, 27727, 27934,  27140, 27934, 27348,  \n14579, 427, 426,  27139, 27931, 27135,  23617, 22491, 6366,  \n7746, 17502, 12594,  1426, 1172, 5479,  4538, 8390, 10301,  \n8606, 12321, 14393,  22491, 8844, 6366,  804, 16637, 7383,  \n13625, 2326, 8705,  9712, 15181, 11139,  16475, 23566, 13428,  \n27554, 27729, 27351,  20953, 1074, 20638,  13179, 19714, 20623,  \n27342, 27935, 27556,  24110, 22813, 20995,  27555, 27352, 27557,  \n28321, 27556, 27935,  24110, 20995, 2238,  11734, 20610, 2245,  \n27557, 27937, 27936,  13422, 14319, 13359,  27937, 27557, 27356,  \n27354, 27556, 27558,  4548, 9564, 11946,  1590, 11426, 9032,  \n5273, 21169, 11861,  9964, 19441, 9883,  17568, 8197, 13216,  \n11301, 7774, 6574,  27730, 27938, 27937,  5890, 8489, 8854,  \n8027, 6074, 20992,  27730, 27559, 27732,  27939, 27734, 27560,  \n27939, 27560, 27731,  27561, 27734, 27562,  4793, 8401, 3141,  \n20911, 20452, 11548,  27737, 27940, 27565,  27565, 27940, 27736,  \n3426, 1887, 26958,  27366, 27155, 27738,  22745, 718, 19158,  \n17659, 17660, 19934,  3676, 16512, 16513,  6572, 7774, 22133,  \n14970, 20826, 16119,  13395, 13394, 13046,  27943, 27368, 26939,  \n15746, 1528, 16254,  7132, 16622, 16621,  7303, 9933, 19262,  \n6047, 12700, 4045,  10365, 18083, 11894,  14912, 18424, 22248,  \n15649, 6852, 3631,  14492, 27946, 18992,  26610, 25088, 25090,  \n19774, 11279, 24041,  5272, 17407, 18028,  26941, 27947, 27370,  \n11075, 13801, 4319,  2556, 2799, 5150,  27368, 26609, 26939,  \n26939, 27366, 27738,  26939, 27738, 27943,  13650, 21207, 6499,  \n4177, 13378, 4590,  27159, 26429, 27371,  1748, 4806, 19605,  \n21391, 2824, 2825,  12935, 19829, 16174,  17151, 17152, 22162,  \n18990, 26498, 8329,  27371, 26612, 27373,  15465, 8694, 12518,  \n27739, 26265, 26942,  13291, 16624, 3069,  27948, 27740, 26785,  \n22531, 9489, 23437,  10868, 10869, 10783,  26612, 26946, 27373,  \n4016, 8526, 2387,  8443, 12154, 4,  14113, 5640, 14112,  \n7560, 7559, 14239,  11450, 11451, 16629,  17579, 8688, 13835,  \n4715, 20136, 5010,  12047, 14465, 15548,  2738, 19921, 11681,  \n16058, 16059, 12437,  21192, 3936, 6175,  12979, 12980, 15897,  \n12916, 19527, 17418,  13217, 6998, 2404,  27743, 27163, 26949,  \n5753, 9828, 3336,  6137, 9760, 6744,  14632, 10979, 7910,  \n8058, 21576, 13276,  511, 23346, 5181,  11515, 12917, 18790,  \n6705, 6706, 16922,  26950, 27164, 27375,  7068, 7482, 7723,  \n24724, 23284, 7697,  8057, 19278, 4876,  12635, 6020, 14891,  \n10356, 19365, 19218,  12297, 14790, 18276,  10222, 7766, 1748,  \n27744, 27747, 27382,  2251, 2839, 12636,  27745, 27566, 27170,  \n19579, 20674, 7781,  27953, 27748, 27568,  27567, 25948, 26790,  \n27571, 27177, 27955,  22634, 14480, 18435,  27955, 27177, 27747,  \n20877, 3580, 3581,  5672, 5671, 16579,  11229, 17531, 9748,  \n5496, 5495, 20177,  11215, 7479, 11216,  27569, 27954, 27956,  \n27748, 27954, 27569,  5175, 6273, 17870,  18585, 5479, 1172,  \n27957, 27749, 27750,  5711, 491, 10444,  6327, 19398, 822,  \n22869, 12943, 9276,  1869, 20615, 21663,  8742, 14979, 4090,  \n15616, 19826, 15887,  18194, 16589, 636,  27958, 27170, 26796,  \n17039, 12988, 16125,  24391, 1557, 6531,  19427, 7507, 19075,  \n27956, 27960, 27569,  27570, 25952, 26954,  4239, 14312, 11618,  \n6111, 9395, 15045,  3076, 15471, 22728,  16225, 10007, 20902,  \n10309, 22887, 13652,  12520, 12519, 16476,  27960, 27751, 27569,  \n15801, 12495, 19620,  20652, 10177, 6267,  10690, 10674, 20843,  \n13745, 15029, 8198,  13752, 19264, 12847,  26955, 26440, 27756,  \n26264, 26442, 27173,  26442, 28157, 27173,  3086, 3372, 11129,  \n27573, 27751, 27961,  6005, 16747, 2518,  7696, 17057, 7697,  \n1465, 13180, 6306,  18306, 1694, 1693,  5547, 17221, 19289,  \n27573, 27961, 27386,  3306, 4069, 4070,  23149, 7589, 13477,  \n8407, 5662, 5661,  27578, 26449, 27576,  885, 12238, 10403,  \n14737, 12870, 22495,  14409, 4984, 4792,  8849, 8489, 8488,  \n11136, 6059, 4291,  27388, 27579, 27181,  14050, 2420, 2779,  \n2129, 22149, 2956,  5488, 4307, 4306,  4059, 1774, 10702,  \n3544, 18660, 7397,  27389, 26625, 27759,  17492, 15125, 17494,  \n21568, 12993, 16005,  16640, 8873, 3100,  27760, 26966, 27182,  \n10854, 22340, 22540,  26454, 27393, 27965,  13742, 3027, 13666,  \n4406, 14154, 17295,  20724, 8415, 8414,  4080, 20915, 8219,  \n23905, 7315, 21418,  27394, 26969, 27966,  11824, 6782, 16809,  \n27941, 18525, 3426,  27764, 21390, 24029,  1530, 18951, 732,  \n27766, 27768, 26970,  26460, 27968, 27581,  22599, 18752, 332,  \n9129, 16128, 9876,  16078, 4504, 7072,  26630, 27761, 27767,  \n9335, 10467, 20200,  1847, 411, 2120,  26973, 27968, 26460,  \n22384, 1553, 6557,  20368, 684, 16979,  26972, 27767, 27769,  \n19934, 15677, 17659,  27186, 26463, 27585,  18817, 17809, 906,  \n12876, 10746, 20384,  12628, 3681, 16069,  3590, 13805, 13702,  \n20242, 18911, 15496,  5050, 8132, 18076,  20096, 2991, 7057,  \n27585, 26463, 26278,  27969, 27397, 27395,  8592, 12362, 8742,  \n23148, 16372, 19643,  8647, 659, 2614,  3849, 4199, 10946,  \n1573, 16368, 17552,  27193, 27589, 27770,  27588, 26976, 27771,  \n26470, 26979, 27772,  9578, 20668, 7588,  10364, 18083, 10365,  \n11276, 10723, 11275,  4199, 8264, 3429,  22862, 7279, 1249,  \n11285, 18835, 7041,  9376, 17854, 8003,  2639, 9502, 18553,  \n19787, 10190, 7652,  2154, 2153, 20328,  19473, 837, 2170,  \n13196, 20283, 19520,  9423, 3433, 3379,  6711, 9654, 13368,  \n8024, 12490, 19184,  22402, 13659, 10203,  13734, 18108, 13735,  \n1767, 1766, 2107,  12701, 21620, 23695,  27971, 26473, 26130,  \n14479, 16229, 8436,  28172, 27196, 27592,  27592, 27196, 26636,  \n27775, 27197, 27591,  545, 11017, 543,  27199, 27197, 27775,  \n20191, 11599, 12188,  9859, 3011, 1676,  26638, 25697, 26814,  \n16177, 23378, 14026,  14385, 15159, 4997,  26987, 26986, 27777,  \n4660, 21388, 21387,  3579, 17411, 15884,  13839, 5922, 8651,  \n26813, 27594, 27778,  19362, 15457, 5251,  26986, 26476, 27778,  \n27974, 26986, 27778,  27595, 26477, 27201,  27204, 27200, 27975,  \n27595, 27781, 26478,  1779, 5955, 4358,  3612, 15548, 15547,  \n27976, 27780, 27206,  27207, 26478, 27781,  24391, 17776, 7599,  \n7444, 14161, 11750,  18498, 21228, 21099,  18972, 16533, 3447,  \n15132, 9860, 4538,  5143, 5144, 1065,  27781, 27977, 27207,  \n14497, 19583, 14498,  9798, 12458, 19372,  9861, 16615, 363,  \n27207, 27977, 27978,  17240, 4086, 4472,  16956, 12530, 19890,  \n20376, 13758, 16734,  19682, 20544, 6880,  1344, 6354, 1671,  \n16675, 12455, 19445,  27207, 27978, 27403,  15067, 21118, 16821,  \n10217, 15585, 10406,  9568, 14025, 18015,  26990, 26816, 27597,  \n21912, 26143, 19466,  27401, 27596, 27980,  26134, 26815, 27405,  \n2462, 2461, 12062,  21169, 6365, 11861,  4490, 2448, 4489,  \n17867, 14976, 5499,  16394, 19127, 14015,  27783, 27404, 27786,  \n10698, 20638, 4894,  7243, 419, 16706,  5189, 12391, 24360,  \n11087, 4812, 4811,  13748, 17412, 10490,  2863, 19838, 18604,  \n26994, 25993, 27788,  15576, 5989, 14133,  13143, 4313, 17642,  \n27406, 27408, 27786,  2616, 8846, 667,  27601, 25992, 26996,  \n25149, 27982, 25148,  7944, 6898, 7943,  27792, 26289, 26486,  \n11796, 11797, 14885,  22318, 20399, 20398,  11007, 14331, 2266,  \n15068, 7284, 15069,  12172, 6929, 12173,  11595, 20938, 18227,  \n25122, 24686, 25462,  17874, 4104, 13412,  2255, 19848, 19760,  \n2179, 12715, 5914,  27793, 27002, 27600,  21651, 3635, 6968,  \n5231, 4387, 15600,  26486, 27796, 27792,  18096, 8006, 6120,  \n27413, 27409, 27795,  1069, 2985, 1061,  27791, 27412, 27417,  \n5617, 3286, 4267,  8124, 11244, 11243,  27409, 27602, 27795,  \n13645, 5365, 16308,  6807, 16163, 2667,  17074, 12070, 17075,  \n1678, 5294, 977,  4782, 13041, 11784,  27605, 27413, 27795,  \n4612, 4613, 799,  3489, 20206, 7286,  20172, 21398, 7996,  \n27002, 27793, 26290,  27416, 26485, 25995,  6850, 9698, 4936,  \n16102, 18009, 7518,  7389, 2992, 12750,  3800, 17432, 12622,  \n12369, 20854, 1799,  10796, 1192, 1191,  18108, 13272, 13735,  \n8184, 9902, 13646,  27985, 27798, 27422,  18997, 16877, 20611,  \n17809, 1364, 6441,  12509, 22034, 5039,  2891, 13237, 2892,  \n7309, 1180, 13424,  8418, 8419, 12704,  10587, 2826, 13290,  \n1592, 5483, 22226,  25996, 26828, 27420,  6074, 8026, 6075,  \n1204, 1111, 17896,  27605, 27987, 27606,  6420, 2514, 1757,  \n27985, 27422, 26834,  7823, 25557, 19850,  19079, 8409, 13003,  \n27985, 27424, 27988,  16311, 18690, 16310,  27608, 27607, 27989,  \n27988, 27424, 27425,  11276, 27990, 10723,  27425, 27802, 27988,  \n1209, 2771, 17622,  4867, 13889, 16487,  16256, 13810, 14167,  \n11869, 9682, 14207,  10207, 14229, 17663,  12691, 11475, 12690,  \n13331, 9665, 5233,  9836, 9838, 19189,  27991, 20959, 17550,  \n3402, 11440, 12616,  22033, 1019, 4234,  3727, 3728, 21047,  \n9824, 18574, 19593,  14030, 16155, 1474,  27609, 26294, 27610,  \n619, 22305, 10961,  22218, 19990, 5493,  14548, 8124, 7537,  \n15446, 15445, 15887,  481, 480, 12562,  20049, 11910, 21749,  \n8526, 4016, 3959,  7127, 590, 15262,  8724, 5720, 5664,  \n4031, 7518, 16230,  27800, 27234, 27611,  21286, 9870, 9869,  \n26836, 27611, 27234,  26294, 26295, 27610,  1608, 16309, 1606,  \n27992, 27237, 28198,  516, 7911, 515,  7278, 16989, 4050,  \n27610, 26295, 27019,  21444, 11675, 19506,  18232, 5732, 5731,  \n14789, 9801, 2987,  27428, 27801, 27993,  26836, 26298, 27994,  \n4784, 17008, 21448,  18206, 13918, 10332,  18339, 8437, 17801,  \n27433, 26297, 27804,  27019, 27022, 27807,  27807, 36, 27019,  \n12601, 27995, 6723,  14720, 14719, 7108,  20338, 1845, 19678,  \n27808, 27805, 27996,  27808, 27238, 27805,  13654, 5947, 13653,  \n14021, 6389, 15479,  4789, 7066, 4790,  2515, 2517, 16205,  \n7014, 15755, 4907,  14497, 6044, 19583,  16792, 27997, 12601,  \n9682, 11869, 11660,  10356, 9936, 9937,  18739, 20686, 5604,  \n6616, 5572, 18336,  6496, 6500, 10929,  21247, 9847, 14406,  \n27809, 27238, 27808,  27435, 27020, 27809,  27616, 25715, 26499,  \n2359, 13452, 2918,  27809, 27808, 27999,  27436, 27025, 27998,  \n1721, 1723, 8880,  20103, 14735, 14736,  14857, 14858, 11395,  \n11987, 14857, 11395,  15387, 16099, 8656,  27812, 26499, 26839,  \n7378, 14957, 5305,  3853, 10846, 21404,  27814, 26840, 27027,  \n26839, 27437, 27813,  26841, 26503, 28000,  23836, 22714, 22713,  \n27437, 28001, 28002,  27435, 27809, 27239,  1066, 18264, 3039,  \n27027, 27815, 27814,  14510, 7227, 5369,  27437, 27438, 28001,  \n16528, 20871, 22255,  16386, 18000, 15512,  5455, 17909, 10507,  \n27818, 27438, 26667,  21506, 11709, 18907,  13406, 2315, 17071,  \n13490, 6349, 6288,  18494, 4253, 5259,  14168, 360, 3807,  \n26501, 27817, 27028,  15333, 9021, 9022,  27819, 26667, 26154,  \n6358, 18538, 12821,  10448, 525, 15316,  2443, 6077, 5205,  \n26503, 26504, 27622,  28003, 26503, 27622,  4668, 17327, 11167,  \n2983, 22250, 13941,  941, 2359, 2918,  26507, 27440, 27820,  \n27823, 27820, 27440,  28004, 28005, 28006,  27240, 27821, 28007,  \n3793, 22926, 10347,  28008, 28009, 27823,  5232, 11162, 15795,  \n4643, 4896, 12000,  4278, 8475, 6689,  13520, 20630, 16989,  \n27824, 27240, 28007,  16091, 12977, 14355,  2326, 8145, 8705,  \n14989, 4172, 15785,  3081, 12595, 16851,  26315, 28010, 27241,  \n27439, 28010, 26315,  9924, 4005, 5906,  26671, 27822, 26844,  \n5632, 18469, 1750,  27240, 27824, 27442,  27443, 27823, 27034,  \n9454, 18652, 2405,  27624, 27825, 28012,  17188, 13021, 2027,  \n28014, 19548, 16704,  716, 6417, 19045,  14398, 1982, 9342,  \n13235, 5283, 15848,  886, 6176, 7561,  306, 12199, 14091,  \n17236, 19866, 7595,  27625, 28406, 27825,  12331, 7154, 6073,  \n13706, 13872, 15459,  27625, 27444, 28015,  3814, 4930, 10281,  \n21725, 3061, 5183,  6359, 6361, 23913,  10772, 12894, 22871,  \n7250, 13435, 21665,  27442, 28016, 26848,  14975, 6149, 4878,  \n28018, 26848, 28016,  10107, 12450, 9161,  6225, 962, 21754,  \n7166, 7165, 6837,  12113, 12112, 1945,  28019, 27827, 27629,  \n28020, 27629, 27449,  891, 893, 16357,  27829, 27826, 27445,  \n14873, 11086, 14874,  1533, 15036, 3601,  1760, 6539, 5574,  \n28020, 27449, 27830,  16982, 1400, 8912,  11603, 6878, 10131,  \n10938, 2090, 17826,  2201, 18547, 5808,  7656, 5623, 7655,  \n6291, 3599, 3598,  2483, 10994, 10399,  27833, 28021, 27829,  \n17413, 14869, 1145,  11561, 18269, 21761,  7905, 15753, 7906,  \n11151, 2308, 10214,  27632, 27835, 28221,  27831, 28022, 27832,  \n14180, 10998, 17096,  3874, 19405, 11042,  18389, 4032, 12180,  \n6642, 6526, 6643,  13964, 10985, 9542,  27457, 27835, 27632,  \n6525, 1944, 7193,  19600, 23510, 2073,  9659, 780, 23287,  \n27634, 27251, 27633,  9387, 3862, 12059,  27835, 27834, 27836,  \n16524, 1966, 11266,  3535, 15836, 9511,  12019, 5990, 12681,  \n11492, 3595, 12838,  18418, 13379, 19817,  22619, 3606, 10635,  \n22018, 22406, 2878,  14671, 17053, 11086,  1162, 1163, 19562,  \n28025, 27834, 27636,  27641, 27459, 27634,  21360, 20055, 15055,  \n17336, 16046, 20897,  18236, 20192, 14478,  27044, 28024, 27466,  \n27837, 28027, 27460,  11717, 8078, 16132,  11696, 17345, 4673,  \n7039, 20790, 14889,  27460, 27462, 27837,  28025, 27636, 27638,  \n4410, 6587, 5333,  21863, 16094, 17678,  5971, 13145, 15577,  \n27837, 27462, 28028,  27462, 27639, 28028,  736, 13834, 6931,  \n23806, 21830, 4935,  27468, 27459, 27641,  28029, 28028, 27639,  \n27257, 27838, 28030,  28031, 27838, 27640,  28031, 27640, 28032,  \n28032, 27640, 27464,  22107, 11647, 21577,  28033, 27464, 27465,  \n19267, 1337, 1336,  14790, 15113, 431,  5401, 1608, 5400,  \n12628, 9586, 3768,  10511, 14343, 1687,  18971, 1563, 1562,  \n27257, 28030, 26855,  27465, 27839, 28033,  27841, 28029, 27639,  \n19708, 1231, 18164,  8336, 1475, 12346,  27639, 27253, 27841,  \n17266, 15375, 17265,  11712, 4730, 483,  20419, 20418, 2237,  \n27649, 27645, 27646,  11198, 13070, 1867,  2052, 3807, 12836,  \n10137, 13213, 12208,  1412, 18512, 11018,  27644, 27055, 27648,  \n7918, 20962, 6744,  826, 2873, 6078,  18002, 6392, 754,  \n16410, 5254, 9259,  8115, 12455, 16675,  5113, 6380, 6379,  \n22571, 22652, 4079,  6322, 6321, 7925,  11980, 4673, 19882,  \n6191, 13417, 1003,  4212, 9891, 4821,  27844, 27642, 27651,  \n27845, 27648, 27055,  27843, 27260, 27050,  10184, 12958, 6902,  \n27842, 27473, 27261,  7489, 22624, 10819,  3016, 3987, 10298,  \n27845, 27647, 27648,  27654, 28034, 27844,  27844, 27651, 27654,  \n15679, 15005, 18875,  28240, 26688, 27474,  1054, 8625, 11130,  \n5220, 21663, 20615,  27470, 27653, 27847,  28035, 27845, 26861,  \n27267, 26696, 27847,  19242, 28039, 27026,  26688, 28240, 27057,  \n18197, 7166, 6837,  27848, 27849, 26860,  20619, 10113, 10114,  \n5395, 5396, 4960,  979, 6819, 980,  16129, 10151, 7038,  \n20949, 13944, 21612,  18654, 2722, 13719,  15459, 2262, 13707,  \n27846, 28040, 27652,  27847, 27653, 28040,  27267, 27847, 28041,  \n18347, 11644, 20699,  11190, 3121, 11354,  22879, 6305, 6597,  \n21316, 6743, 14815,  28040, 27653, 27652,  7159, 7158, 20517,  \n3466, 5020, 22908,  8779, 12852, 19398,  16535, 12763, 11428,  \n14865, 18082, 3454,  12889, 908, 11777,  21190, 13054, 4895,  \n18130, 2868, 14179,  5731, 4928, 734,  10780, 12321, 21839,  \n2585, 2584, 14532,  20968, 2585, 9150,  28042, 27851, 27852,  \n27852, 27851, 27266,  12929, 12686, 8375,  19242, 27026, 17320,  \n6303, 21592, 15763,  12003, 21841, 12004,  830, 5361, 831,  \n27268, 27850, 27853,  15499, 5083, 20518,  27064, 27063, 27856,  \n4966, 12745, 4964,  27268, 27853, 27857,  10180, 10179, 893,  \n4358, 2065, 985,  19901, 3332, 3331,  4031, 1691, 7518,  \n7303, 11644, 7302,  28044, 27271, 27270,  14752, 7836, 7835,  \n15068, 15543, 7284,  23485, 24752, 7551,  27857, 27657, 27268,  \n3059, 2688, 5677,  2130, 22149, 2129,  14819, 8173, 23580,  \n27860, 27480, 27858,  27481, 28046, 27275,  3137, 15712, 14547,  \n12518, 5200, 12578,  6397, 6396, 1761,  27657, 28047, 27658,  \n3150, 10327, 7342,  27862, 27071, 26705,  23791, 28048, 1500,  \n28046, 27481, 28049,  7310, 18551, 17204,  28050, 26875, 27861,  \n8362, 21392, 1893,  10800, 16113, 16272,  8583, 8582, 14070,  \n28049, 27481, 27659,  28050, 27661, 26875,  1466, 9689, 10764,  \n17010, 17009, 7520,  15417, 4195, 21472,  22823, 20403, 10341,  \n28051, 27658, 28047,  6581, 12002, 9939,  27483, 28052, 27659,  \n4467, 13139, 14354,  28051, 27863, 27658,  10591, 20294, 3881,  \n27483, 27484, 28052,  1571, 4001, 13594,  27863, 28051, 28053,  \n28053, 27864, 27863,  27864, 28053, 27865,  19694, 2276, 2229,  \n27866, 27865, 28054,  27488, 28055, 27869,  9636, 8554, 8711,  \n17642, 7680, 13143,  27485, 27667, 27867,  5660, 18447, 8205,  \n27868, 27866, 28054,  28056, 27868, 28054,  11620, 4178, 1356,  \n4494, 9363, 16370,  6569, 9458, 5519,  598, 17543, 6520,  \n28057, 27869, 28058,  11666, 13757, 11667,  11539, 13220, 3462,  \n19473, 21056, 21055,  21130, 19284, 19471,  5193, 5194, 20709,  \n9029, 10842, 10843,  15526, 18550, 15527,  27288, 27875, 27492,  \n28056, 27669, 27868,  28056, 28060, 27669,  11079, 17650, 17649,  \n14994, 10781, 18030,  28057, 27670, 27084,  9939, 16846, 4595,  \n27870, 28061, 27666,  28059, 27668, 27871,  16477, 13108, 17308,  \n20021, 16851, 20599,  22304, 9270, 17282,  5570, 2048, 13883,  \n27870, 28062, 28061,  28063, 27666, 28061,  27666, 28063, 27081,  \n19458, 14758, 13616,  9154, 16639, 18038,  28060, 28064, 27669,  \n27081, 28063, 27872,  27873, 27871, 27496,  28065, 27871, 27873,  \n10820, 21547, 10181,  2415, 1659, 15055,  17721, 17040, 13135,  \n11500, 1890, 13615,  27877, 28068, 27870,  28068, 28062, 27870,  \n6920, 16751, 11341,  4383, 12205, 782,  27873, 27496, 27878,  \n27882, 27677, 27675,  27089, 26723, 27676,  18555, 13164, 13013,  \n391, 18234, 21388,  27877, 27880, 28069,  27877, 28069, 28068,  \n27881, 27872, 28063,  7618, 12640, 16058,  28070, 27873, 27878,  \n27882, 28071, 27501,  10771, 2287, 2286,  27292, 27879, 27499,  \n15445, 20677, 15887,  3455, 1434, 1484,  18513, 20884, 21454,  \n27674, 27883, 27878,  10109, 15312, 14866,  15421, 9666, 8455,  \n22632, 16654, 16453,  11191, 2898, 2899,  17262, 7344, 8808,  \n27292, 26368, 27091,  1466, 5512, 9689,  27506, 27501, 28071,  \n27884, 25895, 26052,  27497, 27678, 27883,  11769, 10755, 19150,  \n27883, 27678, 28074,  3578, 11337, 17411,  27885, 27293, 28075,  \n28074, 27678, 27679,  27509, 27095, 28076,  8939, 8938, 16670,  \n10287, 3567, 19261,  21862, 2051, 18173,  15796, 15704, 13321,  \n27297, 28077, 27293,  3766, 15563, 3764,  20364, 5381, 5380,  \n27889, 27680, 28078,  27889, 28078, 28079,  27889, 28079, 27890,  \n4907, 10310, 7014,  28080, 27888, 27887,  28081, 27680, 27681,  \n27680, 28081, 28078,  21666, 17607, 3343,  5579, 11630, 2158,  \n11080, 12962, 1863,  13532, 11469, 894,  27891, 28081, 27681,  \n21056, 19950, 11646,  3632, 2646, 9323,  14241, 21508, 19114,  \n27508, 27683, 27895,  27893, 27895, 27892,  10488, 2645, 2500,  \n27508, 27895, 27893,  13543, 24005, 16550,  28077, 27297, 27896,  \n27894, 27895, 27683,  27102, 26212, 28083,  5073, 5072, 20668,  \n27097, 27896, 27297,  16142, 7069, 21468,  28082, 27511, 27102,  \n28089, 27685, 27890,  28085, 28086, 27693,  28086, 27897, 27693,  \n27691, 27894, 27687,  4078, 19588, 25138,  27699, 28085, 27693,  \n4292, 21400, 7273,  8752, 10951, 6960,  28087, 27686, 27899,  \n28087, 27900, 27686,  12002, 21331, 9940,  12201, 3305, 2678,  \n17393, 16295, 10649,  6047, 23200, 21285,  19047, 7124, 19048,  \n27902, 28090, 27518,  28092, 27518, 28090,  7440, 13621, 2430,  \n27899, 27903, 28087,  27686, 27900, 27516,  27696, 28093, 27691,  \n27697, 27107, 27688,  3853, 3852, 6569,  6454, 1439, 3637,  \n28094, 27699, 27692,  28095, 28091, 27907,  27907, 28091, 27902,  \n27902, 28091, 28090,  27899, 27904, 27903,  27519, 27516, 27908,  \n27516, 28096, 27908,  28097, 28093, 27908,  6894, 12448, 8514,  \n27698, 27685, 27905,  27698, 27905, 27700,  27700, 27905, 28094,  \n27692, 27700, 28094,  3292, 3293, 14129,  17006, 25584, 8848,  \n27906, 28098, 27524,  16722, 5379, 9112,  27907, 27909, 28095,  \n27518, 28092, 27702,  12589, 16687, 3507,  7701, 21188, 14533,  \n28099, 27903, 27904,  13816, 15796, 14921,  2382, 3768, 7533,  \n6428, 6427, 8602,  16919, 11914, 16915,  27514, 27906, 27524,  \n12263, 17363, 6459,  8962, 7101, 11661,  14927, 13994, 13995,  \n10552, 3909, 7926,  27524, 28100, 27704,  27524, 28098, 28100,  \n27704, 28100, 28101,  27909, 28101, 28095,  27909, 27704, 28101,  \n27703, 27910, 27526,  27527, 27910, 27904,  12487, 3180, 14496,  \n6740, 13787, 8524,  20801, 16348, 22352,  27317, 28103, 27530,  \n22362, 7670, 15445,  14332, 6100, 1375,  3904, 17302, 1916,  \n10850, 6215, 14450,  26398, 25917, 28104,  6997, 12640, 3715,  \n10157, 2403, 2402,  2534, 2507, 1070,  27916, 27533, 27120,  \n4384, 19500, 13899,  22433, 9100, 19059,  14502, 3663, 16668,  \n9703, 9123, 21070,  27320, 28747, 27917,  5779, 20400, 11982,  \n6898, 820, 5878,  27534, 27535, 27710,  27706, 27707, 27709,  \n27918, 27708, 28106,  27707, 27534, 27710,  27324, 27708, 27918,  \n10355, 5270, 11716,  27710, 27535, 28107,  14811, 16400, 13780,  \n27711, 28108, 27712,  27919, 27712, 28108,  1322, 1321, 849,  \n1191, 17265, 15375,  3268, 11535, 4094,  28107, 27535, 27541,  \n7068, 6075, 7729,  28109, 27537, 27919,  27920, 27537, 28109,  \n28110, 27325, 27920,  3551, 2732, 2731,  27541, 28111, 28107,  \n27538, 27325, 28110,  27538, 28112, 27922,  11092, 11093, 14450,  \n27539, 27922, 28113,  27923, 27539, 28113,  26198, 1051, 12661,  \n27544, 27924, 27921,  7816, 5112, 23473,  27544, 27546, 27924,  \n27545, 28114, 27327,  27924, 27546, 28115,  28114, 27926, 27327,  \n28115, 27546, 27925,  8975, 18575, 8974,  6530, 11248, 11247,  \n3531, 13942, 9345,  11100, 11099, 3655,  26770, 27128, 27333,  \n27714, 26595, 27713,  27334, 27333, 27332,  20638, 10698, 10685,  \n15910, 5851, 9067,  10891, 19106, 12241,  16865, 12138, 15324,  \n26598, 26770, 26413,  26766, 27715, 28117,  28118, 27330, 27329,  \n27716, 27330, 28118,  10287, 16786, 5060,  1749, 2710, 9971,  \n21906, 13602, 1919,  10842, 20034, 10843,  27130, 28119, 27332,  \n27716, 27927, 27718,  27130, 27338, 28119,  14633, 14019, 745,  \n13328, 9621, 5154,  6547, 934, 1987,  6580, 6579, 14248,  \n17006, 28102, 25584,  13588, 7887, 7886,  17078, 15844, 4514,  \n27719, 27718, 27927,  15469, 12408, 2311,  14138, 4634, 9724,  \n28313, 27338, 27720,  18995, 11026, 19689,  3520, 14906, 3519,  \n27719, 27927, 27721,  19002, 17274, 11011,  9828, 19059, 13159,  \n17348, 16594, 17349,  27928, 27720, 27548,  3016, 13352, 3987,  \n26777, 27929, 27928,  7677, 7679, 20355,  12171, 4832, 19229,  \n27932, 27549, 27721,  20472, 18362, 18058,  10408, 1894, 5038,  \n13546, 8053, 7488,  27931, 27930, 26418,  27724, 27722, 27341,  \n26605, 27722, 27343,  27724, 27723, 27933,  27727, 27552, 28124,  \n10842, 23296, 20034,  27727, 27138, 27552,  28123, 27931, 27139,  \n14280, 7492, 15458,  11032, 12670, 21561,  16002, 18893, 16003,  \n28124, 27934, 27727,  4062, 1036, 10110,  4167, 458, 12332,  \n12209, 4471, 15099,  27348, 27934, 28125,  28123, 27348, 28125,  \n14014, 22540, 20643,  28123, 27139, 27348,  8205, 18447, 1759,  \n27553, 27729, 27725,  12307, 5384, 15347,  27935, 27342, 27549,  \n7092, 21252, 7093,  523, 18739, 524,  27554, 28126, 27729,  \n9456, 21989, 4030,  28127, 27554, 27555,  3662, 12530, 11423,  \n28127, 27555, 27557,  12787, 13302, 1841,  18681, 18680, 20877,  \n11497, 18564, 12621,  18260, 2359, 2360,  28129, 27558, 27556,  \n15632, 11328, 4229,  27356, 27730, 27937,  28130, 27938, 27730,  \n27356, 27355, 27730,  3378, 1628, 1437,  12408, 4192, 4191,  \n7018, 11031, 16546,  28130, 27730, 28133,  4059, 12846, 1774,  \n28133, 27730, 27732,  27733, 28133, 27732,  13680, 28135, 15800,  \n27563, 28134, 27733,  28136, 28134, 27563,  21962, 11157, 2024,  \n10608, 9868, 9867,  28136, 27736, 27940,  27563, 27736, 28136,  \n28137, 13988, 11005,  27735, 28138, 27737,  7634, 14249, 18079,  \n19955, 8118, 14714,  18441, 28139, 28140,  18441, 28140, 28141,  \n28141, 25627, 18440,  2002, 7209, 2003,  22296, 13224, 22619,  \n5174, 23353, 15862,  18907, 11709, 10732,  16647, 16494, 16646,  \n18441, 28141, 18440,  17128, 3178, 921,  18471, 8797, 14451,  \n6738, 17654, 14805,  10852, 5102, 3871,  22676, 16855, 573,  \n18173, 19868, 22583,  11403, 10495, 11402,  5342, 16891, 10561,  \n9844, 6006, 8018,  20143, 23734, 20144,  4336, 19211, 19886,  \n26941, 27158, 27947,  27158, 28143, 27947,  987, 18094, 8710,  \n15581, 16429, 11792,  21824, 8157, 20307,  11671, 19404, 20884,  \n602, 4900, 9194,  10189, 15939, 11704,  27370, 27947, 27948,  \n27945, 27369, 26786,  7529, 18958, 20854,  26265, 27739, 28145,  \n19913, 14057, 15906,  26786, 26787, 27949,  17073, 22748, 14289,  \n6863, 10954, 5965,  14091, 17749, 7918,  27945, 26786, 27949,  \n27950, 26613, 26944,  14705, 20265, 8697,  9772, 8536, 12222,  \n27373, 27162, 28146,  6532, 11242, 6531,  27742, 26614, 27372,  \n26787, 27741, 27949,  26613, 27950, 27161,  5317, 13981, 16016,  \n26118, 24980, 19379,  5268, 25549, 1024,  17389, 9755, 17390,  \n11250, 11249, 11158,  27739, 26945, 26948,  3275, 1365, 1366,  \n4708, 6226, 6227,  8481, 15952, 19063,  12616, 10566, 19143,  \n18781, 15617, 1310,  1950, 12285, 19042,  17553, 4419, 11813,  \n7158, 568, 21966,  4498, 2752, 19912,  17587, 15610, 8550,  \n27376, 28146, 27162,  17261, 5488, 19660,  11528, 14980, 10229,  \n20252, 11436, 6764,  2721, 15270, 11473,  23866, 17174, 5106,  \n15847, 12026, 14482,  11051, 5552, 3730,  6490, 2055, 1374,  \n22108, 17311, 4986,  14150, 6860, 6861,  13975, 5161, 16148,  \n7777, 21488, 13458,  6908, 15952, 14800,  17538, 16944, 17539,  \n27161, 28148, 27377,  10437, 1516, 22067,  27375, 27164, 28147,  \n28149, 27376, 27745,  12525, 14599, 9278,  28333, 26431, 27374,  \n27744, 27955, 27747,  18851, 7263, 16416,  7609, 9312, 11154,  \n17946, 11273, 7390,  16809, 8775, 11824,  28333, 26794, 26431,  \n9162, 1810, 13557,  27164, 27176, 27752,  12596, 10710, 5267,  \n3609, 11421, 14133,  28151, 27954, 27748,  27748, 27953, 28151,  \n27953, 27568, 27957,  27749, 27957, 27568,  1673, 17059, 2846,  \n19825, 7526, 2137,  23962, 28967, 14476,  20176, 14824, 6602,  \n14054, 19816, 21500,  27749, 27378, 27750,  771, 11286, 1525,  \n9788, 16801, 13628,  16092, 5593, 11557,  27958, 26796, 27959,  \n17018, 19531, 19927,  2591, 1472, 8651,  4422, 19503, 10093,  \n10989, 1413, 4508,  28154, 27960, 27956,  10315, 13089, 6895,  \n1857, 19612, 11924,  28154, 28155, 27960,  14825, 14826, 1664,  \n9195, 13990, 8163,  27752, 27176, 27755,  22745, 14228, 1696,  \n29133, 10250, 28156,  5372, 2628, 14380,  16996, 17335, 16997,  \n18482, 8698, 1778,  6847, 22376, 23292,  28157, 26442, 27754,  \n27754, 26442, 26798,  6285, 9979, 6286,  414, 25126, 22229,  \n20018, 4516, 3456,  15466, 13490, 15916,  27962, 26955, 27756,  \n10938, 9441, 14937,  27757, 28158, 28159,  16471, 8993, 563,  \n2727, 13954, 17869,  27961, 27757, 27386,  10294, 10242, 9054,  \n18926, 11434, 780,  5906, 13837, 10692,  24241, 22264, 21166,  \n8971, 8850, 14503,  3646, 22445, 1227,  12684, 1703, 11107,  \n27388, 27757, 27579,  12672, 13167, 22890,  10718, 22413, 11658,  \n16983, 2899, 2898,  26803, 27580, 28160,  8330, 15799, 410,  \n18053, 13085, 11593,  8430, 7893, 14792,  3810, 11486, 4792,  \n27579, 28162, 27390,  23048, 13619, 18105,  20626, 2406, 16421,  \n15122, 9289, 14632,  27963, 27390, 28162,  9606, 2175, 4950,  \n12099, 20216, 9614,  27759, 27761, 27389,  1812, 1813, 11588,  \n4136, 15066, 4135,  27963, 27182, 27390,  10920, 11591, 12747,  \n18881, 16883, 10469,  27391, 27760, 27392,  27760, 28164, 27392,  \n6896, 15763, 17593,  26627, 28163, 26967,  27762, 26454, 27965,  \n27184, 26627, 26967,  26457, 27389, 27761,  28163, 26627, 27581,  \n3070, 3069, 16624,  21499, 7436, 12534,  3343, 16217, 20190,  \n27967, 26968, 27765,  27967, 27766, 26968,  16509, 1437, 13823,  \n1168, 10191, 1873,  7980, 7979, 12923,  16628, 7408, 16627,  \n13789, 3092, 3093,  9695, 17658, 17735,  788, 20801, 17119,  \n27582, 28166, 27583,  13774, 16990, 15534,  5057, 17244, 8438,  \n18232, 14755, 18233,  19955, 14714, 17880,  17734, 1267, 19297,  \n2498, 13278, 10379,  8239, 5622, 8240,  6711, 13368, 10194,  \n15233, 19422, 19423,  27583, 27969, 27395,  18129, 14969, 8588,  \n6088, 4524, 1239,  11482, 5871, 8804,  14958, 19670, 15466,  \n5709, 4097, 10063,  19429, 23414, 19828,  7994, 21232, 16730,  \n20953, 12517, 1074,  21098, 11021, 827,  335, 5560, 312,  \n4773, 10244, 10708,  22178, 20414, 12966,  18725, 10017, 4680,  \n5437, 9508, 10923,  20547, 1075, 7920,  8876, 8875, 11042,  \n27397, 27969, 27192,  28168, 27586, 27587,  5134, 20376, 10977,  \n17359, 17956, 16663,  13915, 6598, 777,  27192, 27970, 27589,  \n21004, 12865, 15064,  5733, 15147, 7495,  17887, 11223, 17886,  \n4385, 13124, 6077,  2742, 2741, 15737,  28170, 27396, 27194,  \n25713, 14202, 4649,  26976, 26470, 27772,  17201, 4828, 17202,  \n11738, 1829, 13630,  27770, 28171, 27590,  27773, 26472, 27196,  \n27398, 27770, 27590,  27399, 27772, 26979,  7461, 17217, 1882,  \n4413, 2805, 2806,  27590, 28171, 27591,  21005, 19569, 3926,  \n27591, 28171, 28173,  27774, 27971, 26130,  11142, 9842, 9170,  \n27775, 27591, 27972,  27775, 27972, 27973,  498, 21132, 18527,  \n3250, 6831, 21122,  11797, 8918, 6231,  5498, 10354, 19663,  \n12340, 738, 16102,  10859, 20784, 12656,  3937, 13297, 20934,  \n17691, 22671, 17814,  27777, 26986, 27776,  20643, 15526, 15528,  \n5555, 5554, 17871,  3775, 2469, 21452,  28174, 27201, 27777,  \n26987, 27777, 27201,  27778, 27594, 28175,  10372, 17903, 22061,  \n20927, 4910, 4909,  858, 11331, 18620,  12828, 1194, 1572,  \n5789, 19306, 3751,  27200, 27199, 27973,  27200, 27973, 27975,  \n17443, 16506, 18808,  864, 3012, 9859,  21024, 8172, 6156,  \n911, 28178, 26838,  26132, 28180, 26815,  28178, 28181, 26838,  \n27593, 27205, 27782,  27205, 27402, 27782,  27206, 26990, 28182,  \n28183, 26993, 27979,  3247, 11556, 15025,  27401, 27204, 27596,  \n26838, 12726, 911,  7422, 6589, 7423,  14630, 3983, 14631,  \n28184, 26815, 28180,  859, 18620, 1760,  2585, 6694, 16030,  \n27401, 27980, 27210,  18443, 4606, 22092,  25703, 27403, 27981,  \n8753, 20453, 20150,  18341, 7275, 13555,  9182, 9024, 2247,  \n19338, 18141, 11544,  367, 1398, 12523,  7763, 17435, 10306,  \n10084, 13358, 13359,  10973, 4727, 8215,  835, 12325, 18023,  \n13692, 25846, 25490,  12726, 28186, 8765,  25990, 27405, 26996,  \n20571, 5189, 24360,  6055, 15340, 15312,  7633, 2133, 11024,  \n6042, 4638, 10054,  11160, 11344, 11343,  2849, 11502, 2850,  \n27408, 27790, 27786,  28188, 27786, 27790,  27427, 18987, 8765,  \n16530, 22570, 19659,  27790, 27791, 28188,  27600, 28190, 27793,  \n20674, 7118, 7781,  20086, 11626, 2446,  27417, 28188, 27791,  \n22996, 2316, 20949,  8202, 8201, 15742,  27409, 27789, 27602,  \n12521, 14567, 12522,  28188, 27417, 27983,  13331, 11192, 9665,  \n27603, 26485, 27416,  11285, 2216, 18835,  13031, 8765, 28186,  \n26034, 28189, 27427,  16387, 13415, 13977,  11202, 5513, 5512,  \n12894, 10772, 6262,  27983, 27417, 27797,  6144, 19325, 11430,  \n1559, 8584, 13101,  12805, 2172, 4512,  28191, 27796, 27006,  \n3885, 7109, 4701,  5328, 11061, 10767,  1437, 11983, 14382,  \n2434, 15984, 7521,  27984, 27797, 27798,  26140, 27604, 27226,  \n23938, 14104, 14246,  12750, 2992, 5802,  8238, 10660, 12818,  \n13558, 20406, 1587,  20470, 18018, 14994,  19052, 17216, 21029,  \n6268, 22876, 589,  29502, 3405, 3404,  17799, 941, 17801,  \n23596, 25267, 14737,  9545, 8901, 324,  20295, 21166, 24241,  \n18034, 21139, 13693,  750, 5099, 751,  18355, 892, 13444,  \n12293, 12696, 12294,  11876, 10789, 17473,  819, 10396, 16283,  \n26648, 26829, 27986,  8766, 8768, 5728,  12696, 16249, 16248,  \n27226, 28195, 26487,  9271, 10870, 14615,  12053, 16724, 12054,  \n27987, 27605, 27795,  27608, 27986, 26829,  4710, 13517, 11736,  \n9414, 17347, 5581,  8807, 7462, 11899,  12251, 11628, 8318,  \n12369, 1799, 1800,  21158, 7216, 7536,  19708, 11600, 1229,  \n14748, 20622, 4280,  6172, 5174, 15862,  18530, 9202, 9203,  \n14661, 21146, 17646,  8232, 18940, 18941,  5589, 18090, 20894,  \n13459, 11741, 9190,  16815, 9453, 9452,  13669, 1986, 11393,  \n17563, 9437, 5819,  21834, 3619, 18639,  6105, 13864, 3885,  \n4773, 678, 13492,  4779, 9099, 13803,  27801, 27606, 28197,  \n2349, 3504, 3505,  27992, 27613, 27237,  399, 412, 11900,  \n18738, 2047, 19833,  10641, 2804, 2803,  1150, 5835, 10751,  \n27801, 28197, 27993,  15093, 8663, 13970,  7423, 6589, 6588,  \n6782, 6781, 12798,  27806, 28198, 27237,  13568, 13567, 12931,  \n11787, 17850, 19141,  18366, 13647, 11820,  9235, 18584, 1314,  \n18774, 22894, 6493,  6572, 5678, 5677,  5611, 6484, 17904,  \n581, 19435, 2718,  13109, 17357, 11615,  27807, 27022, 27021,  \n9969, 6382, 14050,  5858, 20950, 12115,  16121, 3820, 14673,  \n15340, 19222, 14662,  7779, 444, 443,  14616, 4929, 9164,  \n21641, 21824, 20307,  8326, 435, 4458,  1056, 19664, 18826,  \n21830, 11364, 4935,  19498, 13831, 12633,  17529, 17528, 17144,  \n21332, 6006, 6007,  2087, 12971, 2088,  6253, 9685, 7358,  \n22178, 22177, 20414,  13557, 13558, 13885,  20812, 10926, 8328,  \n387, 17466, 17087,  27616, 26499, 27812,  14238, 7157, 4378,  \n17529, 22914, 3675,  8858, 1980, 11650,  6274, 16632, 6275,  \n22583, 22721, 18173,  17187, 4669, 7649,  982, 11621, 1356,  \n13733, 10253, 18342,  16246, 2083, 5768,  16983, 752, 2703,  \n13171, 3124, 16214,  9309, 18048, 8054,  16837, 14666, 9642,  \n27809, 27999, 27620,  28202, 27437, 28002,  28203, 28202, 28002,  \n28202, 27813, 27437,  27813, 28202, 28201,  7768, 8032, 11446,  \n6658, 8827, 15388,  28001, 28201, 28202,  28002, 28203, 28204,  \n28002, 28001, 28202,  2153, 13410, 20328,  28204, 27810, 28002,  \n1912, 9188, 9189,  28001, 27818, 28201,  20795, 18236, 14478,  \n28001, 27438, 27818,  7278, 18688, 7219,  14365, 2586, 9662,  \n1274, 14695, 16904,  508, 3584, 2540,  27239, 27809, 27620,  \n18036, 11493, 18035,  27618, 27816, 26842,  12870, 28205, 25113,  \n20917, 10639, 10638,  5855, 17138, 14306,  581, 2788, 582,  \n16884, 567, 3183,  15647, 23157, 12181,  14204, 14205, 17032,  \n7451, 14401, 4798,  27819, 26154, 27030,  20971, 15647, 14677,  \n27823, 28009, 28207,  15049, 6544, 6034,  28208, 28209, 28009,  \n4922, 20072, 6161,  28210, 26670, 26843,  27441, 28003, 27622,  \n12883, 16351, 7345,  12108, 13450, 21095,  20164, 13728, 16575,  \n28009, 28008, 28208,  29739, 11905, 3649,  23100, 28211, 22496,  \n11224, 2944, 3739,  1013, 12086, 18409,  14727, 16703, 15036,  \n11761, 6680, 1257,  4306, 10976, 6715,  18841, 21981, 983,  \n11585, 14767, 10973,  21762, 4395, 10267,  983, 21981, 2536,  \n2341, 12473, 15654,  27822, 28212, 28013,  28213, 28013, 28212,  \n28013, 26844, 27822,  27823, 27443, 28008,  28012, 27825, 28214,  \n27626, 27624, 28216,  7419, 15302, 11549,  28214, 27825, 28406,  \n4814, 15347, 5843,  3449, 17904, 19509,  8722, 8721, 16762,  \n12970, 17863, 4778,  2840, 6499, 6498,  23132, 2146, 11760,  \n1977, 1978, 12943,  1525, 5170, 1524,  22608, 21758, 14225,  \n17349, 16594, 12014,  4764, 11352, 12476,  27627, 39, 27441,  \n27627, 27441, 27033,  4446, 20903, 3635,  6224, 16541, 6223,  \n21351, 14421, 21613,  9926, 15766, 13807,  27826, 27627, 27033,  \n3229, 7717, 2931,  5671, 7321, 18426,  28019, 28015, 27444,  \n2322, 11380, 4623,  4820, 14466, 16297,  27827, 28019, 27444,  \n1153, 1835, 1217,  17427, 11212, 10429,  16613, 15082, 13027,  \n5816, 5817, 20528,  27448, 28013, 27828,  10555, 8778, 16163,  \n28020, 28219, 27629,  2410, 22735, 4484,  17472, 5740, 14463,  \n14450, 6215, 11092,  10529, 8492, 5897,  24586, 1862, 4852,  \n5988, 15239, 15240,  27830, 28221, 28020,  14337, 2937, 13881,  \n10420, 10421, 10316,  13050, 2052, 17868,  28221, 27830, 27632,  \n5483, 3063, 19463,  27250, 27628, 27455,  28021, 27833, 28223,  \n28226, 28223, 27833,  5053, 3370, 4564,  27635, 27455, 28224,  \n22592, 27385, 10522,  28226, 27833, 28023,  27831, 28225, 28022,  \n12427, 5618, 18930,  14315, 15287, 20278,  3543, 6717, 5620,  \n27832, 28022, 27633,  8875, 8877, 3590,  27836, 28227, 27835,  \n16390, 3677, 14418,  28228, 27633, 28022,  28229, 27634, 27633,  \n9515, 7868, 16145,  27833, 27637, 28023,  22250, 2566, 13941,  \n28230, 28227, 27836,  27836, 27834, 28025,  27637, 27460, 28231,  \n28231, 27460, 28027,  28230, 27836, 28025,  22096, 13118, 3770,  \n10963, 11485, 15391,  9535, 15566, 8022,  8109, 3855, 3856,  \n6000, 6189, 2550,  27638, 27642, 28025,  27641, 28233, 28234,  \n2650, 15083, 11453,  28030, 27838, 28235,  7960, 22036, 14903,  \n28430, 28031, 28032,  28033, 28032, 27464,  13084, 18379, 9564,  \n5067, 5173, 18858,  1070, 2966, 2534,  5580, 2157, 9631,  \n14533, 7700, 7701,  20516, 16682, 6027,  8167, 1997, 6764,  \n13310, 5266, 13249,  20798, 11816, 13384,  4053, 4054, 13264,  \n27051, 27466, 28024,  8566, 15907, 11574,  18426, 16579, 5671,  \n2767, 20456, 12758,  6653, 20930, 3125,  14650, 10090, 4710,  \n10661, 869, 21665,  27258, 28434, 27474,  27051, 28237, 27843,  \n15171, 6169, 8212,  28434, 28240, 27474,  2247, 16797, 11003,  \n22474, 23451, 10418,  5727, 4877, 12583,  27473, 28239, 27054,  \n27843, 28036, 27260,  20206, 3096, 23103,  17857, 6119, 521,  \n27473, 27842, 28239,  17893, 14909, 5674,  27260, 28036, 27848,  \n5294, 412, 977,  2800, 12196, 2801,  10850, 6214, 6215,  \n12088, 22953, 23467,  28037, 27846, 27468,  20579, 15986, 4618,  \n6899, 21504, 6900,  338, 20995, 26502,  14893, 19643, 16372,  \n11847, 15573, 9317,  20421, 17152, 5522,  28035, 26861, 26862,  \n16305, 19429, 1630,  28242, 27846, 28037,  14710, 18351, 1750,  \n18572, 8282, 19362,  1229, 16593, 1230,  19780, 11236, 15142,  \n28243, 27261, 27263,  28241, 27261, 28243,  19252, 9171, 18367,  \n14192, 3198, 13633,  28244, 27846, 28242,  28244, 28040, 27846,  \n24304, 15483, 10429,  8946, 8160, 8945,  10116, 20748, 10117,  \n28246, 28040, 28244,  28041, 28040, 28246,  28041, 27847, 28040,  \n28041, 27850, 27267,  28245, 27655, 27849,  28245, 27475, 27655,  \n11371, 364, 18672,  3218, 21390, 20463,  11188, 6927, 11050,  \n1239, 14253, 1240,  5075, 23828, 7113,  13223, 17875, 3234,  \n27850, 28247, 27853,  21725, 19357, 7822,  28248, 27476, 27854,  \n27853, 28247, 28249,  27265, 27477, 28043,  10570, 16409, 11138,  \n19511, 7196, 7197,  11943, 2432, 14909,  19066, 24612, 1156,  \n16548, 11071, 394,  28250, 27854, 27855,  27853, 28249, 27857,  \n1240, 519, 6119,  1500, 16714, 1501,  1197, 15659, 22785,  \n27855, 27271, 28044,  26704, 27064, 28045,  27856, 28045, 27064,  \n10679, 15218, 14926,  15411, 5610, 1058,  17677, 3367, 4485,  \n26704, 28045, 27858,  26869, 26704, 27858,  16680, 871, 14566,  \n27857, 28252, 27657,  4730, 11765, 9261,  28044, 27270, 27656,  \n8853, 9468, 5858,  28251, 28044, 27656,  4756, 14795, 11565,  \n27071, 27859, 27477,  27657, 28252, 28253,  28254, 27656, 27273,  \n7849, 3872, 3871,  28046, 28254, 27275,  4614, 20153, 9949,  \n28254, 27273, 27275,  27657, 28253, 28255,  8893, 13767, 8891,  \n28255, 28047, 27657,  12691, 979, 11475,  1857, 20847, 9524,  \n28256, 28046, 28049,  6937, 4918, 6634,  28255, 28257, 28047,  \n6937, 21629, 4918,  19516, 6489, 12011,  11692, 16283, 11781,  \n28051, 28047, 28257,  28052, 28049, 27659,  27661, 28258, 27487,  \n4247, 10895, 15584,  28257, 28259, 28051,  13279, 5276, 22225,  \n23200, 10474, 10442,  14189, 14595, 1237,  16556, 22627, 12991,  \n28051, 28259, 28053,  510, 6857, 6489,  20950, 10666, 12115,  \n19408, 22161, 7895,  13082, 12104, 13796,  11990, 16462, 13446,  \n28053, 28259, 27865,  27865, 28259, 28260,  28260, 28054, 27865,  \n13912, 13911, 14183,  17773, 4024, 17772,  6998, 6997, 3715,  \n5226, 1789, 4265,  9450, 9449, 20491,  28261, 28054, 28260,  \n2041, 9152, 17420,  28262, 28054, 28261,  28056, 28054, 28262,  \n28262, 28263, 28056,  18904, 11719, 19418,  27668, 28264, 27667,  \n28057, 27084, 27869,  28060, 28056, 28263,  7461, 22753, 4586,  \n3990, 3989, 13338,  28062, 28266, 28061,  28062, 28265, 28266,  \n28061, 28267, 28063,  28061, 28266, 28267,  28268, 26719, 26718,  \n27670, 28268, 26718,  20544, 19682, 7192,  1969, 3347, 2889,  \n28265, 28062, 28269,  28059, 27871, 28065,  20005, 1094, 4699,  \n27879, 28066, 27499,  27499, 28066, 27676,  26719, 28268, 27672,  \n28064, 27876, 27669,  28269, 28062, 28068,  28073, 28267, 28271,  \n4362, 21090, 17123,  12941, 15344, 5109,  1218, 3747, 12761,  \n14064, 18908, 21826,  27291, 27089, 27676,  4014, 2503, 6938,  \n11304, 14855, 20830,  28270, 27500, 27672,  20009, 8149, 2818,  \n27876, 28069, 27880,  27876, 28064, 28069,  11528, 10493, 14980,  \n28068, 28069, 28269,  28063, 28267, 28073,  15867, 19353, 21867,  \n6857, 2481, 8099,  12627, 4507, 19356,  23005, 5628, 1068,  \n28272, 28071, 27882,  10266, 21427, 19108,  11951, 11348, 7818,  \n17075, 29782, 14780,  28274, 27878, 27883,  11337, 19618, 15884,  \n28274, 28070, 27878,  5807, 16343, 2119,  3155, 15280, 3380,  \n15075, 15303, 18400,  27500, 28275, 27884,  28276, 28274, 27883,  \n7354, 7355, 9536,  18923, 3787, 10326,  5307, 8331, 13708,  \n27287, 27293, 27885,  1495, 20028, 18812,  28074, 28276, 27883,  \n8259, 18487, 8661,  28076, 27095, 27506,  11150, 22953, 18593,  \n12994, 14875, 16383,  27881, 28073, 27886,  28073, 27887, 27886,  \n17257, 7848, 7847,  9867, 912, 913,  4693, 18774, 4694,  \n8572, 7918, 12177,  14486, 2467, 8934,  20136, 16735, 20137,  \n956, 769, 7354,  6123, 825, 4788,  22628, 21712, 19189,  \n21858, 2704, 2705,  28074, 27679, 28277,  28083, 26212, 26737,  \n14631, 3983, 12345,  28077, 28075, 27293,  28078, 28278, 28079,  \n28078, 28279, 28278,  10136, 13353, 2325,  27684, 28277, 27679,  \n28083, 26737, 28280,  11242, 6532, 10067,  28282, 28279, 28081,  \n28078, 28081, 28279,  27890, 28079, 28283,  28283, 28079, 28278,  \n10238, 2457, 17952,  5338, 5339, 15871,  9043, 4795, 18395,  \n3846, 2909, 726,  13928, 7497, 9208,  18693, 771, 772,  \n26737, 27509, 28280,  6209, 6210, 6747,  21998, 28332, 10581,  \n8367, 24367, 25873,  2350, 4844, 4846,  28080, 28284, 27888,  \n27888, 28284, 27891,  27891, 28284, 28081,  2422, 21324, 20336,  \n8916, 9754, 16501,  4534, 6099, 4985,  27893, 28285, 27684,  \n28287, 28082, 27102,  28287, 27102, 28083,  12881, 7221, 9019,  \n28288, 27895, 27894,  27895, 28288, 27892,  10208, 8236, 10811,  \n28288, 27894, 28290,  27511, 28286, 28291,  11070, 1238, 3795,  \n1403, 10520, 1404,  28089, 27890, 28283,  28086, 28293, 27897,  \n6176, 12240, 2856,  28293, 28294, 27897,  27691, 28290, 27894,  \n14315, 1430, 15287,  27511, 28082, 28286,  28291, 27688, 27511,  \n6627, 7752, 18332,  28294, 27898, 27897,  2581, 2580, 12912,  \n28296, 28297, 28091,  28295, 28090, 28091,  28291, 28088, 27688,  \n18075, 11251, 7046,  1329, 16782, 20313,  28085, 27699, 28094,  \n9234, 18528, 12222,  14859, 22813, 13922,  2601, 22994, 12443,  \n28087, 27903, 28298,  17644, 17224, 9321,  7589, 3440, 10541,  \n27517, 27901, 27896,  27905, 27685, 28089,  28089, 28300, 27905,  \n14180, 9704, 10998,  14621, 14410, 6564,  28095, 28296, 28091,  \n28099, 28298, 27903,  28097, 27908, 28096,  15665, 16119, 20826,  \n28093, 27696, 27908,  27691, 28093, 28299,  12087, 21178, 17381,  \n27905, 28300, 28094,  17975, 17937, 9187,  27898, 28294, 27906,  \n5949, 9343, 9635,  1788, 4233, 2852,  16165, 11007, 6383,  \n18989, 28302, 12162,  21594, 1726, 482,  10784, 6734, 13956,  \n4677, 9505, 11371,  28100, 28098, 28101,  27904, 28303, 28099,  \n27904, 27910, 28303,  27901, 27517, 27529,  27901, 27529, 27912,  \n13939, 12023, 13391,  1887, 14491, 9232,  11909, 6738, 18209,  \n14827, 20594, 1956,  4413, 6907, 4414,  12617, 4802, 6033,  \n9545, 19072, 5432,  23671, 646, 8391,  11202, 5177, 8229,  \n646, 8392, 8391,  16695, 4726, 16737,  13019, 18908, 14064,  \n7615, 18119, 19598,  12243, 20317, 7012,  25917, 26579, 28104,  \n17762, 16794, 1338,  26398, 28104, 28304,  3816, 19870, 1324,  \n28747, 27320, 26752,  5902, 6751, 10296,  2729, 19494, 14605,  \n6514, 9683, 11872,  27916, 27706, 28306,  28105, 27708, 27917,  \n14802, 8432, 8433,  6676, 13018, 2762,  28306, 27706, 27709,  \n27708, 28105, 28106,  13524, 8192, 16035,  18029, 20366, 7780,  \n6917, 19932, 4374,  27710, 28308, 27709,  4365, 10515, 10514,  \n28307, 27711, 27918,  27710, 28107, 28308,  6902, 12958, 8479,  \n28307, 28108, 27711,  9078, 10368, 13943,  11642, 2025, 792,  \n13342, 11592, 6274,  13218, 15329, 4094,  28111, 27541, 27542,  \n27538, 28110, 28112,  28111, 27542, 27921,  28111, 27921, 28309,  \n12162, 12163, 18989,  28112, 28113, 27922,  18893, 16855, 22676,  \n27923, 28310, 27545,  27545, 28310, 28114,  27924, 28115, 28311,  \n317, 2124, 3667,  6145, 6144, 23201,  9900, 373, 11854,  \n27926, 27713, 27327,  19091, 20583, 7662,  2773, 2772, 9041,  \n26765, 28312, 28116,  28116, 26230, 26765,  9984, 9983, 13919,  \n27333, 27334, 27127,  3613, 14762, 12046,  4596, 4905, 9573,  \n497, 2965, 3833,  12570, 12571, 9726,  9067, 7803, 17988,  \n9682, 7003, 11538,  12064, 1247, 15744,  1310, 21046, 18781,  \n565, 16056, 13307,  14271, 8287, 1480,  16765, 8665, 6406,  \n27329, 26766, 28117,  4355, 17461, 4353,  28118, 27927, 27716,  \n2457, 18811, 11256,  2970, 2792, 2791,  4020, 6674, 979,  \n4010, 12181, 20623,  27338, 28313, 28119,  5247, 2006, 5246,  \n10992, 14840, 23046,  18621, 10928, 2942,  1538, 406, 405,  \n27927, 28120, 27721,  27932, 28120, 28314,  13157, 20253, 1998,  \n11815, 11050, 13020,  14305, 626, 625,  2050, 20240, 20239,  \n4487, 9872, 12887,  26777, 27930, 27929,  14849, 14837, 3528,  \n9987, 18357, 3798,  11484, 12731, 10568,  28316, 27930, 27931,  \n23470, 21390, 337,  19518, 9899, 9714,  4010, 20623, 17522,  \n3931, 3212, 14940,  9867, 6841, 912,  27341, 27723, 27724,  \n8540, 4180, 18616,  27345, 27343, 27552,  17741, 20601, 15864,  \n5245, 9825, 2474,  7271, 20244, 4873,  2079, 17489, 17207,  \n28319, 27933, 27726,  10684, 7778, 6375,  27725, 28319, 27726,  \n27935, 27549, 27932,  27725, 28320, 28319,  27729, 28320, 27725,  \n27932, 28321, 27935,  28126, 28320, 27729,  14246, 7704, 4861,  \n28127, 28126, 27554,  2338, 2339, 11772,  15742, 10320, 6709,  \n338, 26502, 21675,  27556, 28321, 28129,  19544, 14331, 16165,  \n28531, 27558, 28129,  27938, 27936, 27937,  27558, 28131, 27731,  \n16945, 486, 3645,  28133, 28324, 28130,  27939, 28325, 27734,  \n11739, 14360, 6867,  22680, 22038, 7549,  12180, 13082, 13796,  \n28326, 28134, 28136,  15183, 1287, 3558,  28134, 28133, 27733,  \n27562, 28138, 27735,  14345, 11502, 19679,  2409, 2869, 3778,  \n28138, 28328, 27737,  28328, 28327, 27737,  28327, 27940, 27737,  \n28327, 28136, 27940,  14848, 4176, 13526,  21423, 22475, 10418,  \n19585, 11152, 20056,  2331, 20100, 3953,  7996, 21717, 7997,  \n20395, 7603, 3436,  9999, 496, 18527,  6525, 17138, 1634,  \n14007, 18764, 21448,  15050, 8113, 2967,  17518, 13262, 5586,  \n6935, 6934, 21466,  16549, 9263, 8704,  5525, 25706, 17409,  \n7779, 2428, 444,  28143, 27158, 27368,  12147, 12759, 4478,  \n15743, 15740, 5525,  1540, 1539, 2855,  15743, 28329, 15740,  \n15700, 9490, 15699,  19642, 8006, 347,  9314, 17277, 16184,  \n12943, 17241, 18906,  11304, 11303, 1652,  16679, 3884, 16680,  \n4876, 10839, 3744,  17070, 12384, 2841,  27372, 27740, 27951,  \n21588, 22149, 21587,  27372, 26947, 27740,  7042, 13875, 17837,  \n9033, 13963, 8878,  19906, 6581, 9939,  4567, 15372, 3555,  \n17672, 7215, 8091,  4293, 5456, 11209,  27374, 26250, 19829,  \n13330, 8648, 17276,  1491, 3308, 12299,  28330, 27161, 27950,  \n28146, 27376, 28331,  27743, 27744, 27163,  28147, 27741, 27375,  \n15610, 11242, 8550,  28331, 27376, 28149,  2210, 12416, 2537,  \n14439, 5943, 14440,  8176, 16215, 20476,  14542, 10184, 6902,  \n11250, 11158, 19634,  18477, 16648, 10098,  10797, 1296, 14930,  \n17409, 28332, 19853,  19992, 22204, 2167,  8197, 2314, 13745,  \n5200, 12518, 8694,  15921, 3454, 11686,  8408, 5661, 9287,  \n2144, 3716, 12988,  28334, 28149, 27745,  27170, 28334, 27745,  \n14726, 8724, 5713,  27952, 26948, 26956,  3999, 19098, 16606,  \n17596, 2357, 3091,  20874, 12614, 2178,  15447, 28335, 15448,  \n28336, 28151, 27953,  16663, 17956, 19282,  4523, 15383, 10123,  \n19587, 1835, 7903,  9151, 3548, 13437,  18733, 6984, 9659,  \n28337, 26794, 28333,  28151, 28338, 27954,  8911, 16011, 1946,  \n27957, 28336, 27953,  16937, 22389, 16935,  26790, 26789, 27746,  \n10941, 19054, 18942,  11912, 14677, 15831,  26952, 26794, 28337,  \n28338, 28154, 27954,  27954, 28154, 27956,  17042, 13014, 22740,  \n28341, 28342, 28343,  27750, 27567, 28152,  27567, 26790, 28152,  \n26790, 27746, 28152,  9379, 7118, 12087,  12159, 687, 10361,  \n7369, 8206, 8207,  7644, 20355, 13881,  17106, 15710, 12826,  \n27574, 27572, 27753,  28155, 27961, 27960,  27961, 27751, 27960,  \n6202, 14015, 19127,  8020, 5939, 8019,  7464, 18913, 10923,  \n20467, 17021, 13786,  17924, 17263, 21109,  4499, 5906, 10693,  \n8988, 15280, 3955,  8173, 21492, 23580,  13621, 19991, 17936,  \n4749, 6826, 9499,  21174, 17800, 13685,  1605, 8822, 5684,  \n28155, 28346, 28158,  18977, 5898, 18913,  11189, 16490, 6927,  \n7747, 5641, 5642,  27961, 28158, 27757,  7464, 18977, 18913,  \n851, 852, 3496,  27756, 27387, 28347,  28348, 27757, 28159,  \n3364, 3289, 15516,  8483, 15143, 4976,  27579, 27757, 28348,  \n2832, 13544, 12600,  28161, 27579, 28348,  27759, 26620, 27578,  \n1760, 4750, 18347,  28162, 27579, 28161,  26270, 27394, 27580,  \n1583, 1582, 23529,  27580, 27394, 28350,  24089, 12321, 20461,  \n27963, 28352, 27182,  12000, 15462, 22557,  12381, 18615, 11196,  \n27182, 28352, 27760,  9815, 15799, 7473,  22250, 9260, 10793,  \n27393, 27392, 27964,  14750, 5771, 17807,  27964, 28165, 27393,  \n28165, 27965, 27393,  25522, 25658, 10922,  17595, 12565, 2357,  \n13394, 21741, 3995,  21241, 19463, 12359,  28354, 26456, 27762,  \n10922, 28349, 10923,  6614, 4608, 6615,  28354, 27765, 26456,  \n1928, 16865, 15324,  13820, 18666, 21149,  22727, 13482, 14417,  \n941, 2918, 8546,  27581, 27968, 28163,  622, 621, 5564,  \n27967, 28355, 27766,  11843, 20975, 21864,  27966, 26969, 27186,  \n2541, 2791, 13484,  28355, 27768, 27766,  27966, 27186, 28167,  \n9202, 10797, 14930,  8810, 3719, 8695,  7412, 2007, 1928,  \n27768, 28355, 27582,  21328, 22094, 2937,  18248, 2253, 17877,  \n8517, 21427, 16873,  3709, 13247, 8876,  28356, 26973, 27584,  \n2294, 2290, 2289,  1634, 17138, 5855,  9557, 3754, 8717,  \n27767, 28357, 27769,  20968, 21407, 741,  11172, 14435, 22018,  \n8972, 6754, 12516,  14400, 18789, 20585,  28359, 27584, 27586,  \n27970, 27192, 27969,  7107, 13607, 20513,  3244, 21169, 5273,  \n5263, 18928, 22950,  27585, 27396, 28169,  9564, 13715, 19447,  \n27589, 27970, 28360,  1037, 13889, 11690,  15041, 6486, 3500,  \n11387, 13668, 9812,  27589, 28360, 27770,  14067, 7544, 13262,  \n9872, 6618, 12483,  16881, 6653, 6652,  2483, 16755, 15176,  \n11233, 12324, 10545,  20565, 23933, 17254,  9579, 9578, 16636,  \n1625, 9995, 10236,  5382, 12299, 16053,  28173, 28171, 28361,  \n19712, 5979, 1913,  14078, 8772, 8773,  6714, 7448, 6715,  \n17157, 19535, 15442,  11198, 12582, 11199,  19500, 13997, 18213,  \n19995, 18015, 19996,  17232, 11260, 13976,  19298, 7372, 20634,  \n16196, 10869, 10868,  4954, 3026, 6916,  28363, 28172, 27592,  \n11041, 7468, 21325,  16045, 16044, 17080,  22278, 1340, 10374,  \n18757, 10904, 19596,  19610, 349, 9988,  4243, 3287, 16384,  \n18470, 14399, 21568,  28364, 27592, 27203,  12039, 3795, 1238,  \n18087, 11837, 15370,  21683, 18287, 3284,  8803, 19690, 19689,  \n27975, 27973, 28177,  27974, 27778, 28365,  13026, 20156, 21159,  \n4987, 8689, 5627,  5997, 12861, 19522,  28180, 26132, 27202,  \n21366, 11027, 20925,  11882, 1480, 8598,  28366, 27593, 27782,  \n6975, 9528, 8397,  3776, 19212, 887,  8352, 9435, 6915,  \n26989, 26993, 28183,  21500, 19816, 3494,  14778, 2894, 10763,  \n5820, 22926, 5216,  17287, 14441, 14533,  9976, 14559, 9977,  \n16286, 13529, 639,  6054, 21137, 13755,  4376, 17674, 4296,  \n27785, 27782, 27402,  14038, 14176, 14037,  18942, 19053, 12517,  \n26990, 27597, 28367,  6406, 8665, 22291,  6407, 11735, 4453,  \n6524, 7852, 1944,  16757, 19251, 20684,  27597, 28368, 28367,  \n27784, 25703, 27981,  27597, 27783, 28368,  20630, 13520, 17209,  \n9317, 11464, 5465,  27785, 26994, 27787,  11594, 9959, 1392,  \n10948, 4181, 3157,  6383, 3024, 3023,  9983, 9984, 1422,  \n27598, 26289, 27599,  16578, 4883, 15308,  28370, 27783, 27786,  \n8200, 8202, 17517,  28371, 27786, 28188,  5957, 14620, 21995,  \n8938, 8168, 16670,  28188, 27983, 28371,  27788, 25993, 27603,  \n9196, 16337, 15960,  13141, 3150, 7342,  2445, 12314, 20098,  \n5636, 9780, 17534,  14635, 4888, 19971,  10525, 14792, 16566,  \n27984, 27983, 27797,  7121, 20930, 17436,  9301, 7787, 4785,  \n21545, 16224, 1918,  680, 10747, 4454,  5265, 1172, 1426,  \n1708, 1707, 9927,  27984, 27798, 28193,  18703, 20994, 6396,  \n28191, 27006, 28587,  3862, 4662, 8678,  6858, 14771, 8555,  \n28587, 27006, 26648,  15974, 19166, 16511,  27986, 28587, 26648,  \n26290, 27793, 28372,  6907, 3736, 16738,  19266, 18393, 15077,  \n2095, 15722, 15389,  28192, 27795, 27602,  26828, 26290, 28372,  \n6032, 9478, 9477,  7181, 8240, 4569,  7111, 22514, 13957,  \n27795, 28192, 27987,  28373, 27798, 27985,  7257, 15186, 17107,  \n2365, 16650, 2366,  3351, 16424, 18155,  5047, 17617, 1700,  \n28373, 27985, 27988,  3697, 19143, 3698,  12437, 14771, 743,  \n15678, 1429, 883,  27799, 27416, 27609,  8820, 18375, 12560,  \n26487, 28195, 26142,  14748, 4280, 17744,  26647, 27420, 28196,  \n6619, 9898, 6620,  18617, 8069, 11051,  17018, 17019, 19531,  \n27987, 28192, 28374,  2744, 6951, 2743,  20060, 21864, 3867,  \n5905, 1520, 1519,  11756, 2910, 11757,  17353, 604, 867,  \n10079, 10080, 12128,  28376, 26647, 28196,  27987, 28374, 28197,  \n3173, 11606, 15881,  16832, 5375, 7467,  14028, 14832, 8461,  \n10392, 15848, 7207,  1314, 10881, 1313,  15970, 18423, 9371,  \n11705, 13625, 7957,  28197, 27606, 27987,  27612, 27802, 27235,  \n3444, 5260, 4093,  28377, 27800, 27611,  11577, 23479, 22197,  \n17978, 19094, 16523,  27612, 27613, 27992,  4216, 17752, 15121,  \n21735, 5037, 1181,  13519, 11465, 12604,  7886, 17038, 16314,  \n17603, 22745, 1696,  12018, 16393, 15474,  17735, 19970, 9695,  \n26827, 25574, 10031,  27993, 28197, 28378,  4097, 4096, 6832,  \n27611, 26836, 28379,  8155, 13141, 8156,  5371, 6036, 17217,  \n9741, 9740, 4485,  1458, 3223, 14892,  27993, 28378, 27805,  \n8665, 16765, 5932,  27994, 28379, 26836,  11432, 13837, 13838,  \n21318, 21317, 10626,  12461, 4125, 4126,  5438, 11069, 5437,  \n1440, 1441, 6380,  10212, 12243, 12511,  20458, 9077, 9078,  \n12447, 13908, 9401,  27996, 27805, 28378,  9974, 15873, 6838,  \n10183, 2080, 2382,  17691, 15782, 15104,  16111, 2633, 16072,  \n20876, 19828, 1488,  28200, 27433, 27804,  5482, 7143, 5481,  \n4600, 16045, 17080,  2744, 28381, 6952,  13809, 13810, 16256,  \n3600, 3599, 14237,  18383, 22116, 20792,  14957, 14822, 5305,  \n17757, 22007, 12428,  22228, 20433, 18369,  6828, 15489, 8249,  \n11363, 8198, 11714,  18582, 20991, 15665,  12040, 9228, 3693,  \n723, 15204, 11477,  27434, 27433, 28200,  13641, 8764, 20140,  \n16934, 12564, 3404,  2262, 8751, 13707,  27814, 27617, 26840,  \n7081, 776, 12797,  16378, 2555, 4614,  29731, 15098, 13560,  \n27999, 27808, 28389,  27808, 27996, 28389,  6398, 952, 6399,  \n21521, 15023, 4659,  5714, 5486, 5487,  27434, 28383, 27618,  \n15637, 673, 672,  10151, 12388, 13317,  28385, 28386, 28387,  \n4670, 4669, 17187,  27816, 27618, 28383,  20057, 7709, 9490,  \n28201, 28390, 28204,  28201, 28386, 28390,  19050, 20810, 21079,  \n27810, 27812, 27813,  9578, 7588, 10541,  28203, 28201, 28204,  \n28203, 27813, 28201,  27813, 28203, 28002,  28002, 27810, 27813,  \n8451, 6505, 11963,  4915, 11684, 8900,  17689, 21327, 17647,  \n27810, 28204, 28391,  27620, 27999, 28389,  28204, 28392, 28391,  \n10124, 9345, 13942,  28606, 28393, 27816,  1919, 3048, 21906,  \n28392, 27818, 28391,  27818, 28394, 28391,  17002, 13854, 18848,  \n28000, 26503, 28395,  27821, 27620, 28389,  12903, 12129, 18957,  \n26503, 28003, 28395,  27818, 27819, 28396,  8340, 2978, 2977,  \n27817, 28397, 27028,  25574, 2744, 10031,  22893, 9620, 9619,  \n9068, 19625, 9069,  13910, 5695, 16878,  27621, 27028, 28397,  \n21665, 513, 7250,  11291, 23149, 12235,  27819, 27030, 28005,  \n28399, 27820, 27823,  28399, 27823, 28207,  28207, 28009, 28209,  \n5525, 5899, 2744,  10020, 623, 18932,  13737, 13668, 11387,  \n1583, 3028, 2245,  28005, 27032, 28006,  28210, 26843, 27621,  \n28398, 28210, 27621,  15887, 8816, 15616,  5653, 10586, 10585,  \n27030, 27032, 28005,  28210, 27242, 26670,  3561, 8503, 1259,  \n10981, 16666, 20120,  11742, 8052, 2412,  18240, 8019, 8548,  \n28401, 28006, 27032,  9368, 13747, 2844,  19701, 16238, 16237,  \n27439, 27242, 28402,  6190, 20068, 14077,  28403, 28008, 28215,  \n28404, 28012, 28214,  8368, 8369, 8833,  28405, 28213, 28212,  \n28008, 27443, 28215,  27626, 28216, 28215,  2270, 21696, 10632,  \n569, 8707, 11635,  28408, 28405, 28212,  28016, 27824, 28007,  \n19809, 7127, 11896,  23699, 14881, 20124,  17768, 13426, 17727,  \n12902, 12901, 9390,  17816, 11999, 1363,  14646, 28400, 24921,  \n39, 27627, 28409,  28411, 28018, 28016,  18685, 6719, 726,  \n5421, 371, 15562,  1827, 4325, 4324,  28412, 28410, 28413,  \n5622, 19472, 8240,  28616, 28415, 28417,  28016, 27442, 27824,  \n27625, 28015, 28406,  9408, 21351, 21613,  28011, 17311, 17310,  \n28406, 28015, 28217,  3256, 3661, 20142,  20801, 22352, 17119,  \n2567, 5654, 6883,  28217, 28414, 28406,  28013, 28213, 27828,  \n3809, 7975, 10596,  28410, 28418, 28416,  24921, 28419, 4989,  \n20492, 17619, 8728,  27627, 27826, 28409,  28410, 28412, 28418,  \n28415, 28416, 28418,  14669, 14668, 13657,  28015, 28019, 28217,  \n28420, 28418, 28412,  28217, 28019, 28219,  6306, 13180, 11339,  \n960, 21311, 961,  22820, 18585, 1174,  28421, 28417, 28415,  \n12772, 8902, 10648,  28219, 28019, 27629,  3661, 3256, 11460,  \n28422, 28415, 28418,  14652, 14651, 23133,  28421, 28415, 28422,  \n27628, 26848, 28018,  10262, 4980, 16043,  6475, 10903, 10900,  \n28423, 28219, 28020,  15621, 21843, 16610,  27829, 52, 27826,  \n28018, 28218, 27628,  10231, 766, 21245,  5808, 5560, 12877,  \n6863, 6862, 3552,  15647, 12181, 15397,  1630, 20876, 1488,  \n28020, 28221, 28423,  10471, 18092, 869,  12102, 20439, 11308,  \n52, 27829, 28021,  28422, 28418, 28420,  12738, 1523, 1522,  \n5896, 9256, 10959,  28425, 28221, 27835,  7604, 8646, 15303,  \n4166, 18054, 11302,  27628, 28222, 27455,  27831, 28426, 28225,  \n28427, 28223, 28226,  28021, 28223, 28427,  7869, 7871, 2000,  \n13381, 21663, 5219,  6413, 6894, 19116,  1864, 22007, 9518,  \n5876, 3047, 7402,  3963, 14379, 3964,  15517, 21788, 8150,  \n12824, 16828, 17652,  11696, 5783, 17345,  1548, 8008, 20753,  \n15287, 2944, 20278,  21105, 4058, 7151,  1626, 18396, 12811,  \n14744, 15265, 18714,  27635, 28224, 27044,  16148, 6398, 6399,  \n21376, 8784, 8785,  16530, 20735, 22570,  28428, 28022, 28225,  \n3105, 14499, 10577,  27633, 28228, 28229,  8784, 8384, 20215,  \n9612, 12702, 13001,  7630, 16538, 6325,  28228, 28022, 28428,  \n1832, 1831, 14773,  28028, 28027, 27837,  3238, 3239, 9216,  \n20482, 3122, 12345,  19858, 14987, 8465,  7992, 4865, 4864,  \n17095, 14629, 15521,  10670, 9404, 10737,  11909, 3581, 17654,  \n1080, 21366, 22425,  612, 4119, 4121,  27641, 27634, 28229,  \n5316, 4261, 20165,  28029, 28232, 28028,  10027, 10431, 10026,  \n8251, 21534, 9119,  8922, 12211, 12607,  28030, 28235, 28429,  \n25423, 1522, 27944,  8738, 7006, 2346,  28430, 27838, 28031,  \n28235, 27838, 28430,  28431, 28430, 28032,  7856, 9040, 13992,  \n28030, 28429, 26855,  28025, 27642, 27844,  7757, 9650, 7690,  \n3809, 6246, 7975,  18436, 957, 10316,  13325, 10364, 10365,  \n15354, 5685, 17287,  2008, 14006, 2159,  20643, 22540, 15526,  \n20803, 16394, 4491,  5059, 1907, 17244,  18410, 2368, 2370,  \n22514, 14979, 8860,  4395, 11445, 18510,  27647, 28236, 27839,  \n13508, 17326, 13509,  27051, 28432, 28237,  27641, 28234, 28433,  \n12027, 23856, 14681,  25064, 12856, 26812,  28236, 27647, 28238,  \n4681, 13530, 14309,  27468, 27641, 28433,  14400, 11618, 18789,  \n6512, 9395, 6111,  9771, 13795, 1472,  15457, 9177, 5251,  \n12091, 4028, 4029,  4937, 7089, 14703,  7925, 3697, 3698,  \n17816, 1363, 12611,  14742, 4939, 11173,  18348, 16560, 15385,  \n12960, 6371, 12918,  19192, 17570, 18726,  8719, 874, 9650,  \n11044, 1277, 16801,  10415, 11375, 4435,  28433, 28037, 27468,  \n27261, 28241, 27842,  3105, 11057, 14499,  448, 10548, 3678,  \n17011, 13251, 19616,  15679, 16007, 19249,  13449, 1008, 1007,  \n28664, 27845, 28035,  6698, 21627, 17105,  16122, 10844, 10845,  \n1962, 19644, 746,  28035, 28876, 28664,  2860, 2692, 16209,  \n26862, 28876, 28035,  6619, 7157, 9556,  26862, 28435, 28436,  \n26862, 28436, 28876,  28435, 27264, 27851,  26862, 27264, 28435,  \n1958, 2629, 12186,  28041, 28246, 28437,  28041, 28437, 27850,  \n16618, 12547, 12548,  28248, 28243, 27476,  8711, 8151, 9763,  \n27850, 28437, 28438,  28247, 27850, 28438,  28243, 27263, 27476,  \n15609, 23330, 18088,  12913, 395, 2929,  27475, 28245, 27852,  \n7119, 10103, 18146,  28439, 28247, 28438,  18493, 12007, 11245,  \n8703, 3276, 22828,  27265, 28043, 27654,  28247, 28439, 28249,  \n6394, 19187, 19818,  28439, 28441, 28249,  19931, 16265, 13351,  \n3659, 19891, 4564,  10077, 11329, 11328,  28442, 28250, 27855,  \n28249, 28443, 27857,  28441, 28443, 28249,  28044, 28442, 27855,  \n28443, 28252, 27857,  18001, 13857, 8499,  13823, 1437, 14382,  \n19826, 15616, 15615,  16485, 10257, 12927,  21667, 4551, 13293,  \n28253, 28252, 28445,  28251, 27656, 28254,  1109, 13334, 6601,  \n24884, 18249, 23499,  28446, 28253, 28445,  28255, 28253, 28446,  \n28446, 28447, 28255,  27859, 27071, 27862,  28255, 28447, 28448,  \n28255, 28448, 28257,  28448, 28450, 28257,  2791, 2792, 20562,  \n28049, 28052, 28449,  28450, 28259, 28257,  13155, 9443, 13330,  \n28450, 28451, 28259,  28452, 28453, 28451,  6990, 10273, 15694,  \n28453, 28259, 28451,  28259, 28453, 28260,  20748, 21687, 18352,  \n28260, 28453, 28261,  21236, 21361, 345,  17385, 20772, 22489,  \n28055, 27488, 27489,  11384, 21326, 15264,  2883, 2884, 2328,  \n18530, 15632, 4944,  27486, 28454, 27484,  8619, 14846, 15773,  \n17837, 25369, 29511,  1751, 20206, 3489,  3291, 14738, 6586,  \n28457, 27867, 27667,  20368, 14353, 9865,  28457, 27667, 28264,  \n22828, 4295, 20161,  1175, 5970, 8194,  28264, 27668, 28059,  \n14545, 21343, 9877,  11919, 6870, 6871,  12700, 11398, 10523,  \n27875, 27662, 27492,  6721, 15209, 17361,  28458, 28060, 28263,  \n28459, 28460, 28265,  28461, 28266, 28460,  28265, 28460, 28266,  \n28264, 28059, 28462,  9441, 21221, 14936,  22787, 17301, 14363,  \n12306, 5383, 5384,  28461, 28267, 28266,  8411, 13984, 1323,  \n16663, 17257, 7847,  12355, 12354, 11613,  7435, 7434, 13348,  \n8498, 23323, 14072,  28265, 28269, 28459,  28271, 28267, 28461,  \n28462, 28059, 28065,  5895, 5452, 5016,  28268, 28463, 27672,  \n28463, 28270, 27672,  28064, 28060, 28458,  9231, 19030, 1155,  \n28458, 28697, 28064,  8108, 13042, 20205,  22887, 21070, 13652,  \n23325, 15807, 15806,  3701, 5999, 6001,  27879, 28465, 28066,  \n12615, 4469, 12763,  28064, 28464, 28069,  28064, 28697, 28464,  \n28269, 28069, 28464,  14002, 12160, 15733,  28073, 27881, 28063,  \n20110, 4851, 4850,  27873, 28070, 28065,  12048, 16353, 1036,  \n27879, 27292, 28273,  19663, 4702, 3437,  28072, 28466, 27091,  \n27500, 28270, 28275,  7973, 547, 19815,  28466, 28273, 27292,  \n28466, 27292, 27091,  27884, 28072, 27091,  28276, 28470, 28274,  \n28470, 28471, 28274,  28471, 28472, 28070,  7575, 17854, 2050,  \n23807, 10253, 2763,  7656, 10593, 5623,  27887, 28073, 28473,  \n28470, 28276, 28474,  1513, 20830, 14855,  21730, 14564, 17591,  \n20609, 17861, 16049,  28474, 28074, 28475,  28474, 28276, 28074,  \n7540, 8543, 17714,  9112, 5379, 9113,  28709, 28279, 28476,  \n28477, 28278, 28279,  28477, 28279, 28709,  16884, 3183, 4019,  \n28277, 28475, 28074,  28075, 28077, 28281,  28478, 28080, 27887,  \n28476, 28279, 28282,  12346, 1475, 1474,  1148, 8769, 14275,  \n5020, 16785, 22908,  27684, 28480, 28277,  2414, 13372, 2934,  \n28480, 28475, 28277,  779, 778, 3067,  4325, 23025, 16932,  \n22919, 11227, 7626,  28080, 28479, 28284,  28284, 28479, 28481,  \n28284, 28282, 28081,  28284, 28481, 28282,  6428, 8382, 7727,  \n24833, 26695, 7136,  26985, 13507, 3387,  11769, 19150, 8687,  \n28285, 27893, 27892,  28285, 27892, 28482,  19318, 4221, 8120,  \n27684, 28285, 28480,  18179, 9933, 11629,  6416, 6415, 21230,  \n17682, 3277, 19680,  28717, 28086, 28292,  28288, 28483, 28289,  \n28288, 28289, 27892,  7032, 4813, 5844,  8526, 21233, 2387,  \n6123, 15384, 6122,  28085, 28292, 28086,  2110, 14440, 2109,  \n28290, 28484, 28288,  22170, 9498, 3455,  5253, 5254, 16410,  \n16745, 15451, 15450,  28485, 28295, 28297,  19991, 7774, 11161,  \n27691, 28299, 28290,  9149, 19944, 5744,  10919, 6916, 21783,  \n28085, 28723, 28292,  7277, 9242, 9241,  28296, 28487, 28297,  \n28297, 28295, 28091,  15781, 1507, 587,  28489, 28087, 28298,  \n28490, 28087, 28489,  27900, 28087, 28490,  28491, 27900, 28490,  \n673, 15637, 22232,  28484, 28299, 28492,  28299, 28484, 28290,  \n28077, 27896, 28493,  7401, 15491, 17643,  5912, 19195, 17086,  \n28094, 28494, 28723,  19196, 20847, 23510,  28085, 28094, 28723,  \n13189, 13188, 21370,  3875, 3876, 19777,  28488, 28092, 28090,  \n28488, 28495, 28092,  28489, 28298, 28496,  7812, 18124, 17625,  \n2291, 11052, 9262,  27900, 28491, 28096,  27516, 27900, 28096,  \n15685, 8367, 15686,  25387, 29333, 3722,  8269, 1194, 1195,  \n17272, 5592, 1989,  27896, 27901, 28493,  28300, 28089, 28084,  \n28094, 28300, 28494,  2234, 629, 2235,  28497, 28498, 28294,  \n28099, 28496, 28298,  28097, 28499, 28093,  28093, 28492, 28299,  \n28093, 28499, 28492,  9619, 9340, 12210,  524, 5604, 17912,  \n27688, 28301, 27697,  8094, 12450, 20070,  28498, 27906, 28294,  \n1823, 16221, 8320,  28095, 28486, 28296,  28092, 28495, 27703,  \n11812, 14218, 9806,  28500, 28496, 28099,  3542, 16710, 7915,  \n10825, 7523, 15362,  13528, 1972, 18217,  7517, 13283, 6485,  \n27906, 28498, 28098,  15402, 16908, 8716,  28101, 28501, 28486,  \n28101, 28486, 28095,  28502, 27703, 28495,  2777, 13793, 21312,  \n27702, 28092, 27703,  27697, 28503, 27522,  28503, 27523, 27522,  \n7556, 9073, 15029,  28098, 28501, 28101,  695, 17150, 694,  \n27703, 28303, 27910,  27703, 28502, 28303,  8813, 15229, 4160,  \n27911, 27528, 27523,  11818, 1925, 12204,  19800, 21225, 17843,  \n15292, 8169, 8170,  3199, 8097, 6339,  22291, 8665, 10469,  \n27913, 28505, 27914,  28505, 28506, 27914,  16701, 13638, 18108,  \n20872, 23671, 8391,  27317, 27705, 28103,  27531, 28507, 26579,  \n28507, 28104, 26579,  26752, 26218, 28304,  26398, 28304, 26218,  \n19704, 17148, 9561,  17884, 17883, 12485,  13977, 13415, 14099,  \n2959, 14055, 14954,  20394, 6479, 18411,  14850, 9236, 12933,  \n28306, 27709, 28509,  20542, 20278, 2944,  5921, 10876, 3830,  \n18176, 622, 1965,  948, 9055, 3421,  28510, 28307, 27918,  \n27709, 28308, 28511,  18872, 14992, 10452,  20126, 11679, 3103,  \n20070, 12450, 5287,  7374, 21052, 3317,  2128, 13246, 7969,  \n28308, 28111, 28512,  28111, 28308, 28107,  12607, 993, 12012,  \n28108, 28513, 27919,  12729, 21642, 1695,  27920, 28514, 28110,  \n19444, 8575, 3860,  14726, 5713, 6418,  28514, 28515, 28110,  \n17327, 14899, 16464,  28110, 28515, 28112,  27921, 28311, 28309,  \n20686, 9498, 5605,  28112, 28515, 28113,  27924, 28311, 27921,  \n28517, 28113, 28515,  28518, 28113, 28517,  19382, 2789, 2788,  \n16416, 8181, 10445,  20345, 14886, 12488,  28518, 27923, 28113,  \n4283, 3393, 13192,  27923, 28519, 28310,  28115, 28516, 28311,  \n28518, 28519, 27923,  27926, 28114, 28520,  27336, 27925, 26919,  \n4508, 1413, 6537,  17322, 600, 21328,  27334, 27336, 27127,  \n27713, 28521, 27714,  27547, 27714, 28522,  12440, 12695, 1307,  \n15986, 9170, 9843,  13422, 13421, 14320,  26765, 27547, 28522,  \n28312, 26765, 28522,  26919, 27328, 27333,  5837, 20596, 4719,  \n5910, 3575, 1210,  27335, 27332, 28119,  16379, 9346, 21007,  \n27329, 28524, 28118,  28524, 27927, 28118,  28524, 28120, 27927,  \n7647, 17949, 4398,  11836, 1627, 12811,  5479, 2117, 5480,  \n5493, 5492, 14273,  21099, 21228, 3711,  20692, 14851, 4320,  \n28120, 28525, 28314,  11158, 2715, 22404,  27932, 27721, 28120,  \n11031, 10479, 4033,  20239, 20240, 8704,  27930, 28526, 27929,  \n12663, 7110, 22828,  12126, 20101, 18362,  20004, 13425, 14209,  \n20004, 17652, 13425,  10014, 8602, 10015,  27722, 28527, 27343,  \n27343, 28527, 28122,  27343, 28122, 27552,  20516, 6027, 15395,  \n5494, 14217, 24315,  28316, 27931, 28123,  7266, 4952, 5238,  \n16608, 14667, 11505,  17317, 17949, 21332,  10598, 2793, 10597,  \n28124, 28529, 27934,  27934, 28529, 28125,  15220, 9909, 2658,  \n17389, 14150, 9755,  28530, 27724, 27933,  2701, 3422, 16129,  \n3382, 2747, 2746,  27932, 28317, 28322,  12363, 19612, 11463,  \n12896, 15403, 18344,  2188, 15811, 15085,  9791, 13010, 9789,  \n28323, 28129, 28321,  28127, 27557, 27936,  28127, 27936, 28128,  \n8452, 5794, 5793,  9627, 19644, 6501,  11885, 1271, 3134,  \n27936, 27938, 28764,  28764, 27938, 28130,  27558, 28531, 28131,  \n28132, 28131, 28532,  6064, 2485, 2486,  27731, 28131, 27939,  \n10337, 6638, 17034,  28131, 28132, 27939,  20098, 4801, 13658,  \n13310, 13249, 4159,  28324, 28133, 28134,  28326, 28533, 28134,  \n19654, 16550, 18761,  27562, 27734, 28534,  10422, 14326, 1998,  \n28534, 28138, 27562,  7063, 2539, 16441,  2335, 2334, 14919,  \n28535, 28328, 28138,  28136, 28327, 28326,  10052, 15284, 10662,  \n18506, 17614, 21478,  10905, 4756, 16568,  23025, 7555, 28536,  \n20223, 6292, 15136,  5135, 21115, 5134,  26898, 11313, 9823,  \n11968, 7254, 16882,  13251, 17011, 20955,  27944, 27369, 27945,  \n28540, 27948, 27947,  28537, 28538, 27371,  28358, 26310, 26309,  \n19615, 21028, 19616,  16807, 12124, 8419,  11882, 9116, 2288,  \n27740, 28144, 28539,  27948, 26785, 27370,  1524, 771, 1525,  \n27371, 28146, 28537,  3810, 4792, 17674,  25091, 25425, 13251,  \n3964, 14379, 5884,  27740, 27948, 28144,  20698, 11529, 15453,  \n28146, 27371, 27373,  6496, 20575, 17757,  680, 2023, 6027,  \n493, 492, 19133,  17356, 17355, 7669,  12719, 20146, 7802,  \n18022, 20088, 13547,  12460, 9420, 17532,  20202, 24306, 21892,  \n28543, 27739, 26948,  4361, 7228, 14510,  27742, 28544, 27743,  \n21257, 2000, 7871,  3837, 3028, 16676,  17188, 2027, 8082,  \n10411, 4597, 15073,  20202, 13251, 11310,  20771, 6972, 14631,  \n21378, 5881, 9439,  8456, 7123, 7122,  7911, 9391, 2748,  \n28331, 28149, 28334,  18601, 3219, 17911,  10658, 6742, 828,  \n23792, 13690, 10373,  17968, 14151, 17845,  10586, 3944, 11806,  \n12571, 10367, 14461,  8728, 17619, 17003,  9357, 18122, 15754,  \n28546, 28547, 27955,  10223, 11552, 21373,  21127, 3774, 15350,  \n20335, 16929, 14265,  424, 8880, 425,  28548, 28147, 27164,  \n28150, 27377, 28148,  15156, 18940, 15155,  27164, 27752, 28548,  \n17238, 12199, 16863,  19845, 4208, 9697,  27170, 27958, 28549,  \n13257, 21485, 16409,  13482, 21184, 22013,  28550, 28151, 28336,  \n17652, 20150, 13425,  907, 757, 7323,  28549, 27958, 28551,  \n8719, 17823, 10887,  856, 11908, 18326,  26956, 26955, 27952,  \n28151, 28550, 28338,  20230, 10768, 10769,  28341, 28550, 28336,  \n27957, 28341, 28336,  14906, 21062, 14196,  28341, 27957, 28342,  \n28552, 28152, 27746,  11365, 12886, 9637,  26793, 27377, 28150,  \n9363, 13119, 13118,  27959, 26796, 27171,  4213, 9733, 9891,  \n28553, 27959, 27171,  28553, 27171, 26952,  27962, 28554, 26955,  \n27957, 27750, 28342,  28342, 27750, 28344,  27750, 28152, 28344,  \n28344, 28152, 28153,  6836, 12831, 12830,  28552, 28153, 28152,  \n19030, 18723, 8615,  24419, 23133, 28555,  26789, 26436, 27570,  \n28556, 26789, 27570,  7698, 14490, 23236,  13805, 10969, 13702,  \n12964, 2379, 13743,  26954, 28558, 27570,  19705, 9270, 22304,  \n10283, 963, 25549,  7984, 14987, 8670,  9558, 6483, 6385,  \n18605, 23655, 17550,  3486, 7299, 2597,  14011, 11952, 22458,  \n18213, 13997, 24039,  28561, 27173, 28157,  28561, 28157, 28562,  \n6438, 2165, 2166,  12680, 19638, 12454,  21524, 20470, 14994,  \n26793, 28559, 26964,  28158, 27961, 28155,  15720, 12515, 20853,  \n13494, 4335, 5596,  28562, 28157, 28563,  28563, 28157, 27754,  \n18347, 20699, 6539,  12482, 16038, 9871,  9461, 6154, 6155,  \n10404, 16273, 10405,  12089, 9293, 5026,  14227, 20256, 617,  \n12431, 10094, 7712,  28346, 28159, 28158,  20420, 669, 668,  \n5471, 14445, 5472,  6510, 22841, 28566,  8522, 8521, 23856,  \n27575, 26803, 28160,  21418, 13193, 23905,  879, 8803, 6306,  \n28159, 28567, 28348,  18510, 8125, 8139,  6637, 2355, 16354,  \n5707, 13193, 21418,  1543, 17644, 4959,  17110, 1752, 12371,  \n6522, 5851, 10488,  6284, 5115, 6066,  6930, 3874, 13639,  \n3139, 3960, 3324,  7669, 7668, 17356,  28161, 28348, 28567,  \n19914, 14693, 13195,  14641, 12995, 12996,  27758, 28784, 27387,  \n28782, 28568, 28161,  4679, 7367, 20241,  13037, 5599, 13156,  \n4579, 1564, 4580,  28568, 28162, 28161,  8555, 12437, 16059,  \n27758, 26967, 28784,  12342, 16301, 5284,  4683, 21845, 3568,  \n28351, 26967, 28163,  6547, 1986, 6546,  22863, 11708, 15145,  \n18503, 18268, 6590,  19869, 6605, 20918,  15493, 21788, 14030,  \n18756, 6657, 18755,  4858, 15246, 1260,  27767, 27761, 28353,  \n14483, 8896, 10646,  16949, 8563, 8565,  7368, 15190, 15192,  \n18849, 20398, 3182,  27582, 28355, 28571,  4244, 20083, 10995,  \n27968, 26973, 28570,  1425, 13249, 5266,  1014, 13803, 2077,  \n14620, 11966, 21995,  17405, 19222, 17403,  20985, 12132, 16400,  \n20443, 19495, 16887,  17422, 3885, 2134,  8484, 1553, 3009,  \n7370, 17271, 15341,  27584, 28573, 28356,  27969, 27583, 28166,  \n13875, 29509, 25369,  9471, 938, 940,  20062, 12097, 12098,  \n15080, 20923, 6856,  12744, 4830, 4829,  14694, 13194, 13195,  \n3506, 365, 14399,  22285, 12178, 15193,  3519, 16630, 15962,  \n7718, 13030, 7719,  3433, 16980, 14511,  8110, 4817, 12212,  \n27585, 26278, 27396,  2981, 17663, 14539,  1725, 17260, 21355,  \n10311, 21160, 4646,  5449, 20190, 16217,  27587, 27588, 28168,  \n28790, 28360, 27970,  7881, 10498, 21566,  15177, 9495, 8459,  \n15167, 21176, 11035,  20812, 3964, 19098,  27771, 28168, 27588,  \n18859, 8953, 8954,  7981, 10531, 17155,  14326, 18609, 15437,  \n27773, 28170, 27194,  5659, 9736, 17089,  18566, 13345, 10038,  \n28171, 27770, 28360,  28361, 28171, 28360,  8738, 14446, 16282,  \n26978, 27195, 28362,  27773, 27196, 28172,  11989, 16733, 18875,  \n9244, 17072, 2436,  18899, 10878, 10877,  27400, 26473, 28574,  \n28574, 26473, 27971,  8953, 18859, 28575,  11904, 15562, 6926,  \n4741, 6036, 13600,  26978, 28362, 28576,  3790, 3792, 5034,  \n27774, 28577, 27971,  11510, 17543, 11511,  19705, 21865, 18244,  \n19251, 9171, 19252,  23229, 20091, 5220,  28578, 27973, 27972,  \n5952, 10572, 19516,  6990, 10274, 10273,  1185, 12649, 17387,  \n323, 5625, 13215,  27592, 28364, 28363,  11856, 11441, 1089,  \n27203, 26989, 28183,  10128, 20922, 14310,  27776, 26986, 27974,  \n28175, 28365, 27778,  4278, 17400, 7614,  16457, 23824, 10116,  \n27779, 27593, 28366,  27594, 28176, 28175,  9530, 20933, 10791,  \n27594, 27780, 28176,  1373, 19142, 3171,  14291, 19956, 14289,  \n17473, 1169, 10127,  27975, 28177, 28579,  2862, 9616, 10978,  \n790, 9159, 791,  6732, 6731, 12430,  19627, 4093, 18902,  \n27781, 27595, 28580,  12537, 3822, 18111,  20392, 6978, 23182,  \n12964, 13743, 10872,  10694, 3521, 9279,  12870, 25113, 22495,  \n3885, 4701, 2134,  19515, 11935, 21167,  954, 5071, 5070,  \n2174, 11165, 918,  28579, 27596, 27975,  27976, 27206, 28182,  \n13347, 10938, 10939,  5034, 5743, 5035,  20009, 2818, 6477,  \n5185, 7949, 5184,  11050, 1832, 13020,  7054, 15603, 1444,  \n27979, 26993, 28802,  26990, 28367, 28182,  27405, 26815, 28184,  \n22226, 5483, 19463,  13870, 15368, 19621,  6684, 20494, 11292,  \n21379, 13559, 11933,  11067, 16002, 11068,  11792, 15582, 15581,  \n22542, 20432, 7933,  18904, 1123, 3194,  4010, 7856, 7855,  \n22426, 22254, 2637,  21159, 20156, 14434,  28368, 27783, 28370,  \n27210, 28582, 28187,  24303, 10898, 23011,  13383, 21950, 18245,  \n27407, 27210, 28187,  28187, 27789, 27407,  28370, 27786, 28371,  \n7433, 3424, 15319,  20919, 3691, 20386,  12725, 27787, 27788,  \n4611, 17672, 8466,  2356, 22977, 5946,  28583, 27599, 28584,  \n14976, 8369, 5499,  11937, 22676, 573,  12620, 11176, 6086,  \n9456, 435, 21989,  18072, 1586, 17916,  17328, 9193, 19325,  \n27796, 28584, 27792,  1313, 2632, 8395,  15503, 6599, 2600,  \n27789, 28586, 27602,  5846, 5327, 15484,  1078, 9386, 441,  \n3328, 10932, 9003,  14802, 14801, 8432,  21750, 17766, 5562,  \n12762, 19783, 21086,  12101, 11341, 9267,  701, 8710, 11084,  \n8147, 15215, 13076,  5182, 7839, 16785,  9241, 22285, 15193,  \n27986, 28588, 28587,  18018, 10265, 10264,  8584, 4287, 22367,  \n10587, 10588, 2826,  9945, 1470, 11325,  16224, 21545, 20109,  \n669, 793, 11110,  619, 9229, 10097,  12782, 19145, 12800,  \n10412, 19634, 21096,  5860, 2322, 2321,  13607, 17723, 13608,  \n15529, 12821, 6354,  13112, 4919, 14503,  5623, 21215, 3247,  \n8494, 14598, 15661,  16551, 11099, 11101,  28192, 28813, 28374,  \n7032, 3619, 2720,  28591, 27988, 27802,  1912, 9189, 17994,  \n15069, 20086, 10679,  2903, 15274, 2904,  28592, 27607, 27800,  \n16678, 952, 12858,  5944, 15557, 14044,  13258, 7656, 7655,  \n14079, 7648, 22996,  20418, 12568, 12292,  26647, 28376, 27426,  \n28377, 28592, 27800,  18339, 20262, 16693,  6847, 13719, 13756,  \n1058, 14537, 6961,  11488, 12457, 12650,  12106, 16630, 3519,  \n8498, 14072, 15655,  5676, 5675, 4075,  28377, 27611, 28379,  \n19156, 16232, 7142,  28374, 28378, 28197,  19418, 1122, 18904,  \n13250, 5595, 17383,  11708, 16409, 15145,  28596, 27429, 27426,  \n13839, 12676, 20190,  478, 5342, 8894,  2599, 9745, 5392,  \n18499, 13462, 15923,  803, 16449, 16454,  3847, 3138, 1579,  \n9720, 7731, 4083,  5145, 12718, 21889,  27616, 28598, 27994,  \n27994, 27614, 27616,  13173, 1909, 14723,  592, 6913, 15768,  \n14196, 13527, 9641,  18538, 16296, 2714,  18067, 19363, 17668,  \n27432, 28382, 26662,  28599, 27615, 27617,  18558, 722, 11477,  \n10963, 6501, 8003,  10448, 1325, 525,  8459, 16325, 6238,  \n15686, 8367, 3288,  28600, 27617, 27814,  18957, 4178, 11620,  \n27025, 26662, 28382,  20815, 13217, 2405,  306, 6744, 9760,  \n28388, 27616, 27812,  28384, 27021, 26841,  13126, 13692, 16637,  \n3339, 1373, 3340,  13061, 12584, 5464,  27996, 28199, 28389,  \n28199, 28602, 28389,  11787, 10421, 11788,  13196, 19335, 11926,  \n28603, 22592, 24661,  28388, 27812, 27811,  28604, 27436, 27998,  \n26841, 28000, 28601,  27814, 28605, 28600,  8539, 7828, 14524,  \n953, 954, 2903,  27815, 28605, 27814,  13159, 19059, 13217,  \n28606, 27816, 28383,  16304, 9884, 24005,  10315, 6895, 6470,  \n28607, 28601, 28000,  4012, 18555, 3438,  16249, 12293, 13043,  \n27818, 28392, 28201,  4802, 16641, 17880,  19985, 28603, 24661,  \n4144, 14713, 12146,  22715, 14373, 20793,  28604, 27619, 27436,  \n12470, 7226, 17036,  1034, 5663, 3529,  3225, 10676, 3224,  \n2291, 7060, 14697,  10530, 6235, 1721,  28394, 27810, 28391,  \n27027, 27820, 27815,  28608, 28393, 28606,  1095, 1096, 21582,  \n18952, 12217, 11683,  28607, 28000, 28395,  16993, 19025, 19921,  \n3900, 1384, 18466,  9370, 8952, 13331,  28394, 27818, 28396,  \n1959, 1858, 2686,  27821, 28389, 28828,  1844, 28826, 28772,  \n27816, 28393, 27822,  25113, 28772, 28826,  28007, 27821, 28828,  \n4221, 10866, 17888,  7691, 8838, 14357,  23167, 7885, 9015,  \n6010, 20433, 5988,  16643, 2730, 12289,  28206, 27819, 28005,  \n7948, 2167, 2168,  19487, 21085, 20166,  28008, 28403, 28208,  \n25565, 4034, 28610,  28005, 28004, 28206,  4855, 4856, 12384,  \n6945, 15403, 6944,  11047, 14634, 5577,  28611, 23272, 21489,  \n28210, 28402, 27242,  19338, 19124, 21010,  5972, 9489, 15700,  \n28393, 28212, 27822,  18053, 19653, 18052,  3279, 15358, 872,  \n28613, 4430, 25284,  902, 16442, 901,  20203, 15726, 15727,  \n13729, 6919, 19647,  17169, 17168, 8916,  15712, 5032, 14547,  \n1062, 21168, 9151,  9572, 15528, 15527,  27241, 28401, 27032,  \n16858, 5815, 17773,  7487, 13270, 3181,  779, 10328, 762,  \n28407, 28615, 28214,  916, 14841, 21089,  15164, 12336, 6481,  \n25443, 6278, 5558,  6221, 11552, 10223,  14262, 11441, 5335,  \n9613, 20622, 14748,  9592, 20182, 15271,  301, 9534, 3291,  \n63, 27441, 39,  6737, 14805, 9290,  28216, 28617, 28215,  \n28404, 28617, 28012,  28617, 28216, 28012,  28406, 28407, 28214,  \n4780, 16054, 13263,  28410, 28416, 28413,  2448, 3203, 20334,  \n9135, 8735, 14171,  4925, 12268, 17512,  28012, 28216, 27624,  \n20194, 3201, 1796,  24315, 8143, 8649,  12652, 6823, 19271,  \n28616, 28416, 28415,  19045, 6417, 17169,  9051, 12324, 11233,  \n6044, 9510, 19583,  5207, 5208, 13012,  28411, 28016, 28612,  \n14563, 8195, 20964,  28841, 28616, 28417,  18480, 16024, 4698,  \n28406, 28414, 28407,  28414, 28619, 28407,  28408, 28620, 28405,  \n9827, 7229, 3358,  28408, 28618, 28620,  5524, 16145, 5818,  \n14190, 16799, 9633,  16840, 18040, 5172,  2360, 17799, 17798,  \n27828, 28213, 28405,  28621, 28417, 28622,  28219, 28414, 28217,  \n20053, 4018, 11511,  19830, 20332, 12043,  28620, 28850, 28405,  \n27828, 28405, 28220,  22321, 21089, 10041,  28624, 28219, 28423,  \n10741, 19786, 17591,  10486, 9668, 6991,  8791, 17265, 10605,  \n7979, 19501, 12923,  8850, 20455, 14503,  27630, 27828, 28220,  \n17821, 16582, 13367,  15343, 16595, 12898,  28412, 28626, 28627,  \n28412, 28623, 28626,  28417, 28421, 28622,  22355, 24133, 12641,  \n28628, 28629, 28423,  2062, 16211, 13581,  9684, 9683, 6514,  \n28622, 28421, 28630,  28222, 27628, 28218,  19568, 18017, 18775,  \n12710, 12711, 5027,  11011, 7595, 12082,  3789, 1345, 1085,  \n27831, 27630, 28220,  18359, 12884, 1046,  10231, 21245, 19389,  \n28625, 6091, 22474,  4650, 20574, 26424,  7750, 7751, 12204,  \n6770, 21317, 20994,  11330, 14284, 14890,  13599, 9185, 10962,  \n28424, 28021, 28427,  28855, 28421, 28631,  28222, 28224, 27455,  \n29405, 133, 103,  15801, 8445, 7924,  28420, 28632, 28422,  \n28421, 28422, 28631,  28419, 14991, 28634,  15827, 20404, 15826,  \n10370, 14052, 17448,  28635, 26309, 28636,  28637, 28638, 28627,  \n28633, 28422, 28632,  13381, 1869, 21663,  24574, 28640, 28048,  \n1356, 4178, 4177,  28631, 28422, 28633,  28632, 28641, 28633,  \n7813, 1662, 9782,  2426, 8881, 2427,  28225, 28426, 28639,  \n8575, 1708, 13806,  15566, 15425, 19119,  28644, 28227, 28645,  \n11293, 11292, 20494,  28024, 27044, 28224,  28023, 27637, 28231,  \n21118, 13651, 15852,  28646, 28231, 28027,  28643, 28647, 28225,  \n28647, 28428, 28225,  16664, 4630, 4631,  15540, 24271, 16900,  \n767, 20560, 21245,  28646, 28027, 28648,  28428, 28647, 28649,  \n6003, 11419, 17662,  6654, 16300, 3660,  9930, 614, 17025,  \n28233, 28229, 28228,  28027, 28028, 28232,  9641, 12106, 14196,  \n7346, 15018, 866,  22336, 13020, 1832,  20880, 9998, 14131,  \n8796, 25143, 27026,  2060, 4006, 12030,  27641, 28229, 28233,  \n22906, 1365, 13110,  11894, 11893, 2116,  1617, 12617, 1618,  \n21636, 4256, 5708,  17876, 2914, 2915,  28651, 28429, 28235,  \n28867, 28430, 28431,  28867, 28235, 28430,  10976, 7488, 21299,  \n28232, 28029, 27841,  28654, 26855, 28429,  2278, 19549, 2279,  \n28033, 28431, 28032,  28656, 28232, 27841,  28653, 28011, 19469,  \n14890, 6890, 9892,  27051, 28024, 28432,  13050, 20345, 12488,  \n27844, 28655, 28025,  16220, 5509, 16874,  6326, 16096, 15353,  \n27258, 26855, 28654,  28033, 27839, 28431,  28625, 22474, 22475,  \n12520, 16476, 6109,  7244, 15958, 4684,  28656, 27841, 27840,  \n27258, 28654, 28434,  1982, 14619, 9342,  16032, 5415, 16073,  \n11436, 467, 16177,  16008, 10267, 14013,  28657, 28433, 28234,  \n16215, 7054, 5245,  3545, 1220, 10556,  15534, 10196, 13586,  \n15943, 9972, 19560,  6105, 3885, 17422,  11085, 11084, 1289,  \n15048, 12041, 4974,  12196, 5384, 5383,  12978, 7844, 8999,  \n20466, 20221, 8595,  6496, 17757, 12428,  7357, 11362, 5875,  \n21854, 5229, 19097,  3626, 15114, 20573,  18960, 16178, 21423,  \n23172, 20437, 1510,  4339, 22449, 20775,  28240, 28434, 28659,  \n25381, 11172, 3322,  28660, 28236, 28238,  28036, 27843, 28658,  \n13707, 17726, 13706,  22989, 24390, 11313,  11391, 21271, 6622,  \n8516, 22080, 16001,  5869, 20956, 16227,  28659, 28667, 28240,  \n28238, 27647, 27845,  28433, 28661, 28037,  28663, 27842, 28241,  \n28238, 27845, 28664,  21519, 1615, 12300,  28243, 28663, 28241,  \n28661, 28242, 28037,  2286, 6801, 1107,  13882, 1457, 17340,  \n3052, 13105, 19018,  28242, 28661, 28666,  27057, 28240, 28667,  \n3850, 19206, 4037,  28666, 28244, 28242,  28437, 28668, 28669,  \n28042, 27852, 28670,  28244, 28666, 28671,  28671, 28246, 28244,  \n28671, 28668, 28246,  28437, 28246, 28668,  28438, 28437, 28669,  \n25181, 26502, 22813,  11713, 1725, 11363,  28439, 28438, 28672,  \n28673, 27852, 28245,  28672, 28441, 28439,  27856, 28667, 28440,  \n27057, 28667, 27856,  11270, 20059, 20694,  7046, 6240, 18075,  \n1033, 2034, 2036,  28441, 28674, 28443,  3113, 23770, 12274,  \n28442, 28444, 28885,  28442, 28044, 28444,  28675, 27477, 27859,  \n1378, 5022, 1379,  4212, 13122, 4213,  28252, 28443, 28676,  \n8985, 8413, 7288,  27858, 28045, 27860,  28252, 28676, 28445,  \n8940, 17255, 26084,  20964, 10741, 17591,  28676, 28446, 28445,  \n3512, 11955, 6685,  3958, 17350, 3959,  18694, 18696, 1320,  \n28254, 28046, 28678,  27860, 28677, 27861,  28679, 28447, 28446,  \n28678, 28046, 28256,  17712, 16867, 20961,  6070, 18134, 15213,  \n1444, 21892, 24306,  28050, 28681, 27661,  18558, 19103, 5681,  \n28256, 28049, 28682,  27661, 28681, 28258,  28683, 27859, 27862,  \n378, 18006, 371,  28682, 28049, 28449,  28450, 28684, 28451,  \n28685, 28453, 28452,  10699, 4132, 9797,  28686, 28685, 28452,  \n28687, 28682, 28449,  27487, 28258, 27489,  14830, 10403, 1681,  \n13136, 14651, 23360,  18920, 18919, 21346,  13147, 4705, 19117,  \n1301, 3086, 12524,  28688, 28449, 28052,  28261, 28453, 28685,  \n8585, 5618, 882,  28688, 28052, 27484,  2695, 22016, 14188,  \n28455, 27862, 27662,  496, 9999, 22064,  28685, 28262, 28261,  \n11731, 1576, 14774,  15591, 21276, 20669,  1016, 11114, 12335,  \n27486, 27867, 28454,  27869, 28456, 28058,  28454, 27867, 28457,  \n9155, 18418, 19817,  4606, 4607, 816,  28691, 27670, 28057,  \n28692, 28458, 28263,  9610, 8749, 8750,  28461, 28460, 28693,  \n10286, 2380, 2880,  2329, 8593, 6369,  20334, 9235, 5003,  \n5981, 5982, 6588,  1305, 881, 882,  28264, 28462, 28694,  \n28695, 28268, 27670,  10611, 9453, 8707,  6091, 23451, 22474,  \n28461, 28698, 28271,  11037, 21520, 11038,  3280, 12360, 9342,  \n10036, 15566, 9535,  2666, 4153, 4406,  21076, 1255, 18983,  \n14406, 12753, 3093,  28700, 28462, 28065,  28700, 28694, 28462,  \n12313, 12312, 15129,  13348, 7434, 10645,  28702, 28696, 28467,  \n14858, 11899, 13078,  28697, 28699, 28464,  28699, 28269, 28464,  \n7417, 857, 7416,  28067, 22738, 24021,  5993, 5994, 19430,  \n11997, 12479, 4880,  28701, 28703, 28272,  2470, 16534, 15732,  \n27882, 27675, 28701,  19826, 615, 11191,  25549, 963, 1024,  \n15461, 2576, 9703,  6822, 11921, 6820,  28065, 28070, 28704,  \n28700, 28065, 28704,  28705, 28071, 28272,  28703, 28705, 28272,  \n22298, 2742, 10604,  28072, 28469, 28466,  403, 2559, 402,  \n3612, 12047, 15548,  14157, 19019, 17458,  28706, 28072, 27884,  \n28706, 27884, 28275,  2935, 18407, 21775,  28470, 28707, 28471,  \n28274, 28471, 28070,  28076, 27506, 28071,  12170, 1902, 1901,  \n28466, 28708, 28273,  13170, 13120, 3915,  18060, 7830, 8614,  \n17495, 9523, 19957,  28469, 28072, 28706,  28467, 27885, 28075,  \n28073, 28271, 28473,  5067, 9470, 5173,  28709, 28711, 28710,  \n6377, 23693, 7628,  452, 9105, 11670,  6474, 6473, 23974,  \n5110, 1432, 2045,  21569, 15325, 8354,  28713, 28711, 28476,  \n22819, 16014, 4455,  28714, 28712, 28474,  28470, 28474, 28712,  \n15504, 14087, 13389,  28711, 28709, 28476,  10107, 3461, 19491,  \n11954, 17730, 8116,  8893, 8892, 18656,  27887, 28473, 28478,  \n6109, 3935, 14959,  12000, 11752, 12001,  17271, 13624, 15341,  \n28715, 28278, 28477,  28714, 28474, 28475,  6495, 24724, 25420,  \n28476, 28716, 28713,  28282, 28716, 28476,  28283, 28278, 28715,  \n12542, 6963, 15663,  28719, 28714, 28475,  25086, 15088, 15483,  \n13077, 15161, 2662,  28281, 28720, 28075,  5340, 10254, 8409,  \n20803, 13711, 16394,  28479, 28080, 28478,  10803, 11383, 5794,  \n17306, 14459, 15591,  17304, 19298, 5866,  28283, 28715, 28913,  \n28717, 28721, 28086,  28293, 28086, 28721,  28480, 28719, 28475,  \n20109, 16225, 16224,  10688, 9739, 23529,  18719, 18295, 22765,  \n14142, 14638, 10291,  28481, 28716, 28282,  19378, 19986, 15974,  \n9271, 14615, 9270,  28722, 28292, 28723,  15495, 6605, 19869,  \n5599, 17951, 3473,  28285, 28482, 28724,  28285, 28724, 28480,  \n9874, 9875, 22585,  21790, 2777, 21312,  20172, 10879, 2171,  \n6843, 759, 592,  28913, 28084, 28283,  19233, 6428, 7727,  \n21555, 6586, 14738,  19288, 4242, 1563,  19619, 1904, 13407,  \n28483, 28484, 28725,  28484, 28483, 28288,  28289, 28482, 27892,  \n7298, 10028, 16114,  22782, 17682, 19680,  20062, 9297, 5136,  \n19120, 1964, 15621,  19010, 7171, 18079,  8463, 22107, 15615,  \n3485, 16974, 3484,  9540, 8767, 9072,  14798, 18614, 20676,  \n28918, 28297, 28487,  28726, 14835, 6582,  10388, 12646, 14766,  \n7051, 19298, 17304,  2139, 13516, 2140,  18267, 15001, 7291,  \n28281, 28077, 28493,  13627, 10181, 15525,  28089, 28283, 28084,  \n28913, 28727, 28084,  7261, 8616, 17661,  12778, 20325, 12777,  \n28485, 28488, 28295,  6529, 19582, 5086,  11166, 11167, 17327,  \n23365, 11324, 1370,  6009, 5988, 15240,  17146, 5401, 19335,  \n24343, 1140, 1139,  6025, 8660, 11995,  3206, 4867, 20350,  \n28294, 28293, 28497,  5093, 8078, 15972,  28488, 28090, 28295,  \n28730, 28731, 28496,  23365, 1370, 7764,  3956, 2525, 17565,  \n18853, 19013, 13744,  28492, 28725, 28484,  10465, 8939, 16670,  \n28084, 28727, 28300,  28729, 28494, 28300,  28729, 28300, 28727,  \n28494, 28729, 28723,  4450, 6024, 1385,  3100, 12660, 4220,  \n21186, 13561, 15338,  28486, 28487, 28296,  22161, 2988, 9314,  \n10157, 5427, 1145,  7963, 1448, 20175,  28731, 28489, 28496,  \n18234, 391, 634,  18481, 19274, 19620,  888, 890, 10420,  \n17301, 12982, 16543,  29365, 5158, 17833,  7656, 9372, 20022,  \n15978, 7351, 7352,  13325, 10397, 10364,  28730, 28496, 28500,  \n28096, 28491, 28097,  2757, 5440, 4920,  28097, 28732, 28499,  \n28499, 28732, 28492,  17668, 12520, 18067,  15054, 14201, 24231,  \n27688, 28088, 28301,  28497, 28733, 28498,  21126, 2438, 18184,  \n28737, 28088, 28736,  28088, 28737, 28301,  19973, 5806, 5241,  \n13993, 18039, 17229,  2879, 2878, 16089,  16459, 20929, 9841,  \n28498, 28733, 28098,  28098, 28733, 28501,  28502, 28495, 28734,  \n28303, 28735, 28099,  28735, 28500, 28099,  28739, 27697, 28301,  \n19629, 2005, 21122,  6113, 2040, 4681,  18121, 17039, 16125,  \n28502, 28735, 28303,  28771, 28740, 999,  1059, 11567, 6686,  \n28741, 27901, 27912,  23387, 11067, 13730,  14139, 8169, 15292,  \n12780, 13111, 15345,  14427, 14428, 18667,  17771, 28742, 3708,  \n6202, 15099, 14015,  11450, 20095, 11451,  28504, 27913, 27911,  \n18156, 21031, 21572,  7498, 5841, 6563,  27913, 28504, 28505,  \n3883, 3882, 8563,  27912, 27530, 28103,  20759, 11307, 25581,  \n18755, 11249, 11250,  15158, 15439, 20236,  2894, 14778, 1803,  \n14455, 14229, 10741,  19557, 14424, 16866,  9551, 2605, 1711,  \n18306, 18099, 1694,  28743, 27531, 27915,  28743, 28507, 27531,  \n27533, 28508, 27532,  28745, 28746, 22285,  843, 842, 10758,  \n14474, 6834, 17808,  11406, 1856, 18005,  2559, 2558, 10874,  \n15860, 23849, 15861,  27917, 28747, 28748,  17581, 9589, 1419,  \n28105, 28749, 28106,  28510, 27918, 28749,  28106, 28749, 27918,  \n333, 332, 10815,  28512, 28511, 28308,  28307, 28750, 28108,  \n28513, 28108, 28750,  28109, 28514, 27920,  28751, 27919, 28513,  \n23099, 23655, 8394,  28751, 28109, 27919,  28309, 28512, 28111,  \n28946, 28515, 28514,  14731, 19221, 16825,  28752, 28309, 28311,  \n28516, 28752, 28311,  3425, 10246, 15199,  3524, 7066, 3523,  \n18839, 3882, 19272,  9523, 2141, 19957,  14866, 15311, 12157,  \n28753, 28115, 27925,  20652, 6267, 18994,  19647, 6919, 11008,  \n28520, 27713, 27926,  17345, 8682, 13999,  7513, 14081, 14082,  \n12109, 4323, 15520,  11626, 10211, 11627,  21249, 15285, 10969,  \n4828, 20779, 6583,  17910, 1754, 1753,  15070, 7824, 12333,  \n6083, 15669, 21280,  23001, 20574, 4650,  27715, 28523, 28754,  \n2543, 4530, 2542,  28524, 28525, 28120,  28755, 28119, 28313,  \n5003, 4489, 20334,  12041, 15048, 5862,  20432, 18369, 20433,  \n3478, 3477, 10804,  28313, 27928, 27929,  18576, 11650, 17863,  \n14421, 21351, 14454,  11383, 11382, 10462,  754, 755, 18002,  \n28316, 28757, 27930,  17663, 1901, 6503,  27932, 28314, 28317,  \n28125, 28529, 28123,  8764, 13641, 19458,  28758, 28123, 28529,  \n27724, 28121, 27722,  2949, 14913, 580,  27722, 28121, 28527,  \n28122, 28527, 28759,  28122, 28528, 27552,  28528, 28124, 27552,  \n4494, 13117, 13119,  8214, 18399, 12892,  17018, 12223, 8112,  \n11296, 10639, 15660,  2772, 6025, 11995,  8224, 19988, 7853,  \n27933, 28319, 28530,  2814, 15448, 7786,  3088, 11875, 6575,  \n8781, 8398, 13167,  19429, 16305, 5125,  28321, 27932, 28322,  \n5125, 17109, 19429,  28322, 28317, 28760,  18443, 22092, 19986,  \n2557, 1230, 6019,  8327, 3999, 3998,  28761, 28126, 28127,  \n8214, 3442, 8213,  28762, 28128, 28763,  28323, 28321, 28322,  \n16266, 19355, 1447,  6767, 20487, 16578,  28129, 28323, 28531,  \n28764, 28128, 27936,  12041, 12096, 3027,  17477, 18103, 16852,  \n28764, 28130, 28765,  28531, 28532, 28131,  28765, 28130, 28324,  \n8223, 20021, 1993,  15317, 15316, 15099,  28132, 28325, 27939,  \n3625, 19346, 15699,  20929, 4372, 21832,  8025, 2262, 15459,  \n14000, 13999, 13042,  15955, 27946, 4543,  6463, 5558, 750,  \n27734, 28325, 28534,  4622, 8973, 4621,  5341, 14757, 19497,  \n28766, 28533, 28326,  6010, 16465, 18630,  28533, 28324, 28134,  \n14597, 15689, 15690,  28965, 28535, 28534,  2725, 11630, 11974,  \n13922, 24110, 7760,  21724, 6452, 4250,  8442, 17417, 16517,  \n28328, 28535, 28767,  28328, 28766, 28327,  28767, 28766, 28328,  \n28327, 28766, 28326,  28535, 28138, 28534,  19985, 3078, 23451,  \n1555, 11827, 13465,  15911, 2514, 9422,  16412, 1225, 11554,  \n26308, 24439, 26309,  4648, 8946, 21695,  20698, 17816, 12611,  \n25437, 25089, 1888,  12768, 1039, 3608,  20462, 26109, 3218,  \n17325, 3714, 2243,  25267, 28205, 12870,  19445, 12455, 6423,  \n1019, 6429, 2872,  22592, 28768, 27385,  25284, 28610, 28613,  \n28769, 28141, 28140,  28769, 25627, 28141,  3986, 12127, 23790,  \n14163, 1348, 1688,  19833, 12693, 12598,  1887, 25089, 25088,  \n16617, 24438, 20434,  28011, 18421, 12398,  18344, 20713, 10225,  \n2994, 11588, 22294,  28540, 28144, 27948,  12357, 2145, 1186,  \n9378, 12790, 4057,  27945, 27949, 28541,  18450, 20336, 19559,  \n16918, 5636, 17534,  20079, 13420, 13419,  28770, 28145, 27739,  \n16911, 10837, 16279,  27742, 27372, 27951,  27950, 26944, 28771,  \n17114, 3724, 17270,  20078, 14863, 8847,  14656, 3736, 6907,  \n11813, 15830, 17553,  11687, 19839, 10204,  20994, 21317, 21318,  \n28146, 28331, 28772,  1372, 361, 6163,  20606, 11529, 20698,  \n28546, 27744, 27743,  7755, 20513, 13608,  11939, 23919, 4371,  \n7956, 18052, 19653,  1613, 9827, 1614,  28546, 27955, 27744,  \n21620, 12701, 16174,  2193, 9690, 10790,  28545, 27741, 28147,  \n22052, 11411, 15525,  28543, 26948, 27952,  20019, 14374, 11776,  \n18916, 18623, 5257,  13441, 17430, 1718,  21138, 5192, 11309,  \n26424, 28680, 14202,  12612, 1363, 1644,  15381, 10962, 12401,  \n16094, 21863, 14920,  1729, 5738, 5737,  28549, 28334, 27170,  \n22263, 12029, 12028,  28547, 27571, 27955,  10304, 4201, 2735,  \n19850, 24438, 13380,  21892, 28542, 20202,  1343, 15878, 4926,  \n7658, 8374, 7657,  28337, 28553, 26952,  28773, 28338, 28550,  \n28550, 28341, 28773,  28339, 28552, 27746,  27746, 26789, 28339,  \n9186, 14378, 17201,  14396, 16365, 20133,  28775, 28154, 28338,  \n4627, 4626, 14482,  17488, 13246, 17487,  21156, 10264, 24100,  \n27572, 27571, 28774,  24134, 19829, 25089,  28155, 28154, 28775,  \n28343, 28344, 28776,  28343, 28342, 28344,  3495, 22409, 851,  \n19946, 16466, 756,  9191, 9193, 17328,  20890, 19197, 20952,  \n8258, 13258, 7655,  15986, 9169, 9170,  26793, 28150, 28559,  \n28777, 28776, 28344,  28344, 28153, 28777,  28558, 26954, 27173,  \n17459, 12201, 2678,  12703, 16758, 15962,  8102, 8103, 10391,  \n28560, 28775, 28779,  28155, 28775, 28560,  28345, 27173, 28561,  \n7689, 11274, 10323,  8978, 9131, 2249,  2108, 10156, 12330,  \n27753, 28563, 27754,  12607, 12012, 8923,  16632, 11407, 6275,  \n28560, 28346, 28155,  8694, 15465, 14818,  13801, 11075, 11074,  \n4663, 4662, 3862,  27575, 28564, 27755,  9737, 12635, 9738,  \n28346, 28560, 28780,  28346, 28780, 28159,  25089, 1887, 1888,  \n12525, 21082, 14599,  6444, 4644, 5822,  28780, 28565, 28159,  \n28781, 28565, 28780,  15515, 1258, 3839,  8779, 1078, 8780,  \n12223, 17018, 19927,  2606, 12956, 14376,  27962, 27756, 28347,  \n13470, 12503, 12502,  17924, 12528, 4265,  28159, 28565, 28567,  \n28567, 28565, 28782,  5865, 5864, 10438,  9177, 20219, 5251,  \n3767, 9663, 13115,  28347, 27387, 28784,  7735, 20335, 289,  \n28567, 28782, 28161,  11487, 8232, 18941,  2476, 1843, 17099,  \n28568, 28352, 27963,  28162, 28568, 27963,  11108, 9817, 8789,  \n9040, 24271, 15540,  3096, 14852, 23103,  8847, 17830, 20078,  \n8201, 1661, 16173,  18129, 16961, 6341,  23170, 13153, 5614,  \n27761, 27759, 11608,  11987, 11394, 6158,  28352, 28164, 27760,  \n13866, 11220, 28680,  4036, 16977, 15081,  20881, 13221, 17248,  \n17875, 20855, 22366,  27392, 28164, 27964,  6383, 17195, 15078,  \n27964, 28164, 28786,  28786, 28165, 27964,  1772, 21521, 21387,  \n7308, 19586, 7722,  18982, 20451, 6225,  7494, 1264, 14688,  \n8261, 13091, 13952,  28788, 27765, 28354,  18589, 7123, 22408,  \n8887, 6530, 14499,  15820, 20068, 18886,  5191, 20098, 13658,  \n27967, 28789, 28355,  10483, 21154, 21378,  17760, 17537, 21542,  \n18721, 18550, 17823,  28570, 26973, 28356,  20002, 16093, 13775,  \n13233, 19870, 20819,  28571, 28166, 27582,  9645, 9646, 16888,  \n8227, 22290, 3704,  14034, 4345, 16424,  14781, 5747, 7968,  \n27585, 28167, 27186,  8919, 14213, 8920,  1864, 22965, 1863,  \n21131, 12280, 7770,  27969, 28166, 28571,  10618, 11013, 21460,  \n7630, 6325, 2922,  11220, 13866, 28771,  11055, 12116, 11056,  \n28573, 27584, 28359,  8121, 14901, 8457,  17563, 1167, 9355,  \n26276, 27769, 28357,  3772, 15966, 12174,  18031, 8194, 20837,  \n18002, 16733, 6392,  12705, 12124, 14034,  13568, 12931, 12930,  \n4681, 2040, 2345,  13530, 4681, 2345,  28636, 6057, 18525,  \n17461, 14586, 16938,  10358, 10359, 12185,  10072, 12125, 16807,  \n5322, 9758, 5321,  13807, 22197, 9420,  11387, 9812, 7293,  \n19694, 17872, 21969,  21579, 9770, 702,  8852, 4956, 3368,  \n16867, 14425, 20961,  4051, 568, 569,  15237, 21494, 2273,  \n9019, 4872, 12881,  8997, 8988, 3838,  4093, 19627, 7815,  \n10720, 12695, 23357,  27972, 28794, 28578,  27972, 27591, 28173,  \n11220, 28771, 999,  791, 9159, 13634,  13311, 11400, 4173,  \n12489, 3945, 11551,  10820, 5082, 21547,  27198, 26474, 12274,  \n11490, 21739, 8834,  21192, 7878, 3936,  26474, 26638, 12274,  \n6421, 20479, 19180,  27779, 26638, 26814,  6266, 6267, 3237,  \n28183, 28364, 27203,  23216, 27779, 28366,  5941, 18211, 3143,  \n5222, 20231, 12310,  28174, 28796, 27201,  21642, 17264, 1695,  \n5370, 21644, 4360,  11052, 1378, 15994,  27595, 27201, 28580,  \n28176, 27780, 28797,  27781, 28580, 28179,  22034, 12167, 22106,  \n11821, 10880, 11822,  1189, 2016, 15436,  9234, 9233, 9999,  \n19608, 3030, 21789,  16021, 23533, 3464,  7103, 11661, 7101,  \n10009, 10010, 10251,  15964, 18090, 11553,  22606, 16753, 20567,  \n10887, 20838, 875,  6460, 6053, 6461,  20145, 15190, 19814,  \n28798, 27979, 28800,  27596, 28579, 28581,  13860, 22240, 18765,  \n4623, 17670, 13972,  20189, 14343, 7001,  27980, 27596, 28581,  \n10426, 6482, 11499,  28367, 28368, 28999,  1313, 17879, 1314,  \n18402, 7895, 7894,  13806, 16957, 8575,  7134, 14154, 14614,  \n27784, 28803, 26824,  28582, 27210, 27980,  6833, 14221, 8986,  \n16108, 3817, 18152,  2202, 17735, 17734,  2464, 1036, 16353,  \n12871, 1110, 4190,  16513, 10834, 20601,  11714, 4730, 11712,  \n11602, 8584, 15964,  2428, 453, 2873,  4130, 17641, 4131,  \n8272, 8038, 7171,  2447, 8086, 2709,  28584, 27599, 27792,  \n19343, 11091, 908,  28371, 27983, 27984,  19187, 23791, 25143,  \n2189, 16582, 2972,  27600, 28585, 28190,  7774, 19991, 22133,  \n21226, 21448, 17008,  27789, 28187, 28586,  19512, 4311, 23083,  \n16178, 28625, 22475,  5682, 1905, 5324,  28191, 28806, 27796,  \n11598, 11599, 618,  28193, 27798, 28809,  3745, 21576, 8058,  \n27603, 27416, 28807,  27604, 28808, 27226,  28191, 28587, 28810,  \n28191, 28810, 28806,  17570, 19192, 5399,  8660, 8661, 18487,  \n4510, 1352, 14176,  28810, 28587, 28812,  28192, 27602, 28586,  \n9374, 9370, 10580,  28589, 28812, 28587,  10492, 3189, 10501,  \n626, 18473, 625,  22820, 11875, 12050,  28192, 28586, 28813,  \n28589, 28587, 28588,  943, 12773, 20978,  5769, 4840, 3658,  \n15955, 25420, 18992,  27989, 28588, 27608,  11224, 3739, 8786,  \n13885, 8300, 1097,  28374, 28813, 28817,  8493, 23194, 21893,  \n15955, 6500, 25420,  11359, 3483, 7324,  16739, 624, 1853,  \n12905, 3681, 12627,  10981, 16664, 16666,  8553, 3135, 4752,  \n28640, 1500, 28048,  14327, 13157, 1998,  28318, 18960, 19021,  \n17678, 14227, 617,  10112, 14055, 2959,  27609, 28593, 27799,  \n21317, 2555, 10626,  1010, 6318, 1009,  16567, 21764, 12014,  \n6221, 17141, 17928,  21072, 21764, 16567,  12325, 834, 7438,  \n11326, 5247, 588,  28593, 27609, 27610,  8368, 8833, 10565,  \n28819, 27612, 27992,  14634, 11047, 21384,  906, 3551, 11610,  \n16296, 3220, 2714,  28374, 28818, 28594,  10186, 15637, 17580,  \n10995, 13413, 13484,  594, 13187, 14223,  28376, 28595, 27426,  \n1808, 23071, 20804,  20567, 16753, 24274,  5701, 24574, 6395,  \n2467, 2258, 21661,  9288, 18416, 17710,  4565, 4644, 4564,  \n19663, 3437, 11808,  22728, 17164, 21798,  28378, 28374, 28594,  \n3067, 4690, 7685,  26985, 28572, 13507,  14429, 3844, 10487,  \n3394, 4179, 4180,  774, 8089, 12481,  23742, 4116, 9521,  \n3349, 13654, 9079,  1884, 13465, 11827,  21750, 10980, 21602,  \n15889, 23334, 15890,  441, 9386, 442,  742, 777, 18996,  \n10761, 25490, 25846,  27804, 27429, 28596,  18725, 18080, 10017,  \n15606, 13679, 5049,  14523, 16727, 4107,  28378, 28597, 27996,  \n28380, 27806, 27615,  15897, 17478, 12979,  9467, 4043, 5185,  \n5566, 18797, 829,  27432, 27431, 28820,  20838, 16245, 13690,  \n13128, 7484, 12739,  15798, 15799, 9815,  28597, 28199, 27996,  \n22653, 14366, 25158,  13604, 2014, 9923,  20223, 13459, 14334,  \n19916, 13532, 894,  7269, 8298, 6929,  8389, 8064, 17800,  \n23974, 7186, 7187,  9054, 2141, 1407,  15828, 18384, 16354,  \n18745, 22214, 19609,  27998, 28382, 28821,  25680, 13792, 26845,  \n14157, 17458, 2503,  13977, 15278, 16387,  12960, 12918, 12917,  \n18290, 8762, 6812,  6214, 8089, 8090,  60, 27021, 28384,  \n22290, 17578, 28305,  16016, 5900, 13411,  16890, 478, 12511,  \n1369, 1370, 8775,  5600, 20063, 4517,  21472, 4194, 5551,  \n28823, 27616, 28388,  27025, 28382, 27998,  22454, 22058, 7668,  \n28824, 18024, 16646,  26406, 28825, 11801,  12045, 10234, 9826,  \n28601, 28384, 26841,  19471, 7809, 8594,  14477, 15630, 21968,  \n13982, 13636, 9630,  8514, 12448, 3095,  12675, 10174, 977,  \n15537, 4286, 20417,  9642, 1963, 9647,  13628, 13970, 9788,  \n13078, 7463, 539,  28385, 28390, 28386,  2857, 3307, 4368,  \n27810, 29197, 27811,  10187, 20025, 6356,  9062, 18718, 22430,  \n16252, 19479, 21883,  28201, 28392, 28386,  9960, 3617, 9787,  \n28390, 28392, 28204,  6108, 2594, 18673,  19912, 1781, 607,  \n28606, 28827, 28608,  9499, 6826, 11672,  16508, 12466, 4834,  \n60, 44, 27021,  12135, 15890, 3910,  12006, 12007, 8720,  \n14190, 12734, 10807,  11883, 10398, 9347,  13373, 8804, 22299,  \n4635, 28468, 21427,  20461, 12320, 22861,  28609, 27817, 27619,  \n10633, 10415, 15864,  15591, 13285, 1611,  662, 18211, 5941,  \n28744, 21877, 5818,  5190, 2683, 19646,  13809, 3270, 13810,  \n17650, 22837, 23284,  6533, 9718, 5975,  28208, 28830, 28209,  \n8677, 11672, 7333,  5558, 6278, 3164,  28397, 28398, 27621,  \n28208, 28833, 28832,  4460, 14161, 7444,  13262, 14068, 14067,  \n15288, 11913, 10200,  28833, 28208, 28403,  28835, 28004, 28006,  \n8654, 14660, 16151,  4184, 12255, 995,  28838, 28836, 28616,  \n14301, 6343, 19007,  661, 2120, 5520,  12230, 15954, 8793,  \n14392, 15175, 2615,  11102, 12790, 9378,  8011, 8919, 10036,  \n28010, 27439, 28402,  28416, 28616, 28836,  28416, 28836, 28837,  \n12277, 8165, 6209,  826, 2428, 2873,  28614, 28401, 28010,  \n28401, 27241, 28010,  28833, 28403, 28215,  23287, 780, 11434,  \n28833, 28215, 29028,  18130, 9752, 2868,  12727, 11891, 11890,  \n4655, 4912, 22100,  5881, 16037, 5792,  28416, 28837, 28839,  \n12507, 8082, 8130,  29028, 28215, 28617,  6563, 14174, 7498,  \n15362, 7581, 15363,  16350, 5274, 16351,  28615, 28404, 28214,  \n28413, 28416, 28839,  14522, 3212, 12942,  3846, 726, 18765,  \n11806, 11864, 10586,  28408, 28212, 28618,  28537, 28205, 25267,  \n18593, 22953, 5025,  28619, 28842, 28407,  7785, 775, 7177,  \n4575, 10821, 22551,  13992, 11133, 12166,  11668, 320, 9921,  \n29032, 28841, 28621,  22890, 446, 447,  28417, 28621, 28841,  \n11903, 5341, 11902,  3866, 3865, 8482,  14216, 18559, 2912,  \n22369, 14262, 13712,  18235, 2288, 9116,  19474, 7733, 7732,  \n6891, 1332, 11087,  503, 916, 504,  28412, 28413, 28623,  \n11517, 19778, 11518,  28219, 28624, 28414,  14665, 14419, 13340,  \n15119, 14494, 1138,  10062, 12552, 18822,  28622, 28847, 28621,  \n28218, 28018, 28411,  28423, 28848, 28624,  28849, 28405, 28850,  \n2145, 3716, 2144,  1447, 15681, 7437,  5661, 19355, 12401,  \n11033, 4024, 12670,  7101, 3622, 15357,  17260, 3772, 21355,  \n307, 2607, 18388,  18681, 20877, 3581,  28847, 28622, 28851,  \n2580, 1546, 6400,  14354, 7695, 4467,  28629, 28848, 28423,  \n18610, 20901, 18677,  28852, 13933, 11695,  8823, 5061, 2232,  \n28220, 28405, 28849,  11610, 19951, 20496,  28420, 28412, 28627,  \n8659, 22187, 6219,  19392, 11920, 7659,  18021, 15104, 19380,  \n943, 8861, 12773,  28846, 28626, 28623,  15811, 2188, 2187,  \n4489, 18690, 4619,  12461, 3974, 2976,  28220, 28849, 28426,  \n17744, 18546, 14747,  28626, 28637, 28627,  5459, 6954, 5290,  \n28628, 28423, 28221,  6466, 21207, 14895,  6228, 8430, 16084,  \n28851, 28622, 28630,  14162, 12255, 4184,  28854, 28426, 28849,  \n17938, 4342, 18989,  8177, 15367, 6536,  28426, 27831, 28220,  \n1151, 457, 17702,  2095, 8310, 23491,  28425, 28628, 28221,  \n5351, 21835, 16478,  5559, 12244, 10212,  28421, 28855, 28630,  \n20192, 557, 9571,  702, 5668, 1637,  28856, 28855, 28631,  \n11208, 11128, 19312,  28642, 56, 28226,  28420, 28627, 28632,  \n728, 2780, 4777,  28226, 28023, 28642,  5342, 10561, 8894,  \n22551, 10821, 21560,  9847, 9846, 14406,  17948, 25698, 28824,  \n28638, 28632, 28627,  17447, 22702, 17448,  28858, 28633, 28641,  \n10433, 1418, 5938,  28633, 28858, 28857,  28631, 28633, 28859,  \n28644, 28425, 27835,  28641, 28632, 28638,  22062, 15817, 17713,  \n28859, 28633, 28857,  20483, 20439, 24013,  28644, 27835, 28227,  \n476, 9779, 11170,  8405, 21854, 9727,  28646, 28023, 28231,  \n15039, 21228, 18498,  28861, 21866, 6951,  18243, 1969, 2378,  \n5892, 1146, 14136,  2339, 3942, 19581,  28643, 28862, 28647,  \n10961, 1769, 619,  5180, 3467, 14707,  28649, 28228, 28428,  \n28863, 28027, 28232,  28863, 28648, 28027,  21779, 5011, 476,  \n28864, 28228, 28649,  13835, 2491, 21555,  28865, 28233, 28864,  \n28233, 28228, 28864,  29250, 28863, 28232,  28233, 28865, 28234,  \n10191, 13827, 10190,  10845, 18481, 16122,  22376, 6847, 651,  \n28227, 28230, 28645,  16359, 14172, 2896,  15732, 11803, 2706,  \n28866, 28429, 28651,  23770, 3113, 3608,  28867, 28651, 28235,  \n28025, 28655, 28230,  28234, 28865, 28652,  28656, 28868, 28232,  \n19390, 5123, 7169,  28869, 28654, 28429,  28870, 28869, 28429,  \n432, 17896, 18811,  28340, 2814, 5739,  5958, 5584, 16157,  \n21031, 7422, 18143,  11145, 16079, 7068,  1263, 3758, 4447,  \n28431, 28236, 28871,  23972, 7993, 19617,  17078, 4514, 11399,  \n8909, 6311, 19353,  440, 18165, 1341,  28024, 28650, 28432,  \n4265, 14477, 5340,  2554, 1057, 10913,  28236, 28431, 27839,  \n28872, 28657, 28652,  28234, 28652, 28657,  16454, 1451, 2808,  \n11106, 10537, 4548,  8108, 20205, 5289,  2488, 14092, 2489,  \n27054, 28239, 28873,  28335, 8824, 15448,  9308, 18466, 19908,  \n14435, 11172, 25381,  28873, 28239, 28662,  28655, 27844, 28034,  \n9570, 1165, 10319,  28657, 28661, 28433,  6324, 18350, 22734,  \n24738, 4408, 3411,  28874, 28661, 28657,  28239, 27842, 28662,  \n12721, 817, 13474,  14854, 8524, 6471,  2374, 2375, 6797,  \n3014, 8810, 8695,  18091, 5226, 5225,  3525, 21652, 4345,  \n28660, 28238, 28664,  22290, 28305, 8079,  13127, 20504, 4389,  \n18647, 7816, 23473,  28875, 28661, 28874,  3592, 3591, 8921,  \n28665, 28663, 28243,  22129, 14561, 13618,  28661, 28875, 28666,  \n9880, 720, 15134,  9709, 901, 16442,  28877, 28436, 28435,  \n28034, 27654, 28878,  28666, 28875, 28671,  12612, 1644, 2390,  \n28880, 28672, 28879,  3499, 20633, 21106,  7042, 17061, 13875,  \n14658, 8508, 8684,  19684, 16739, 1852,  1175, 17899, 4293,  \n28881, 28673, 28245,  12223, 9395, 6512,  28669, 28879, 28438,  \n28438, 28879, 28672,  1793, 21659, 16715,  14175, 14048, 14047,  \n28670, 27852, 28673,  15015, 3628, 20823,  5163, 9550, 642,  \n4181, 2245, 20610,  28882, 28441, 28672,  28248, 27854, 28883,  \n27854, 28250, 28883,  6942, 3016, 6943,  28674, 28441, 28882,  \n18237, 18236, 20795,  15204, 17839, 7501,  28884, 28443, 28674,  \n2929, 2096, 14143,  15598, 10281, 6400,  27856, 28886, 28045,  \n20110, 7055, 7056,  13093, 11841, 17022,  14269, 12151, 6136,  \n10132, 12663, 8014,  28443, 28884, 28676,  10972, 15518, 5873,  \n8692, 3176, 10147,  28675, 28043, 27477,  10526, 19365, 13784,  \n6162, 4367, 15293,  28044, 28251, 28444,  6091, 19985, 23451,  \n17440, 786, 18274,  28887, 28444, 28251,  20645, 10614, 6132,  \n1368, 12486, 18320,  28887, 28251, 28254,  28254, 28678, 28887,  \n28050, 27861, 28888,  13519, 17209, 13520,  28447, 28679, 28448,  \n28679, 28889, 28448,  1612, 10554, 14248,  1141, 13944, 20949,  \n10993, 20696, 21251,  28451, 28684, 28890,  11492, 11493, 18036,  \n28451, 28891, 28452,  11561, 21761, 17309,  26958, 26610, 26943,  \n28448, 28889, 28450,  28889, 28684, 28450,  16829, 14953, 10269,  \n21514, 854, 17117,  9451, 21026, 18498,  3920, 18106, 18130,  \n22542, 14788, 20432,  13220, 17896, 1111,  19810, 1253, 4084,  \n28455, 28683, 27862,  22278, 10374, 700,  16060, 12573, 12572,  \n28688, 28892, 28449,  28892, 28687, 28449,  7046, 15702, 2674,  \n28686, 28893, 28685,  28690, 28892, 28688,  15493, 3425, 21788,  \n15455, 16769, 14107,  28636, 6582, 6057,  19921, 16684, 11681,  \n27484, 28454, 28688,  28454, 28690, 28688,  17057, 22035, 17056,  \n28690, 28454, 28894,  15818, 6197, 7660,  28894, 28454, 28457,  \n28262, 28692, 28263,  28460, 28459, 28895,  15759, 13504, 5424,  \n20714, 4140, 14075,  28264, 28896, 28457,  28896, 28894, 28457,  \n28057, 28058, 28691,  27662, 28696, 28455,  1215, 16688, 9252,  \n17446, 6177, 17325,  23414, 19429, 17109,  28696, 27662, 27875,  \n13481, 17226, 16327,  3638, 1733, 21150,  28693, 28698, 28461,  \n28896, 28264, 28694,  28694, 28899, 28896,  18766, 14492, 25557,  \n18757, 18211, 1668,  28695, 27670, 28691,  28458, 28692, 28697,  \n3551, 906, 17809,  7560, 15681, 18973,  4430, 28613, 21397,  \n10351, 6359, 23913,  5085, 17602, 11987,  2986, 16601, 4426,  \n28465, 27675, 28066,  28467, 28696, 27875,  28467, 27875, 27885,  \n3799, 9890, 10222,  28899, 28694, 28700,  28272, 27882, 28701,  \n27676, 28066, 27675,  5163, 7164, 6900,  1302, 10858, 3980,  \n28900, 28899, 28700,  19762, 9579, 9621,  28538, 25267, 23596,  \n29100, 28705, 28703,  23207, 17830, 1199,  13766, 15417, 3347,  \n19447, 8722, 22081,  28465, 27879, 28901,  28903, 28709, 28710,  \n28700, 28704, 28900,  17634, 11271, 18753,  28076, 28071, 28904,  \n28904, 28071, 28705,  2082, 17025, 12521,  27879, 28273, 28901,  \n14160, 11257, 7083,  27421, 24274, 26177,  28070, 28472, 28704,  \n6269, 18382, 1216,  21532, 22954, 10251,  28861, 15041, 575,  \n4707, 4184, 17155,  28707, 28470, 28905,  28471, 28906, 28472,  \n7563, 12824, 2099,  12583, 4778, 14796,  26883, 26265, 28902,  \n18016, 9766, 9765,  28469, 28706, 28907,  10403, 14830, 18516,  \n28709, 29097, 28908,  12303, 6977, 9026,  28905, 28470, 28712,  \n14529, 19573, 10480,  10107, 18196, 12450,  20049, 11911, 11910,  \n28469, 28910, 28466,  2046, 10910, 11555,  12851, 22418, 357,  \n4277, 9154, 19817,  28715, 28709, 28908,  28911, 28712, 28714,  \n1154, 11207, 13829,  20675, 8897, 11723,  23443, 4085, 16447,  \n20771, 12345, 926,  9258, 14436, 14437,  15549, 20182, 17722,  \n19870, 18059, 4115,  28719, 28911, 28714,  16175, 22355, 12636,  \n9583, 16946, 3188,  14195, 774, 8627,  5534, 14550, 6207,  \n8700, 22488, 19788,  28280, 27509, 28076,  28478, 28915, 28479,  \n7738, 26406, 11801,  28912, 28716, 28915,  18886, 20068, 18521,  \n28713, 28716, 28912,  28718, 28721, 28717,  28479, 28915, 28481,  \n28481, 28915, 28716,  5939, 2681, 10433,  7328, 17092, 3865,  \n28916, 28719, 28480,  28720, 28281, 28917,  28918, 28919, 28297,  \n28920, 28921, 28725,  28289, 28483, 28922,  23668, 4268, 16826,  \n11321, 13827, 10191,  28480, 28724, 28916,  8205, 1759, 8204,  \n2019, 1639, 19404,  4640, 22738, 12296,  15405, 13292, 13291,  \n28485, 28297, 28924,  28725, 28921, 28483,  11450, 19972, 15180,  \n10608, 13785, 9868,  10882, 2559, 10874,  17868, 2644, 2783,  \n17028, 15516, 16053,  28729, 28722, 28723,  28332, 25706, 10581,  \n6785, 1325, 11873,  686, 13764, 24191,  28918, 28487, 28728,  \n12581, 2308, 17643,  18162, 18009, 11184,  22600, 21039, 21038,  \n13887, 20673, 14070,  20169, 8267, 12867,  28913, 28923, 28727,  \n28923, 28729, 28727,  7975, 10965, 12143,  21577, 11647, 19950,  \n4542, 13524, 16035,  28925, 28489, 28731,  28925, 28490, 28489,  \n28925, 28926, 28490,  12802, 21361, 9674,  25499, 13584, 19804,  \n10611, 10404, 4552,  17237, 7658, 22240,  28728, 28487, 28486,  \n18275, 3895, 6067,  28926, 28491, 28490,  28492, 28930, 28725,  \n8148, 26080, 20414,  1229, 11600, 9220,  28082, 28931, 28286,  \n587, 15246, 4858,  20959, 1483, 14378,  1418, 10433, 5326,  \n14378, 9187, 20959,  18224, 10672, 10673,  28927, 28728, 28486,  \n24134, 25089, 25437,  12007, 12006, 11245,  6525, 6524, 1944,  \n28492, 28732, 28930,  19463, 3063, 12359,  1020, 8956, 15809,  \n28733, 28497, 28932,  28932, 28927, 28733,  11836, 19354, 2056,  \n28495, 28488, 28734,  3947, 23807, 3946,  28488, 28738, 28734,  \n1760, 17374, 4750,  21519, 2268, 22391,  28928, 28730, 28500,  \n28933, 28491, 28934,  28933, 28097, 28491,  10933, 18278, 10711,  \n28097, 28933, 28732,  19073, 20617, 21945,  28493, 28935, 28936,  \n28733, 28927, 28501,  28501, 28927, 28486,  28735, 28928, 28500,  \n3994, 14357, 2526,  19086, 19085, 23118,  28493, 27901, 28935,  \n14734, 4197, 4198,  28502, 28734, 28735,  12529, 3598, 9505,  \n5318, 6376, 3266,  28736, 28088, 28937,  23302, 5091, 2651,  \n7687, 7686, 16469,  14576, 20038, 11120,  21877, 17970, 5525,  \n28739, 28301, 28737,  16743, 10004, 5032,  27697, 28739, 28938,  \n5588, 4853, 4852,  28935, 27901, 28741,  27523, 28503, 27911,  \n5566, 6468, 22324,  8439, 10266, 19108,  3879, 3268, 3267,  \n16969, 12736, 22344,  28103, 28939, 27912,  27914, 28506, 28743,  \n28743, 27915, 27914,  9779, 9780, 5636,  15286, 2779, 16520,  \n1231, 1230, 2557,  13936, 16839, 20880,  27532, 28508, 28940,  \n27705, 27532, 28940,  7822, 14507, 7683,  16837, 14842, 14420,  \n26752, 28304, 28747,  25126, 27026, 28039,  1703, 8371, 11976,  \n9854, 20897, 16046,  14314, 17755, 11740,  2915, 10602, 12195,  \n27917, 28748, 28105,  14292, 8883, 4968,  8708, 8709, 19017,  \n9079, 2724, 3349,  13517, 21232, 11736,  27709, 28511, 28509,  \n23272, 10939, 12102,  20065, 16140, 20064,  28942, 28307, 28510,  \n10679, 22137, 15218,  11307, 2301, 2300,  1089, 11454, 18894,  \n28942, 28750, 28307,  11094, 19271, 6823,  28943, 28513, 28750,  \n28944, 28512, 28309,  2525, 14481, 17565,  28944, 28309, 28752,  \n28752, 28516, 28947,  22035, 18005, 1856,  28310, 28519, 28949,  \n28949, 28114, 28310,  28516, 28115, 28950,  28753, 28950, 28115,  \n28949, 28520, 28114,  2237, 21156, 24100,  8882, 18772, 13481,  \n27336, 28753, 27925,  28521, 28951, 27714,  27335, 27717, 27334,  \n2014, 1021, 16422,  28523, 27715, 28116,  28754, 28117, 27715,  \n28119, 29134, 27335,  1358, 9380, 13858,  10044, 3841, 2194,  \n28952, 25557, 15255,  28954, 28525, 28524,  28954, 28955, 28525,  \n8362, 1893, 8360,  19932, 6538, 4155,  28313, 28956, 28755,  \n28525, 28955, 28314,  28955, 28756, 28314,  6125, 16414, 6126,  \n28956, 28313, 27929,  21476, 18456, 14938,  3420, 9816, 4588,  \n28757, 28526, 27930,  28317, 28314, 28756,  28316, 28123, 28758,  \n6942, 5962, 4219,  28756, 28760, 28317,  20418, 12292, 23828,  \n6260, 14944, 17764,  28121, 27724, 28530,  28530, 28957, 28121,  \n3852, 9458, 6569,  2039, 10790, 1593,  28959, 28319, 28320,  \n28958, 28319, 28959,  28960, 28959, 28320,  28960, 28320, 28126,  \n28960, 28126, 28761,  28128, 28761, 28127,  28322, 28760, 28323,  \n8199, 4190, 1110,  28763, 28128, 28764,  28531, 28323, 28961,  \n2155, 13130, 9664,  14924, 11123, 770,  9647, 1963, 1964,  \n28962, 28763, 28764,  18224, 10801, 18833,  8572, 20962, 7918,  \n28764, 28765, 28962,  16820, 5276, 20916,  28532, 28964, 28132,  \n12453, 3061, 3060,  28132, 28965, 28325,  17421, 9282, 9281,  \n28325, 28965, 28534,  4737, 4599, 4600,  28767, 29145, 28766,  \n10821, 3875, 21560,  10090, 11770, 5765,  29145, 28767, 28966,  \n12095, 20419, 19066,  28965, 28966, 28535,  28966, 28767, 28535,  \n20192, 9572, 14478,  21311, 17838, 18715,  2108, 17838, 21311,  \n1365, 22906, 1366,  26943, 26360, 26958,  22837, 7696, 23284,  \n14519, 20234, 18675,  28538, 28537, 25267,  999, 28740, 911,  \n26985, 28143, 28572,  27943, 13507, 28572,  27943, 18711, 13507,  \n28967, 25467, 14476,  7738, 11801, 7736,  24390, 25565, 20486,  \n10345, 6336, 6335,  12187, 2213, 17011,  18988, 25698, 22549,  \n8826, 10311, 17386,  27944, 27945, 28541,  21493, 3842, 20855,  \n28539, 27951, 27740,  28539, 28144, 28613,  10516, 7420, 8338,  \n20402, 17340, 1457,  19642, 16685, 19641,  11898, 15751, 1961,  \n28611, 27944, 28541,  15956, 16064, 6817,  4917, 1540, 2664,  \n19030, 17987, 19208,  28544, 27742, 29482,  27742, 27951, 29482,  \n2165, 20515, 2166,  27739, 28358, 28770,  12468, 4572, 3397,  \n25423, 27944, 28611,  11316, 11077, 11076,  21599, 11333, 22369,  \n27739, 28543, 28358,  12067, 4187, 11702,  4922, 23940, 20072,  \n28969, 28772, 28331,  2950, 5714, 5487,  16652, 12794, 14286,  \n17079, 7665, 17834,  28148, 28330, 28970,  1611, 14248, 6579,  \n19316, 3738, 4866,  18784, 21900, 15428,  18711, 27943, 27738,  \n813, 16295, 15674,  28331, 28334, 28969,  13091, 8261, 21444,  \n13987, 15943, 8001,  1933, 11807, 3162,  5825, 17179, 7427,  \n17695, 1492, 8538,  28148, 27161, 28330,  13441, 17431, 17430,  \n28540, 27947, 26985,  12372, 1806, 5816,  8116, 16675, 16843,  \n23262, 23243, 22153,  15817, 21975, 18014,  7545, 23507, 14359,  \n6638, 907, 7323,  4250, 1807, 15222,  24134, 25437, 21620,  \n4178, 12329, 12328,  2494, 18770, 7639,  4558, 20952, 19197,  \n26139, 21176, 10032,  11883, 9347, 11884,  7522, 7523, 13540,  \n20130, 4490, 4489,  16367, 18768, 18767,  6425, 18162, 6424,  \n22576, 22577, 4360,  2349, 3468, 3504,  28775, 28338, 28773,  \n28775, 28773, 28971,  28971, 28773, 28341,  5380, 8048, 20364,  \n15562, 3778, 2869,  28775, 28971, 28779,  18606, 16629, 19031,  \n28971, 28341, 28343,  5726, 5727, 9878,  28339, 28972, 28552,  \n26789, 28556, 28339,  28556, 28973, 28339,  2504, 1381, 15071,  \n5936, 9487, 20222,  15531, 14914, 13985,  22606, 13499, 16753,  \n28779, 28971, 28974,  28971, 28343, 28974,  28343, 28776, 28974,  \n28975, 28777, 28153,  28552, 28975, 28153,  3046, 11963, 9980,  \n27570, 28558, 28556,  28558, 28976, 28556,  16553, 14937, 19585,  \n12718, 8256, 21889,  28779, 28974, 28977,  11899, 14857, 17602,  \n17038, 10261, 10260,  28974, 28776, 28978,  5679, 19414, 3060,  \n28777, 28978, 28776,  28777, 28979, 28978,  28979, 28777, 28778,  \n2530, 2529, 21393,  3871, 13843, 13844,  23682, 1184, 14590,  \n10904, 22620, 10944,  1252, 7059, 11395,  1810, 18702, 13557,  \n12721, 816, 817,  2758, 2757, 5812,  11981, 5891, 10023,  \n19206, 12421, 19161,  18010, 19124, 17984,  23533, 6543, 17923,  \n12350, 12349, 6753,  28558, 27173, 28345,  6720, 21610, 17938,  \n14936, 29152, 28545,  12063, 12062, 11187,  8433, 13205, 20854,  \n16191, 9121, 12895,  16083, 12249, 12248,  12509, 5039, 7558,  \n28974, 28978, 28977,  837, 17586, 17585,  20046, 3117, 15244,  \n28978, 28979, 28981,  28779, 28977, 28560,  7558, 11062, 12509,  \n28981, 28977, 28978,  28560, 28977, 28780,  28977, 28781, 28780,  \n6038, 774, 773,  19445, 16844, 16675,  15324, 3284, 3285,  \n487, 14262, 486,  27576, 26964, 28559,  486, 14262, 22369,  \n4423, 9116, 14363,  5919, 14750, 13219,  4038, 10589, 20304,  \n23695, 22108, 12701,  20932, 16076, 838,  28575, 14572, 8953,  \n28565, 28983, 28984,  28781, 28983, 28565,  19659, 14225, 8298,  \n1367, 3441, 12892,  20799, 8917, 25069,  6831, 637, 5046,  \n1244, 23685, 9429,  28565, 28984, 28782,  20011, 27575, 28160,  \n13868, 22357, 8246,  4685, 3887, 12752,  28985, 28782, 28984,  \n21127, 3517, 3329,  23630, 20941, 11465,  19758, 26695, 20321,  \n9112, 9113, 5578,  12063, 7099, 2383,  28160, 27580, 28350,  \n14045, 3148, 3147,  26872, 26502, 20813,  20033, 13554, 805,  \n27578, 28783, 27759,  629, 14035, 630,  14297, 16019, 16018,  \n28569, 27759, 28783,  5439, 17488, 15667,  28350, 27394, 29168,  \n7106, 5335, 10757,  6121, 13703, 12817,  28352, 28568, 28785,  \n7933, 20432, 20431,  28986, 28352, 28785,  19340, 18461, 18462,  \n28352, 28986, 28164,  9143, 6252, 9144,  3928, 20495, 19864,  \n19427, 10659, 13219,  9870, 17630, 4443,  18931, 8280, 7459,  \n28987, 28786, 28164,  5879, 5880, 7377,  1312, 18807, 13361,  \n10352, 17997, 10027,  2486, 18637, 11942,  28786, 28988, 28165,  \n28816, 26284, 26285,  28988, 27965, 28165,  11140, 9711, 9712,  \n16852, 11831, 2198,  17082, 14877, 9566,  28163, 27968, 28787,  \n27968, 28570, 28787,  6465, 6467, 13938,  28355, 28789, 28989,  \n27967, 27765, 28789,  15703, 13284, 2625,  20901, 6225, 20451,  \n19186, 8856, 7538,  8415, 5977, 5336,  26898, 10455, 22989,  \n4488, 6564, 14410,  20017, 25126, 6227,  10990, 4854, 6655,  \n20097, 1288, 14753,  7946, 7945, 8441,  4627, 14482, 9547,  \n8768, 17129, 17532,  9036, 1469, 20092,  17005, 11981, 21671,  \n5105, 13170, 3915,  5370, 4360, 14510,  18541, 17229, 12770,  \n27195, 26276, 28792,  28791, 28359, 28168,  27586, 28168, 28359,  \n457, 1151, 12161,  26827, 25466, 25574,  7402, 3047, 16777,  \n26276, 28357, 28792,  17844, 8802, 22082,  13889, 1037, 16487,  \n337, 21390, 3218,  14982, 16012, 15578,  3077, 16195, 7141,  \n28169, 27396, 28170,  5867, 1712, 1017,  7910, 5562, 15122,  \n5233, 11948, 11947,  2298, 4645, 4644,  7281, 21048, 1630,  \n18602, 5095, 2204,  27771, 27772, 28793,  28360, 28991, 28994,  \n27195, 28792, 28362,  15051, 15257, 1383,  28360, 28994, 28361,  \n27772, 27399, 28793,  27773, 28172, 28992,  9802, 13118, 7355,  \n20436, 11911, 20440,  28173, 28994, 28794,  28994, 28173, 28361,  \n14903, 14576, 7048,  11120, 20038, 11121,  22164, 28577, 27774,  \n27972, 28173, 28794,  28172, 28363, 28995,  14338, 15496, 17321,  \n26983, 26978, 28576,  6907, 4413, 14656,  27973, 28578, 28996,  \n28177, 27973, 28996,  27202, 26983, 24272,  28996, 28795, 28177,  \n5122, 7170, 5123,  14747, 1072, 18867,  23919, 19391, 25475,  \n9770, 7362, 5667,  9218, 2946, 19216,  12598, 25424, 22785,  \n12499, 2824, 12712,  6414, 28768, 22592,  28579, 28177, 28795,  \n28580, 27201, 28796,  20560, 11957, 4382,  28180, 27202, 28997,  \n19412, 19789, 20493,  10331, 10332, 16713,  28797, 27780, 27976,  \n9818, 15319, 15320,  1126, 22881, 16332,  13983, 18745, 19609,  \n19636, 1666, 4791,  9770, 5667, 702,  28366, 27782, 28799,  \n16386, 20642, 22453,  27781, 28179, 27977,  1875, 869, 6481,  \n9226, 1193, 13027,  8301, 13603, 1710,  15760, 576, 8233,  \n11065, 6807, 2667,  12628, 16069, 9586,  7849, 3871, 10209,  \n5344, 11842, 3412,  27976, 28182, 28998,  3388, 7134, 13531,  \n28800, 27979, 28802,  10385, 18053, 18052,  28182, 28367, 28998,  \n28801, 27403, 27978,  25594, 28375, 10031,  20054, 19127, 16146,  \n20054, 10703, 19127,  12865, 7576, 12866,  27981, 27403, 28801,  \n3897, 10770, 19005,  17782, 12619, 12618,  12071, 15139, 3445,  \n8189, 12866, 6813,  29000, 28999, 28368,  28803, 27784, 27981,  \n28805, 28802, 27598,  27785, 27787, 28804,  3837, 16676, 3838,  \n28368, 28370, 29000,  21176, 26139, 11034,  23133, 24419, 23361,  \n28805, 27598, 27599,  27600, 26824, 28803,  2981, 2980, 10207,  \n293, 4609, 19517,  10018, 11560, 10019,  1447, 18973, 15681,  \n11512, 14445, 11217,  13834, 17437, 6931,  28369, 27601, 26996,  \n14994, 18018, 10780,  17726, 12593, 17725,  6032, 6031, 23410,  \n8276, 8277, 3549,  27421, 8279, 24274,  1483, 12981, 4828,  \n10886, 23139, 4166,  29001, 28371, 27984,  19517, 9952, 292,  \n28902, 3426, 25804,  2081, 4507, 2382,  27984, 28193, 29002,  \n2902, 4328, 13578,  639, 16635, 16634,  28806, 28584, 27796,  \n19846, 16973, 21094,  12937, 641, 7724,  13337, 7744, 7569,  \n27604, 27601, 29003,  24462, 14121, 10282,  8961, 13110, 12368,  \n25211, 25437, 24786,  21397, 28613, 28540,  12147, 4477, 14997,  \n4669, 4670, 9517,  18867, 1071, 9613,  28808, 27604, 29003,  \n3098, 17164, 3584,  5368, 14636, 10297,  2166, 5910, 9575,  \n1031, 4163, 3879,  27798, 28373, 28809,  18667, 20457, 5822,  \n14282, 5565, 8049,  2229, 2276, 3490,  5381, 20364, 21844,  \n28814, 28373, 27988,  28814, 27988, 28591,  13010, 9791, 15708,  \n27420, 26828, 28372,  27989, 28589, 28588,  8931, 10769, 8932,  \n4170, 6778, 21712,  28588, 27986, 27608,  594, 5574, 595,  \n17383, 6923, 8393,  18114, 8981, 540,  18562, 11828, 7861,  \n19089, 24236, 5114,  11568, 15866, 2086,  3287, 4243, 20925,  \n6248, 18664, 14939,  13916, 2123, 11829,  13285, 15591, 14460,  \n27607, 28592, 27989,  26293, 26142, 28590,  28374, 28817, 28818,  \n27802, 28819, 28591,  6666, 19344, 13726,  5533, 20932, 839,  \n10132, 8014, 2833,  5154, 16636, 7451,  14788, 22542, 9799,  \n4506, 9881, 6469,  8002, 21011, 5074,  12236, 16485, 12927,  \n27802, 27612, 28819,  5175, 13643, 22655,  28572, 27368, 27943,  \n2073, 18483, 2072,  10055, 14397, 15949,  5288, 8108, 5289,  \n408, 1495, 1494,  4948, 4536, 4949,  26985, 27947, 28143,  \n29006, 28377, 28379,  7452, 3374, 19942,  28596, 27426, 28595,  \n6750, 14495, 14494,  14380, 2628, 16708,  28379, 29007, 29006,  \n28378, 28594, 29009,  6983, 13671, 17834,  28379, 27994, 29007,  \n3670, 14125, 5569,  12484, 15813, 5855,  29010, 29007, 27994,  \n662, 5941, 9142,  19728, 11789, 8899,  28200, 27804, 29011,  \n27994, 28598, 29010,  28598, 29012, 29010,  12861, 7396, 5668,  \n17717, 9462, 7240,  28599, 28380, 27615,  2486, 11942, 18474,  \n3837, 8988, 3955,  18818, 17395, 1869,  7373, 15934, 7374,  \n28382, 27432, 28820,  18595, 10647, 10646,  16860, 17492, 4837,  \n12187, 2212, 2213,  2059, 15102, 18877,  21080, 10497, 20834,  \n27434, 28200, 29195,  731, 7216, 15258,  19573, 14529, 17661,  \n5005, 8734, 10358,  5919, 5920, 17902,  2017, 17985, 4316,  \n28598, 27616, 28823,  21880, 19702, 17603,  20859, 379, 20006,  \n29195, 28383, 27434,  29195, 29014, 28383,  9465, 2112, 12359,  \n322, 9338, 11959,  9514, 11433, 9515,  29521, 28602, 29015,  \n5591, 5592, 17272,  18190, 18229, 21520,  28605, 29013, 28600,  \n683, 14507, 22682,  28383, 29016, 28606,  28827, 28606, 29016,  \n7360, 339, 340,  3357, 8752, 9562,  12623, 9753, 8916,  \n678, 10707, 1790,  2282, 3740, 2572,  28390, 28386, 28392,  \n1187, 1188, 14117,  16482, 23537, 5687,  583, 582, 6987,  \n10566, 10565, 8833,  28605, 27815, 28399,  432, 6387, 17896,  \n4232, 9731, 10549,  19675, 3209, 5192,  28394, 29197, 27810,  \n28389, 28602, 28828,  13535, 9389, 9390,  10897, 19559, 6889,  \n3528, 14837, 16198,  16674, 3257, 11657,  27619, 28604, 28609,  \n27815, 27820, 28399,  6520, 13770, 1766,  29019, 28608, 28827,  \n10188, 17057, 7696,  6731, 23471, 10217,  18086, 11003, 16797,  \n11091, 3104, 17913,  29020, 28829, 28209,  3712, 3713, 2740,  \n28396, 29018, 28394,  3840, 3839, 19449,  28207, 28829, 28399,  \n19193, 1317, 19891,  3877, 9067, 17988,  28827, 29021, 29019,  \n29021, 28827, 29016,  29018, 28396, 28831,  27819, 28831, 28396,  \n20727, 22857, 455,  10955, 13932, 4442,  17053, 7564, 2831,  \n28829, 28207, 28209,  29020, 28209, 28830,  28830, 28832, 29023,  \n11518, 19778, 13548,  19876, 4341, 18136,  19239, 21203, 26965,  \n2293, 15623, 8667,  28832, 28830, 28208,  10134, 11065, 20692,  \n28831, 27819, 28206,  619, 16170, 22305,  8218, 11790, 5145,  \n15286, 16520, 5829,  14298, 5131, 16263,  28608, 28834, 28393,  \n7858, 7895, 16185,  1263, 7493, 16382,  10181, 13627, 5578,  \n5659, 17089, 28993,  332, 18752, 10815,  8072, 4418, 4417,  \n13813, 17638, 17639,  28007, 28828, 29022,  3620, 15097, 6999,  \n1989, 1988, 10754,  28832, 28833, 29024,  7873, 12687, 1898,  \n28835, 29025, 28004,  15383, 10891, 10123,  5658, 5659, 29026,  \n8690, 3634, 11449,  12414, 14459, 10736,  16879, 4248, 9982,  \n5128, 9591, 13230,  551, 552, 861,  7511, 7510, 16904,  \n6469, 12790, 11104,  3826, 13091, 21444,  6424, 18162, 11184,  \n17213, 5640, 13362,  28212, 28393, 28834,  28835, 28006, 28840,  \n14974, 17935, 1757,  6532, 12684, 10066,  7544, 7703, 11725,  \n2925, 15412, 5259,  28614, 28010, 28402,  28615, 29029, 28404,  \n28212, 28834, 29030,  23997, 912, 21549,  7002, 776, 1985,  \n19965, 21598, 14098,  28404, 29029, 28617,  19162, 6665, 6664,  \n9765, 1269, 20662,  28839, 29031, 28413,  1147, 14137, 1146,  \n7267, 6039, 679,  28007, 28612, 28016,  402, 14171, 5457,  \n29032, 29033, 28841,  28842, 28615, 28407,  6544, 19204, 1633,  \n7189, 2769, 12911,  13283, 13282, 6485,  15217, 5724, 7294,  \n4705, 7566, 13350,  20467, 9413, 17021,  7788, 18578, 18518,  \n7788, 18518, 5805,  29036, 29034, 28843,  28413, 29031, 29035,  \n21131, 4771, 9167,  4837, 23728, 6710,  18106, 9752, 18130,  \n29038, 29032, 28621,  13561, 10848, 13563,  13238, 9582, 16812,  \n12029, 28375, 15575,  10146, 3657, 3295,  17094, 8585, 14786,  \n2178, 12533, 2177,  19209, 5097, 19421,  5931, 3727, 16883,  \n28620, 28618, 28845,  28623, 28413, 29035,  28619, 28624, 29039,  \n28624, 28848, 29039,  28619, 28414, 28624,  28623, 29035, 28846,  \n10423, 3473, 19220,  3509, 3508, 19201,  16735, 13232, 17748,  \n810, 3938, 8408,  29038, 28621, 29041,  2713, 2714, 3220,  \n5371, 17217, 7461,  29041, 28621, 28847,  4598, 1006, 20047,  \n17022, 11841, 13854,  28620, 28845, 29044,  28620, 29044, 28850,  \n7102, 7101, 15357,  6320, 6322, 6563,  9892, 1086, 6381,  \n20147, 12719, 13038,  12187, 17011, 21028,  7954, 11575, 14943,  \n29044, 29045, 28853,  28853, 28850, 29044,  23905, 12010, 18125,  \n6326, 17187, 17186,  29046, 28218, 28411,  12528, 17924, 21109,  \n16769, 15455, 13451,  17823, 8720, 8135,  5353, 17623, 2271,  \n5185, 4043, 15465,  10581, 15740, 28329,  28850, 28853, 28854,  \n15829, 3395, 18663,  28849, 28850, 28854,  2388, 11912, 15900,  \n16476, 28315, 3935,  24029, 3218, 27764,  1036, 19873, 12048,  \n16180, 12629, 3587,  28853, 29047, 29048,  7172, 7046, 6734,  \n29049, 28854, 28853,  17787, 22188, 1332,  28426, 28854, 28639,  \n2363, 3992, 21770,  13369, 18490, 2209,  10414, 16191, 12895,  \n3867, 18389, 18390,  28224, 28222, 29050,  6123, 14775, 825,  \n6710, 2058, 4837,  7954, 14982, 11575,  29051, 28628, 28425,  \n26965, 6866, 19239,  29051, 28425, 28644,  14344, 3698, 8095,  \n21397, 28540, 26985,  9244, 2436, 8033,  10535, 2471, 13497,  \n28225, 28639, 28643,  23140, 18683, 22344,  3021, 5004, 10358,  \n2429, 19893, 2204,  29053, 28860, 28639,  318, 10547, 2124,  \n15575, 28375, 21175,  19271, 11094, 6409,  28856, 28631, 28859,  \n15329, 13218, 13883,  3894, 2485, 2561,  28639, 28860, 28643,  \n10474, 17035, 13811,  892, 891, 13444,  28224, 29050, 28024,  \n28646, 28642, 28023,  12543, 15663, 20834,  6500, 12426, 6147,  \n4419, 17553, 4417,  11806, 18618, 11864,  5714, 18686, 17687,  \n13743, 13188, 14316,  22397, 720, 9880,  8116, 17730, 9897,  \n29238, 28024, 29050,  7368, 6741, 18909,  3129, 20983, 10274,  \n16184, 1075, 16185,  21652, 19787, 22078,  10197, 3776, 887,  \n16085, 21549, 15652,  12165, 12166, 11133,  28862, 28643, 29056,  \n28643, 28860, 29056,  4499, 9924, 5906,  29055, 28646, 28648,  \n29055, 28648, 29057,  4691, 17626, 6813,  8622, 17963, 15436,  \n14607, 15501, 20068,  28862, 29058, 28647,  28647, 29058, 28649,  \n28648, 28863, 29057,  18667, 17371, 20457,  29058, 28864, 28649,  \n28864, 29058, 29060,  14062, 17631, 18894,  28865, 28864, 29060,  \n19551, 4142, 19478,  6208, 16077, 16076,  29060, 28872, 28865,  \n28232, 29061, 29250,  28870, 28866, 29062,  28429, 28866, 28870,  \n29062, 28866, 29063,  29063, 28866, 28651,  29063, 28651, 28867,  \n29064, 28867, 28431,  28645, 28230, 29059,  28652, 28865, 28872,  \n1412, 12351, 7224,  28431, 28871, 29064,  1744, 15352, 15297,  \n17240, 16345, 1913,  29059, 28230, 28655,  29066, 28868, 28656,  \n19525, 7237, 5146,  9959, 6195, 13151,  10035, 12674, 1354,  \n14629, 20724, 8414,  7061, 8211, 15593,  10241, 10240, 6925,  \n7468, 5406, 21325,  13105, 3052, 5800,  24320, 29059, 28034,  \n27840, 27054, 28873,  27843, 28237, 29070,  28658, 27843, 29070,  \n12080, 19957, 11853,  6182, 22966, 16243,  28660, 26302, 28236,  \n1262, 8290, 919,  17840, 15637, 10186,  28036, 25376, 27848,  \n13479, 10822, 10823,  27842, 28663, 28662,  12729, 3621, 21642,  \n14325, 9309, 22942,  2149, 15556, 21882,  1594, 18420, 12319,  \n15380, 5485, 3391,  8330, 7473, 15799,  28875, 28874, 29073,  \n29073, 28874, 29072,  9294, 12088, 17437,  1831, 12134, 18206,  \n28665, 29260, 28663,  4613, 4612, 18773,  11342, 13954, 2727,  \n29073, 28671, 28875,  9430, 8679, 13906,  29073, 29076, 28671,  \n29076, 29074, 28669,  28669, 29074, 28879,  14166, 6134, 6067,  \n15405, 13291, 3069,  5728, 8768, 17532,  28436, 29077, 28876,  \n22724, 8186, 6166,  18353, 9114, 18780,  26488, 28877, 27851,  \n18844, 20579, 19418,  17767, 4502, 22634,  7051, 22302, 19298,  \n28671, 29076, 28668,  28668, 29076, 28669,  4318, 12723, 473,  \n28672, 28880, 28882,  27738, 24723, 18711,  3431, 21466, 6934,  \n21775, 13778, 6832,  15172, 890, 889,  25015, 5274, 16350,  \n18743, 20566, 9917,  7832, 7831, 14681,  19820, 17422, 13595,  \n28878, 27654, 28043,  26087, 28440, 28667,  20142, 13131, 13130,  \n16513, 2872, 10834,  28250, 29078, 28883,  16310, 24955, 16311,  \n15777, 16424, 12855,  6517, 7733, 14589,  28250, 28442, 29078,  \n3723, 15268, 10942,  3388, 13531, 621,  28143, 27368, 28572,  \n17603, 19702, 22745,  24740, 19380, 15104,  29080, 28885, 29081,  \n27860, 28045, 28886,  1542, 4958, 5332,  8619, 8618, 14846,  \n28676, 28884, 29082,  28740, 28178, 911,  1238, 5761, 14543,  \n28444, 28887, 29083,  9222, 2247, 11003,  28683, 28675, 27859,  \n28446, 28676, 29082,  28679, 28446, 29082,  4861, 13672, 7983,  \n14930, 11799, 9754,  16321, 21079, 20810,  18143, 21572, 21031,  \n3192, 17747, 13660,  28887, 28678, 29083,  8257, 19299, 3821,  \n1107, 13775, 2286,  28451, 28890, 28891,  2105, 6868, 20999,  \n11650, 18576, 11541,  6674, 4020, 21253,  29084, 28678, 28256,  \n9588, 3744, 17397,  18986, 3588, 20310,  28686, 28452, 28891,  \n3956, 3112, 8376,  7996, 15778, 10879,  28682, 29084, 28256,  \n19069, 12618, 22975,  6360, 16127, 6361,  5114, 15431, 19089,  \n28682, 28687, 29084,  27489, 28258, 28055,  17844, 22082, 14037,  \n29085, 28683, 28455,  17391, 18896, 17541,  3166, 6203, 13352,  \n19853, 15447, 19852,  19853, 29086, 15447,  29089, 28892, 28690,  \n28685, 28893, 28692,  28460, 28895, 29087,  29088, 29089, 28894,  \n29089, 28690, 28894,  28058, 28456, 29090,  28262, 28685, 28692,  \n17810, 2329, 2337,  28691, 28058, 28897,  28898, 28895, 28459,  \n14390, 22115, 4102,  4999, 7383, 23146,  29092, 28894, 28896,  \n29092, 29088, 28894,  11034, 26139, 5898,  28269, 28699, 28459,  \n18599, 18737, 18738,  21839, 17326, 17472,  29092, 28896, 29093,  \n28699, 28697, 29095,  28899, 29093, 28896,  16357, 893, 20001,  \n28697, 28692, 29095,  23005, 5508, 5628,  28702, 29094, 28696,  \n944, 564, 11543,  3512, 1740, 4410,  29096, 29097, 28903,  \n29098, 29096, 28903,  29099, 29093, 28899,  8206, 7370, 15341,  \n3733, 19718, 20176,  28635, 18525, 27941,  19065, 9911, 7958,  \n2422, 13059, 21324,  28710, 29098, 28903,  17250, 11396, 11390,  \n29099, 28899, 28900,  13059, 2421, 6193,  11259, 7349, 10812,  \n29101, 29100, 28703,  28635, 28636, 18525,  23734, 19069, 22975,  \n6237, 11152, 8726,  1114, 10935, 13927,  28711, 29098, 28710,  \n11566, 7381, 10275,  28709, 28903, 29097,  4703, 1203, 19350,  \n6944, 14875, 6945,  18182, 13071, 6291,  2666, 4406, 18660,  \n18146, 454, 21728,  28909, 28465, 28901,  17467, 5222, 22357,  \n28270, 29102, 28275,  10208, 471, 7928,  14103, 8171, 21239,  \n475, 802, 17157,  7427, 7426, 7487,  28900, 28704, 28472,  \n14465, 12047, 10492,  29102, 28907, 28275,  28275, 28907, 28706,  \n29105, 28702, 28467,  28271, 29103, 28473,  28715, 28477, 28709,  \n28142, 2657, 22388,  21011, 19560, 11111,  8125, 20965, 2696,  \n7762, 815, 18066,  28906, 28471, 28707,  21803, 14453, 8427,  \n5418, 11209, 5456,  13821, 3144, 3143,  4538, 9860, 4539,  \n7633, 11146, 17585,  29104, 28905, 28712,  14796, 20924, 9878,  \n28478, 28473, 29103,  29103, 29106, 28478,  21082, 22214, 8529,  \n28711, 28713, 28912,  29107, 28721, 28718,  6569, 9847, 18955,  \n28911, 29104, 28712,  28466, 28910, 28708,  7539, 14198, 12559,  \n21787, 12750, 1551,  13346, 10029, 10038,  28720, 28467, 28075,  \n28720, 29105, 28467,  11695, 13933, 17917,  8981, 13492, 6580,  \n17466, 16024, 17086,  14203, 16910, 1132,  20219, 5252, 5251,  \n28913, 28715, 28908,  21567, 17712, 20561,  28717, 28722, 29109,  \n29109, 28718, 28717,  14328, 4697, 21498,  17753, 18405, 19896,  \n22966, 8042, 16243,  10837, 3858, 21856,  1431, 4113, 1430,  \n7415, 4542, 16035,  29106, 28915, 28478,  29106, 29108, 28915,  \n29108, 28912, 28915,  12019, 13556, 6933,  7654, 838, 8627,  \n11243, 11244, 19396,  28719, 29110, 28911,  7666, 994, 18404,  \n28917, 29105, 28720,  14100, 9389, 13535,  2095, 295, 8310,  \n28717, 28292, 28722,  28293, 28721, 29111,  9564, 3569, 13084,  \n22116, 18383, 4674,  16487, 17930, 22573,  21661, 16380, 16381,  \n1510, 7424, 1511,  11202, 4807, 5177,  19873, 20983, 12048,  \n12009, 10370, 2689,  1417, 1418, 24596,  28924, 28297, 28919,  \n897, 4765, 6774,  18214, 4896, 4642,  9613, 14748, 18867,  \n28916, 29110, 28719,  8270, 11110, 8271,  4862, 10189, 11703,  \n19374, 8608, 12989,  580, 579, 2949,  13391, 21347, 13269,  \n29113, 28722, 28923,  21347, 18488, 10550,  10756, 5507, 23005,  \n8778, 18623, 15050,  28920, 29112, 28921,  28483, 28921, 28922,  \n28482, 28289, 29116,  1034, 2036, 19165,  28482, 29116, 29117,  \n28724, 28482, 29117,  28916, 28724, 29117,  17578, 19468, 28305,  \n14328, 21498, 2274,  28923, 28722, 28729,  10058, 5947, 13654,  \n29303, 28918, 28728,  28925, 28731, 29115,  29114, 29115, 28730,  \n5724, 5725, 10767,  14136, 1146, 14137,  28917, 28281, 28936,  \n3160, 6601, 6602,  16188, 12253, 16186,  28932, 29303, 28728,  \n28731, 28730, 29115,  13961, 11283, 3718,  28925, 29119, 29120,  \n28930, 28920, 28725,  21998, 19853, 28332,  29121, 28931, 28082,  \n28917, 28936, 29122,  28493, 28936, 28281,  29309, 28932, 29111,  \n28932, 28497, 29111,  10479, 4682, 4033,  14230, 9479, 10701,  \n28488, 28485, 29118,  23317, 16360, 19329,  4225, 3390, 3389,  \n22709, 18920, 7088,  17731, 4879, 6458,  16384, 3287, 548,  \n11818, 12204, 15823,  1461, 5310, 1462,  8828, 10536, 14362,  \n21351, 15373, 15375,  3424, 3719, 3423,  28927, 28932, 28728,  \n2592, 1525, 11286,  16505, 17712, 21567,  17109, 5125, 3732,  \n8429, 10417, 28102,  2938, 2939, 4835,  28931, 28291, 28286,  \n29124, 28291, 28931,  6082, 18456, 3524,  6607, 16320, 1242,  \n28934, 28491, 28926,  4009, 7868, 4008,  14423, 22773, 14732,  \n17840, 6477, 2819,  4114, 11846, 5134,  2379, 2880, 2380,  \n29124, 28931, 29125,  11645, 3266, 295,  28734, 29314, 28928,  \n28738, 29314, 28734,  4310, 23083, 4311,  8300, 9322, 13261,  \n834, 836, 17710,  28734, 28928, 28735,  28937, 28088, 28291,  \n7110, 8703, 22828,  16314, 5365, 13645,  9488, 12749, 12748,  \n6410, 5784, 4255,  9573, 9574, 20140,  28503, 28504, 27911,  \n21293, 28340, 13503,  1603, 19906, 15937,  28939, 28741, 27912,  \n28939, 29126, 28741,  29127, 28939, 29128,  29127, 29126, 28939,  \n14253, 519, 1240,  27705, 29128, 28939,  4156, 14957, 8260,  \n14383, 4280, 20622,  988, 3541, 989,  19542, 8930, 8932,  \n16318, 13506, 4467,  13234, 20567, 24274,  12868, 19867, 10641,  \n13685, 14810, 21174,  12086, 1013, 1014,  28508, 27916, 29129,  \n28508, 27533, 27916,  16183, 10588, 19973,  27916, 28306, 29129,  \n2915, 12195, 17876,  403, 16143, 16142,  403, 16142, 2558,  \n14563, 17591, 14564,  28749, 28105, 28941,  7336, 6321, 6320,  \n11089, 15754, 22560,  28749, 29131, 28510,  1331, 1330, 19226,  \n15207, 3514, 18506,  28511, 28512, 29325,  28510, 29327, 28942,  \n21249, 18378, 15285,  5703, 10503, 18778,  6407, 9819, 11735,  \n6814, 7563, 16507,  28751, 28513, 28943,  1452, 9071, 1686,  \n28947, 28944, 28752,  28517, 28515, 28946,  28950, 28947, 28516,  \n28517, 29132, 28948,  28011, 12398, 19469,  28518, 28517, 28948,  \n28518, 28948, 29133,  13525, 13593, 11992,  21156, 2237, 20418,  \n7469, 18671, 7470,  4045, 2567, 10742,  29331, 28753, 27336,  \n14498, 17913, 3104,  29331, 27336, 27717,  28521, 27713, 28520,  \n20554, 7783, 1327,  9025, 580, 22260,  20664, 12413, 9373,  \n21085, 4793, 20166,  10936, 9301, 10120,  7710, 10617, 4592,  \n28523, 28116, 28312,  12245, 18938, 14003,  1190, 13323, 17346,  \n28754, 28523, 29135,  10453, 18634, 1527,  28117, 28754, 29136,  \n27329, 28117, 28953,  14241, 14240, 21508,  10001, 9740, 9741,  \n28953, 28524, 27329,  29134, 28119, 28755,  28953, 29137, 28524,  \n28524, 29137, 28954,  10346, 10347, 17441,  8897, 20675, 8992,  \n1533, 9150, 19062,  12760, 1751, 12761,  6707, 11508, 7154,  \n12279, 11614, 9315,  21182, 14518, 5949,  13882, 13006, 5074,  \n20389, 21232, 21233,  28956, 27929, 28526,  18969, 6207, 14550,  \n17413, 11840, 16971,  721, 720, 1389,  23596, 27159, 28538,  \n3943, 14415, 8052,  28316, 28758, 29139,  6248, 17859, 15092,  \n12831, 6836, 6835,  28316, 29139, 28757,  11336, 11335, 13326,  \n28756, 29138, 28760,  28528, 28122, 28759,  28528, 29140, 28124,  \n19931, 15550, 16265,  18075, 6239, 5542,  10628, 4343, 15138,  \n28758, 28124, 29140,  28529, 28124, 28758,  8182, 7382, 2141,  \n28527, 28957, 28759,  23538, 14442, 12259,  11985, 8656, 4480,  \n29141, 29142, 28530,  6591, 19427, 19075,  28527, 28121, 28957,  \n28319, 28958, 28530,  27159, 23596, 18987,  1557, 15725, 12684,  \n2659, 17401, 2657,  16645, 11721, 11720,  28760, 28961, 28323,  \n28531, 28961, 28963,  22108, 17635, 12701,  28532, 28531, 28963,  \n15394, 12959, 10656,  2168, 2167, 8806,  3585, 16102, 7518,  \n28740, 26944, 28178,  18055, 5246, 1497,  29144, 28765, 28324,  \n29147, 28132, 28964,  6596, 16272, 16113,  2143, 4620, 10590,  \n22509, 12897, 12898,  29146, 28533, 28766,  29146, 28766, 29145,  \n29147, 28965, 28132,  15741, 16173, 16748,  17429, 11747, 14839,  \n18393, 3024, 15077,  4904, 18477, 4278,  4294, 2621, 8635,  \n2059, 2254, 2255,  27738, 27155, 24723,  1587, 11994, 6260,  \n29148, 17975, 12121,  28381, 15041, 6952,  15199, 22224, 3425,  \n17726, 12399, 12593,  17578, 22790, 19468,  17578, 8228, 22790,  \n16145, 28744, 5818,  29086, 28335, 15447,  8228, 19594, 22790,  \n13554, 9411, 9412,  24135, 2956, 13486,  19972, 11450, 16629,  \n6443, 9427, 20050,  27951, 28539, 29482,  16833, 14438, 15975,  \n28771, 26944, 28740,  28205, 28537, 28146,  792, 2025, 16116,  \n21489, 23272, 12102,  20506, 15775, 3487,  4232, 10549, 18122,  \n29149, 24694, 25627,  22161, 16184, 7895,  14544, 2396, 2395,  \n7982, 25467, 17089,  28968, 28546, 29345,  28546, 27743, 29345,  \n29345, 27743, 28544,  28330, 27950, 29150,  18848, 747, 19644,  \n27949, 27741, 29152,  29152, 27741, 28545,  29151, 28772, 28969,  \n2298, 19160, 6983,  4925, 17512, 17121,  20874, 21081, 8308,  \n28333, 27374, 19829,  19306, 6071, 11716,  11926, 19335, 11925,  \n22250, 10793, 2566,  20959, 27991, 1483,  28549, 28969, 28334,  \n2184, 5317, 9086,  21448, 18764, 4784,  27571, 28547, 29153,  \n15485, 4241, 19615,  5119, 6334, 18213,  24439, 28726, 27942,  \n17355, 11221, 7669,  1749, 6962, 1509,  5053, 5052, 15402,  \n15239, 18656, 8892,  7794, 14778, 11935,  2626, 2625, 12970,  \n3596, 3117, 14183,  16274, 12418, 4820,  14302, 4238, 20927,  \n27959, 29154, 27958,  8523, 16372, 13597,  16146, 19249, 20054,  \n2693, 18791, 2692,  20425, 5440, 25153,  27959, 28553, 29154,  \n1177, 14462, 18468,  5776, 8053, 13546,  6007, 17317, 21332,  \n28972, 28339, 28973,  28980, 27753, 28774,  1814, 1815, 18931,  \n28552, 28972, 28975,  29349, 28972, 28973,  10248, 4692, 7248,  \n6187, 20191, 870,  20992, 11373, 12189,  7586, 7585, 4847,  \n14978, 3087, 3086,  1943, 19988, 7376,  21139, 25086, 26929,  \n27753, 27572, 28774,  14981, 18535, 22663,  28150, 29157, 28559,  \n1119, 20200, 8081,  15383, 4523, 16632,  9095, 17079, 17100,  \n28952, 28726, 24438,  21468, 9349, 19136,  28563, 28561, 28562,  \n6337, 2960, 18794,  522, 17174, 9992,  11094, 6410, 6409,  \n603, 604, 17353,  12529, 16928, 3598,  2449, 6179, 2450,  \n11390, 716, 1427,  28981, 28979, 29158,  28778, 29158, 28979,  \n13667, 15672, 3278,  23182, 12164, 14884,  28375, 22263, 26827,  \n16675, 16844, 16843,  28983, 28781, 28982,  28981, 28781, 28977,  \n28781, 28981, 28982,  22965, 13482, 16194,  22147, 27576, 28559,  \n7903, 7843, 7902,  19218, 13478, 19440,  28178, 28185, 26838,  \n795, 14933, 14934,  14801, 9718, 16563,  22147, 27577, 27576,  \n1577, 6416, 10139,  6137, 863, 16780,  16708, 17375, 17572,  \n28564, 27575, 20011,  29159, 27962, 28347,  16027, 12647, 17331,  \n1328, 20408, 3366,  2406, 8535, 16421,  2734, 9956, 10595,  \n16908, 9557, 8717,  13686, 1700, 1701,  28984, 28983, 29160,  \n28783, 27578, 27577,  28347, 28784, 29161,  28347, 29161, 4634,  \n5780, 20813, 25181,  1122, 1123, 18904,  28568, 28782, 28985,  \n6941, 1555, 7780,  6459, 6458, 4879,  16140, 8224, 20064,  \n29162, 28785, 28568,  28784, 26967, 28351,  21107, 14322, 3654,  \n341, 21911, 11459,  29163, 28785, 29162,  4386, 28603, 1410,  \n3646, 3647, 14024,  27159, 18987, 27427,  4198, 3523, 7066,  \n14351, 20985, 14811,  12304, 701, 10374,  27759, 28569, 11608,  \n13517, 10090, 10089,  28785, 29163, 28986,  13904, 11609, 6779,  \n28987, 28986, 29163,  5676, 4075, 4076,  28987, 28164, 28986,  \n29164, 28786, 28987,  29165, 28988, 28786,  14333, 22833, 16577,  \n29166, 28351, 28163,  29167, 27965, 28988,  27965, 29167, 27762,  \n29168, 27394, 27966,  28353, 27761, 11608,  420, 16121, 13817,  \n27762, 28788, 28354,  28178, 26944, 28185,  10301, 18934, 4538,  \n28570, 19540, 29169,  27765, 28788, 28789,  8365, 6625, 8177,  \n20671, 15066, 15065,  5257, 18781, 21046,  16489, 13061, 5464,  \n9614, 13494, 5596,  11151, 8986, 18722,  12674, 7980, 12923,  \n27367, 1522, 1521,  2037, 20197, 19193,  7397, 620, 7396,  \n16252, 19551, 19479,  22302, 665, 15399,  28790, 27970, 27969,  \n6553, 28359, 19255,  11299, 6491, 6492,  4451, 4450, 7989,  \n1696, 14228, 16287,  16642, 14275, 16643,  16546, 2131, 7018,  \n8721, 2842, 13039,  10078, 16589, 10715,  4563, 4562, 10776,  \n26034, 27159, 27427,  24100, 18031, 2237,  16640, 3100, 12974,  \n2655, 15064, 12865,  5846, 15441, 13782,  29172, 28169, 28170,  \n19648, 17972, 17973,  3543, 11262, 3542,  29171, 28360, 28790,  \n28185, 12726, 26838,  12208, 19968, 19648,  17296, 4903, 7614,  \n14521, 19357, 14638,  28170, 27773, 28992,  28360, 29171, 28991,  \n2756, 2560, 1416,  7457, 13691, 18331,  6963, 12542, 1619,  \n14081, 7513, 21151,  5720, 14554, 5664,  10838, 20670, 10839,  \n5104, 23595, 2708,  2464, 1458, 14069,  17255, 27400, 28574,  \n9517, 9396, 10329,  14903, 7048, 7960,  29173, 28794, 28994,  \n2172, 12805, 956,  10190, 1873, 10191,  4862, 13769, 9816,  \n18819, 14347, 15177,  12660, 3101, 7796,  10008, 17623, 7846,  \n17444, 27777, 27776,  9717, 6533, 384,  28653, 19469, 22606,  \n4761, 4760, 14467,  17490, 22735, 2410,  20642, 16386, 15512,  \n7314, 11019, 3135,  11380, 15124, 549,  27160, 28174, 29174,  \n18248, 18249, 22288,  11492, 12838, 12541,  20592, 16304, 17052,  \n362, 3980, 7850,  28183, 27979, 28798,  19955, 16641, 18442,  \n4808, 11202, 5512,  28581, 28579, 29175,  15485, 25434, 28542,  \n16203, 8631, 4482,  5677, 6573, 6572,  28998, 28367, 28999,  \n17144, 17528, 2053,  7235, 10867, 15568,  6820, 2118, 6821,  \n27405, 28184, 26996,  15886, 4347, 15626,  11090, 17858, 10061,  \n10790, 9690, 2478,  26958, 25088, 26610,  28369, 26996, 29178,  \n772, 606, 18692,  16078, 7072, 7520,  20606, 8924, 8925,  \n3650, 13128, 727,  7288, 8413, 11603,  28803, 28585, 27600,  \n6073, 7154, 5698,  12651, 13951, 19534,  5989, 9952, 19517,  \n8890, 6103, 3985,  584, 14817, 12454,  29002, 29001, 27984,  \n17560, 5716, 5751,  4611, 19017, 17672,  29179, 28586, 28187,  \n8911, 21824, 2019,  28193, 28809, 29002,  14993, 336, 19416,  \n3528, 16198, 3422,  28824, 23450, 18024,  28582, 29179, 28187,  \n10967, 19695, 10989,  16485, 15071, 10257,  21844, 23851, 2301,  \n16247, 14444, 850,  16811, 18234, 16812,  28372, 28190, 29629,  \n16178, 22475, 21423,  11422, 12928, 15717,  16085, 19562, 1131,  \n12101, 15241, 6256,  9255, 5896, 6145,  16733, 18002, 15327,  \n28589, 28810, 28812,  14119, 12315, 8141,  28372, 27793, 28190,  \n4904, 4278, 7614,  3909, 10552, 10553,  28586, 29183, 28813,  \n27226, 28808, 28195,  29184, 28589, 27989,  20203, 554, 21764,  \n16163, 3509, 12339,  6717, 8589, 14641,  28813, 29183, 28817,  \n11802, 14480, 8108,  29185, 27989, 28592,  16558, 17280, 14530,  \n2424, 3356, 12143,  5640, 14113, 17443,  28196, 27420, 28815,  \n1338, 2620, 7242,  28592, 29187, 29185,  11898, 14341, 6093,  \n28815, 29188, 28196,  17062, 7865, 17063,  1169, 1171, 10127,  \n28594, 28818, 29189,  10417, 25584, 28102,  29187, 28592, 28377,  \n28819, 27992, 28198,  28819, 28198, 29005,  29188, 28595, 28376,  \n20903, 12724, 12044,  4279, 10438, 2886,  29190, 28377, 29006,  \n7358, 22170, 1484,  931, 17044, 12499,  1420, 1911, 1912,  \n6416, 18846, 6415,  28198, 27806, 29005,  3971, 4425, 13629,  \n18326, 7804, 11498,  16373, 3549, 8277,  27431, 27803, 29008,  \n9674, 4114, 21115,  19664, 23705, 5592,  13332, 1526, 1528,  \n11761, 1257, 1256,  8172, 8171, 14103,  7679, 14337, 13881,  \n15129, 12312, 8922,  28378, 29009, 28597,  2114, 15040, 19444,  \n5535, 4113, 15288,  27804, 28596, 29011,  3688, 21692, 12644,  \n8095, 561, 14344,  12613, 19164, 8613,  4418, 14734, 4789,  \n15371, 6434, 3555,  9016, 18583, 17860,  20036, 8712, 16864,  \n16112, 29289, 25584,  5179, 19956, 12060,  19316, 4866, 19315,  \n2587, 5336, 2997,  29192, 28599, 27617,  28382, 28820, 29194,  \n4177, 4590, 23036,  29011, 29195, 28200,  28600, 29013, 29192,  \n15714, 18064, 11228,  28382, 29194, 28821,  25557, 14492, 15255,  \n27617, 28600, 29192,  29193, 28598, 28823,  5753, 3336, 2753,  \n28566, 14184, 6510,  736, 1398, 1397,  28602, 28199, 29015,  \n28383, 29014, 29016,  4828, 4108, 20779,  29197, 28823, 28388,  \n29196, 28605, 29017,  4878, 6149, 3757,  4543, 27946, 14492,  \n2089, 20483, 24013,  29197, 28388, 27811,  3302, 22065, 3645,  \n17420, 2531, 8441,  2197, 7088, 7750,  29198, 28604, 27998,  \n13782, 1672, 12900,  28605, 28399, 29017,  4952, 7266, 9606,  \n9676, 22620, 11897,  15702, 11656, 1898,  29521, 28828, 28602,  \n12670, 333, 21561,  11510, 13852, 2760,  13075, 13074, 20143,  \n16620, 14255, 16618,  29197, 28394, 29018,  1487, 17560, 1717,  \n9734, 479, 13814,  28829, 29017, 28399,  28538, 27159, 27371,  \n3948, 3968, 3949,  849, 12880, 1322,  18757, 1668, 16877,  \n16694, 11267, 4480,  18646, 4738, 16044,  29199, 29020, 28830,  \n29023, 29199, 28830,  21728, 6829, 13887,  3669, 11668, 9920,  \n1970, 3201, 7421,  28836, 29201, 28837,  8757, 12588, 15840,  \n16526, 14888, 20790,  28609, 29200, 27817,  28838, 29203, 28836,  \n13291, 13292, 10657,  26938, 27159, 13031,  29200, 28397, 27817,  \n7161, 4255, 4254,  27159, 26034, 13031,  12366, 2413, 11551,  \n16120, 6579, 6580,  29204, 28398, 28397,  21578, 21643, 21526,  \n26940, 12726, 28185,  29205, 29019, 29021,  26940, 28186, 12726,  \n28831, 28206, 29206,  16122, 15953, 4185,  13412, 4104, 9350,  \n11185, 10672, 6527,  675, 18651, 12908,  29202, 28839, 28837,  \n28838, 28616, 29027,  28608, 29208, 28834,  13032, 1596, 15694,  \n6391, 6392, 21761,  29208, 29019, 29207,  29208, 28608, 29019,  \n4672, 20047, 715,  28210, 28398, 29210,  2210, 2537, 1823,  \n457, 12161, 18082,  5544, 8558, 20510,  29211, 29024, 28833,  \n1522, 27369, 27944,  23674, 11483, 29569,  29025, 28835, 29212,  \n18912, 14797, 7796,  19942, 1783, 17081,  29033, 29027, 28841,  \n28007, 29022, 28612,  29028, 29211, 28833,  29029, 29211, 29028,  \n28840, 29212, 28835,  9437, 17563, 8897,  28840, 28006, 28401,  \n7243, 22101, 18410,  19939, 15028, 8162,  17343, 16048, 17341,  \n10410, 11902, 4597,  18149, 7959, 20329,  17007, 20980, 4807,  \n26872, 15148, 26502,  9845, 23267, 3254,  457, 5208, 2828,  \n29027, 28616, 28841,  29028, 28617, 29029,  2811, 17631, 2812,  \n29390, 29029, 28615,  11684, 4663, 9387,  7942, 2242, 2972,  \n16541, 7312, 17072,  18004, 5351, 19117,  11912, 299, 5242,  \n764, 765, 21865,  318, 8773, 3678,  1596, 13032, 14088,  \n10421, 890, 9360,  29216, 28618, 29030,  29034, 29527, 28843,  \n29217, 29034, 29218,  29219, 29217, 29218,  3352, 18484, 6316,  \n13919, 20909, 5207,  23074, 5736, 8522,  29036, 29218, 29034,  \n27155, 23382, 24723,  4486, 13737, 14966,  15641, 21696, 6375,  \n4143, 11467, 10033,  22211, 11305, 18513,  28619, 29039, 28842,  \n19082, 14085, 20575,  29040, 29222, 29036,  29222, 29221, 29218,  \n29222, 29218, 29036,  29031, 29221, 29224,  14394, 15148, 26872,  \n29221, 29222, 29223,  29220, 29032, 29225,  29036, 28843, 29040,  \n17299, 9966, 13036,  28411, 28612, 29037,  19714, 632, 20623,  \n15960, 11457, 7238,  16875, 9269, 9601,  29040, 28844, 29222,  \n29223, 29222, 28844,  28842, 29039, 29227,  9346, 16379, 11110,  \n4965, 7459, 20947,  7747, 16846, 16882,  29039, 29043, 29227,  \n28845, 29228, 29044,  4645, 3659, 4564,  7406, 4982, 1539,  \n4026, 22473, 22640,  10398, 10399, 10994,  11730, 10231, 19389,  \n29042, 29046, 28411,  10349, 687, 12159,  373, 9900, 8681,  \n4420, 7879, 16920,  23901, 4529, 4531,  22451, 9178, 18286,  \n13193, 12010, 23905,  4319, 472, 11075,  13360, 11705, 20528,  \n25064, 27367, 1521,  799, 812, 4612,  29045, 29230, 28853,  \n28853, 29230, 29047,  6782, 11824, 6781,  12970, 4877, 18139,  \n28218, 29046, 28222,  29047, 29230, 29048,  2738, 8176, 5412,  \n1162, 15652, 10966,  28222, 29046, 29050,  10124, 5298, 13443,  \n16417, 11632, 12065,  4785, 13804, 6181,  28628, 29051, 28629,  \n14172, 531, 14173,  15171, 11622, 22074,  28853, 29048, 29049,  \n29289, 9029, 25584,  2415, 7285, 1659,  25181, 20813, 26502,  \n29232, 29049, 29048,  8230, 5176, 1868,  28854, 29049, 28639,  \n28851, 28630, 29233,  29049, 29232, 29053,  29049, 29053, 28639,  \n10009, 6380, 1441,  28851, 29233, 29231,  18092, 15164, 869,  \n2269, 713, 8674,  56, 28642, 93,  1995, 11116, 5561,  \n6979, 6978, 14806,  29233, 28630, 28855,  21099, 8005, 19086,  \n28637, 29237, 29052,  14316, 13188, 1430,  29236, 29053, 29235,  \n13573, 13572, 13248,  20970, 14019, 4206,  23157, 20623, 12181,  \n28637, 29052, 28638,  29233, 28855, 28856,  6479, 5696, 18411,  \n6173, 1647, 5691,  28646, 29055, 28642,  29233, 28856, 29054,  \n10372, 22061, 11033,  16020, 16021, 3464,  12596, 20717, 10710,  \n29053, 29236, 28860,  5667, 19522, 12861,  22895, 16626, 14270,  \n9736, 7982, 17089,  15248, 20204, 20901,  7259, 7258, 12672,  \n479, 3771, 480,  16791, 14818, 4044,  7864, 16724, 12053,  \n15048, 12396, 5862,  7728, 9257, 16026,  21877, 26202, 17970,  \n28641, 28638, 29239,  1445, 11312, 2969,  4284, 11295, 12232,  \n29240, 28641, 29239,  8229, 12171, 19229,  11081, 3973, 17004,  \n20452, 16715, 20453,  14379, 17163, 10725,  12905, 14043, 12906,  \n28856, 28859, 29243,  29056, 28860, 29236,  369, 15067, 370,  \n4585, 8666, 4586,  28641, 29240, 29244,  28858, 29244, 29241,  \n28858, 28641, 29244,  28857, 29241, 29242,  28857, 28858, 29241,  \n29245, 28856, 29243,  28645, 29246, 28644,  21180, 20890, 20952,  \n8435, 12431, 14592,  29247, 28857, 29242,  29247, 28859, 28857,  \n8375, 18310, 10061,  22249, 8306, 15642,  12391, 7671, 24360,  \n29248, 28862, 29056,  5936, 5926, 10971,  29249, 29057, 29250,  \n20849, 5330, 14106,  19131, 945, 791,  20039, 21591, 20407,  \n28862, 29251, 29058,  29248, 29251, 28862,  12515, 5298, 11351,  \n28863, 29250, 29057,  29252, 29058, 29251,  29060, 29058, 29252,  \n17699, 16887, 9904,  29060, 29252, 29253,  19828, 23414, 6779,  \n28645, 29059, 29246,  28872, 29060, 29253,  5974, 6533, 5975,  \n9544, 23070, 14988,  28868, 29061, 28232,  18129, 6341, 14969,  \n4191, 5198, 28877,  29064, 29063, 28867,  6217, 4823, 19505,  \n5060, 23682, 21069,  9701, 16057, 13649,  4424, 16543, 868,  \n4060, 14431, 20118,  20978, 12773, 17628,  5120, 4341, 11258,  \n7768, 7767, 7065,  7279, 11238, 7860,  29066, 28656, 29067,  \n27840, 29067, 28656,  29068, 28871, 28236,  28874, 28657, 28872,  \n29065, 28874, 28872,  29068, 28236, 26302,  10156, 12331, 12330,  \n29067, 27840, 28873,  28434, 28654, 29069,  12926, 7014, 8591,  \n1955, 18158, 14207,  4595, 16846, 8144,  3103, 3102, 13670,  \n6452, 5076, 9367,  29059, 28655, 28034,  28659, 28434, 29257,  \n21766, 23235, 16858,  7312, 12306, 12305,  13137, 11959, 20478,  \n28662, 29256, 28873,  28658, 21817, 28036,  29065, 29072, 28874,  \n5767, 5156, 2902,  28663, 29258, 28662,  18635, 11207, 1154,  \n17237, 9277, 9831,  14621, 6564, 4017,  27849, 27848, 25376,  \n28879, 29074, 29263,  29260, 29071, 28663,  28659, 29075, 28667,  \n17493, 19957, 12080,  29261, 28660, 28664,  13173, 14723, 20031,  \n659, 2972, 17821,  15041, 28381, 25466,  29073, 29072, 29262,  \n2719, 14423, 9609,  3444, 4815, 13663,  11523, 22789, 16040,  \n22975, 2994, 22294,  11909, 8373, 17239,  6272, 6273, 5175,  \n14447, 20680, 21021,  1005, 1419, 16900,  29073, 29262, 29076,  \n29076, 29262, 29264,  3105, 3106, 1866,  29076, 29264, 29074,  \n23861, 16248, 12117,  18587, 8959, 5253,  4468, 11896, 8888,  \n29077, 28436, 29266,  28243, 28248, 28665,  28883, 29267, 28248,  \n28952, 14834, 14835,  21098, 827, 17309,  14611, 8135, 17273,  \n26488, 27851, 28042,  17659, 3750, 8154,  12067, 11702, 18069,  \n7259, 7854, 13661,  2970, 13060, 2792,  8510, 1052, 8511,  \n29079, 28882, 28880,  29267, 28665, 28248,  2453, 22653, 13900,  \n3957, 19825, 13612,  14995, 14304, 1273,  21856, 21886, 16279,  \n6642, 312, 6526,  7301, 4934, 4465,  28442, 29268, 29078,  \n27856, 28440, 28886,  28878, 28043, 28675,  28885, 29268, 28442,  \n17053, 14671, 20592,  10239, 20563, 13320,  28884, 28674, 29082,  \n17418, 7483, 6244,  2529, 2528, 9649,  17130, 1213, 19805,  \n29081, 29271, 29270,  10786, 11671, 1266,  11816, 3054, 13384,  \n27860, 28886, 28677,  29081, 28885, 29083,  342, 11459, 1846,  \n28885, 28444, 29083,  29080, 29081, 29270,  27861, 28677, 29272,  \n5927, 5464, 12584,  6864, 15873, 1182,  28679, 29082, 29269,  \n13272, 13638, 4527,  29081, 29083, 29273,  29272, 28888, 27861,  \n4830, 1809, 20804,  28889, 28679, 29275,  28890, 28684, 29275,  \n29273, 29083, 28678,  3859, 2527, 8837,  28684, 28889, 29275,  \n29273, 28678, 29084,  5560, 5809, 6357,  29278, 28686, 28891,  \n29276, 29273, 29084,  16086, 13651, 21118,  22858, 8068, 22337,  \n2762, 13583, 6676,  13882, 5074, 1457,  15000, 1427, 716,  \n14228, 12269, 16287,  28687, 29276, 29084,  6728, 1513, 9981,  \n16043, 13827, 12033,  7907, 7763, 7761,  16887, 19495, 9904,  \n28687, 28892, 29277,  22081, 15467, 19447,  12426, 20260, 19499,  \n15061, 1943, 7376,  27869, 28055, 28689,  13470, 9247, 18408,  \n29089, 29279, 28892,  29085, 28455, 29091,  2459, 15380, 3391,  \n17794, 5446, 6998,  29280, 28693, 29087,  29089, 29088, 29281,  \n19592, 17568, 14204,  6973, 20771, 2447,  15694, 13397, 13032,  \n29282, 29090, 28456,  16901, 9858, 12290,  28460, 29087, 28693,  \n28058, 29090, 28897,  28898, 28459, 28699,  29092, 29283, 29281,  \n29088, 29092, 29281,  29091, 28455, 28696,  28893, 29095, 28692,  \n16295, 813, 3136,  11790, 1320, 8468,  6507, 2555, 6769,  \n8056, 19189, 21020,  14559, 16909, 9977,  9637, 4708, 11365,  \n29093, 29283, 29092,  5830, 2905, 23287,  17904, 6484, 6485,  \n29093, 29285, 29283,  29284, 29094, 28702,  14174, 3698, 14344,  \n18773, 4612, 21402,  12800, 19145, 12130,  29286, 28701, 27675,  \n29286, 27675, 28465,  2298, 6444, 19160,  19704, 23974, 7187,  \n7145, 683, 3133,  29099, 29285, 29093,  1616, 15417, 21213,  \n29287, 29286, 28465,  7303, 19262, 11644,  8574, 5603, 7833,  \n5730, 3891, 9418,  29289, 22547, 10842,  29290, 29285, 29099,  \n2518, 707, 6005,  29291, 28705, 29100,  8399, 18396, 8809,  \n5020, 3467, 16785,  29290, 28900, 29292,  29099, 28900, 29290,  \n16894, 16895, 10642,  1834, 7718, 7719,  169, 29749, 11826,  \n3520, 15962, 16758,  8518, 13723, 5897,  28271, 28698, 29103,  \n16585, 20260, 21394,  28711, 28912, 29288,  28711, 29288, 29098,  \n28900, 28472, 29292,  28472, 28906, 29292,  8018, 15377, 9844,  \n28076, 28904, 28914,  1534, 10239, 341,  29105, 29284, 28702,  \n9208, 17133, 17134,  9977, 16909, 4758,  12849, 20491, 6888,  \n28905, 29451, 28707,  20435, 11522, 16968,  2867, 15386, 2898,  \n5635, 5579, 5580,  2626, 15703, 2625,  10396, 8016, 11782,  \n11289, 11290, 22490,  29296, 29297, 29104,  28905, 29104, 29294,  \n29108, 29288, 28912,  28038, 19242, 25266,  5091, 5093, 4305,  \n29295, 29296, 28911,  28911, 29296, 29104,  1681, 22330, 4448,  \n28901, 28273, 29298,  11338, 3579, 16081,  10465, 488, 6183,  \n15082, 9226, 13027,  28722, 29113, 29109,  6150, 15279, 10852,  \n13256, 3375, 3916,  29289, 25081, 9029,  11011, 17274, 11246,  \n3929, 18124, 3930,  17040, 28901, 29298,  1933, 3162, 1932,  \n28908, 29299, 28923,  29299, 29113, 28923,  22575, 12095, 1157,  \n28721, 29308, 29111,  23387, 13730, 13731,  29300, 28919, 28918,  \n29295, 28911, 29110,  28917, 7795, 29105,  28923, 28913, 28908,  \n7277, 29302, 9242,  17349, 21764, 17348,  25627, 17948, 29149,  \n7451, 8062, 14401,  29305, 29112, 29458,  29306, 29112, 29305,  \n512, 15276, 4095,  19945, 19545, 19378,  16088, 1605, 1604,  \n28920, 29307, 29304,  29304, 29458, 29112,  29112, 29306, 28921,  \n9757, 8501, 671,  24997, 7795, 28917,  13257, 18452, 4833,  \n12133, 5984, 10650,  29309, 29111, 29308,  4877, 8004, 18139,  \n9119, 2005, 8251,  6591, 21073, 19427,  28920, 29304, 29112,  \n28289, 28922, 29116,  28916, 29117, 29462,  15356, 14049, 5642,  \n28293, 29111, 28497,  28932, 29309, 29303,  12816, 14999, 7857,  \n1711, 2605, 2033,  11790, 11997, 5145,  20017, 20016, 20612,  \n13830, 6748, 12309,  18082, 12161, 5223,  14187, 14774, 1468,  \n18599, 2936, 15658,  15307, 6767, 16578,  29311, 29114, 28730,  \n28920, 28930, 29312,  7858, 1075, 20547,  29313, 28738, 29118,  \n29313, 29314, 28738,  4511, 8529, 15031,  29315, 9188, 1912,  \n28185, 26254, 26940,  28926, 28925, 29120,  29316, 29121, 28082,  \n28287, 29316, 28082,  13593, 16462, 11990,  3529, 5358, 5359,  \n5663, 5358, 3529,  10466, 23414, 3733,  28934, 28926, 29123,  \n29123, 29317, 28934,  28930, 29317, 29312,  1747, 9750, 3798,  \n12317, 3782, 16979,  29317, 28933, 28934,  28933, 29317, 28732,  \n28732, 29317, 28930,  11531, 4797, 11532,  4747, 4748, 9634,  \n8948, 3108, 19375,  12212, 8922, 12312,  28931, 29121, 29318,  \n29125, 28931, 29318,  3667, 15106, 5918,  19746, 13644, 10243,  \n4832, 4831, 3356,  2858, 9661, 6426,  28937, 28291, 29319,  \n17258, 29122, 29322,  13212, 18652, 4763,  27697, 28938, 28503,  \n29320, 28736, 29321,  8920, 11776, 15425,  29322, 28935, 29126,  \n29126, 28935, 28741,  712, 3390, 713,  13373, 1133, 8804,  \n27705, 28939, 28103,  21941, 6726, 14599,  28506, 28505, 29323,  \n28506, 29323, 28743,  1809, 1808, 20804,  29128, 27705, 28940,  \n4251, 19869, 4252,  9220, 15133, 9213,  12407, 17496, 12406,  \n28186, 26427, 26938,  3117, 20046, 14183,  5038, 12194, 10408,  \n28508, 29129, 28940,  4091, 8046, 391,  28104, 29324, 28304,  \n28104, 28507, 29324,  3263, 4248, 4247,  22254, 11195, 2637,  \n9962, 16125, 3716,  18037, 14682, 22077,  27369, 1522, 27367,  \n29129, 29130, 26005,  7918, 306, 14091,  6349, 16284, 8502,  \n29130, 28306, 28509,  28105, 28748, 28941,  21095, 13277, 11360,  \n14854, 13486, 21191,  29325, 29326, 28509,  22734, 18350, 8119,  \n28941, 29131, 28749,  20057, 9489, 16029,  6469, 8220, 12790,  \n29131, 29327, 28510,  12451, 22519, 12452,  29327, 28750, 28942,  \n28943, 28750, 29327,  28947, 29329, 28944,  28514, 29330, 28946,  \n1387, 16564, 9265,  27155, 27156, 23382,  23678, 23679, 4143,  \n11227, 7100, 21250,  29331, 28950, 28753,  7431, 20693, 13473,  \n20458, 9233, 8434,  15747, 1805, 18698,  26541, 28521, 29332,  \n27717, 29607, 29331,  1371, 4760, 8187,  27714, 28951, 28522,  \n16756, 2010, 2668,  1974, 4978, 1292,  25387, 28522, 29333,  \n8816, 8817, 22417,  27717, 27335, 29134,  28953, 28117, 29136,  \n12271, 10174, 12675,  22001, 17997, 17996,  4592, 10617, 20424,  \n29334, 28954, 29137,  9173, 5670, 7402,  28755, 28956, 29335,  \n7944, 11691, 19907,  2004, 2003, 18094,  16990, 17454, 16156,  \n10957, 8728, 17003,  16180, 3587, 3588,  15783, 12199, 17238,  \n9578, 9577, 20668,  3677, 15179, 6874,  28756, 28955, 29138,  \n21314, 7520, 17009,  29138, 28955, 29336,  28757, 29139, 29337,  \n25698, 18988, 23283,  28726, 6582, 27942,  11171, 7773, 11895,  \n28759, 29140, 28528,  29142, 28957, 28530,  29141, 28530, 28958,  \n3991, 16539, 22155,  8984, 4138, 12706,  24179, 29171, 4254,  \n28960, 28761, 29339,  29339, 29338, 28960,  28128, 28762, 28761,  \n29340, 28761, 28762,  28763, 29341, 28762,  6697, 16507, 8130,  \n28962, 29341, 28763,  28962, 29478, 29341,  14976, 17867, 4678,  \n4459, 14571, 3082,  28765, 29478, 28962,  22547, 23296, 10842,  \n29478, 28765, 29144,  28964, 28532, 28963,  29144, 28324, 28533,  \n28533, 29146, 29144,  29344, 29614, 29145,  29614, 29146, 29145,  \n29344, 29147, 29343,  3957, 13612, 17456,  13112, 9328, 15345,  \n13884, 7892, 7891,  16911, 16278, 12195,  6753, 18354, 3823,  \n4491, 14016, 18735,  28965, 29147, 29344,  29344, 28966, 28965,  \n29344, 29145, 28966,  28048, 23791, 19187,  2825, 7399, 7400,  \n29086, 19853, 21998,  6720, 17938, 17937,  14707, 3467, 1281,  \n14177, 19974, 7736,  12183, 21610, 6720,  10572, 5952, 6671,  \n22837, 10188, 7696,  27367, 26783, 27369,  26254, 28185, 26944,  \n21355, 13216, 11363,  20147, 15172, 2711,  24271, 19326, 16900,  \n13031, 28186, 26938,  13416, 14020, 9018,  28186, 26940, 26427,  \n27157, 12856, 23382,  5176, 5178, 9045,  19103, 17200, 1906,  \n27156, 27157, 23382,  11903, 12929, 5341,  8539, 8540, 7828,  \n14409, 9129, 9876,  23382, 12856, 23383,  12508, 2984, 16044,  \n6341, 6908, 8042,  12176, 28349, 10922,  16310, 18690, 5003,  \n16470, 8271, 378,  12552, 17858, 20525,  21072, 9642, 14666,  \n14800, 8043, 8042,  1302, 361, 1303,  5256, 7336, 8477,  \n25113, 28205, 28772,  10417, 16112, 25584,  6861, 6860, 7148,  \n12896, 16383, 6944,  25565, 28610, 20486,  26309, 24439, 28636,  \n13233, 18059, 19870,  28547, 28546, 28968,  18344, 10225, 12896,  \n6302, 4234, 18150,  3622, 7101, 14483,  29346, 28543, 29347,  \n29346, 28358, 28543,  17263, 1791, 10708,  12527, 14995, 16540,  \n15022, 19833, 12598,  13225, 22296, 11879,  2673, 21159, 13829,  \n15448, 8824, 7786,  1311, 14186, 7979,  7926, 9615, 7927,  \n18106, 16523, 9752,  10594, 22109, 21457,  29616, 28969, 28549,  \n28551, 29616, 28549,  5015, 4762, 5895,  13009, 8764, 7624,  \n5092, 7349, 5093,  8761, 6811, 8762,  10471, 869, 10661,  \n28545, 28147, 28548,  21652, 3525, 19787,  16416, 7263, 12120,  \n29156, 28148, 28970,  14817, 14359, 9206,  28774, 27571, 29153,  \n29156, 28150, 28148,  8781, 8780, 8398,  6013, 4238, 9419,  \n12608, 13540, 818,  12733, 14873, 12734,  19718, 14824, 20176,  \n17737, 10245, 3362,  7056, 7055, 20673,  324, 325, 21992,  \n13924, 21250, 6186,  15025, 14958, 15636,  27952, 26955, 28554,  \n11264, 8279, 27421,  29348, 28975, 28972,  29348, 28972, 29349,  \n13722, 13647, 5271,  11093, 1819, 1820,  7937, 15035, 4915,  \n29350, 28973, 28556,  6284, 6851, 5115,  1132, 12381, 18455,  \n28778, 28777, 28975,  4503, 1174, 1173,  831, 9715, 830,  \n13171, 14848, 16463,  5235, 5236, 3349,  29350, 28556, 28976,  \n17815, 19268, 16374,  28558, 29351, 28976,  4426, 22011, 1415,  \n4714, 17254, 6696,  29351, 28558, 28345,  6318, 14696, 19477,  \n20955, 25091, 13251,  701, 12304, 1976,  8068, 20727, 8067,  \n11687, 14097, 19839,  27755, 28564, 25153,  29158, 28982, 28981,  \n29158, 28778, 29353,  12859, 9414, 14579,  20410, 3498, 6631,  \n28985, 28984, 29160,  4305, 19092, 15083,  6221, 10224, 20108,  \n18609, 3958, 13751,  11027, 11165, 1485,  9464, 15396, 20014,  \n14697, 9932, 1795,  9844, 15377, 9845,  5179, 6721, 19956,  \n29160, 28568, 28985,  5911, 386, 19195,  29161, 28784, 29166,  \n16941, 5033, 9722,  21546, 7813, 6749,  12832, 12831, 949,  \n28568, 29160, 29162,  1669, 16091, 6455,  6569, 5519, 9846,  \n607, 1782, 7591,  4573, 3804, 6045,  28145, 28770, 28635,  \n29163, 29355, 28987,  18498, 21099, 23118,  29164, 28987, 29355,  \n3654, 12526, 21107,  9369, 28335, 29086,  28784, 28351, 29166,  \n8209, 1409, 15729,  12971, 7970, 2088,  28786, 29164, 29356,  \n20034, 23296, 10747,  28786, 29356, 29165,  5169, 5168, 21044,  \n29167, 28988, 29165,  19646, 5999, 11149,  29166, 28163, 28787,  \n13638, 13272, 18108,  27762, 29167, 28788,  12728, 8001, 5074,  \n14111, 7455, 9573,  28570, 29169, 28787,  8961, 7368, 6515,  \n28788, 29357, 28789,  28571, 28355, 28989,  8316, 644, 7612,  \n28570, 28356, 19540,  13098, 2471, 9424,  9530, 4199, 20933,  \n16074, 17638, 8295,  7442, 28167, 27585,  28357, 27767, 28353,  \n27969, 29358, 28790,  27969, 28571, 29358,  23728, 24917, 6710,  \n4104, 1577, 10139,  29302, 11034, 5898,  2270, 10632, 19979,  \n16000, 14636, 4995,  6553, 28573, 28359,  738, 10628, 4329,  \n18117, 27585, 28169,  2639, 2999, 2640,  15155, 19180, 15156,  \n22663, 10130, 21395,  19648, 19649, 17972,  12145, 14466, 18730,  \n23748, 23836, 22713,  28792, 28357, 22025,  28791, 19255, 28359,  \n17959, 17958, 22874,  28168, 29170, 10064,  14428, 14672, 18667,  \n8517, 16873, 22187,  4051, 12425, 14836,  9176, 3071, 11950,  \n16154, 12067, 13697,  27771, 29170, 28168,  28793, 29170, 27771,  \n7024, 11136, 7272,  11602, 9102, 7561,  8526, 20389, 21233,  \n4273, 4272, 20931,  11309, 5192, 10466,  14841, 9643, 21088,  \n5319, 1066, 3038,  17633, 5065, 9797,  14009, 10968, 16190,  \n11089, 13643, 11848,  28793, 27399, 27400,  28793, 27400, 17255,  \n16703, 12538, 15756,  28994, 28991, 29173,  6545, 13935, 1372,  \n28574, 27971, 29360,  6587, 490, 17410,  28577, 29360, 27971,  \n14239, 10458, 7560,  28995, 28992, 28172,  14119, 6743, 16538,  \n15242, 13154, 1178,  22164, 27198, 12273,  22164, 27774, 27198,  \n12274, 12273, 27198,  28996, 28578, 28794,  19426, 3204, 9888,  \n25227, 26423, 26812,  2556, 8609, 17926,  26638, 27779, 12274,  \n28997, 27202, 24272,  11168, 4651, 1591,  2268, 12300, 12301,  \n17444, 27776, 27974,  14586, 1150, 10752,  28174, 27777, 29174,  \n28365, 28175, 29503,  18631, 11681, 16684,  376, 7892, 377,  \n28796, 28174, 27160,  2799, 16631, 5150,  18418, 2061, 13615,  \n28364, 28183, 28798,  643, 642, 24396,  2231, 2097, 4513,  \n5469, 10285, 2880,  16237, 21494, 15237,  27976, 28998, 29361,  \n28797, 27976, 29361,  27978, 27977, 29362,  20256, 9858, 16901,  \n28802, 29177, 28800,  16934, 3404, 21916,  14872, 518, 15305,  \n28805, 29177, 28802,  9361, 11788, 10421,  14458, 22548, 1990,  \n9202, 9753, 9203,  29178, 26996, 28184,  1072, 21331, 12002,  \n16063, 493, 11265,  18469, 4731, 16781,  9782, 17438, 7813,  \n10607, 12179, 20467,  27980, 25653, 28582,  22908, 13399, 7551,  \n12725, 28804, 27787,  28370, 29001, 29000,  10677, 9121, 16191,  \n28805, 27599, 28583,  28370, 28371, 29001,  7520, 7519, 16078,  \n12015, 12016, 6780,  9302, 12494, 1305,  15091, 3712, 2740,  \n7967, 16722, 9112,  5046, 5045, 7601,  3564, 16115, 14934,  \n14817, 9206, 12454,  17146, 12224, 16309,  15945, 16047, 16048,  \n13787, 20015, 17187,  21766, 8545, 23235,  5848, 14512, 285,  \n22084, 16651, 22083,  1444, 24306, 11310,  11806, 3944, 12489,  \n28190, 28585, 29180,  17101, 29365, 28583,  570, 10434, 23036,  \n521, 22022, 17857,  21753, 18045, 10177,  4412, 14862, 950,  \n13944, 6392, 4868,  19005, 2337, 7497,  29003, 27601, 29182,  \n17161, 23051, 12302,  28810, 29181, 28806,  6327, 9386, 1078,  \n21177, 20895, 4932,  6274, 11592, 11591,  9559, 20767, 20474,  \n5164, 17951, 13037,  15794, 21815, 19126,  4726, 4725, 2250,  \n6574, 7774, 6572,  4055, 9473, 8914,  3972, 22879, 4744,  \n15605, 10520, 16128,  29183, 28586, 29179,  28814, 28809, 28373,  \n20193, 18650, 18667,  12317, 16914, 3782,  28195, 28808, 29366,  \n28807, 27416, 27799,  19298, 20634, 3326,  28590, 28195, 29366,  \n28768, 21785, 27385,  22682, 11839, 683,  15085, 1538, 15557,  \n13013, 4239, 8731,  3713, 11736, 20389,  4653, 10342, 19157,  \n7193, 17138, 6525,  5518, 1106, 1105,  2022, 20016, 4709,  \n11955, 19129, 8679,  28653, 17311, 28011,  29185, 29367, 27989,  \n26142, 28195, 28590,  22653, 2455, 14366,  23172, 20867, 20372,  \n14182, 1350, 2307,  27803, 26293, 28590,  20190, 5922, 13839,  \n13938, 12252, 16188,  2752, 2751, 19912,  9621, 15023, 16610,  \n8132, 18617, 5842,  8681, 16623, 8682,  15874, 692, 6127,  \n7670, 7009, 13923,  28815, 28816, 29188,  6655, 601, 600,  \n15635, 3249, 3248,  10810, 3845, 13747,  10129, 17986, 6355,  \n10518, 3227, 16484,  9085, 9084, 7493,  22958, 17021, 13854,  \n17951, 14897, 3473,  13763, 1822, 1956,  6125, 15430, 16414,  \n5194, 6433, 6434,  29005, 29004, 28819,  28376, 28196, 29188,  \n29190, 29187, 28377,  13072, 18182, 16642,  15324, 15805, 1928,  \n10593, 7656, 20022,  9465, 7930, 11791,  2130, 2129, 11203,  \n28595, 29188, 29369,  26118, 11264, 24980,  1297, 3378, 1437,  \n9967, 12021, 10393,  19923, 19897, 14456,  12767, 14566, 871,  \n8564, 14877, 5792,  6416, 7807, 18846,  28820, 27431, 29008,  \n18038, 16639, 22544,  29007, 29370, 29006,  29005, 27806, 28380,  \n29370, 29007, 29010,  29008, 24898, 28820,  13332, 19413, 1526,  \n5292, 6706, 5893,  16513, 20601, 17741,  6482, 6483, 3002,  \n29371, 28597, 29009,  13144, 18846, 26657,  21048, 7280, 21503,  \n29195, 29011, 29372,  23480, 15848, 5283,  16554, 4592, 20424,  \n28598, 29193, 29012,  7878, 12954, 340,  29015, 28199, 28597,  \n29372, 29373, 29195,  6991, 17191, 10160,  5661, 8408, 8407,  \n6439, 751, 322,  7373, 8242, 2562,  3929, 15083, 19092,  \n20929, 21832, 9841,  395, 742, 396,  15057, 23157, 8312,  \n29013, 29374, 29192,  6374, 5939, 5938,  9739, 2749, 2748,  \n18502, 4610, 16593,  956, 10419, 2172,  9382, 9820, 15284,  \n11539, 11257, 11256,  29013, 28605, 29376,  15603, 21892, 1444,  \n12532, 16866, 23115,  11438, 7176, 11793,  17052, 16304, 11205,  \n1023, 963, 964,  11503, 14345, 21601,  29198, 27998, 28821,  \n8471, 2019, 19404,  1676, 7140, 1675,  19635, 6350, 7062,  \n17977, 645, 14703,  21007, 16162, 16379,  6176, 11764, 18516,  \n7923, 15801, 7924,  15844, 11895, 20445,  22938, 22144, 21385,  \n16103, 13241, 13240,  3702, 21709, 20830,  29380, 29196, 29017,  \n18736, 16066, 1326,  8951, 9519, 14085,  15988, 21254, 19931,  \n29202, 28837, 29201,  28826, 1844, 28211,  11091, 19343, 10889,  \n3630, 20705, 6934,  29524, 28838, 29383,  20784, 13081, 12656,  \n4815, 3444, 779,  28604, 16251, 28609,  3867, 7726, 15431,  \n17328, 1134, 9191,  29203, 29201, 28836,  4593, 387, 386,  \n6312, 17561, 1196,  17650, 23284, 24724,  29017, 28829, 29381,  \n20386, 9738, 14891,  1147, 1146, 5892,  8145, 1738, 10539,  \n375, 14793, 7893,  29020, 29199, 29384,  29521, 29022, 28828,  \n9354, 10824, 12188,  7865, 7864, 12053,  29020, 29386, 28829,  \n12777, 11751, 12778,  1908, 3233, 5252,  28838, 29027, 29383,  \n22565, 29022, 29521,  17792, 14456, 17577,  7705, 7969, 5439,  \n21578, 17264, 21643,  12838, 15618, 12541,  13924, 6186, 22152,  \n19335, 5401, 11925,  29387, 29023, 29024,  29023, 28832, 29024,  \n19547, 28831, 29206,  18961, 18055, 3610,  1734, 2046, 18180,  \n29027, 29033, 29383,  19046, 10203, 13659,  29019, 29205, 29207,  \n28206, 28004, 29206,  16937, 15711, 2712,  16699, 4424, 868,  \n12856, 27157, 25227,  7350, 2187, 4429,  29025, 29206, 28004,  \n29388, 29210, 28398,  6609, 17354, 6610,  14712, 16187, 15418,  \n12157, 14661, 6094,  3438, 22422, 1103,  7622, 17020, 7739,  \n15366, 10824, 12767,  3318, 8485, 8242,  25227, 27157, 26423,  \n29030, 28834, 29208,  28402, 28210, 29210,  10820, 2606, 7443,  \n22355, 9502, 18717,  29022, 25372, 28612,  10297, 9415, 18447,  \n20329, 5598, 5961,  29389, 28840, 28401,  11492, 5800, 11493,  \n8929, 9543, 21619,  11689, 12246, 2220,  8242, 7373, 6373,  \n28843, 29527, 29214,  14926, 3259, 3258,  17033, 2699, 2698,  \n25652, 9494, 9612,  29211, 29029, 29390,  29211, 29390, 29387,  \n4661, 13172, 20031,  5261, 6994, 20128,  22486, 12874, 20674,  \n29213, 29217, 29219,  29213, 29219, 29031,  18028, 1480, 8287,  \n7462, 7463, 11899,  13157, 14327, 23720,  29390, 29215, 29391,  \n8100, 3491, 4718,  29215, 29390, 28615,  18551, 7310, 4684,  \n28618, 28212, 29030,  29213, 29031, 28839,  28842, 29215, 28615,  \n19667, 17724, 8100,  29220, 29033, 29032,  13087, 18973, 9272,  \n29218, 29221, 29219,  29221, 29031, 29219,  3585, 11558, 3586,  \n20145, 9141, 13344,  4886, 18170, 4887,  20145, 13344, 15191,  \n20573, 5371, 7985,  25372, 29037, 28612,  29712, 5502, 21298,  \n29215, 29393, 29392,  15254, 17959, 23207,  2072, 18483, 15630,  \n29032, 29038, 29225,  29393, 29215, 29227,  29216, 29228, 28845,  \n28845, 28618, 29216,  9203, 10533, 10532,  29221, 29223, 29226,  \n29035, 29031, 29224,  29215, 28842, 29227,  630, 14035, 2934,  \n9731, 18841, 983,  11805, 6328, 822,  18950, 13994, 8370,  \n29224, 29221, 29226,  11423, 4667, 3662,  13303, 16008, 13304,  \n25562, 19833, 2047,  848, 10309, 5656,  28846, 29035, 29224,  \n11355, 17701, 8301,  1225, 1224, 4732,  12146, 610, 9373,  \n2705, 3714, 21858,  13016, 11513, 842,  8612, 4657, 8924,  \n10568, 19605, 19604,  3787, 3789, 4616,  729, 3650, 727,  \n28846, 29224, 29394,  15022, 12598, 22785,  29044, 29228, 29045,  \n3771, 849, 1321,  9001, 28557, 22801,  4137, 12662, 4736,  \n12525, 10680, 19609,  10729, 5536, 8737,  10465, 6183, 17189,  \n29042, 25519, 29046,  12997, 12403, 2272,  2041, 19374, 12989,  \n6832, 11144, 21775,  3153, 494, 16063,  23046, 14840, 12054,  \n4177, 946, 1356,  3280, 874, 13504,  29398, 28848, 28629,  \n9072, 8767, 8766,  28626, 28846, 29234,  9519, 20575, 14085,  \n28637, 28626, 29234,  28847, 28851, 29229,  2634, 2269, 4225,  \n29048, 29230, 29400,  17762, 12887, 16794,  13622, 11246, 17274,  \n29401, 28629, 29051,  28629, 29401, 29398,  16572, 17986, 17987,  \n13971, 1188, 7460,  1417, 10684, 5938,  16213, 9008, 5495,  \n18566, 13947, 13345,  1307, 12695, 10720,  29402, 29403, 29232,  \n29402, 29232, 29048,  29229, 28851, 29231,  22789, 11934, 22455,  \n2205, 8597, 2206,  15398, 15397, 12181,  14157, 10506, 16036,  \n23035, 13813, 13699,  5293, 16528, 22255,  29235, 29053, 29232,  \n14163, 8486, 14162,  8729, 15422, 8730,  757, 907, 758,  \n15845, 15846, 1047,  22277, 17915, 14760,  28822, 17006, 25138,  \n29233, 29404, 29231,  28427, 40, 28424,  14691, 12422, 1574,  \n15858, 10564, 17669,  29404, 29233, 29054,  15577, 4811, 5971,  \n28642, 29055, 103,  22220, 4827, 1755,  29051, 28644, 29406,  \n17661, 10257, 19573,  29055, 29405, 103,  28638, 29052, 29239,  \n15343, 12897, 5072,  28822, 28929, 17006,  17060, 19214, 16833,  \n5395, 4300, 303,  29407, 29239, 29052,  15790, 20334, 3203,  \n13615, 13379, 18418,  8159, 10578, 21062,  8879, 4561, 9225,  \n10765, 17974, 10766,  11352, 4764, 6175,  14643, 14642, 12190,  \n9165, 16915, 16914,  10803, 8451, 11728,  4152, 3413, 14271,  \n21208, 22346, 21741,  20237, 5902, 20238,  7179, 12491, 9398,  \n28856, 29245, 29054,  28024, 29238, 28650,  24360, 7671, 7673,  \n5564, 13532, 19916,  11277, 11976, 8371,  19810, 821, 1253,  \n17899, 7405, 7404,  29243, 28859, 29247,  22101, 23720, 14327,  \n4537, 4536, 4948,  12143, 10965, 11296,  19559, 20336, 6889,  \n29410, 29241, 29244,  10164, 8889, 8888,  9370, 9369, 29086,  \n29251, 29248, 29408,  964, 18915, 14695,  29408, 29252, 29251,  \n2604, 4118, 11381,  29253, 29252, 29409,  4473, 17686, 17685,  \n9092, 18794, 3448,  11153, 12592, 8573,  29065, 29253, 29675,  \n28872, 29253, 29065,  15415, 8992, 20675,  28870, 29411, 28869,  \n28870, 29412, 29411,  29412, 28870, 29062,  29412, 29062, 29413,  \n13378, 9201, 8607,  15896, 19565, 17926,  7552, 3624, 15784,  \n22966, 14969, 6341,  21055, 4931, 20895,  29413, 29062, 29063,  \n29064, 29413, 29063,  11131, 5832, 22184,  29246, 29059, 29414,  \n15201, 12991, 7420,  23272, 13347, 10939,  16120, 6580, 6089,  \n11132, 5832, 11131,  23136, 29414, 24320,  28654, 28869, 29415,  \n6080, 17792, 17577,  28871, 29416, 29064,  21319, 20799, 12643,  \n15693, 9532, 12833,  29255, 28432, 29254,  20441, 22688, 3921,  \n2904, 15274, 10871,  4024, 4025, 5098,  14462, 14463, 2813,  \n7903, 7902, 6030,  26424, 13865, 28680,  17565, 14317, 19340,  \n13342, 13341, 11592,  5953, 4433, 4434,  28432, 19053, 28237,  \n14953, 16829, 2960,  7321, 2357, 12853,  28434, 29069, 29257,  \n1055, 23705, 19664,  24039, 9204, 6425,  12191, 17314, 9803,  \n14573, 14574, 1954,  3091, 2357, 7321,  24877, 10854, 14014,  \n13629, 4449, 2341,  28658, 29070, 21817,  10956, 18251, 13986,  \n19003, 21930, 15724,  29258, 29256, 28662,  11788, 17850, 11787,  \n1617, 16989, 7278,  22111, 23696, 18005,  18611, 12378, 9912,  \n21817, 25376, 28036,  14283, 18268, 18503,  9357, 18841, 4232,  \n17749, 14091, 12231,  10683, 4583, 13852,  29071, 29258, 28663,  \n9635, 3374, 704,  9561, 8776, 19703,  26494, 28881, 28245,  \n1684, 10411, 15072,  15163, 9199, 1064,  29072, 29418, 29262,  \n29759, 29264, 29418,  29264, 29262, 29418,  29759, 29420, 29264,  \n7121, 17436, 7122,  29074, 29264, 29420,  29074, 29420, 29419,  \n29074, 29419, 29263,  16332, 13339, 15643,  18088, 8513, 10150,  \n29422, 29071, 29260,  6169, 21133, 6553,  29075, 28659, 29259,  \n21739, 11490, 6353,  17898, 18864, 13945,  22780, 11661, 7103,  \n29263, 28880, 28879,  8332, 17204, 3568,  28880, 29263, 29421,  \n16895, 1633, 10642,  29265, 29261, 28664,  9494, 19951, 11610,  \n19686, 17377, 10340,  29265, 28664, 28876,  22627, 28034, 28878,  \n21935, 7396, 12861,  15279, 6150, 15278,  5963, 6943, 12938,  \n29266, 28436, 28877,  8973, 19518, 10155,  619, 19952, 9229,  \n22865, 9510, 2354,  28665, 29423, 29260,  29423, 29424, 29260,  \n26087, 28667, 29075,  2482, 5758, 10994,  5424, 3204, 15759,  \n28877, 28435, 27851,  9542, 19625, 9068,  28665, 29267, 29423,  \n6684, 6683, 17471,  28876, 29077, 29265,  3323, 3588, 19847,  \n9168, 14433, 16935,  18797, 395, 1575,  25680, 26845, 4157,  \n29425, 28673, 28881,  16622, 26087, 29075,  29265, 29077, 29426,  \n6709, 17711, 21637,  26488, 28042, 28670,  20510, 11118, 8912,  \n28670, 28673, 29425,  1822, 14827, 1956,  9853, 1045, 616,  \n28883, 29078, 29267,  20760, 6094, 24915,  1346, 13160, 16278,  \n28674, 29079, 29082,  28886, 28440, 26087,  20583, 19091, 5018,  \n9064, 9065, 19698,  28885, 29427, 29268,  9090, 6719, 13863,  \n29427, 28885, 29080,  1798, 353, 355,  19439, 13935, 3405,  \n11820, 13647, 15392,  28891, 28890, 29428,  5302, 18782, 18475,  \n28890, 29275, 29429,  16980, 3433, 14352,  5407, 14688, 6513,  \n29430, 28891, 29428,  6965, 6966, 17930,  28679, 29269, 29275,  \n6965, 17930, 9761,  29432, 29431, 29273,  29273, 29431, 29081,  \n14510, 5369, 5370,  29278, 28891, 29430,  29433, 29432, 29273,  \n5455, 10507, 10506,  28681, 28050, 28888,  11562, 9723, 12098,  \n29276, 29433, 29273,  16230, 7518, 18009,  29435, 29433, 29276,  \n11427, 1158, 5930,  28683, 29085, 29274,  7189, 11858, 13406,  \n29435, 29276, 28687,  3700, 11768, 11769,  29277, 29435, 28687,  \n5268, 1024, 1023,  29278, 28893, 28686,  29087, 28895, 29438,  \n29436, 29277, 28892,  18849, 22318, 20398,  5406, 921, 6845,  \n29279, 29436, 28892,  8607, 8608, 13541,  27869, 28689, 28456,  \n3412, 3413, 4152,  19850, 28952, 24438,  2966, 21175, 15167,  \n29281, 29437, 29089,  16488, 1416, 6181,  28699, 29095, 29438,  \n28698, 29439, 29440,  14692, 12402, 14691,  8994, 16924, 20008,  \n28698, 28693, 29439,  1094, 17948, 4699,  29283, 29441, 29281,  \n10540, 663, 15950,  28897, 22597, 28691,  17523, 19282, 17524,  \n29094, 29091, 28696,  29442, 29696, 29283,  28691, 22597, 28695,  \n13036, 417, 13464,  29445, 29097, 29096,  3622, 14483, 16976,  \n29283, 29285, 29442,  9678, 8881, 2426,  29098, 29443, 29096,  \n29445, 29446, 29097,  28698, 29440, 29103,  18833, 16023, 18224,  \n11450, 18421, 20095,  29446, 28908, 29097,  9800, 9799, 20748,  \n29101, 28703, 28701,  12685, 10114, 21709,  29101, 28701, 29286,  \n5331, 20573, 2323,  14583, 21498, 13343,  3858, 3857, 5205,  \n28268, 19133, 28463,  10995, 9459, 13413,  7771, 7770, 2543,  \n29098, 29288, 29443,  6620, 9898, 19029,  29285, 29290, 29442,  \n11733, 9585, 9587,  28705, 29291, 29447,  3273, 17842, 23300,  \n20456, 2767, 18825,  5375, 4148, 7467,  29286, 29448, 29101,  \n28909, 29287, 28465,  29449, 28270, 28463,  3618, 3619, 11046,  \n29288, 29106, 29450,  16465, 17162, 18630,  1062, 9151, 13437,  \n21216, 2794, 21830,  3957, 11798, 21982,  6524, 24060, 7852,  \n29447, 29584, 28705,  28904, 28705, 29584,  29102, 28270, 29449,  \n1318, 14725, 14620,  29106, 29288, 29108,  6229, 11228, 14189,  \n29293, 28707, 29451,  28906, 29293, 29292,  13653, 23730, 13654,  \n20438, 17537, 17536,  29584, 29454, 28904,  3046, 8725, 11963,  \n773, 15074, 3470,  23507, 4766, 9514,  16609, 28102, 28929,  \n4277, 4276, 9154,  16808, 9628, 11353,  29104, 29297, 29294,  \n4417, 19778, 12678,  29451, 28905, 29294,  28707, 29293, 28906,  \n29102, 29453, 28907,  18348, 9258, 7727,  29109, 29113, 29299,  \n28718, 29109, 29452,  28718, 29452, 29107,  831, 1233, 6635,  \n28914, 28904, 29454,  17618, 16209, 14364,  12066, 15367, 21084,  \n1304, 23522, 15030,  20800, 4626, 7150,  4814, 4813, 11476,  \n9692, 14693, 19889,  16470, 17731, 6458,  10036, 8919, 15425,  \n15003, 17713, 15817,  29456, 28919, 29300,  29456, 28924, 28919,  \n11374, 11373, 20992,  28280, 28076, 28914,  28273, 28708, 29298,  \n17899, 7404, 17900,  28726, 28952, 14835,  29303, 29455, 28918,  \n28918, 29455, 29300,  13182, 14519, 12221,  15782, 15103, 15104,  \n11727, 19069, 13074,  1718, 5751, 13441,  29459, 29458, 29304,  \n29295, 29110, 29301,  11963, 17782, 17469,  11590, 4913, 9440,  \n13244, 606, 11636,  6518, 24997, 6519,  13052, 11417, 16987,  \n29114, 29457, 29115,  29115, 29457, 29119,  4187, 11703, 11702,  \n12070, 12379, 12068,  20436, 21749, 11910,  28922, 28921, 29306,  \n4850, 4849, 3574,  12984, 14655, 22755,  28929, 28822, 21999,  \n15099, 15316, 12209,  16030, 9150, 2585,  8310, 6377, 7628,  \n14330, 10925, 10924,  1132, 19150, 1131,  15115, 9906, 2877,  \n29460, 28485, 28924,  5345, 9733, 9777,  6301, 11802, 5289,  \n29115, 29119, 28925,  5027, 12711, 12024,  4300, 6882, 4301,  \n11941, 16725, 7939,  29116, 28922, 29461,  4099, 2575, 15461,  \n21127, 18184, 15166,  8761, 5086, 20908,  4106, 5030, 13144,  \n1491, 3290, 1492,  2076, 24384, 2077,  29310, 28083, 28280,  \n22224, 15199, 15198,  2327, 12225, 2326,  29118, 28738, 28488,  \n12493, 22230, 12038,  29461, 29462, 29116,  29116, 29462, 29117,  \n29462, 29110, 28916,  22219, 23847, 6422,  8279, 11264, 1843,  \n28730, 28928, 29311,  20398, 5825, 3182,  19891, 1317, 18467,  \n433, 20482, 12345,  14958, 15917, 13401,  29316, 28287, 29463,  \n29313, 29311, 29314,  28928, 29314, 29311,  17948, 25627, 28769,  \n29307, 28920, 29312,  6188, 13436, 10546,  28926, 29120, 29123,  \n21398, 6286, 7996,  9610, 17266, 8792,  29464, 29123, 29596,  \n29121, 29316, 29465,  9958, 10376, 10375,  4127, 3096, 12760,  \n20933, 7504, 10791,  29123, 29464, 29317,  29464, 29312, 29317,  \n3288, 16974, 20496,  15918, 16074, 8295,  21598, 19965, 20199,  \n29122, 28936, 28935,  14081, 21151, 17004,  29122, 28935, 29322,  \n29319, 28291, 29124,  28937, 29319, 29321,  28736, 28937, 29321,  \n14272, 4274, 7896,  2729, 21207, 13650,  28737, 29320, 28739,  \n29320, 28737, 28736,  17709, 12486, 9288,  29322, 29126, 29127,  \n3100, 3101, 12660,  10896, 10895, 10305,  28504, 28503, 29466,  \n28505, 28504, 29467,  11535, 11534, 1130,  21794, 5779, 5778,  \n5972, 19346, 5973,  8110, 12313, 8109,  28505, 29467, 29323,  \n7253, 16882, 7254,  5268, 18027, 2311,  29468, 28743, 29323,  \n29324, 28507, 29468,  17659, 8154, 8153,  29324, 29468, 29470,  \n28507, 28743, 29468,  4340, 20775, 9495,  17345, 5782, 8682,  \n20979, 21522, 20937,  29129, 29469, 28940,  4856, 16057, 9701,  \n29324, 29471, 28304,  1552, 14402, 8321,  29472, 28747, 29471,  \n14553, 556, 555,  28747, 28304, 29471,  14377, 17545, 18420,  \n29472, 28748, 28747,  5438, 5739, 11069,  28748, 29473, 28941,  \n29326, 29130, 28509,  21271, 9400, 18338,  29148, 6720, 17937,  \n28941, 21463, 29131,  14278, 18586, 18580,  10608, 10607, 13786,  \n29328, 28512, 28944,  16527, 17470, 6219,  19805, 11743, 12244,  \n22013, 14417, 13482,  18278, 10933, 10934,  6328, 11805, 3773,  \n4537, 10320, 6678,  29330, 29132, 28946,  29132, 28517, 28946,  \n5710, 17192, 4096,  28947, 28950, 29329,  22054, 22053, 19250,  \n28519, 28518, 29133,  7431, 5984, 20693,  28949, 29332, 28520,  \n9040, 5700, 24271,  15039, 1878, 12394,  9401, 9400, 21271,  \n14718, 7028, 5710,  29474, 29607, 27717,  28951, 28521, 26541,  \n14795, 1262, 11565,  28522, 28951, 29333,  29474, 29134, 29475,  \n29474, 27717, 29134,  21803, 9246, 14453,  6556, 6555, 7534,  \n614, 10459, 3400,  18001, 8499, 7162,  21047, 3728, 3435,  \n16955, 16162, 19650,  29134, 28755, 29475,  16276, 5108, 8652,  \n12836, 3807, 360,  28754, 26074, 29136,  19679, 11502, 3756,  \n24548, 29137, 28953,  24548, 28953, 29136,  3977, 8570, 1992,  \n3520, 16758, 8945,  20439, 10939, 24013,  28954, 29334, 28955,  \n13138, 18731, 18730,  27623, 28956, 28526,  2806, 19390, 7169,  \n3273, 17292, 17842,  27623, 29335, 28956,  14822, 14957, 17637,  \n20168, 10139, 21230,  10117, 16457, 10116,  768, 9802, 769,  \n27623, 28526, 29337,  29337, 28526, 28757,  14422, 24384, 24760,  \n6637, 13025, 6636,  20712, 15582, 21158,  29139, 28758, 29476,  \n28758, 29140, 29476,  9885, 3370, 10623,  23536, 12215, 12609,  \n5387, 5386, 13922,  13390, 15169, 13389,  6976, 15965, 6977,  \n9814, 3382, 14600,  28759, 28957, 29140,  8807, 11899, 17602,  \n28958, 29477, 29141,  29142, 29141, 29477,  28760, 29138, 29143,  \n6369, 6370, 18025,  29477, 28958, 28959,  29338, 29477, 28959,  \n29338, 28959, 28960,  29340, 29339, 28761,  25658, 14635, 12176,  \n28961, 28760, 29143,  2353, 19716, 4632,  7510, 5665, 1274,  \n28762, 29341, 29340,  9039, 9038, 13512,  7126, 15977, 15782,  \n29479, 28963, 28961,  13488, 18329, 7063,  4810, 18751, 11835,  \n16915, 4302, 16914,  19993, 18894, 2811,  11017, 9745, 543,  \n28963, 29480, 28964,  9428, 1143, 9429,  29481, 28964, 29480,  \n29147, 28964, 29481,  2760, 17838, 2108,  29481, 29343, 29147,  \n781, 412, 5294,  19680, 3277, 13859,  13687, 13386, 18971,  \n10885, 9512, 4354,  28745, 18977, 7464,  14087, 16977, 13389,  \n17331, 909, 18556,  7990, 16164, 3901,  4888, 25522, 4886,  \n14000, 8108, 14708,  11261, 1434, 20686,  25658, 12176, 10922,  \n20144, 23734, 18451,  7433, 15319, 9818,  12634, 9058, 8745,  \n28726, 24439, 24438,  20016, 2022, 2021,  8507, 6622, 21944,  \n24786, 1888, 2400,  24786, 25437, 1888,  22471, 22525, 22509,  \n28613, 28144, 28540,  15338, 9003, 10932,  13762, 18708, 13094,  \n4536, 3197, 4949,  2576, 9123, 9703,  2093, 7930, 2094,  \n12231, 14091, 15783,  19833, 25562, 21114,  2818, 20991, 2819,  \n28542, 25434, 20202,  28544, 29482, 29345,  28611, 28541, 29152,  \n28541, 27949, 29152,  28205, 28146, 28772,  7644, 2258, 11346,  \n5278, 18345, 17088,  22098, 10397, 13325,  20065, 17989, 19767,  \n28547, 28968, 29483,  16955, 20326, 16160,  10783, 408, 484,  \n9211, 13929, 5061,  17825, 15647, 20971,  28358, 29346, 26310,  \n21251, 21042, 22479,  13893, 5591, 17272,  15009, 4363, 6127,  \n4860, 22548, 6436,  715, 11636, 1248,  8530, 17330, 8531,  \n4537, 6677, 10320,  665, 22302, 7051,  2317, 8018, 6006,  \n13766, 3347, 1969,  12191, 16912, 5500,  19404, 11671, 8471,  \n17319, 23235, 22874,  6833, 3479, 11232,  7845, 860, 14487,  \n29484, 28551, 29486,  28551, 27958, 29486,  8289, 9759, 15737,  \n4600, 4599, 13687,  29485, 28337, 28333,  15456, 8282, 8283,  \n833, 14728, 19029,  17378, 14571, 4459,  29486, 27958, 29154,  \n3130, 3129, 10274,  14873, 14874, 12734,  8628, 6119, 17857,  \n11699, 11700, 1326,  10427, 20651, 16815,  17900, 3889, 3077,  \n29352, 27753, 28980,  5063, 24191, 3230,  10187, 21594, 20025,  \n11901, 2055, 20426,  2268, 21519, 12300,  20759, 21844, 2301,  \n18618, 2218, 14224,  23952, 29352, 28980,  7670, 20338, 20677,  \n29621, 28975, 29348,  10058, 3349, 5236,  29349, 29487, 29490,  \n29487, 29349, 28973,  29487, 28973, 29350,  813, 6128, 3136,  \n28976, 29351, 29350,  4088, 2861, 22162,  14902, 3480, 8227,  \n28561, 29488, 29351,  5450, 5923, 5922,  28561, 28563, 29488,  \n29489, 28563, 29352,  18783, 9772, 23390,  25153, 27752, 27755,  \n20074, 554, 22525,  15571, 17548, 10560,  29490, 29491, 29349,  \n10007, 9072, 8766,  29351, 28345, 28561,  2955, 20123, 5440,  \n6600, 378, 8271,  9571, 11470, 13303,  18618, 11806, 2218,  \n29353, 28778, 28975,  22722, 7258, 16275,  16417, 12465, 11632,  \n29158, 29353, 28982,  22147, 28559, 29157,  8625, 1054, 8624,  \n28983, 28982, 29354,  27577, 22147, 29492,  20399, 17179, 5825,  \n28983, 29354, 29493,  27577, 29492, 28783,  14784, 28160, 28350,  \n3946, 23807, 24116,  28640, 28811, 1500,  15058, 16808, 4804,  \n13440, 5083, 15499,  20008, 21485, 8009,  8170, 384, 11049,  \n29494, 29162, 29160,  29163, 29162, 29494,  10025, 2870, 11966,  \n29494, 29355, 29163,  5271, 2848, 735,  29495, 29355, 29494,  \n29355, 29496, 29164,  29496, 29356, 29164,  18066, 5333, 7762,  \n5106, 17174, 8495,  22127, 13309, 10300,  4352, 13455, 19586,  \n12581, 17643, 4996,  16222, 3781, 6675,  29167, 29165, 29497,  \n29167, 29497, 29498,  921, 7468, 17128,  2571, 2563, 17498,  \n15317, 15878, 1343,  5575, 5574, 7681,  29167, 29498, 28788,  \n29498, 29357, 28788,  3989, 10424, 13338,  19864, 20495, 7151,  \n1359, 1768, 18070,  8119, 2475, 8009,  8445, 10560, 8446,  \n28989, 29358, 28571,  14987, 19858, 10119,  5106, 5107, 25443,  \n27966, 28167, 7442,  10742, 2567, 7779,  15805, 3285, 15456,  \n8774, 2411, 14194,  1224, 18072, 4732,  12798, 6781, 9017,  \n18217, 1972, 18216,  28990, 28357, 28353,  15612, 5908, 15613,  \n19992, 28357, 28990,  1269, 18253, 12590,  6667, 10216, 9209,  \n29358, 28945, 28790,  4436, 14735, 21171,  4737, 4738, 2565,  \n13770, 6520, 17543,  9091, 3003, 16303,  14734, 4418, 6112,  \n6307, 14267, 22595,  19180, 15155, 13966,  8246, 22357, 12310,  \n22025, 28357, 19992,  2920, 14886, 2919,  28791, 28168, 10064,  \n12289, 6442, 3252,  29499, 29500, 24297,  18281, 1359, 11025,  \n20069, 6685, 11955,  11193, 2942, 654,  8863, 14622, 15987,  \n15504, 13389, 15169,  13602, 21545, 1918,  9944, 9943, 15679,  \n12417, 18278, 10934,  28992, 29172, 28170,  739, 10346, 4258,  \n20562, 4243, 4244,  28634, 5524, 4989,  17830, 8847, 8846,  \n4846, 22737, 14939,  7823, 13380, 18861,  19853, 19852, 29501,  \n9369, 8824, 28335,  11595, 11596, 12839,  12514, 20980, 23583,  \n24055, 29360, 28577,  17479, 5084, 13539,  22164, 24055, 28577,  \n7052, 17143, 12836,  28995, 28363, 9219,  9148, 7641, 6167,  \n24272, 26983, 28576,  10846, 3853, 6569,  19686, 1504, 20825,  \n28794, 25205, 28996,  21681, 28363, 28364,  22980, 22274, 16576,  \n28795, 28996, 25205,  11525, 17350, 18609,  16506, 27974, 28365,  \n13070, 18001, 1979,  25594, 21176, 21175,  2625, 18576, 17863,  \n16515, 7840, 21552,  13241, 7620, 13240,  29502, 28579, 28795,  \n29502, 4092, 28579,  29503, 28175, 28176,  2284, 10960, 10291,  \n21054, 19660, 5827,  2972, 16582, 17821,  29175, 28579, 4092,  \n4757, 4758, 4476,  2368, 20735, 16529,  9476, 1835, 19587,  \n9476, 19587, 9477,  18324, 13581, 16211,  14112, 28179, 28580,  \n16532, 24997, 6518,  3521, 3522, 9279,  28800, 29177, 28798,  \n1282, 13673, 708,  15148, 21675, 26502,  27782, 27785, 29176,  \n8855, 19186, 15544,  28801, 27978, 29362,  20215, 12094, 8784,  \n29178, 28184, 29504,  29176, 27785, 28804,  27981, 28801, 29364,  \n7161, 6409, 6410,  25653, 27980, 28581,  22408, 21280, 5122,  \n6026, 8660, 6025,  719, 22304, 17282,  12858, 952, 951,  \n13602, 21906, 3049,  15746, 16398, 5183,  915, 14348, 14517,  \n29001, 29002, 29506,  18535, 5029, 22663,  15911, 14918, 2514,  \n10125, 13131, 3661,  12725, 27788, 29507,  14623, 14624, 21299,  \n29506, 29002, 29509,  10642, 21677, 20941,  17101, 28583, 28584,  \n15171, 15841, 11622,  729, 7196, 19511,  8460, 16769, 16325,  \n7023, 25698, 6059,  13670, 18889, 1401,  9464, 13904, 20516,  \n5307, 5306, 8830,  15886, 15237, 4347,  6448, 11516, 13211,  \n29511, 29002, 28809,  2630, 5835, 1150,  1918, 16224, 9492,  \n4149, 18815, 15009,  27603, 28807, 29510,  29629, 28190, 29180,  \n16081, 351, 12875,  16037, 20221, 5791,  13053, 15578, 11951,  \n17487, 7339, 15666,  29184, 28810, 28589,  11062, 7558, 7560,  \n20445, 11895, 7773,  25634, 22782, 18256,  27420, 28372, 26284,  \n2334, 16856, 14919,  21462, 4500, 18289,  29184, 27989, 29367,  \n4573, 18329, 3804,  18033, 11214, 8500,  17769, 22781, 7008,  \n22330, 6007, 11936,  20661, 3577, 7398,  7758, 1675, 6060,  \n10054, 4638, 10055,  29367, 29185, 29515,  29188, 28816, 29514,  \n29185, 29187, 29515,  19607, 11681, 18631,  4025, 18349, 6315,  \n29515, 29187, 29516,  9015, 9014, 15719,  2639, 2640, 9502,  \n9596, 8326, 4458,  17561, 15659, 1196,  2030, 15521, 14629,  \n29008, 27803, 29632,  20276, 17354, 12739,  9490, 7709, 4740,  \n13102, 5033, 16941,  16292, 6530, 8462,  4567, 19257, 15372,  \n20130, 18115, 4490,  29190, 29516, 29187,  557, 556, 9571,  \n1297, 16509, 1296,  8133, 8134, 17281,  4188, 13781, 1395,  \n4103, 9174, 502,  29516, 29190, 2680,  1233, 831, 1234,  \n9104, 15431, 7726,  21004, 21946, 7576,  803, 23190, 13125,  \n4174, 4173, 11400,  2680, 29190, 29006,  20617, 19073, 20618,  \n29006, 29370, 2680,  7896, 5117, 9513,  17970, 15743, 5525,  \n2244, 2243, 10042,  9050, 21132, 2621,  17162, 21254, 18630,  \n3450, 14538, 14537,  29191, 28380, 28599,  12644, 13184, 17362,  \n12056, 4908, 4907,  2165, 22017, 20515,  28861, 6951, 6952,  \n29517, 29373, 29372,  21089, 21088, 10041,  29015, 28597, 29371,  \n10186, 8168, 6487,  29373, 29522, 29014,  8340, 2086, 2088,  \n1948, 10617, 7710,  17015, 14825, 8233,  4837, 2058, 16860,  \n29375, 29374, 29013,  2310, 12408, 20635,  1507, 17065, 14570,  \n4336, 13207, 20164,  21513, 9723, 11501,  29375, 29013, 29376,  \n28305, 19468, 12163,  29193, 28823, 29518,  5624, 1441, 7300,  \n28605, 29196, 29376,  16851, 16852, 2198,  28744, 4009, 26202,  \n14979, 14251, 8860,  4562, 316, 10776,  1733, 3639, 1732,  \n29380, 29520, 29196,  29518, 28823, 29197,  8698, 18482, 3419,  \n18691, 9114, 14654,  29014, 29522, 29016,  833, 15208, 3195,  \n18610, 4287, 5693,  29380, 29017, 29381,  1064, 5299, 15163,  \n29197, 3314, 29378,  29198, 16251, 28604,  2830, 15829, 18663,  \n13065, 21365, 6824,  10501, 4664, 10493,  29524, 29203, 28838,  \n29386, 29381, 28829,  4014, 16315, 2503,  11520, 11522, 20435,  \n13583, 1479, 6676,  8672, 8673, 8856,  13318, 15791, 18387,  \n1558, 24391, 7599,  11700, 11699, 1268,  9987, 13959, 19238,  \n29386, 29020, 29384,  1062, 1061, 21168,  29197, 29018, 29382,  \n14975, 708, 17016,  28609, 16251, 29200,  14605, 6970, 7026,  \n15232, 14574, 22911,  26265, 27941, 28902,  11261, 20686, 8573,  \n21150, 1733, 15587,  15159, 18188, 15307,  15207, 20118, 19004,  \n29022, 22565, 21046,  7266, 7265, 6645,  29526, 29202, 29385,  \n25125, 29383, 29033,  25266, 12886, 11365,  29199, 29023, 29387,  \n28397, 20672, 29204,  29202, 29526, 29213,  28839, 29202, 29213,  \n3966, 17035, 14375,  374, 3597, 5319,  17776, 24391, 20797,  \n7803, 7802, 3321,  16221, 8321, 8320,  1365, 12368, 13110,  \n19588, 22062, 28822,  3183, 1503, 350,  1497, 29206, 29025,  \n28398, 29204, 29388,  29209, 29214, 29527,  8519, 5896, 10959,  \n29211, 29387, 29024,  6003, 20217, 6004,  21118, 15852, 1724,  \n8493, 21893, 8841,  4626, 20800, 22903,  29033, 29220, 29529,  \n13242, 3779, 16162,  29530, 29207, 29205,  11709, 22872, 10732,  \n29034, 29528, 29527,  13503, 5739, 5438,  29220, 29531, 29529,  \n29390, 29391, 29387,  6381, 16279, 21886,  19261, 18398, 9837,  \n22488, 12742, 12743,  11935, 14778, 10763,  7031, 5181, 23346,  \n29532, 29389, 28401,  1877, 15039, 18498,  29217, 29528, 29034,  \n29207, 29530, 29534,  19639, 3721, 9025,  29534, 29208, 29207,  \n29534, 29030, 29208,  9246, 21803, 11218,  8914, 3180, 4055,  \n28840, 29389, 29212,  8406, 16158, 10035,  29215, 29392, 29391,  \n6957, 12682, 18475,  2072, 19600, 2073,  17810, 10770, 10771,  \n29030, 29534, 29216,  16764, 14511, 17818,  29225, 29531, 29220,  \n2843, 9421, 19510,  4145, 20141, 4742,  3008, 9582, 13238,  \n29393, 29535, 29392,  12955, 14600, 8551,  29042, 28411, 29037,  \n9089, 2069, 9090,  15652, 1162, 19562,  19128, 13410, 2153,  \n15931, 7010, 12334,  25574, 28381, 2744,  9267, 19207, 12101,  \n29225, 29038, 29041,  9888, 8896, 8962,  9140, 11224, 8786,  \n28844, 29536, 29223,  29536, 29226, 29223,  3533, 14556, 17433,  \n4375, 29225, 29041,  5434, 4310, 13366,  11930, 22309, 15234,  \n29043, 29039, 28848,  6804, 4694, 854,  29224, 29226, 29536,  \n20961, 14425, 3168,  14936, 2955, 9436,  9277, 10130, 9831,  \n4737, 21153, 5047,  29536, 28844, 29395,  17449, 9152, 12989,  \n894, 16246, 6118,  29395, 29397, 29536,  18441, 21785, 28769,  \n17019, 13606, 19531,  18170, 9509, 11069,  1383, 5841, 9733,  \n17844, 1353, 8802,  29398, 29043, 28848,  2697, 21687, 8964,  \n19390, 19238, 4404,  13369, 13368, 4747,  9483, 9473, 14531,  \n19387, 19392, 7659,  29394, 29663, 29537,  18260, 28847, 14870,  \n11092, 9307, 16077,  29045, 29538, 29230,  13387, 15557, 405,  \n28847, 29229, 14870,  3456, 4516, 3457,  29538, 29539, 29230,  \n29539, 29400, 29230,  6797, 10750, 10749,  22366, 798, 17875,  \n7591, 1710, 13603,  29402, 29048, 29400,  10956, 8790, 3705,  \n5039, 22107, 8463,  20191, 15366, 870,  29403, 29402, 29666,  \n15475, 817, 6179,  18359, 2181, 24429,  10425, 10676, 8913,  \n29542, 14870, 29229,  4396, 4395, 16741,  18039, 17094, 17609,  \n29403, 29541, 29543,  29232, 29403, 29543,  23367, 29543, 29541,  \n16901, 12290, 9985,  22074, 12348, 12316,  28637, 29234, 29237,  \n7623, 13616, 7624,  29232, 29543, 29235,  3045, 15169, 3265,  \n9827, 2953, 11030,  22127, 6170, 13309,  29229, 29231, 29542,  \n19973, 11828, 18562,  25420, 6500, 6495,  9929, 11370, 12120,  \n29051, 29406, 29401,  4926, 4927, 3648,  16488, 6735, 2756,  \n15314, 7748, 10861,  1879, 19027, 14829,  10697, 14519, 18675,  \n13717, 13716, 5075,  29236, 29543, 29544,  20157, 4529, 23901,  \n7797, 18912, 7796,  23836, 16637, 13692,  29235, 29543, 29236,  \n11010, 7835, 12189,  13693, 13126, 23948,  3498, 8886, 1570,  \n10061, 10062, 8375,  29405, 29545, 133,  11564, 3922, 9744,  \n25557, 28952, 19850,  28644, 29246, 29406,  12654, 12091, 12459,  \n29056, 29236, 29544,  29545, 29405, 29055,  8453, 22426, 12415,  \n29315, 29404, 29054,  28650, 29238, 29546,  4883, 4997, 14108,  \n29547, 29056, 29544,  10581, 25706, 15740,  9622, 7512, 13266,  \n14642, 21601, 12190,  1688, 1347, 11125,  6579, 18305, 1611,  \n29547, 29248, 29056,  14937, 16553, 2090,  29548, 29252, 29408,  \n1385, 19024, 6263,  13584, 19264, 10888,  29249, 29055, 29057,  \n29249, 29545, 29055,  505, 2989, 2988,  29240, 29239, 29407,  \n2442, 4385, 2443,  15691, 15800, 11422,  16149, 29246, 29414,  \n7791, 6029, 12441,  3169, 3718, 6772,  7704, 11045, 22043,  \n8699, 13587, 13857,  8102, 11747, 20624,  7630, 2922, 12249,  \n5979, 12013, 6969,  1975, 2191, 2193,  22170, 7358, 12662,  \n4533, 5114, 24236,  14749, 13219, 14750,  19281, 1462, 17524,  \n4242, 5328, 8636,  5551, 5550, 20552,  12862, 3737, 10362,  \n5958, 17058, 2122,  21181, 16081, 6995,  12672, 447, 7259,  \n9186, 9187, 14378,  14182, 16658, 8231,  18521, 15501, 16229,  \n19259, 11545, 20125,  11892, 11474, 1439,  29551, 29411, 29412,  \n29551, 29412, 29413,  8659, 8517, 22187,  8146, 1068, 6892,  \n29415, 28869, 29552,  13827, 16043, 7406,  4313, 11938, 12569,  \n9094, 8449, 15097,  29553, 29413, 29064,  28432, 28650, 29254,  \n3490, 9260, 14676,  5965, 18407, 13372,  1092, 29414, 23136,  \n15241, 3154, 18452,  29414, 29059, 24320,  11922, 10024, 5094,  \n22491, 17824, 8844,  29069, 28654, 29415,  29064, 29416, 29553,  \n10613, 10612, 9797,  28868, 29066, 29061,  11675, 17069, 3911,  \n29554, 29065, 29675,  9226, 2536, 21981,  29067, 29555, 29066,  \n29415, 29556, 29069,  29068, 29416, 28871,  16579, 6216, 19935,  \n29255, 29254, 19053,  1328, 1327, 20408,  9545, 324, 19072,  \n28873, 29555, 29067,  9788, 12492, 16801,  10493, 11528, 10492,  \n15470, 21834, 6912,  2169, 2170, 9744,  1723, 14396, 8880,  \n4806, 8643, 2520,  29072, 29065, 29554,  13682, 17396, 15755,  \n29070, 28237, 19053,  29070, 19053, 19054,  15958, 21677, 19204,  \n21126, 867, 2438,  29256, 29557, 28873,  28929, 28102, 17006,  \n633, 9648, 16812,  16199, 21460, 6941,  29259, 28659, 29417,  \n28659, 29257, 29417,  1030, 7959, 16376,  8686, 2558, 1341,  \n21592, 15764, 5995,  18943, 6845, 3179,  24320, 28034, 22627,  \n5794, 8452, 10803,  9246, 8428, 14453,  29422, 29258, 29071,  \n9246, 18859, 8428,  5239, 4952, 4951,  27849, 25376, 26494,  \n1188, 19981, 1265,  1758, 4019, 21692,  8520, 2672, 13829,  \n28245, 27849, 26494,  29559, 29422, 29260,  29289, 10842, 25081,  \n10327, 10756, 7342,  29424, 29559, 29260,  10121, 10120, 14587,  \n3376, 5242, 23164,  29685, 29261, 29265,  10157, 1145, 14869,  \n3634, 6122, 18509,  19507, 13308, 15082,  29561, 29423, 29267,  \n29561, 29424, 29423,  1758, 18658, 19118,  18945, 5964, 9109,  \n2296, 2970, 16583,  15080, 18816, 24007,  16275, 11803, 11805,  \n16485, 2504, 15071,  10669, 2691, 9405,  28145, 28635, 27941,  \n11217, 380, 22046,  29426, 29077, 29266,  21082, 19609, 22214,  \n946, 14059, 935,  29269, 29560, 29563,  28674, 28882, 29079,  \n29149, 16494, 16647,  29078, 29561, 29267,  29564, 29561, 29078,  \n2998, 1408, 5048,  3027, 5956, 13666,  4743, 6334, 3240,  \n29269, 29079, 29560,  29268, 29564, 29078,  28878, 28675, 29565,  \n29427, 29564, 29268,  14321, 26285, 17275,  24303, 18141, 2671,  \n28890, 29566, 29428,  29429, 29566, 28890,  29567, 29428, 29566,  \n29427, 29080, 29270,  29275, 29568, 29429,  5870, 9488, 5936,  \n19367, 6755, 433,  335, 312, 6642,  23676, 3110, 21819,  \n23051, 10049, 17572,  17244, 5057, 5059,  15840, 5335, 11441,  \n12685, 21709, 17798,  8619, 3967, 10695,  29567, 29430, 29428,  \n1958, 4241, 13816,  20196, 1972, 16566,  12392, 1297, 10797,  \n29271, 29081, 29431,  28675, 29274, 22066,  29569, 29431, 29432,  \n21157, 18031, 20837,  28675, 28683, 29274,  29278, 29430, 29570,  \n17826, 10939, 10938,  15733, 14095, 14002,  19015, 15758, 10334,  \n1371, 12419, 18327,  1732, 15587, 1733,  21452, 18087, 3775,  \n9619, 9620, 9340,  14198, 13567, 23936,  29433, 29571, 29432,  \n6458, 6459, 17363,  6921, 6922, 6714,  28258, 28681, 29434,  \n18684, 17486, 11103,  28893, 29278, 29572,  7104, 6911, 17545,  \n2750, 7711, 17703,  29573, 29435, 29277,  3506, 14399, 18463,  \n28893, 29572, 29095,  7959, 5598, 20329,  28895, 28898, 29438,  \n29573, 29277, 29436,  12088, 12089, 22953,  28898, 28699, 29438,  \n29436, 29279, 29574,  29436, 29574, 29573,  20436, 19073, 21945,  \n29282, 28456, 17683,  6147, 12426, 19499,  28693, 29280, 29439,  \n20662, 11699, 18016,  11429, 16477, 17256,  6198, 16841, 4470,  \n29089, 29437, 29279,  13730, 13041, 4782,  5264, 5266, 13310,  \n29437, 29281, 29575,  1976, 12304, 8237,  11998, 2161, 22727,  \n14300, 12883, 16473,  29441, 19185, 29281,  29281, 19185, 29575,  \n25634, 28897, 29090,  25634, 22597, 28897,  4256, 15468, 1835,  \n11080, 11079, 12962,  4070, 21451, 18233,  29283, 29696, 29441,  \n22597, 19132, 28695,  16609, 8429, 28102,  5157, 12825, 14878,  \n22722, 19398, 12852,  989, 19052, 990,  3217, 11376, 15931,  \n19132, 28268, 28695,  29103, 29440, 29576,  8566, 7115, 18126,  \n9007, 19742, 10117,  29444, 29096, 29443,  19031, 8394, 24654,  \n11839, 15636, 13401,  29450, 29103, 29576,  14369, 2752, 21086,  \n12280, 19707, 13714,  12996, 12995, 14041,  2820, 6317, 12591,  \n706, 10725, 15762,  17204, 18551, 3568,  29450, 29106, 29103,  \n29288, 29450, 29443,  12687, 2335, 3991,  29446, 29577, 28908,  \n29578, 29579, 29296,  16190, 4066, 14008,  29296, 29579, 29297,  \n4886, 9508, 18170,  29290, 29580, 29442,  3364, 6837, 6688,  \n4902, 9173, 17449,  15951, 16362, 807,  29100, 29101, 29291,  \n15191, 13344, 3216,  12354, 19144, 3312,  10874, 22719, 16189,  \n19890, 12530, 3663,  12192, 21020, 8297,  29583, 29451, 29294,  \n29583, 29294, 29297,  559, 553, 4824,  14433, 9168, 18635,  \n8484, 3009, 3010,  16981, 3700, 3699,  29292, 29580, 29290,  \n20760, 24915, 14929,  12847, 25499, 17168,  28908, 29577, 29299,  \n14801, 5975, 9718,  29292, 29293, 29580,  5168, 20255, 21044,  \n8334, 8335, 22124,  29299, 29452, 29109,  21737, 29107, 29452,  \n29585, 29578, 29295,  10188, 22035, 17057,  29295, 29578, 29296,  \n7383, 23748, 23146,  22370, 8079, 12162,  10878, 14140, 2171,  \n20017, 6226, 20016,  3777, 1805, 13468,  23679, 11467, 4143,  \n28721, 29107, 22937,  29308, 28721, 22937,  29456, 29300, 29455,  \n13276, 11171, 11895,  10112, 15423, 14056,  19903, 18367, 1730,  \n29586, 29587, 29305,  19187, 25143, 19818,  29287, 28909, 17721,  \n28909, 28901, 17040,  17959, 22874, 23235,  29453, 7347, 28907,  \n975, 8262, 8188,  7631, 17886, 1993,  10785, 10195, 12105,  \n8405, 5229, 21854,  5148, 2771, 1209,  4162, 20946, 4161,  \n29114, 29589, 29457,  29707, 29119, 29457,  1349, 13103, 1347,  \n29458, 29586, 29305,  12052, 6973, 2447,  384, 6533, 6534,  \n28861, 6952, 15041,  10557, 12338, 16542,  7347, 28469, 28907,  \n9716, 2663, 6011,  29309, 29308, 29588,  16521, 18755, 6657,  \n29455, 29303, 29309,  10350, 10349, 7964,  22328, 29707, 29457,  \n20934, 5669, 3937,  17827, 29591, 28910,  17827, 28910, 28469,  \n13752, 12847, 17168,  21531, 1981, 21229,  17827, 28469, 7347,  \n8120, 4221, 4222,  29589, 29311, 29313,  2812, 11810, 16406,  \n9082, 6131, 15523,  29307, 29459, 29304,  29590, 29461, 29306,  \n3952, 17517, 8202,  14624, 21982, 11798,  29590, 29593, 29462,  \n29301, 29462, 29593,  4859, 8310, 7628,  4013, 13915, 14558,  \n29110, 29462, 29301,  29310, 28280, 28914,  19981, 1266, 1265,  \n29118, 28485, 29460,  29460, 29592, 29118,  29313, 29118, 29592,  \n29313, 29592, 29589,  29120, 29119, 29594,  29461, 28922, 29306,  \n5840, 28566, 3189,  29462, 29461, 29590,  9895, 2798, 12702,  \n29120, 29594, 29123,  412, 1374, 11901,  10391, 7206, 8102,  \n12114, 20412, 12599,  29307, 29312, 29596,  14201, 19394, 24231,  \n15942, 1902, 13555,  18344, 15403, 19052,  1798, 14090, 16794,  \n14643, 16041, 16042,  13081, 11139, 14505,  15484, 11868, 7465,  \n29594, 29595, 29123,  29595, 29596, 29123,  8406, 8405, 13694,  \n22458, 15010, 17452,  28287, 28083, 29463,  29312, 29464, 29596,  \n7383, 7382, 804,  24997, 28917, 29122,  14225, 16087, 14224,  \n3378, 15893, 1628,  19640, 12287, 4685,  17802, 4887, 21336,  \n29318, 29121, 29465,  13792, 9311, 26845,  16352, 17786, 5117,  \n29465, 29597, 29318,  29318, 29597, 29598,  5524, 28634, 16145,  \n21944, 18337, 7842,  29599, 29318, 29598,  14798, 2638, 11196,  \n29125, 29318, 29599,  29124, 29125, 26391,  29319, 29124, 26391,  \n8970, 21843, 1964,  16924, 15146, 15145,  12662, 9661, 4637,  \n28739, 29320, 29600,  2030, 8414, 2587,  6575, 16078, 691,  \n29466, 28503, 28938,  6474, 19704, 19703,  8160, 8159, 8945,  \n20596, 4720, 4719,  12183, 6720, 5179,  1627, 3423, 3719,  \n28504, 29466, 29467,  8804, 18284, 22299,  8394, 23655, 24654,  \n29323, 29467, 29468,  29128, 1251, 29127,  7866, 21494, 16236,  \n20168, 15745, 13630,  12614, 5293, 13241,  4898, 4822, 4899,  \n2100, 8866, 1799,  29469, 29128, 28940,  1251, 29128, 29469,  \n29470, 29603, 29324,  2226, 7015, 3550,  8550, 10067, 7827,  \n5124, 1992, 21238,  8354, 13382, 18245,  29603, 29471, 29324,  \n16514, 5495, 3793,  29129, 28306, 29130,  13497, 2706, 16727,  \n29473, 28748, 29604,  29604, 28748, 29472,  12385, 1419, 9589,  \n7545, 4766, 23507,  18384, 13025, 6637,  28509, 28511, 29325,  \n12928, 28135, 29131,  29131, 28135, 29327,  29325, 28512, 29328,  \n15762, 20133, 706,  21578, 28943, 29327,  29605, 29328, 28944,  \n28109, 28751, 8449,  29330, 28514, 28109,  29605, 28944, 29329,  \n1625, 1624, 3815,  29606, 29329, 28950,  9440, 4913, 20415,  \n29606, 28950, 29331,  28949, 28519, 29133,  10249, 28949, 28156,  \n2862, 3920, 18130,  10249, 29332, 28949,  29607, 29606, 29331,  \n1565, 1566, 18387,  28521, 28520, 29332,  11857, 6108, 9968,  \n11554, 15339, 11555,  6817, 20466, 22466,  21329, 11672, 6827,  \n26541, 29333, 28951,  638, 10993, 22479,  2814, 28340, 21293,  \n28523, 28312, 29135,  11012, 11013, 4062,  17357, 13109, 11872,  \n14913, 28754, 22260,  28754, 29135, 22260,  6550, 12928, 21463,  \n21286, 14881, 23699,  29475, 28755, 29335,  8613, 9925, 9927,  \n24396, 3774, 643,  17360, 13695, 771,  21015, 20093, 2067,  \n5078, 3924, 5079,  29140, 28957, 29609,  17059, 7877, 2846,  \n6507, 4614, 2555,  29609, 28957, 29610,  28957, 29142, 29610,  \n29477, 29611, 29142,  20940, 10849, 17955,  29338, 29612, 29477,  \n13052, 19137, 7115,  24188, 9164, 8895,  28961, 29143, 29342,  \n18335, 18336, 4192,  29613, 29339, 29341,  9830, 9829, 16375,  \n29479, 28961, 29342,  7247, 10967, 5390,  1687, 20189, 20844,  \n15082, 2535, 9226,  8152, 9764, 9763,  13757, 8266, 8265,  \n29479, 29480, 28963,  679, 7265, 7267,  5111, 1985, 6062,  \n21875, 17935, 7923,  7198, 22369, 3302,  12351, 7460, 1187,  \n29614, 29343, 29615,  14552, 16891, 16890,  670, 14995, 671,  \n3711, 4990, 8004,  12599, 23048, 12112,  16875, 9601, 13759,  \n29344, 29343, 29614,  6450, 2437, 6403,  11732, 4880, 12479,  \n17142, 3633, 15848,  4345, 4346, 3525,  21877, 28744, 26202,  \n23685, 4699, 9429,  6599, 11277, 5124,  28952, 15255, 14834,  \n28575, 9246, 19572,  28636, 27942, 6582,  28636, 24439, 27942,  \n26265, 28145, 27941,  338, 21675, 23470,  17568, 17567, 14204,  \n2974, 2975, 8000,  28770, 26309, 28635,  25804, 26958, 26360,  \n21999, 16609, 28929,  22865, 19583, 9510,  28811, 16714, 1500,  \n22035, 1856, 17056,  2847, 17033, 4501,  28825, 26406, 7737,  \n28861, 575, 21866,  12519, 16178, 18960,  28826, 23101, 25113,  \n24021, 4078, 4077,  9542, 9068, 9543,  4078, 16010, 19588,  \n28542, 21892, 13069,  12593, 9117, 17725,  9544, 9545, 5431,  \n4543, 14492, 18766,  10776, 8390, 14525,  11185, 6527, 12677,  \n28539, 28613, 29482,  5672, 20207, 15351,  1421, 1420, 18252,  \n3833, 12967, 21416,  18666, 16781, 17916,  19357, 21725, 14638,  \n27950, 28771, 13866,  28211, 25017, 22496,  2568, 10340, 12886,  \n28745, 9242, 18977,  8650, 19089, 5494,  29719, 28968, 29345,  \n4929, 488, 9163,  2855, 16497, 16123,  28653, 22606, 17311,  \n1002, 1001, 2175,  8434, 10987, 5454,  7388, 7387, 7124,  \n487, 486, 14655,  27763, 28330, 29150,  6819, 12691, 18949,  \n29616, 29151, 28969,  12768, 3608, 12769,  15256, 8477, 6320,  \n27763, 28970, 28330,  28551, 29618, 29616,  29485, 28333, 19829,  \n22170, 12662, 4137,  13752, 18901, 19264,  17313, 11156, 17079,  \n965, 9889, 966,  13297, 14358, 9813,  1540, 2855, 16123,  \n21629, 11580, 8971,  22459, 28640, 24574,  18801, 2105, 20999,  \n3158, 14156, 7606,  18731, 12144, 12145,  28774, 29153, 28980,  \n21010, 10376, 9958,  3195, 15208, 3194,  8524, 14854, 21191,  \n29156, 28970, 10240,  25265, 29619, 24986,  28337, 17464, 28553,  \n25265, 25263, 29619,  27952, 13946, 28543,  5750, 2776, 2777,  \n22711, 23952, 28980,  11370, 9994, 8181,  2332, 3626, 20573,  \n28548, 27752, 20123,  5953, 18448, 10911,  10067, 10066, 7827,  \n27952, 28554, 13946,  16228, 5490, 5491,  16972, 20104, 15832,  \n29352, 28563, 27753,  12285, 15232, 12284,  19977, 20485, 21912,  \n22204, 28990, 11607,  9398, 19673, 2327,  13056, 29157, 28150,  \n29620, 15378, 25149,  1998, 1997, 10422,  3979, 9414, 558,  \n29489, 29488, 28563,  7358, 7514, 6253,  7391, 11273, 7377,  \n17434, 7761, 7760,  6054, 18187, 6055,  11767, 6440, 12668,  \n3322, 11172, 2879,  19066, 1156, 12095,  8192, 7731, 9720,  \n2356, 4678, 22977,  5572, 6616, 11348,  5952, 14012, 9330,  \n29351, 29720, 29350,  19827, 7218, 14308,  14674, 11054, 12536,  \n15175, 5955, 1779,  29621, 29353, 28975,  4848, 17158, 22070,  \n7253, 19696, 7747,  20425, 25153, 28564,  7981, 17598, 9856,  \n9824, 17376, 5692,  9987, 3798, 13959,  29354, 28982, 29353,  \n20560, 4382, 21245,  2404, 6998, 3715,  15287, 8730, 15422,  \n18085, 9864, 13901,  20867, 17329, 17600,  21835, 15429, 16478,  \n29160, 28983, 29493,  14784, 20011, 28160,  14837, 2695, 14838,  \n10332, 19485, 18206,  13453, 14399, 365,  22367, 18090, 15964,  \n19665, 19315, 11736,  29160, 29493, 29494,  29494, 29493, 29622,  \n17261, 7642, 22770,  1272, 5614, 3134,  3663, 3662, 4667,  \n28569, 28783, 19003,  4919, 13111, 4918,  29495, 29494, 29623,  \n5670, 15047, 11246,  21851, 7780, 1555,  6257, 10405, 16273,  \n29355, 29495, 29496,  19034, 883, 18509,  23025, 19740, 16932,  \n16853, 9456, 8069,  20940, 782, 14181,  3830, 13590, 3829,  \n29496, 29624, 29356,  885, 7561, 9102,  18216, 22818, 18217,  \n29356, 29624, 29625,  29165, 29356, 29625,  29497, 29165, 29625,  \n13819, 12431, 8435,  3584, 14544, 2395,  895, 13273, 15090,  \n7758, 16780, 5199,  13234, 4986, 17311,  29358, 28989, 19271,  \n5330, 2333, 2332,  27966, 7442, 21580,  6007, 20935, 11936,  \n19540, 28356, 28573,  2611, 1446, 17453,  6329, 18502, 9220,  \n12599, 6360, 22129,  28575, 19572, 14572,  10972, 13880, 15611,  \n5845, 10650, 12182,  8263, 7448, 6922,  4462, 4463, 8959,  \n6211, 3188, 8174,  18117, 28169, 29359,  2184, 5523, 5317,  \n29172, 29359, 28169,  2021, 2020, 6739,  12094, 16847, 12093,  \n18087, 21452, 11837,  17891, 29359, 29172,  16442, 6536, 15367,  \n11051, 8069, 5552,  6302, 17945, 11375,  8603, 18430, 12746,  \n392, 13428, 13427,  3641, 10385, 3640,  9582, 14843, 1771,  \n17059, 1673, 1674,  28362, 22025, 3946,  28362, 28792, 22025,  \n18876, 29426, 5573,  29170, 28793, 17255,  7934, 21254, 8964,  \n5543, 20551, 18621,  8099, 5636, 5719,  13690, 13689, 20838,  \n7120, 3574, 20515,  25211, 24786, 11406,  12688, 11623, 11376,  \n16910, 18615, 12381,  21652, 22078, 18154,  17386, 3603, 5925,  \n22869, 4275, 20501,  16754, 12468, 10730,  23848, 28574, 29360,  \n18469, 4732, 4731,  950, 14862, 951,  4298, 4299, 21514,  \n14083, 4112, 10015,  21627, 11052, 2291,  24272, 28576, 24116,  \n429, 16814, 10076,  24272, 24116, 20653,  1372, 6676, 361,  \n18589, 2544, 7121,  8488, 8850, 8849,  8383, 16879, 9982,  \n1703, 11976, 9013,  29502, 28795, 25205,  23138, 28364, 28798,  \n17444, 27974, 16506,  29174, 27777, 17444,  17435, 7763, 7907,  \n9910, 18556, 7473,  13947, 13946, 13345,  11848, 1193, 9358,  \n7297, 10348, 1020,  288, 5982, 10001,  6595, 4521, 12864,  \n19875, 22340, 16245,  8620, 5037, 18386,  21598, 29503, 28176,  \n15027, 7582, 8495,  28799, 19197, 28366,  7844, 7845, 11478,  \n20092, 3611, 8454,  7329, 1320, 18696,  7637, 28798, 29177,  \n15955, 18992, 27946,  4773, 6988, 10244,  14701, 20262, 8764,  \n28184, 28180, 29504,  28180, 25422, 29504,  29627, 28998, 29363,  \n28801, 29362, 21553,  7941, 1448, 7963,  28581, 29175, 25873,  \n15761, 28400, 14646,  7115, 19137, 18126,  13269, 12252, 13938,  \n15373, 21351, 9408,  17260, 17073, 3772,  29363, 28998, 28999,  \n28581, 25873, 24367,  4087, 4861, 7983,  16455, 6403, 15734,  \n15543, 15068, 17679,  25653, 28581, 24367,  12599, 22129, 23048,  \n9155, 6596, 18418,  20584, 10821, 16019,  10156, 960, 6707,  \n19367, 304, 12516,  28585, 28803, 29505,  12229, 3513, 3512,  \n27788, 27603, 29507,  426, 13636, 5523,  17593, 16294, 15224,  \n19919, 8844, 17824,  1621, 13690, 1622,  13776, 14513, 14041,  \n5754, 9207, 1584,  27601, 28369, 29182,  9977, 9975, 9976,  \n15355, 13771, 18849,  25369, 29002, 29511,  2536, 4337, 4171,  \n17102, 28584, 28806,  20025, 482, 16600,  28582, 25653, 29179,  \n29181, 17102, 28806,  21148, 13192, 4839,  4756, 5080, 21421,  \n12291, 1957, 18773,  10772, 22871, 2883,  4409, 13912, 20300,  \n6771, 17254, 8915,  28814, 29511, 28809,  12779, 15544, 13896,  \n21739, 18758, 14961,  22161, 14287, 505,  18881, 5931, 16883,  \n3099, 12771, 12770,  28814, 29630, 29511,  17356, 16916, 19761,  \n1759, 18447, 18446,  5214, 11859, 16472,  28807, 27799, 29513,  \n4481, 2693, 16203,  29183, 29179, 29512,  28814, 28591, 7047,  \n3409, 7047, 28591,  28815, 27420, 26284,  13584, 25499, 12847,  \n29366, 16946, 16947,  29004, 3409, 28591,  21410, 15492, 9807,  \n28746, 28745, 7464,  3941, 7452, 1369,  29620, 24686, 8979,  \n28815, 26284, 28816,  29004, 28591, 28819,  29631, 29183, 20504,  \n7297, 3159, 10348,  3616, 7827, 17781,  6439, 322, 11959,  \n29631, 28817, 29183,  17260, 1725, 14405,  19098, 3999, 10926,  \n18642, 2766, 21882,  22823, 10341, 13989,  29632, 27803, 28590,  \n13915, 20510, 6598,  13663, 13283, 13662,  3283, 3083, 4689,  \n10553, 28818, 28817,  29368, 29188, 29514,  8404, 9778, 19211,  \n10536, 1007, 14362,  23646, 5135, 22911,  28680, 11220, 14202,  \n9027, 523, 12538,  26424, 9153, 13865,  3982, 21672, 7850,  \n9899, 16849, 22415,  1785, 1786, 11126,  9599, 6699, 2497,  \n25017, 1843, 26118,  3728, 18207, 22445,  1166, 15633, 14411,  \n29634, 29188, 29368,  19901, 10237, 3332,  29189, 28818, 10553,  \n11709, 21506, 17405,  18651, 466, 5262,  7495, 12920, 17673,  \n1325, 6785, 525,  1556, 10873, 1730,  11808, 3437, 11809,  \n21753, 10176, 15238,  18089, 5543, 18322,  2367, 767, 766,  \n28595, 29369, 29635,  360, 14168, 14170,  1402, 14442, 16516,  \n29189, 29009, 28594,  28596, 28595, 29635,  4909, 2024, 20927,  \n11473, 18004, 14916,  21115, 4114, 5134,  10876, 10875, 13590,  \n7426, 5201, 9486,  24429, 12884, 18359,  7021, 4727, 10973,  \n6751, 1828, 1827,  6140, 885, 9102,  14599, 6726, 9278,  \n29011, 28596, 29635,  28820, 24898, 23679,  28380, 29191, 29636,  \n13988, 22823, 13989,  29370, 29010, 29012,  29194, 28820, 23679,  \n9274, 15600, 5285,  29191, 28599, 29192,  29370, 29012, 12843,  \n9926, 9925, 15766,  23678, 29194, 23679,  18585, 12049, 5479,  \n9711, 15181, 9712,  14035, 2415, 2414,  14367, 2455, 2454,  \n17623, 4326, 2271,  7182, 4569, 4570,  8570, 13603, 7740,  \n14982, 11574, 11575,  9729, 15934, 10477,  1116, 2065, 13804,  \n29732, 9651, 6321,  29195, 29373, 29014,  23392, 23671, 20872,  \n15739, 5655, 15695,  3894, 12554, 21632,  12250, 14376, 12956,  \n29517, 29639, 29373,  5860, 16653, 2322,  29373, 29639, 29638,  \n29373, 29638, 29522,  12097, 14101, 11562,  28821, 29194, 23678,  \n29521, 29015, 29371,  10829, 1155, 14102,  29196, 29641, 29376,  \n8323, 7129, 21131,  3206, 6903, 3207,  11034, 29302, 7277,  \n26109, 21584, 337,  29196, 29520, 29641,  29518, 29197, 29378,  \n846, 8714, 20640,  29641, 29520, 29740,  23851, 2299, 2301,  \n10831, 10830, 16396,  25466, 28381, 25574,  6079, 10302, 6080,  \n9416, 9415, 1117,  3503, 983, 4171,  29645, 29643, 29642,  \n4870, 13798, 4869,  16436, 11458, 16437,  19035, 17064, 1692,  \n29383, 24252, 29524,  16809, 7582, 7581,  15547, 13029, 3612,  \n29202, 29201, 29385,  943, 20978, 944,  6352, 6353, 22696,  \n3597, 8553, 18747,  9861, 363, 18956,  29647, 29648, 29384,  \n29016, 29522, 29646,  3314, 29197, 29382,  29642, 29379, 29525,  \n29647, 29384, 29199,  10623, 4733, 9885,  29645, 29642, 29525,  \n16250, 29200, 16251,  5601, 17739, 5602,  14242, 244, 247,  \n20097, 20096, 7057,  29021, 29016, 29646,  29525, 29209, 29645,  \n29199, 29387, 29649,  29645, 29209, 29643,  29643, 29209, 29528,  \n4954, 17225, 4955,  3291, 9076, 20956,  16128, 9130, 15605,  \n19547, 29018, 28831,  9343, 9313, 1783,  14899, 17327, 6298,  \n29643, 29528, 29652,  17534, 9780, 16921,  29526, 29652, 29217,  \n29213, 29526, 29217,  21046, 1309, 29022,  1120, 16033, 3832,  \n29021, 29650, 29205,  16820, 16821, 22225,  15265, 13453, 5935,  \n29653, 29210, 29388,  29528, 29209, 29527,  14989, 8901, 9544,  \n29652, 29528, 29217,  4475, 15413, 7334,  15893, 1410, 1628,  \n29022, 1309, 25372,  2929, 14143, 7409,  7548, 9365, 10386,  \n7822, 7821, 3059,  10972, 15611, 19503,  21257, 7871, 15487,  \n12075, 11319, 28017,  14221, 11232, 8985,  13887, 14071, 7739,  \n14242, 6851, 12692,  29655, 17013, 15376,  29205, 29656, 29530,  \n29210, 29533, 28402,  19470, 17530, 25867,  29654, 29387, 29391,  \n15334, 8932, 10769,  29532, 28401, 28614,  29533, 28614, 28402,  \n29391, 29392, 29654,  29530, 29656, 29657,  11888, 15267, 9005,  \n7334, 11447, 4474,  18935, 6436, 20547,  19092, 14192, 14193,  \n29658, 29530, 29657,  29658, 29534, 29530,  29225, 20055, 21359,  \n12078, 29659, 29392,  29534, 29658, 29660,  29660, 29216, 29534,  \n8600, 5527, 2190,  12078, 29392, 29535,  13391, 16337, 21347,  \n29660, 29228, 29216,  12229, 6685, 18897,  24090, 7726, 18390,  \n14991, 2764, 2765,  21923, 5923, 5450,  9124, 9085, 5249,  \n853, 21498, 4697,  29228, 29660, 29661,  22736, 4556, 4555,  \n7000, 24191, 13764,  5098, 5097, 19209,  8718, 11456, 7544,  \n29662, 29228, 29661,  19007, 10782, 14301,  25698, 23283, 23450,  \n3777, 13468, 19212,  14214, 12057, 14853,  13607, 3185, 3186,  \n13218, 8579, 11199,  16134, 12108, 14008,  23170, 14052, 13153,  \n29396, 29045, 29228,  29662, 29396, 29228,  9872, 12482, 9871,  \n4589, 5859, 4240,  15474, 18607, 12018,  29224, 29536, 29394,  \n386, 5911, 19525,  14355, 6455, 16091,  7567, 10395, 14398,  \n29663, 29536, 29397,  29536, 29663, 29394,  25562, 15593, 17503,  \n3371, 22518, 16556,  5626, 18511, 5625,  15923, 4576, 18499,  \n29663, 29397, 29399,  29396, 29665, 29538,  5297, 12515, 15720,  \n29663, 29399, 29537,  29041, 28847, 18260,  14197, 29046, 25519,  \n29045, 29396, 29538,  29234, 28846, 29394,  29394, 29537, 29234,  \n29537, 29399, 29234,  9242, 28745, 22285,  29050, 14197, 9074,  \n29050, 29046, 14197,  17869, 13954, 12563,  9672, 11739, 348,  \n29539, 29402, 29400,  29666, 29402, 29539,  10533, 23694, 10534,  \n29234, 29399, 29540,  15768, 688, 15769,  29403, 29666, 29541,  \n29399, 29667, 29540,  10339, 10334, 10333,  29540, 29237, 29234,  \n13988, 29155, 16682,  29541, 22848, 23367,  24304, 25086, 15483,  \n26360, 28902, 25804,  16283, 10396, 11781,  2883, 6304, 22556,  \n4685, 4687, 3887,  18326, 442, 8259,  3230, 10818, 16798,  \n13616, 13008, 7624,  23367, 29668, 29543,  18956, 363, 15884,  \n29670, 29668, 23367,  6066, 7896, 4274,  3255, 14300, 3876,  \n19642, 347, 16685,  12298, 4484, 12299,  1499, 657, 4596,  \n29544, 29543, 29668,  15796, 13321, 9026,  29237, 29540, 29671,  \n18936, 8759, 7511,  16533, 14844, 3447,  22547, 4453, 23296,  \n10945, 10946, 3085,  10265, 5075, 13718,  13228, 14123, 13229,  \n10509, 5739, 2814,  18274, 786, 787,  3068, 22219, 10328,  \n29231, 29404, 11652,  21991, 29406, 29246,  488, 4929, 6182,  \n29237, 29674, 29052,  29404, 29315, 11652,  21991, 29246, 16149,  \n29547, 29544, 29668,  14571, 22044, 3082,  29052, 29674, 29407,  \n14094, 12323, 15808,  14782, 20385, 14781,  18995, 878, 17694,  \n13227, 3161, 3162,  29548, 29248, 29547,  14185, 10931, 10930,  \n20698, 15453, 17817,  12440, 6811, 12695,  29674, 29676, 29407,  \n9311, 21803, 26845,  9188, 29315, 17058,  2004, 18094, 7356,  \n22801, 5840, 9001,  29408, 29248, 29548,  29548, 29409, 29252,  \n29253, 29409, 29675,  10111, 10857, 1817,  20842, 7036, 10955,  \n14897, 4666, 5045,  29315, 29054, 17058,  28650, 29546, 1073,  \n29240, 29407, 29677,  5743, 19257, 5035,  10073, 12425, 3174,  \n19875, 14036, 18550,  29240, 29677, 29678,  29242, 29241, 29410,  \n7693, 3607, 10534,  8324, 8323, 8314,  14952, 2064, 1742,  \n29249, 29250, 29549,  21016, 417, 416,  29244, 29678, 29410,  \n12755, 21325, 11860,  2377, 6512, 2797,  6316, 18844, 6317,  \n17106, 18221, 16141,  4498, 14419, 18821,  29679, 29410, 29678,  \n9485, 29245, 20181,  4857, 11284, 11666,  29245, 3797, 29054,  \n29411, 29680, 28869,  14073, 5138, 1609,  29681, 29551, 29413,  \n2117, 12049, 12051,  3233, 18572, 5251,  17731, 2971, 9902,  \n29250, 29061, 29549,  29549, 29061, 29682,  29550, 29242, 29410,  \n29247, 29242, 29550,  29245, 29243, 20181,  29552, 28869, 29680,  \n29413, 29553, 29681,  10280, 9707, 4441,  22714, 25117, 26070,  \n5945, 3943, 11742,  6755, 20482, 433,  18452, 3154, 4833,  \n336, 335, 6642,  14275, 19574, 1148,  4544, 12625, 4808,  \n1936, 15535, 1937,  4625, 2051, 1613,  29061, 29066, 29682,  \n16162, 16955, 5755,  8589, 5303, 12995,  21577, 2444, 615,  \n29555, 29683, 29066,  8171, 18534, 21239,  4755, 6031, 10063,  \n19053, 29254, 5649,  12146, 12413, 18927,  15866, 6773, 6774,  \n18516, 16576, 22274,  29069, 29556, 18542,  16520, 15015, 5829,  \n15216, 4916, 2109,  660, 13366, 661,  29255, 19053, 28432,  \n29555, 28873, 29557,  25537, 29068, 26302,  331, 5324, 16798,  \n29257, 11794, 29417,  10141, 11582, 1100,  15375, 17266, 21351,  \n22409, 5708, 851,  7993, 7994, 19617,  29557, 29256, 29558,  \n15824, 17134, 19453,  29554, 29418, 29072,  8021, 16458, 8035,  \n3633, 17142, 20569,  29258, 29558, 29256,  5430, 11756, 7299,  \n12429, 6496, 12428,  29558, 29258, 29422,  14335, 14334, 13459,  \n28660, 29261, 26302,  10662, 7413, 10663,  9821, 12736, 22046,  \n22226, 18579, 1593,  29333, 26541, 19190,  15166, 18184, 2438,  \n12810, 14299, 12809,  626, 3499, 18473,  13648, 9669, 14869,  \n5569, 3669, 3670,  29559, 29424, 29684,  16323, 7165, 5162,  \n17991, 14554, 5719,  20669, 21276, 10903,  15798, 18308, 18602,  \n16855, 23387, 573,  16855, 11067, 23387,  29266, 28877, 5198,  \n1873, 12125, 1168,  3310, 2836, 3311,  13639, 4527, 13638,  \n19979, 8548, 8019,  19533, 20684, 15268,  29686, 29424, 29561,  \n17602, 5085, 22059,  6036, 6037, 17217,  19148, 18256, 13859,  \n19772, 17122, 4643,  6157, 11175, 19505,  15943, 19560, 8002,  \n18876, 29265, 29426,  22894, 18945, 16562,  29269, 29082, 29079,  \n29686, 29561, 29564,  6141, 10276, 9284,  29688, 29564, 29427,  \n29568, 29275, 29793,  29269, 29563, 29793,  29688, 29427, 29689,  \n8244, 11693, 8245,  29269, 29793, 29275,  4505, 9881, 4506,  \n29427, 29270, 29689,  21018, 22714, 21895,  14780, 1204, 15454,  \n29690, 29691, 29270,  19804, 27358, 12623,  13279, 28677, 28886,  \n13279, 29272, 28677,  29690, 29431, 29692,  8418, 11064, 19827,  \n18933, 18570, 18569,  29690, 29271, 29431,  6063, 11437, 20333,  \n29569, 29692, 29431,  17777, 9274, 9273,  29432, 29571, 29569,  \n28888, 29272, 22225,  10438, 21394, 21393,  20699, 11644, 19262,  \n14260, 8994, 20008,  19910, 11466, 15922,  3054, 7703, 11456,  \n21210, 13793, 2777,  4078, 24021, 16010,  29435, 29693, 29433,  \n28258, 29434, 28055,  11935, 16034, 14086,  4971, 11335, 15197,  \n21192, 3191, 12954,  29572, 29438, 29095,  13837, 11432, 3355,  \n29087, 29694, 29280,  29694, 16661, 29280,  29693, 29435, 29573,  \n28055, 1724, 28689,  4023, 3562, 10666,  15906, 2292, 15130,  \n21787, 1551, 1552,  23046, 10991, 10992,  29574, 29437, 29695,  \n28689, 17683, 28456,  21114, 17503, 17525,  29437, 29575, 29695,  \n29279, 29437, 29574,  14155, 14156, 10988,  16536, 8701, 8700,  \n29576, 29440, 29697,  7201, 5544, 14295,  10100, 10110, 10098,  \n11874, 21201, 930,  29440, 29439, 29697,  22081, 11946, 15467,  \n16409, 18452, 13257,  6166, 8186, 8185,  16080, 14656, 14847,  \n16002, 16001, 22080,  11525, 18609, 14326,  10995, 20083, 16680,  \n29699, 29443, 29450,  8471, 11671, 16011,  29444, 29700, 29096,  \n29096, 29700, 29445,  13653, 17410, 490,  29700, 25545, 29445,  \n8545, 3408, 14864,  1357, 7364, 7365,  19746, 17463, 7798,  \n6974, 19422, 6975,  25545, 19626, 29446,  4944, 15632, 9274,  \n29445, 25545, 29446,  901, 9467, 5184,  29580, 29698, 29442,  \n29698, 29696, 29442,  4804, 21440, 2589,  2495, 20514, 18889,  \n3837, 11734, 3028,  10240, 28970, 27763,  14277, 18611, 9912,  \n20925, 4243, 21486,  2171, 13812, 15079,  7511, 5378, 18936,  \n29701, 29579, 29578,  12106, 10278, 16630,  29583, 29297, 21566,  \n356, 18020, 357,  2522, 17197, 11122,  19312, 18813, 1351,  \n21500, 3494, 1125,  29101, 29582, 29291,  29582, 29581, 29291,  \n29448, 29582, 29101,  6606, 2354, 19416,  29287, 29448, 29286,  \n2508, 1585, 9207,  6276, 12924, 19742,  29451, 29583, 29293,  \n29293, 29583, 29580,  11256, 18811, 11539,  11099, 6935, 3655,  \n17039, 18121, 8523,  4342, 28302, 18989,  29577, 29702, 29299,  \n29299, 29702, 29452,  2224, 5077, 2082,  29452, 29702, 21737,  \n2481, 12234, 5637,  13009, 14701, 8764,  5894, 18281, 18356,  \n8964, 21254, 8965,  2002, 9192, 7209,  21093, 13630, 15745,  \n21737, 23858, 29107,  3673, 10814, 3674,  21474, 16143, 5457,  \n29449, 9493, 29102,  15111, 12685, 8437,  12001, 18214, 22833,  \n860, 861, 14487,  21171, 19023, 12782,  29703, 22997, 29586,  \n23791, 17320, 25143,  9493, 29453, 29102,  22937, 29588, 29308,  \n13850, 6239, 6240,  29704, 29455, 29588,  21244, 29455, 29704,  \n29455, 21244, 29456,  17312, 7772, 11171,  12653, 14293, 4956,  \n29703, 29458, 29459,  29458, 29703, 29586,  21764, 21072, 17776,  \n29590, 29306, 29305,  4613, 11315, 3235,  9229, 3692, 3693,  \n29295, 29301, 29585,  19849, 20964, 8195,  19175, 4207, 1917,  \n2417, 7261, 19640,  29309, 29588, 29455,  29705, 28924, 29456,  \n9127, 10813, 13002,  29705, 29460, 28924,  9326, 17365, 9325,  \n2121, 18163, 4422,  29706, 29592, 29460,  20573, 13600, 5371,  \n21652, 18155, 4345,  4974, 12041, 3027,  8099, 5719, 5720,  \n19467, 24818, 10722,  29301, 29593, 29585,  17721, 28909, 17040,  \n8453, 12415, 2210,  4497, 14213, 8919,  29459, 29595, 29594,  \n29459, 29307, 29595,  14809, 13573, 9216,  10130, 5029, 9831,  \n29593, 29590, 29774,  13682, 10738, 13385,  5241, 10629, 11495,  \n29114, 29311, 29589,  6469, 13606, 8220,  29595, 29307, 29596,  \n4231, 2950, 5487,  4333, 15692, 15693,  20918, 29298, 28708,  \n21667, 21338, 4551,  13304, 15528, 9571,  10135, 4004, 10136,  \n9365, 4615, 16095,  10603, 5361, 5950,  3281, 5717, 5718,  \n20036, 16802, 1719,  8713, 3190, 19758,  29463, 28083, 29310,  \n4349, 11082, 16307,  3806, 4589, 15788,  613, 15608, 21330,  \n29463, 15393, 29316,  20551, 5836, 10927,  17530, 25529, 21996,  \n24997, 29122, 17258,  15378, 27982, 25149,  10324, 547, 3828,  \n27982, 15378, 25148,  12872, 8662, 14819,  7117, 2513, 2512,  \n9721, 9419, 18795,  12755, 1612, 5422,  10735, 15929, 8547,  \n5501, 12980, 5502,  17941, 5195, 599,  3179, 10387, 10386,  \n10087, 15984, 2434,  23671, 12857, 646,  7343, 7344, 6910,  \n4607, 18443, 7674,  28938, 28739, 29601,  29127, 1251, 29322,  \n7633, 7632, 13266,  12997, 3377, 12403,  17573, 29600, 29320,  \n10749, 10750, 9169,  9616, 5012, 10978,  10225, 20705, 7017,  \n9017, 11324, 14864,  28938, 29710, 29466,  13718, 10263, 10265,  \n29710, 29467, 29466,  29710, 29470, 29467,  29467, 29470, 29468,  \n1810, 9162, 11006,  9338, 13569, 13570,  13393, 15431, 9104,  \n1251, 29469, 16721,  29470, 29602, 29603,  11829, 9485, 9486,  \n9583, 3187, 9584,  29602, 29471, 29603,  26005, 29469, 29129,  \n2260, 14766, 12646,  29471, 29711, 29472,  13209, 9929, 11655,  \n17384, 13180, 14094,  29604, 29472, 29711,  26005, 29130, 29326,  \n29604, 1745, 29473,  28941, 29473, 28194,  8644, 2163, 22159,  \n1806, 5817, 5816,  21208, 15432, 22346,  29131, 21463, 12928,  \n29326, 29325, 5835,  22775, 21229, 13601,  6046, 1015, 6971,  \n2451, 1170, 2452,  15547, 1257, 3894,  9494, 11610, 10199,  \n29327, 28135, 13681,  29327, 13681, 21578,  28575, 18859, 9246,  \n28109, 8449, 29330,  29329, 29712, 29605,  8448, 29132, 29330,  \n20175, 15137, 7963,  29606, 29712, 29329,  468, 28948, 29132,  \n2147, 9864, 18085,  29133, 28948, 468,  23132, 1862, 3644,  \n2260, 4133, 1532,  20985, 16400, 14811,  2390, 14371, 20043,  \n11277, 8370, 13994,  4624, 19344, 15542,  10790, 2478, 1593,  \n3859, 14431, 4060,  5714, 17687, 5486,  29475, 17314, 29474,  \n7968, 2941, 7725,  24694, 29149, 16647,  26074, 28754, 14913,  \n24548, 29334, 29137,  305, 9394, 19927,  13877, 6679, 10261,  \n29336, 29334, 14267,  16587, 10419, 17562,  29334, 13011, 14267,  \n12105, 16062, 7385,  28955, 29334, 29336,  14016, 2919, 18735,  \n13352, 8147, 3987,  29138, 29336, 29608,  29140, 29609, 29476,  \n6176, 18516, 12240,  6778, 8708, 19017,  5884, 17227, 3964,  \n29611, 29610, 29142,  29143, 29138, 29608,  29477, 29612, 29713,  \n29143, 29608, 16171,  10074, 786, 17440,  29714, 29612, 29338,  \n29714, 29338, 29339,  29613, 29714, 29339,  29339, 29340, 29341,  \n29715, 29479, 29342,  29341, 29478, 29613,  18245, 7456, 18332,  \n29478, 29716, 29613,  29144, 29716, 29478,  29144, 29146, 29716,  \n8097, 8317, 6339,  3548, 14312, 8276,  29715, 29717, 29480,  \n2481, 6857, 10599,  9715, 2942, 10928,  7532, 9216, 3239,  \n5641, 2978, 8340,  10304, 21137, 8555,  18635, 11208, 11207,  \n28902, 27941, 3426,  29480, 29717, 29481,  13701, 5194, 5193,  \n843, 18531, 3770,  12780, 12779, 16137,  29343, 29481, 29718,  \n2616, 1200, 8846,  9150, 8668, 20968,  14184, 6511, 6510,  \n4886, 25522, 9508,  6091, 28625, 809,  25562, 17503, 21114,  \n20955, 17011, 2213,  25088, 26958, 1887,  1830, 20168, 13630,  \n28826, 23100, 23101,  17650, 24724, 6495,  3082, 20325, 21364,  \n25467, 28967, 17089,  12092, 25425, 25091,  24021, 4077, 28067,  \n5180, 14707, 511,  12310, 20231, 8490,  10411, 10410, 4597,  \n5778, 5777, 3861,  28318, 28315, 12519,  29026, 5659, 28993,  \n18523, 27990, 11276,  12954, 7878, 21192,  29148, 12121, 6720,  \n28610, 29482, 28613,  17954, 13748, 17955,  7287, 1659, 7285,  \n3649, 10378, 12042,  26883, 28902, 26360,  12176, 28746, 28349,  \n19833, 21114, 12693,  2036, 2035, 19165,  22822, 28968, 29719,  \n12477, 21887, 11679,  29719, 29345, 29482,  28610, 29719, 29482,  \n336, 6642, 6643,  18473, 21106, 11600,  18083, 10364, 16868,  \n12398, 18421, 11450,  11310, 11312, 1445,  28315, 7203, 19594,  \n25284, 20486, 28610,  22822, 29483, 28968,  10883, 7403, 14391,  \n26310, 29346, 29617,  29617, 26308, 26310,  8918, 11416, 6231,  \n28547, 6313, 29153,  1487, 16802, 844,  5487, 14493, 4231,  \n19470, 25867, 21030,  8486, 14163, 1688,  29484, 29618, 28551,  \n10349, 14002, 7965,  11737, 2834, 15781,  8733, 18276, 16824,  \n10722, 27990, 19467,  29346, 23806, 29617,  28980, 29153, 22711,  \n14483, 8962, 8896,  5660, 10297, 18447,  29346, 29347, 23806,  \n10319, 10561, 9570,  6116, 14466, 4820,  19942, 17081, 7764,  \n28337, 29485, 17464,  13596, 13595, 14121,  21390, 23470, 20463,  \n17934, 29154, 28553,  14399, 13453, 21568,  21216, 29347, 13946,  \n29347, 28543, 13946,  7212, 9549, 3446,  11537, 22296, 10635,  \n29489, 29352, 23952,  25153, 20123, 27752,  4703, 4704, 1201,  \n12887, 17762, 14116,  7404, 16659, 2307,  8260, 15995, 14054,  \n29721, 29488, 29489,  15670, 6199, 20970,  17100, 17079, 11156,  \n29720, 29490, 29487,  29720, 29487, 29350,  29351, 29488, 29720,  \n29720, 29488, 29721,  5386, 22813, 14859,  8490, 457, 2827,  \n29621, 29348, 29491,  29348, 29349, 29491,  20142, 3661, 13131,  \n15817, 22062, 19588,  11269, 6343, 14301,  29722, 29353, 29621,  \n7914, 7940, 13121,  16804, 19580, 9644,  14153, 14154, 4406,  \n3640, 10385, 6660,  12064, 15744, 16527,  3545, 1221, 1220,  \n28554, 27962, 29159,  11116, 3496, 852,  29723, 29354, 29353,  \n29353, 29722, 29723,  4417, 13548, 19778,  11480, 28564, 20011,  \n5604, 5605, 17912,  16376, 18435, 11802,  4445, 8281, 21745,  \n3337, 3336, 9828,  29622, 29493, 29354,  20727, 20729, 8067,  \n17313, 15514, 11156,  21828, 377, 3802,  29622, 29354, 29723,  \n6046, 9195, 12482,  11673, 8905, 11674,  4180, 2611, 3394,  \n10335, 16673, 1764,  29623, 29622, 29786,  10346, 1536, 9563,  \n29622, 29623, 29494,  27183, 29623, 29786,  11348, 6616, 7818,  \n12470, 9065, 9064,  28783, 29492, 19003,  29724, 29623, 27183,  \n22887, 17533, 21070,  29623, 29496, 29495,  29624, 29496, 29623,  \n29624, 29623, 29724,  7237, 4721, 15273,  17523, 17637, 2408,  \n3373, 20513, 12864,  4518, 4517, 21832,  9308, 19908, 5104,  \n21394, 5864, 16585,  19824, 19087, 19086,  29625, 29624, 29725,  \n29725, 29726, 29625,  17768, 7008, 2331,  13533, 13433, 29168,  \n1399, 3158, 14474,  29625, 29726, 29497,  8260, 7378, 15995,  \n29726, 22432, 29497,  29357, 29498, 22432,  29498, 29497, 22432,  \n1706, 14761, 14760,  29166, 28787, 29169,  21735, 18386, 5037,  \n9796, 15055, 9794,  22013, 21184, 9518,  6725, 684, 10681,  \n16873, 29169, 19540,  5140, 13950, 22711,  19096, 2350, 4846,  \n17975, 17201, 12121,  16096, 15354, 15353,  12678, 8071, 4417,  \n11097, 11096, 11073,  14984, 5705, 5170,  22204, 19992, 28990,  \n13644, 2278, 2280,  20108, 12541, 15618,  29626, 28573, 6553,  \n7442, 27585, 18117,  11572, 15724, 1300,  15221, 10384, 10383,  \n11388, 12748, 5453,  5095, 11576, 6847,  8206, 7369, 7370,  \n7149, 2127, 4700,  29171, 28790, 28945,  17251, 8644, 22159,  \n19064, 747, 21258,  20481, 2078, 13803,  18642, 15345, 9328,  \n21080, 14042, 10497,  15996, 29172, 28992,  3946, 22025, 12841,  \n17869, 13193, 2728,  14310, 20922, 11894,  13375, 4883, 16578,  \n4903, 10215, 16648,  10438, 16371, 5865,  23848, 17255, 28574,  \n553, 28991, 24179,  2457, 11256, 14160,  14062, 12984, 8642,  \n11077, 19978, 11078,  16070, 15246, 587,  11622, 15841, 2700,  \n24055, 23849, 29360,  2799, 2556, 15274,  4064, 19306, 5367,  \n15317, 1343, 15316,  17098, 765, 20159,  13185, 21209, 645,  \n28794, 29173, 8469,  28017, 11319, 19548,  15873, 6864, 4823,  \n28794, 8469, 25205,  600, 5279, 21328,  12357, 3716, 2145,  \n6920, 11341, 500,  14897, 19220, 3473,  16147, 11716, 6071,  \n3049, 22775, 13601,  1124, 19512, 14941,  18639, 3619, 3618,  \n15523, 12265, 19375,  11803, 16534, 11804,  23216, 28366, 19197,  \n14759, 19458, 13640,  17974, 17655, 16528,  28176, 28797, 21598,  \n28797, 21909, 21598,  16681, 13904, 19675,  385, 7210, 11049,  \n29361, 21909, 28797,  3668, 20082, 2063,  761, 760, 15264,  \n1553, 13592, 3009,  6349, 6347, 6288,  28179, 29362, 27977,  \n22391, 28798, 7637,  29504, 25422, 20127,  15461, 17533, 13537,  \n22633, 21030, 6758,  5602, 15283, 9396,  10083, 9954, 5301,  \n28799, 27782, 29176,  21030, 6724, 6758,  28998, 29627, 29361,  \n13431, 18175, 17961,  4429, 19413, 20224,  17946, 3145, 327,  \n5613, 13765, 15294,  9111, 1966, 16524,  25873, 29175, 12564,  \n29364, 28801, 21553,  17810, 17811, 2329,  9945, 23164, 10517,  \n8841, 2669, 1289,  29364, 21553, 21552,  5451, 22942, 5452,  \n3971, 22267, 10808,  4066, 11587, 14596,  18693, 772, 18692,  \n29363, 28999, 29000,  29176, 28804, 1765,  11005, 680, 29155,  \n23223, 28805, 28583,  28611, 21489, 25423,  21644, 22576, 4360,  \n15306, 16281, 12577,  28803, 27981, 29364,  22231, 17337, 29505,  \n22231, 29505, 29364,  29505, 28803, 29364,  13413, 2541, 13484,  \n10308, 8017, 17175,  29000, 29506, 29727,  29000, 29001, 29506,  \n21513, 20062, 9723,  15699, 4741, 13600,  9976, 2844, 3845,  \n13392, 11457, 15960,  2626, 12970, 18139,  6032, 23410, 18054,  \n7375, 696, 7142,  29628, 29180, 28585,  29182, 28369, 29508,  \n29509, 29002, 25369,  18290, 6812, 2101,  16118, 22178, 12965,  \n13586, 13312, 19181,  13750, 20365, 2502,  7920, 1075, 7921,  \n29629, 29180, 29628,  16656, 7242, 8487,  8417, 733, 7031,  \n3884, 18099, 2985,  26965, 8977, 2163,  13084, 19251, 19252,  \n2840, 18011, 6499,  29377, 26285, 29629,  13511, 3298, 3297,  \n11109, 2863, 18604,  11594, 21253, 19247,  767, 17098, 20560,  \n29630, 28814, 7047,  9184, 9287, 10962,  22919, 28810, 29184,  \n28808, 29003, 29366,  29629, 26284, 28372,  3006, 13571, 24596,  \n29513, 27799, 29186,  1087, 1088, 5980,  18726, 12144, 20478,  \n10573, 12947, 4323,  1725, 21355, 11363,  23974, 6473, 3806,  \n18800, 8956, 10348,  8203, 11773, 2592,  21783, 6491, 10919,  \n3924, 9023, 18092,  22989, 11313, 26898,  16127, 20412, 11210,  \n16530, 16529, 20735,  5095, 18602, 18308,  17378, 10126, 17664,  \n16233, 3965, 16234,  12651, 21378, 9439,  20128, 1228, 5261,  \n13406, 11858, 14164,  29515, 23661, 29367,  10553, 28817, 29631,  \n880, 6207, 17694,  15392, 13647, 13722,  15303, 15075, 7604,  \n16636, 10541, 7450,  29368, 29514, 20081,  8394, 1483, 27991,  \n10341, 28026, 13989,  29368, 20081, 29633,  10384, 29633, 20081,  \n10020, 7989, 7988,  19222, 20900, 19223,  29368, 29633, 29634,  \n29008, 29632, 16947,  18816, 4149, 24007,  20758, 29004, 29005,  \n24898, 29008, 16947,  6699, 9599, 11052,  29369, 29634, 29728,  \n1679, 17756, 1678,  29188, 29634, 29369,  19239, 6866, 6562,  \n19183, 12024, 12711,  6327, 8779, 19398,  29728, 29635, 29369,  \n21671, 23667, 14582,  20203, 21764, 17776,  19910, 15922, 13461,  \n9242, 29302, 18977,  20677, 19678, 16231,  29637, 29009, 29189,  \n29729, 28380, 29636,  21255, 29729, 29636,  14525, 19618, 11337,  \n5028, 14639, 16464,  12732, 535, 8632,  16081, 12875, 20128,  \n751, 13569, 322,  5605, 11785, 11786,  29011, 29635, 29372,  \n29191, 29192, 26198,  2405, 9455, 9454,  29636, 29191, 29731,  \n26198, 29731, 29191,  29730, 29372, 29635,  29637, 29371, 29009,  \n29372, 29730, 29517,  13014, 19878, 22740,  2384, 19876, 2385,  \n29370, 12843, 19837,  16617, 27347, 609,  26198, 29192, 27794,  \n17467, 17468, 5222,  20674, 12087, 7118,  18295, 18719, 13975,  \n20927, 4238, 4910,  8511, 29192, 29374,  15321, 22205, 15087,  \n29375, 29734, 29374,  13884, 3803, 7892,  4011, 19904, 12638,  \n3240, 6334, 5119,  24410, 29371, 29732,  29375, 29376, 29736,  \n29737, 29736, 29376,  14230, 10701, 8809,  29376, 29641, 29737,  \n21477, 10700, 19372,  22355, 1077, 9502,  25848, 29203, 29644,  \n20485, 18526, 18523,  14121, 13595, 10836,  3811, 10651, 11486,  \n29738, 29523, 29201,  3571, 29738, 29201,  3571, 29201, 25848,  \n29519, 29379, 29642,  29521, 24410, 22565,  1582, 10688, 23529,  \n5701, 3369, 22459,  29521, 29371, 24410,  29385, 29523, 29739,  \n29644, 29203, 29524,  5987, 7271, 15947,  8707, 569, 7159,  \n6580, 22122, 6089,  4495, 4494, 16370,  29385, 29201, 29523,  \n29386, 29740, 29520,  28821, 19551, 29198,  29741, 29742, 29643,  \n1751, 12760, 20206,  25125, 24252, 29383,  13008, 13009, 7624,  \n20087, 16706, 13158,  16350, 2067, 25015,  29381, 29520, 29380,  \n29520, 29381, 29386,  11529, 20606, 11950,  6068, 6169, 18974,  \n7386, 1065, 4860,  9117, 13873, 13872,  12880, 849, 4174,  \n8953, 14572, 7136,  25680, 19974, 14177,  8474, 477, 9147,  \n29741, 29643, 29652,  12092, 25091, 20955,  13126, 16347, 23948,  \n7122, 6809, 8456,  9380, 6346, 9381,  5249, 9125, 9124,  \n6605, 12774, 12775,  29739, 29741, 29526,  14102, 4053, 14101,  \n29739, 29526, 29385,  25125, 29529, 17841,  15457, 9178, 9177,  \n29199, 29649, 29647,  7833, 5603, 21092,  19818, 25143, 8796,  \n22418, 3158, 357,  29650, 29021, 29646,  13141, 7342, 8146,  \n29741, 29652, 29526,  7108, 9749, 2233,  9543, 11866, 21619,  \n5608, 1303, 4824,  29018, 19547, 29382,  28397, 29200, 16250,  \n8029, 21887, 15217,  20881, 19892, 13221,  29529, 25125, 29033,  \n1181, 6864, 1182,  6799, 3973, 11081,  29649, 29654, 29743,  \n13956, 8859, 16176,  6244, 7483, 6222,  5144, 10255, 19923,  \n16250, 20672, 28397,  29387, 29654, 29649,  15065, 29388, 29204,  \n13907, 8317, 8098,  14693, 14694, 13195,  29205, 29650, 29651,  \n15065, 29653, 29388,  15065, 29204, 20672,  9424, 8828, 10019,  \n18353, 18780, 3142,  9371, 4743, 21433,  12209, 526, 4471,  \n29653, 29533, 29210,  28011, 17310, 18421,  23473, 1736, 13047,  \n29656, 29205, 29651,  29532, 28614, 29533,  29533, 29744, 29532,  \n2072, 15630, 14340,  29659, 29654, 29392,  22246, 29657, 29656,  \n20645, 8007, 1548,  11694, 29025, 29212,  11694, 29212, 28852,  \n28852, 29212, 29389,  29532, 28852, 29389,  11721, 6317, 11719,  \n29531, 29225, 21359,  25372, 20521, 29037,  15926, 748, 8436,  \n4964, 7230, 3471,  1344, 15529, 6354,  18116, 17891, 10574,  \n15485, 28542, 13069,  8189, 2655, 12865,  29745, 29660, 29658,  \n4495, 16370, 11855,  29661, 29660, 29745,  1369, 8775, 7523,  \n20055, 29225, 27874,  26424, 25713, 4650,  5739, 13503, 28340,  \n3552, 9794, 27874,  6783, 15115, 20195,  4264, 7664, 17236,  \n16123, 12550, 20002,  29661, 29746, 29662,  8997, 13910, 3380,  \n15033, 29662, 29746,  12430, 10217, 13688,  3085, 10946, 8983,  \n4832, 3356, 2424,  12179, 3641, 3640,  8995, 9722, 22959,  \n23491, 8310, 4859,  11327, 5672, 15351,  5256, 5257, 21046,  \n1309, 10133, 20521,  15171, 22074, 18974,  29042, 21122, 25519,  \n18976, 6061, 19019,  9624, 29393, 29227,  29396, 29662, 29665,  \n7601, 25519, 21122,  29664, 29227, 29043,  15324, 3285, 15805,  \n21728, 454, 6830,  29398, 29664, 29043,  4375, 29041, 18260,  \n7642, 12783, 22770,  11648, 15630, 21264,  19634, 11157, 21962,  \n11133, 15540, 12165,  3396, 10317, 11581,  9624, 29664, 29398,  \n29665, 29539, 29538,  4182, 3911, 3910,  8798, 19402, 302,  \n13910, 8997, 5695,  1259, 3562, 3561,  6385, 6483, 10426,  \n18087, 9693, 3775,  15224, 1849, 1848,  29666, 29791, 22848,  \n29747, 29791, 29666,  6071, 5187, 19593,  12527, 21107, 12526,  \n11344, 12563, 13954,  29539, 3032, 29666,  3032, 29747, 29666,  \n27990, 10722, 10723,  29666, 22848, 29541,  20713, 3431, 6934,  \n11990, 13446, 11991,  29669, 29540, 29667,  10578, 22364, 21062,  \n2223, 13274, 6612,  8648, 16603, 17276,  29050, 9074, 21320,  \n17711, 10320, 9547,  29238, 29050, 21320,  807, 806, 9080,  \n14870, 29542, 21631,  16054, 17611, 13263,  13452, 14870, 21631,  \n9625, 19568, 5248,  19440, 17455, 13355,  29669, 29671, 29540,  \n21133, 6169, 6068,  29669, 29672, 29671,  29669, 29748, 29672,  \n16161, 20342, 4993,  11798, 3957, 17456,  3902, 3901, 21369,  \n20680, 6540, 4526,  12608, 7522, 13540,  4626, 22903, 15847,  \n2454, 10396, 14367,  29674, 29671, 18007,  18007, 29671, 29672,  \n29674, 29237, 29671,  29542, 29231, 11652,  8492, 10529, 10530,  \n16497, 2855, 2854,  15855, 1565, 15856,  390, 11724, 19969,  \n19162, 17453, 9048,  10184, 1784, 12958,  16147, 19593, 10355,  \n29668, 29548, 29547,  29409, 29548, 22939,  29750, 29545, 29249,  \n29749, 29545, 29750,  25467, 23001, 26810,  4732, 5632, 15339,  \n5016, 5015, 5895,  9699, 9701, 14580,  29752, 29750, 29249,  \n1295, 16149, 29414,  12854, 15777, 12855,  14980, 1763, 2386,  \n8913, 3225, 11922,  21307, 11429, 11237,  5664, 14490, 5713,  \n29677, 29407, 29676,  7603, 15815, 14973,  6174, 13084, 3569,  \n6383, 3023, 1715,  19596, 3342, 12890,  7463, 15026, 539,  \n29678, 29677, 23689,  29244, 29240, 29678,  29054, 3797, 17058,  \n4256, 16613, 5708,  3456, 16066, 20018,  16038, 2940, 16039,  \n27112, 29678, 23689,  7329, 18696, 19406,  14885, 12776, 13817,  \n2843, 19510, 14486,  4623, 11380, 11379,  29753, 29411, 29551,  \n29753, 29551, 29681,  11996, 13005, 2773,  8030, 15238, 8031,  \n19145, 6307, 22595,  10165, 2802, 9533,  22989, 4035, 25565,  \n5404, 747, 19064,  14655, 947, 487,  29415, 29552, 29754,  \n29552, 29680, 29754,  2969, 28557, 9001,  29553, 29755, 29681,  \n13383, 29550, 29410,  9845, 17135, 23267,  4206, 4207, 20970,  \n20561, 18071, 15361,  7827, 10066, 11107,  29415, 29754, 29756,  \n1857, 11924, 20847,  20141, 7494, 4742,  6269, 1216, 5455,  \n20081, 28816, 12226,  29243, 29247, 29550,  3797, 29245, 9485,  \n29756, 29556, 29415,  9050, 18528, 21132,  11997, 11175, 8256,  \n6341, 8042, 22966,  13659, 22402, 17761,  20404, 4682, 15826,  \n29682, 29066, 29683,  13738, 18524, 7952,  2249, 9131, 8598,  \n11969, 29243, 29550,  3972, 6305, 22879,  25537, 29553, 29416,  \n10152, 10151, 16129,  20423, 4128, 19257,  19899, 18140, 23011,  \n29757, 29683, 29555,  7711, 10082, 17703,  9789, 26074, 9790,  \n11794, 29257, 29758,  29068, 25537, 29416,  29555, 29760, 29757,  \n29557, 29760, 29555,  29257, 29069, 29758,  28315, 19021, 7203,  \n11538, 7004, 18345,  1873, 3525, 4346,  29554, 29759, 29418,  \n17743, 29263, 29419,  1732, 3639, 17278,  12154, 15048, 8908,  \n29069, 18542, 29758,  18201, 2736, 18877,  10996, 9991, 10458,  \n7975, 3356, 2264,  23073, 8498, 8497,  17743, 29419, 22019,  \n1744, 6550, 1745,  6267, 10177, 18045,  22019, 29419, 29420,  \n28315, 28318, 19021,  5663, 20454, 5358,  29761, 29760, 29558,  \n29760, 29557, 29558,  29362, 16515, 21553,  15807, 5508, 5507,  \n5113, 7458, 1737,  29762, 29761, 29763,  11364, 21830, 2794,  \n29558, 29422, 29761,  22226, 5680, 18579,  7188, 17071, 19520,  \n29560, 28880, 29421,  9984, 9365, 7548,  13774, 15534, 6754,  \n11444, 21095, 13021,  12162, 28302, 22370,  18423, 19304, 18424,  \n29559, 29684, 27167,  26302, 29685, 15101,  26302, 29261, 29685,  \n28881, 26494, 10284,  10284, 29425, 28881,  388, 389, 11999,  \n29079, 28880, 29560,  10366, 8551, 7983,  27167, 29684, 16996,  \n17925, 4871, 19917,  29729, 13560, 21379,  4437, 5533, 4621,  \n16008, 14013, 13304,  17335, 29684, 29424,  16254, 1528, 2285,  \n29562, 29685, 29265,  5198, 29426, 29266,  4996, 4995, 12581,  \n22628, 14099, 21712,  17335, 29424, 29686,  12171, 8229, 8230,  \n10095, 12071, 8683,  28670, 23210, 26488,  29425, 23210, 28670,  \n19487, 13670, 1401,  17632, 13004, 11996,  29562, 29265, 18876,  \n1542, 9555, 9554,  20421, 2645, 5852,  17227, 16607, 16606,  \n10133, 3427, 20521,  7856, 16339, 8206,  3593, 20618, 14032,  \n13495, 17448, 1937,  29564, 29688, 29686,  29688, 7555, 29686,  \n15083, 3929, 11453,  29568, 29764, 29429,  29765, 29566, 29764,  \n29429, 29764, 29566,  11250, 13949, 18756,  15150, 2276, 19694,  \n1424, 17540, 6597,  18637, 18636, 21503,  3287, 20925, 11027,  \n10777, 16038, 16039,  29566, 29765, 29567,  19594, 8228, 3935,  \n2648, 5745, 16549,  29567, 29765, 29570,  29689, 29270, 29691,  \n2649, 18056, 19268,  29565, 28675, 22066,  19919, 17824, 12156,  \n20197, 5193, 12184,  7132, 13279, 28886,  7837, 13196, 17194,  \n29567, 29570, 29430,  17041, 11774, 3914,  12464, 4299, 4298,  \n29271, 29690, 29270,  19915, 345, 11225,  16053, 12299, 22735,  \n11639, 10131, 6878,  7287, 20206, 23103,  17859, 15131, 382,  \n14127, 4603, 18925,  29278, 29570, 29572,  22823, 16681, 20403,  \n23674, 29569, 29571,  11327, 7322, 5672,  22225, 28681, 28888,  \n10851, 2415, 9796,  1576, 18961, 1468,  29434, 28681, 22225,  \n1037, 17931, 16487,  15928, 10594, 2672,  29693, 29571, 29433,  \n14862, 22083, 16651,  2960, 2959, 14953,  20024, 29087, 29438,  \n29766, 20024, 29438,  29694, 29087, 20024,  18238, 18919, 7930,  \n29693, 29767, 29571,  1724, 28055, 29434,  2526, 14357, 2527,  \n29438, 29572, 29766,  15172, 13038, 9360,  10676, 3225, 8913,  \n6433, 3556, 3555,  29768, 29767, 29693,  3953, 21794, 24533,  \n8512, 8513, 5105,  20139, 6208, 13790,  29573, 29768, 29693,  \n17953, 2057, 18697,  15212, 4134, 6903,  16788, 29695, 29575,  \n29574, 29695, 29768,  29574, 29768, 29573,  29026, 28993, 26498,  \n8937, 17560, 1487,  22699, 13200, 13199,  2147, 2151, 5332,  \n8364, 10912, 15791,  29769, 19185, 29441,  10920, 16942, 11591,  \n29090, 29282, 8629,  883, 19034, 14280,  29441, 29696, 29769,  \n28825, 7737, 20483,  29697, 29699, 29576,  14421, 6018, 21613,  \n11045, 7704, 11044,  29576, 29699, 29450,  8330, 410, 411,  \n29699, 29499, 29444,  29499, 29700, 29444,  21080, 29696, 29698,  \n711, 29091, 29094,  29699, 29444, 29443,  12676, 13839, 13795,  \n21610, 12183, 4342,  28268, 19132, 19133,  7295, 8029, 15217,  \n15397, 15398, 21849,  29579, 29701, 24771,  28318, 12519, 18960,  \n20838, 14036, 16245,  29577, 29446, 19626,  12817, 20014, 15396,  \n4545, 11407, 4522,  5210, 16508, 4836,  29579, 21566, 29297,  \n5110, 1985, 5111,  29580, 29583, 29698,  5060, 1184, 23682,  \n20687, 1162, 20688,  19183, 16819, 12024,  29702, 29577, 3261,  \n19884, 22338, 12042,  10717, 29702, 3261,  29770, 29701, 29578,  \n15225, 15596, 11124,  17740, 20991, 22232,  29581, 29447, 29291,  \n29771, 29582, 29448,  29581, 29582, 29771,  5878, 820, 819,  \n29448, 7007, 29771,  19972, 16629, 18606,  16050, 4895, 1554,  \n29702, 10717, 21737,  398, 14621, 6915,  19527, 12918, 11374,  \n13903, 29701, 29770,  24304, 10431, 10430,  14069, 8431, 6194,  \n17909, 23075, 29454,  17909, 29454, 29584,  29447, 10507, 17909,  \n29447, 17909, 29584,  6154, 15126, 22876,  9312, 14702, 858,  \n29454, 23075, 22446,  1041, 9469, 1040,  23858, 21737, 2371,  \n16890, 7012, 14552,  23858, 22937, 29107,  21007, 9656, 760,  \n19958, 21721, 5160,  13989, 28026, 2570,  11007, 6384, 6383,  \n29585, 29770, 29578,  21749, 10593, 20049,  11321, 2336, 12033,  \n29454, 22446, 6528,  28914, 29454, 6528,  11334, 6519, 4354,  \n22937, 29704, 29588,  10854, 3852, 2631,  9553, 25581, 26299,  \n12142, 10161, 3465,  22997, 29703, 20020,  29590, 29305, 29587,  \n16864, 7893, 8430,  29587, 29773, 29590,  15832, 12881, 16972,  \n29770, 29585, 29772,  15989, 1294, 15450,  21526, 21643, 3620,  \n11629, 9933, 6775,  17094, 14786, 17609,  29705, 29456, 4002,  \n29706, 29705, 4003,  29706, 29460, 29705,  3085, 8983, 2545,  \n1699, 18999, 1207,  29707, 5282, 29594,  20020, 29459, 29594,  \n809, 28625, 16178,  20020, 29703, 29459,  3264, 12784, 12783,  \n1660, 19063, 13697,  29772, 29585, 29593,  15367, 12066, 9709,  \n13366, 660, 13365,  13244, 3368, 14293,  20223, 16602, 13459,  \n29706, 29589, 29592,  3952, 9783, 17517,  22328, 29706, 567,  \n22328, 29457, 29706,  29457, 29589, 29706,  12854, 11064, 8418,  \n19394, 14200, 5730,  805, 13554, 9412,  29119, 29707, 29594,  \n17969, 26202, 4009,  11918, 12993, 21790,  29774, 29772, 29593,  \n3421, 11085, 948,  13481, 16327, 1636,  11646, 12167, 19493,  \n29310, 28914, 14324,  14194, 8603, 7105,  5486, 9086, 5330,  \n21730, 6271, 3073,  29298, 29775, 17040,  29775, 29298, 20918,  \n8566, 9638, 15907,  2065, 4358, 6180,  6368, 12655, 6366,  \n29775, 29796, 29776,  20918, 29796, 29775,  4447, 2609, 9645,  \n5248, 19568, 11371,  28708, 28910, 29591,  11564, 9744, 20691,  \n4618, 15986, 9843,  20837, 8194, 5970,  28742, 29777, 29775,  \n29775, 29776, 29795,  7885, 23167, 7886,  28742, 29775, 29795,  \n18371, 11599, 11598,  22422, 8601, 1103,  29463, 29310, 15393,  \n4176, 14848, 13171,  8589, 12995, 14641,  28557, 11312, 12863,  \n15393, 29465, 29316,  18027, 5268, 1023,  10183, 3239, 3238,  \n29598, 29597, 24738,  29778, 29598, 24738,  29598, 29778, 29599,  \n3577, 19204, 6544,  10014, 8382, 8602,  29599, 20505, 29125,  \n26391, 29125, 20505,  21875, 6419, 17935,  17378, 15857, 5458,  \n20991, 23521, 22232,  7607, 3002, 6483,  8525, 18100, 8389,  \n15427, 29319, 26391,  13296, 3937, 570,  24818, 24986, 10722,  \n28739, 29600, 29601,  1560, 15421, 11877,  6116, 12418, 7304,  \n11288, 12798, 9017,  18595, 11266, 1621,  29321, 5585, 29320,  \n29320, 5585, 29709,  29709, 17573, 29320,  10625, 15220, 2658,  \n3158, 7607, 9558,  14252, 4736, 6041,  10664, 3815, 9237,  \n4783, 14486, 17128,  16035, 16258, 7415,  26005, 16721, 29469,  \n12942, 13415, 16387,  29471, 29602, 17531,  17531, 29711, 29471,  \n9404, 17871, 10737,  26109, 20462, 21584,  29604, 29711, 24911,  \n29604, 24911, 1745,  10060, 19559, 15266,  16816, 1186, 2145,  \n28941, 28194, 21463,  969, 17004, 21151,  24574, 19187, 6394,  \n3629, 16551, 11687,  29325, 29328, 5548,  29779, 29328, 29605,  \n6563, 5841, 15256,  29779, 29605, 29712,  21526, 28943, 21578,  \n28751, 28943, 6999,  12691, 12690, 21575,  9036, 4795, 9043,  \n18695, 19406, 18696,  11709, 18928, 22872,  29132, 8448, 468,  \n21076, 6225, 21754,  13754, 6055, 18187,  29607, 29474, 29606,  \n26541, 29332, 10249,  11211, 22571, 4079,  4503, 7072, 4504,  \n14604, 7689, 16898,  21476, 14938, 7320,  28312, 28522, 25387,  \n29135, 28312, 19639,  20584, 13747, 10821,  17077, 17915, 22277,  \n9789, 24548, 29136,  12199, 306, 9760,  18293, 9803, 29335,  \n4005, 11432, 13838,  29335, 9803, 29475,  10530, 1134, 8492,  \n29139, 5169, 29337,  29336, 6307, 29608,  379, 15381, 19199,  \n29139, 29476, 5169,  29609, 29610, 29780,  29780, 29610, 29611,  \n10976, 4307, 5489,  10596, 4013, 7568,  29026, 26498, 18990,  \n29477, 29713, 29611,  18547, 22955, 5808,  29342, 29143, 16171,  \n5129, 5128, 17869,  8504, 16973, 19846,  4342, 12183, 5179,  \n20215, 9619, 16847,  12341, 12340, 16102,  23071, 1808, 13799,  \n20813, 8606, 14394,  29715, 29480, 29479,  3607, 18899, 13467,  \n19912, 2751, 1781,  29614, 29716, 29146,  24821, 17847, 23904,  \n14358, 13836, 8677,  29717, 29718, 29481,  29718, 29615, 29343,  \n10095, 13820, 21149,  14046, 13930, 14045,  11264, 27421, 24980,  \n9154, 1825, 16639,  28603, 6414, 22592,  6435, 5302, 5303,  \n11508, 6707, 15248,  23073, 8497, 16437,  21176, 25594, 10032,  \n12743, 15111, 16693,  10511, 10513, 17693,  12092, 25424, 25425,  \n18724, 9783, 3951,  7474, 19846, 1777,  16519, 9092, 3448,  \n22001, 11211, 4079,  2438, 2439, 15166,  17266, 9610, 8750,  \n11319, 9751, 29708,  10722, 24986, 26468,  9331, 8944, 19960,  \n6758, 27995, 24240,  8351, 12545, 8963,  12545, 29687, 12544,  \n9370, 29086, 21998,  12808, 4719, 20597,  21785, 28768, 6414,  \n7099, 7816, 18647,  19207, 3500, 3154,  785, 14203, 14839,  \n4034, 29719, 28610,  29756, 5171, 1464,  18335, 4192, 8760,  \n21645, 16056, 565,  23001, 12058, 26810,  23001, 4650, 12058,  \n16966, 3888, 15948,  24240, 27995, 24985,  9501, 2998, 5048,  \n29620, 25462, 24686,  23272, 28611, 21221,  29620, 25149, 25462,  \n27995, 6758, 6723,  23742, 17216, 3679,  16618, 14255, 12547,  \n29655, 28014, 25529,  28611, 29152, 21221,  29150, 27950, 13866,  \n4689, 4690, 3283,  853, 4697, 7472,  28017, 19548, 28014,  \n14791, 3036, 15215,  13380, 7823, 19850,  16428, 11699, 1326,  \n1456, 3505, 1455,  2299, 23851, 18991,  26308, 29617, 27347,  \n29483, 6313, 28547,  29150, 6925, 27763,  11740, 12976, 14314,  \n29618, 29151, 29616,  15785, 4172, 22317,  19122, 4235, 6790,  \n13314, 19032, 17803,  504, 22321, 18517,  10275, 18529, 10276,  \n13359, 10083, 10084,  1444, 11310, 1445,  17374, 7844, 4751,  \n29617, 608, 27347,  15223, 2205, 2206,  12092, 22785, 25424,  \n12720, 6522, 13917,  13350, 7566, 7567,  5332, 2151, 18171,  \n13988, 16682, 22823,  11087, 14162, 4812,  6033, 4802, 17880,  \n22344, 12736, 20428,  19329, 16360, 698,  29617, 23806, 608,  \n7107, 15244, 16303,  5584, 2123, 1376,  5999, 19646, 11300,  \n29486, 29154, 18720,  17464, 17934, 28553,  15642, 8306, 12332,  \n3941, 1369, 7522,  18371, 15368, 18557,  19890, 2619, 2618,  \n8376, 2548, 3956,  15510, 15512, 18000,  14116, 4487, 12887,  \n13056, 28150, 29156,  29489, 23952, 24405,  16669, 17580, 672,  \n5328, 4665, 8636,  12966, 12965, 22178,  29781, 29720, 29782,  \n2696, 22016, 2695,  8490, 17702, 457,  29782, 29720, 29721,  \n4015, 10629, 5241,  8160, 8946, 4648,  25594, 21175, 28375,  \n3873, 11042, 11043,  17652, 20004, 20005,  9551, 14125, 3670,  \n29781, 29783, 29490,  29781, 29490, 29720,  2162, 6866, 26965,  \n29783, 29491, 29490,  22989, 25565, 24390,  28554, 29159, 13346,  \n29491, 29722, 29621,  9318, 2201, 12877,  15322, 24304, 10430,  \n29491, 29784, 29722,  17885, 6742, 10013,  29722, 29785, 29723,  \n29722, 29784, 29785,  21930, 29492, 22147,  28332, 17409, 25706,  \n6817, 20554, 15956,  18327, 9159, 790,  14348, 9313, 9343,  \n29785, 29786, 29723,  8487, 14398, 9342,  28347, 14138, 29159,  \n29786, 29622, 29723,  18187, 6054, 13755,  11269, 12602, 4332,  \n2661, 17196, 11758,  3575, 15779, 2853,  29687, 25122, 12544,  \n4634, 29161, 4635,  21839, 17472, 17084,  14486, 19510, 2467,  \n4635, 29161, 28468,  5925, 7587, 7586,  13538, 28350, 29168,  \n20465, 13167, 8398,  29725, 29624, 29724,  11608, 28569, 11607,  \n29161, 29166, 28468,  21813, 7649, 15283,  12103, 11355, 1709,  \n2076, 3048, 24760,  1619, 12337, 20503,  13551, 11525, 6049,  \n21851, 1555, 12835,  12910, 5161, 13975,  18124, 7812, 21546,  \n6706, 5292, 6953,  21427, 28468, 29169,  16225, 20902, 6666,  \n2182, 17547, 4100,  29168, 27966, 13533,  16380, 9364, 7548,  \n12652, 29357, 22432,  13533, 27966, 21580,  12652, 28789, 29357,  \n23974, 23307, 7186,  19271, 28989, 28789,  19271, 28789, 12652,  \n9618, 9990, 3677,  22446, 19582, 6528,  14455, 2954, 7275,  \n7190, 13330, 9443,  28353, 11608, 28990,  19540, 28573, 29626,  \n28945, 29358, 19271,  9375, 2648, 2049,  25867, 17530, 21996,  \n1870, 16880, 865,  2729, 7025, 14895,  5419, 16088, 1604,  \n9919, 18718, 11176,  6752, 12350, 6753,  11298, 965, 18382,  \n20975, 4032, 18389,  18117, 29359, 17891,  15602, 11086, 10592,  \n26143, 11276, 19460,  17548, 9062, 10559,  11204, 6592, 15689,  \n15720, 20853, 14222,  6993, 9435, 13498,  9911, 7400, 14699,  \n2194, 12727, 16619,  1436, 330, 6872,  9732, 16401, 19579,  \n16401, 22486, 19579,  15648, 7163, 17255,  17729, 2303, 8741,  \n22236, 13200, 22699,  4727, 1594, 6648,  28991, 29171, 24179,  \n26084, 17255, 23848,  3336, 3335, 2753,  20758, 11964, 9136,  \n23849, 23848, 29360,  9480, 9479, 6149,  28991, 553, 29173,  \n23630, 16894, 20941,  28992, 28995, 7012,  7012, 28995, 14552,  \n20463, 24089, 20461,  14552, 28995, 9219,  1368, 18319, 1367,  \n14684, 5817, 8845,  15861, 24055, 22164,  16883, 21047, 10354,  \n8469, 29173, 13583,  9219, 28363, 21681,  8786, 2959, 2960,  \n20359, 22067, 8831,  23866, 13739, 9992,  18527, 496, 498,  \n6839, 12052, 6838,  9196, 5214, 16337,  3113, 27779, 23216,  \n4404, 13959, 18917,  12107, 13720, 14008,  29174, 17444, 16268,  \n18655, 1258, 15515,  11706, 10540, 15950,  28580, 28796, 27160,  \n14113, 28580, 27160,  16781, 18072, 17916,  4204, 12605, 4203,  \n1373, 3339, 19142,  28180, 28997, 5255,  17085, 20823, 21300,  \n11329, 10077, 15778,  3229, 2931, 2930,  8828, 2471, 10535,  \n25422, 28180, 5255,  10550, 6813, 12253,  9517, 4670, 4289,  \n11943, 5452, 2432,  28179, 14112, 16515,  5779, 21794, 20400,  \n10278, 6662, 16630,  12376, 1776, 1778,  18500, 2479, 2478,  \n9081, 5760, 6647,  1940, 14618, 14617,  8578, 14017, 3399,  \n10521, 9389, 14100,  19804, 10533, 27358,  11023, 8486, 1688,  \n3602, 4646, 21593,  15410, 16413, 16414,  13603, 8301, 7740,  \n2157, 2158, 5090,  18049, 3674, 14341,  28805, 23223, 7637,  \n29363, 29000, 29727,  4791, 17674, 4792,  17811, 10771, 2286,  \n14537, 5621, 3805,  1717, 5751, 1718,  8367, 15685, 24367,  \n827, 828, 6043,  9436, 2758, 14936,  28369, 29178, 29508,  \n10495, 4572, 16754,  1308, 24231, 19394,  9140, 8786, 6337,  \n1772, 21387, 9582,  28585, 29505, 29628,  29505, 17337, 29628,  \n21335, 14397, 12998,  18768, 12873, 12185,  23866, 9992, 17174,  \n17102, 17101, 28584,  16745, 15450, 1294,  18615, 14798, 11196,  \n10684, 6374, 5938,  9217, 13396, 2845,  7909, 450, 13258,  \n28315, 19594, 3935,  12400, 19902, 9938,  29377, 29628, 20897,  \n29377, 29629, 29628,  22353, 22658, 24041,  17503, 26898, 17525,  \n19703, 19074, 6474,  3624, 324, 15784,  29003, 29182, 23379,  \n29512, 29179, 25652,  11224, 20542, 2944,  21456, 29003, 23379,  \n6341, 6340, 6908,  4143, 14713, 4144,  7626, 29181, 22919,  \n17781, 7827, 11107,  11417, 7818, 21543,  5378, 5377, 21543,  \n8045, 8209, 15729,  17275, 26285, 29377,  10234, 29510, 29513,  \n7474, 11625, 20179,  10234, 29513, 29787,  3006, 20877, 18680,  \n14528, 20029, 5067,  26285, 26284, 29629,  19791, 12113, 2599,  \n6765, 23904, 6766,  8497, 5976, 3469,  17977, 15999, 645,  \n14300, 19687, 19777,  29186, 29787, 29513,  21785, 6414, 4388,  \n12659, 12580, 9267,  5983, 4769, 19809,  8106, 15453, 1056,  \n16789, 3039, 14575,  19052, 15403, 990,  9970, 2469, 2468,  \n7184, 17588, 20386,  15060, 29004, 20758,  12832, 19175, 14143,  \n24985, 27997, 25262,  29632, 28590, 16947,  16364, 9292, 23676,  \n19158, 12269, 22745,  9388, 11364, 10037,  16342, 16343, 20306,  \n572, 23661, 29515,  13428, 23566, 12626,  8562, 17161, 12303,  \n2345, 2344, 16395,  3011, 21336, 11209,  21030, 25867, 6724,  \n572, 29515, 29516,  18189, 2312, 18188,  8980, 29687, 8351,  \n5547, 22153, 5545,  1469, 18961, 3610,  2679, 572, 29516,  \n22151, 25148, 16468,  9583, 24898, 16947,  20485, 19977, 20484,  \n11545, 13044, 20125,  28380, 11964, 29005,  17789, 5675, 14910,  \n17691, 15104, 18021,  21133, 29626, 6553,  10552, 29189, 10553,  \n24231, 1308, 7956,  9623, 2352, 5009,  29637, 29189, 10552,  \n21880, 9334, 22329,  29636, 29731, 21255,  18929, 9159, 17450,  \n29730, 29635, 29728,  27997, 24985, 12601,  2586, 14342, 18240,  \n19095, 4561, 13443,  18951, 462, 11320,  5204, 10816, 2442,  \n4278, 18477, 8431,  29637, 10552, 9651,  12977, 6906, 11830,  \n28993, 28967, 23962,  15859, 1560, 14901,  19649, 25158, 17972,  \n8511, 23407, 29192,  19441, 11802, 6301,  1585, 1584, 9207,  \n613, 14137, 15063,  29517, 29730, 22899,  29639, 29517, 22899,  \n411, 410, 19893,  13184, 21209, 13185,  29371, 29637, 29732,  \n10070, 3472, 4604,  29375, 29736, 29735,  21862, 10585, 13062,  \n10188, 22111, 18005,  22770, 17175, 17261,  29735, 29734, 29375,  \n19351, 23541, 3490,  29012, 29193, 12843,  7446, 25015, 2067,  \n5739, 18170, 11069,  29193, 29640, 12843,  12986, 17905, 12133,  \n3666, 2631, 21404,  22338, 29788, 29742,  7301, 5362, 3760,  \n17299, 20328, 5334,  25848, 29201, 29203,  29644, 29524, 24252,  \n16457, 19742, 16456,  13530, 21226, 17008,  4142, 28821, 23678,  \n29788, 29642, 29742,  29739, 29523, 29738,  15185, 15184, 21953,  \n29788, 29519, 29642,  17789, 11525, 5675,  19037, 6402, 2436,  \n4853, 14617, 3665,  29640, 29193, 29518,  29642, 29643, 29742,  \n26965, 8976, 8977,  29789, 29638, 28142,  29638, 29639, 28142,  \n24041, 22658, 19774,  9005, 1892, 11889,  1103, 1104, 3438,  \n29638, 29789, 29790,  29522, 29638, 29790,  3314, 29518, 29378,  \n23099, 27991, 17550,  678, 1790, 12005,  29741, 29739, 27631,  \n7270, 12638, 19904,  29648, 29740, 29386,  9831, 5029, 4106,  \n29198, 19551, 16251,  3307, 13101, 4368,  20999, 6868, 1063,  \n19501, 18572, 3233,  10616, 15388, 8827,  14991, 16145, 28634,  \n8249, 15489, 8250,  29522, 29790, 29646,  1460, 15835, 10655,  \n4997, 17140, 13097,  29649, 29743, 29647,  2301, 11307, 20759,  \n25266, 2568, 12886,  12248, 6013, 6012,  18408, 9247, 17325,  \n22317, 3771, 9734,  13789, 10267, 4396,  8796, 6282, 6283,  \n2366, 14604, 2364,  27728, 29651, 29650,  22007, 17757, 9518,  \n28770, 28358, 26309,  6256, 15241, 18452,  16335, 9969, 14050,  \n29529, 29531, 26186,  6550, 1744, 15297,  16679, 18099, 3884,  \n14325, 20553, 4226,  5642, 8340, 2088,  3771, 1321, 9590,  \n6234, 12213, 11678,  29533, 29653, 29744,  13268, 2584, 10115,  \n29659, 24343, 29654,  14904, 19502, 14576,  4892, 1157, 4891,  \n1497, 29025, 1498,  8999, 858, 14702,  29744, 28852, 29532,  \n3884, 2985, 1069,  886, 11764, 6176,  8079, 28305, 12163,  \n10069, 1269, 9765,  5327, 4364, 5326,  11694, 12631, 29025,  \n6683, 13509, 17471,  21166, 17983, 24241,  19686, 6249, 1504,  \n22083, 19940, 394,  18462, 19392, 19340,  21360, 21359, 20055,  \n21974, 8537, 7745,  29657, 2426, 29658,  29658, 2426, 29745,  \n3291, 11698, 301,  16896, 20438, 17536,  29746, 29661, 29745,  \n23972, 24086, 21758,  18441, 28769, 28140,  21365, 17923, 6543,  \n19644, 1962, 6501,  14573, 11419, 8874,  28993, 23962, 26498,  \n824, 823, 4052,  13421, 2434, 7521,  27874, 29225, 4375,  \n8052, 11742, 3943,  10277, 544, 8288,  29535, 16022, 12078,  \n18175, 12642, 25069,  29042, 19629, 21122,  15236, 11800, 15218,  \n9762, 12031, 16740,  13006, 12728, 5074,  8861, 7474, 20179,  \n29535, 9624, 16022,  29665, 29662, 15033,  11740, 17755, 14577,  \n21577, 19826, 15615,  29664, 9624, 29227,  6939, 13209, 8811,  \n9342, 12360, 8487,  16099, 15387, 13370,  28826, 28211, 23100,  \n29665, 3033, 29539,  29747, 20259, 15195,  28038, 13024, 19242,  \n15195, 29791, 29747,  4050, 20630, 17209,  28026, 2568, 2570,  \n22738, 28067, 28811,  6673, 14371, 17667,  16713, 13918, 17068,  \n1438, 354, 353,  9148, 6168, 20801,  18170, 5739, 12320,  \n16086, 369, 5656,  17177, 13783, 3310,  9142, 5941, 9141,  \n14409, 2328, 9129,  10128, 1171, 1170,  2551, 18461, 2552,  \n2646, 18042, 18678,  5144, 1990, 1065,  13968, 6557, 16012,  \n29401, 29406, 11499,  471, 3132, 14600,  12927, 19208, 11531,  \n11879, 5034, 5035,  2318, 6113, 8190,  29670, 23367, 22144,  \n3432, 20713, 21029,  7549, 22038, 7550,  21991, 14516, 29406,  \n3920, 2863, 7466,  21385, 29409, 22939,  18767, 18768, 12185,  \n6094, 20760, 6093,  3924, 18092, 5079,  11411, 29675, 11047,  \n11780, 18923, 11778,  29675, 29409, 11047,  19113, 13446, 16462,  \n16990, 16156, 15534,  29238, 6630, 29546,  29668, 22938, 29548,  \n29548, 22938, 22939,  21753, 10177, 10176,  18430, 2410, 7230,  \n20729, 20727, 20728,  29751, 29674, 18007,  14695, 16544, 16904,  \n10814, 12216, 20356,  10526, 16136, 22276,  29751, 29676, 29674,  \n16700, 13008, 13616,  1985, 4759, 7002,  8242, 3735, 3734,  \n24752, 23485, 12713,  4823, 14630, 6839,  5085, 9466, 4170,  \n14818, 4043, 4044,  23223, 29365, 17833,  29752, 29249, 29549,  \n1295, 29414, 1092,  29676, 23689, 29677,  1073, 5649, 28650,  \n13563, 17340, 20402,  9420, 23479, 17532,  10698, 13037, 13156,  \n22313, 29411, 29753,  19758, 3190, 22841,  6280, 16097, 662,  \n29254, 28650, 5649,  29675, 22052, 29554,  29682, 17037, 12207,  \n29549, 29682, 12207,  4146, 27112, 23689,  7072, 18787, 17010,  \n13489, 13490, 15933,  9893, 6663, 1653,  16853, 8069, 18617,  \n22402, 29754, 29680,  22402, 29680, 22313,  22313, 29680, 29411,  \n29681, 29755, 29753,  17217, 5325, 1882,  1197, 22785, 12092,  \n27112, 29679, 29678,  17984, 877, 784,  21950, 29410, 29679,  \n14920, 6745, 19055,  20491, 12849, 9450,  7358, 9685, 12662,  \n19416, 6294, 6606,  8202, 6709, 3952,  13383, 29410, 21950,  \n16089, 18873, 5959,  4903, 4904, 7614,  18543, 1463, 16719,  \n29556, 29756, 1463,  14348, 5244, 11154,  22052, 17541, 29554,  \n10375, 15936, 16301,  18905, 17037, 29683,  17037, 29682, 29683,  \n7450, 16200, 5613,  13517, 10089, 14286,  19716, 2353, 11845,  \n18542, 29556, 1463,  29755, 29553, 25537,  12224, 17146, 15608,  \n11908, 21829, 441,  29683, 29757, 18905,  9490, 4740, 15699,  \n11322, 21520, 6733,  20181, 29243, 11969,  2851, 2431, 9432,  \n28419, 28634, 4989,  7044, 20355, 7644,  9894, 3494, 19816,  \n9104, 15458, 7721,  15028, 11572, 8162,  5923, 21923, 19807,  \n15801, 7923, 12495,  17935, 12495, 7923,  18483, 11923, 15630,  \n13235, 10392, 13678,  29420, 29759, 22019,  13009, 12810, 11985,  \n13024, 28038, 11365,  9659, 6984, 7707,  15519, 21694, 12097,  \n3869, 3868, 14954,  17743, 29421, 29263,  17743, 17742, 29421,  \n6855, 16521, 6656,  29757, 29760, 29792,  4020, 980, 21253,  \n22640, 29421, 17742,  7573, 11582, 9497,  11137, 8515, 2239,  \n9075, 7622, 7739,  29792, 29760, 29761,  8571, 863, 20962,  \n29762, 29792, 29761,  19926, 11333, 21599,  29070, 10941, 21817,  \n17132, 6454, 3637,  13115, 9663, 9662,  29761, 29422, 29763,  \n15102, 26302, 15101,  7842, 18337, 18338,  29422, 29559, 29763,  \n29762, 29763, 27167,  21747, 3371, 15170,  13522, 12075, 29655,  \n29559, 27167, 29763,  29259, 29417, 11794,  10284, 26494, 18915,  \n18520, 17159, 5391,  3277, 3278, 13859,  18066, 5334, 5333,  \n12075, 28017, 28014,  16996, 29684, 17335,  29075, 29259, 6897,  \n22099, 8611, 8613,  16421, 1021, 20626,  28877, 14307, 4191,  \n10284, 10283, 29425,  7554, 17335, 7555,  15101, 29685, 4040,  \n2535, 4337, 2536,  20635, 23210, 29425,  28878, 29565, 22627,  \n29686, 7555, 17335,  3273, 3272, 7454,  29562, 18876, 20781,  \n14763, 9859, 5199,  17585, 11146, 2069,  3236, 3235, 11315,  \n12499, 12712, 13948,  12991, 22627, 29565,  12575, 12576, 2924,  \n7829, 14073, 1609,  26143, 18523, 11276,  13598, 1957, 13599,  \n29075, 6897, 16622,  14521, 14520, 13870,  301, 2900, 9534,  \n1009, 6662, 10278,  28877, 26488, 14307,  29793, 29764, 29568,  \n3200, 9507, 7666,  6580, 13492, 22122,  16000, 3430, 14636,  \n29764, 22472, 29765,  20094, 29765, 22472,  29688, 28536, 7555,  \n3620, 15197, 11335,  3706, 3705, 8790,  16692, 2427, 12282,  \n29689, 28536, 29688,  10035, 1775, 6378,  3529, 5238, 3530,  \n2010, 4014, 6938,  1381, 1382, 15532,  29570, 29765, 13275,  \n13275, 29765, 20094,  9265, 16564, 14269,  3419, 8797, 11870,  \n15378, 16468, 25148,  29689, 29691, 28536,  17333, 12634, 9737,  \n29691, 29690, 19740,  11905, 6926, 3649,  8420, 4046, 8421,  \n12991, 29565, 22066,  5702, 1160, 6604,  29692, 20503, 29690,  \n3276, 19622, 22828,  8054, 2805, 4414,  9504, 20034, 10747,  \n7471, 22526, 15692,  13275, 15413, 29570,  12170, 14229, 14455,  \n15413, 29572, 29570,  9628, 3020, 19148,  29572, 15413, 29766,  \n6311, 13492, 678,  16821, 29434, 22225,  3870, 10852, 3871,  \n13423, 17368, 10786,  15417, 1615, 4195,  18378, 4065, 8293,  \n10936, 7787, 9301,  19227, 5744, 20511,  20024, 4475, 29694,  \n29571, 29767, 23674,  29274, 29085, 8338,  22066, 29274, 8338,  \n17948, 28824, 16494,  15761, 17976, 575,  15917, 7542, 12081,  \n2365, 6070, 6069,  13024, 28039, 19242,  16273, 6258, 6257,  \n29439, 29280, 16661,  3669, 13518, 11018,  6963, 19185, 15663,  \n13024, 25126, 28039,  29575, 19185, 16788,  14085, 14084, 8951,  \n11871, 10878, 13224,  26109, 337, 3218,  19659, 8298, 16530,  \n6889, 20336, 21324,  8629, 17683, 17682,  10644, 7434, 13399,  \n9625, 5248, 4379,  8383, 17797, 4200,  29696, 21080, 29769,  \n2933, 1979, 2932,  20047, 8852, 3368,  8578, 19130, 14017,  \n29699, 29697, 29500,  29500, 29499, 29699,  14029, 2000, 8051,  \n14498, 3104, 14497,  15618, 6164, 15619,  12656, 6518, 11334,  \n21566, 29579, 24771,  21566, 24771, 7881,  7975, 2264, 10596,  \n16705, 15588, 6063,  20687, 20624, 11747,  29794, 29583, 21566,  \n9664, 9665, 2155,  29794, 14042, 29698,  24771, 29701, 23475,  \n29794, 29698, 29583,  19985, 24661, 3078,  15529, 15614, 2678,  \n711, 29094, 710,  3261, 29577, 19626,  23475, 29701, 13903,  \n19068, 5781, 15168,  18746, 15304, 13650,  29094, 29284, 710,  \n6930, 15038, 7269,  23948, 16347, 13125,  29447, 22266, 10507,  \n22266, 29447, 29581,  4386, 6414, 28603,  18976, 29581, 29771,  \n19133, 29449, 28463,  12258, 4826, 12259,  666, 710, 29284,  \n11038, 11322, 11037,  13053, 11951, 7818,  13234, 8279, 4986,  \n403, 2558, 2559,  2999, 2639, 17388,  8629, 17682, 22782,  \n20108, 15618, 15619,  29587, 29586, 22997,  22325, 29773, 29587,  \n13903, 29770, 29773,  15585, 7959, 10406,  29448, 29287, 7007,  \n23948, 17690, 18034,  12545, 8351, 29687,  7863, 1866, 1979,  \n29773, 29770, 29774,  20881, 6921, 12404,  29774, 29770, 29772,  \n20169, 29704, 22937,  28746, 10923, 28349,  20169, 21244, 29704,  \n13182, 13319, 15855,  1181, 19908, 21735,  29655, 12075, 28014,  \n5282, 29707, 16726,  9729, 10477, 18578,  29773, 29774, 29590,  \n2707, 5104, 2708,  11963, 11726, 8451,  372, 19327, 16162,  \n4985, 6099, 4971,  17296, 9209, 4903,  7973, 18909, 5101,  \n29707, 22328, 16726,  16497, 12550, 16123,  20020, 29594, 5282,  \n318, 3678, 10547,  13513, 13514, 21354,  21602, 3361, 13150,  \n28914, 6529, 14324,  29453, 7252, 7347,  20065, 19767, 19576,  \n17437, 398, 9294,  7795, 24997, 16532,  7694, 19352, 12138,  \n21451, 4069, 2868,  29775, 28555, 17040,  29775, 29776, 28555,  \n8106, 4081, 8107,  14323, 29310, 14324,  13660, 2149, 3192,  \n29777, 28742, 24419,  29775, 29777, 29776,  29777, 29795, 29776,  \n12547, 4537, 4948,  11810, 12470, 17621,  28825, 20483, 2089,  \n21462, 11014, 15957,  29310, 14323, 12343,  7724, 2896, 7725,  \n1165, 21289, 10319,  3883, 4298, 8307,  28742, 29795, 29796,  \n12561, 691, 4176,  29310, 12343, 15393,  28769, 4388, 9428,  \n28746, 12176, 22285,  26424, 14202, 25713,  16944, 16241, 22277,  \n15393, 4408, 29465,  14002, 14095, 7965,  1357, 18966, 20384,  \n10962, 20859, 19248,  29597, 4408, 24738,  18950, 12684, 15725,  \n22688, 29778, 19094,  20753, 7290, 20752,  29778, 22688, 29599,  \n16315, 14157, 2503,  7282, 22095, 13944,  17258, 29322, 4357,  \n20441, 20505, 29599,  20017, 22229, 25126,  17846, 18586, 17847,  \n9462, 17437, 13834,  3539, 4582, 3114,  11789, 15230, 17764,  \n5658, 29026, 23851,  2694, 9749, 3489,  18307, 1768, 1359,  \n29321, 29319, 15427,  16452, 9336, 7829,  5874, 5875, 11362,  \n18252, 4597, 1421,  21577, 615, 19826,  17573, 17574, 29600,  \n5585, 29321, 13315,  15133, 9880, 15134,  28938, 29601, 29600,  \n5460, 474, 12860,  21776, 3628, 11613,  17934, 19539, 17099,  \n11216, 29470, 29710,  29155, 13988, 28137,  29602, 29470, 11216,  \n16721, 1048, 1251,  2599, 1945, 9875,  16654, 9767, 16453,  \n17208, 2793, 10598,  675, 12908, 12909,  26005, 22962, 16721,  \n11229, 29711, 17531,  2868, 9752, 21451,  24911, 29711, 11229,  \n3136, 8553, 16295,  15633, 18243, 8462,  1743, 1745, 24911,  \n1745, 28194, 29473,  3418, 4180, 4179,  8820, 814, 18375,  \n24274, 8279, 13234,  17970, 28329, 15743,  5835, 29325, 7372,  \n29325, 5548, 7372,  13064, 449, 9253,  28135, 12928, 15800,  \n5549, 5548, 29328,  3954, 19599, 2331,  29328, 29779, 20831,  \n13103, 9437, 517,  14458, 1990, 19923,  691, 12561, 690,  \n10169, 11986, 11114,  29779, 29712, 21298,  6186, 11455, 16842,  \n10506, 10507, 16036,  8448, 29330, 8449,  4301, 8166, 303,  \n7564, 9183, 2831,  2254, 19848, 2255,  29606, 17315, 29712,  \n29133, 468, 10250,  28949, 29133, 28156,  29474, 17315, 29606,  \n1342, 4308, 2557,  19465, 329, 4445,  11264, 26118, 1843,  \n10249, 2445, 26541,  16918, 16921, 10594,  11005, 9504, 680,  \n6234, 22704, 1722,  13158, 16706, 20333,  14454, 24384, 14422,  \n552, 551, 7743,  28312, 25387, 19639,  20909, 9839, 5207,  \n29475, 9803, 17314,  24548, 9789, 13010,  3763, 9803, 18293,  \n24548, 13010, 29334,  13010, 13011, 29334,  14774, 1270, 9524,  \n29155, 6027, 16682,  1127, 1380, 10015,  14728, 3195, 4901,  \n12940, 12677, 16023,  18293, 29335, 27623,  12447, 9401, 2513,  \n20008, 8009, 2475,  10341, 10340, 28026,  29337, 3762, 27623,  \n14554, 20343, 13898,  11390, 18215, 17250,  10323, 15164, 18092,  \n13694, 16158, 8406,  9963, 1030, 19441,  1948, 7710, 4674,  \n13868, 8246, 12310,  17491, 2839, 2251,  18652, 20815, 2405,  \n5168, 29609, 29780,  10907, 10908, 9065,  20888, 5007, 18180,  \n29609, 5168, 29476,  29780, 29611, 29713,  20255, 29713, 29714,  \n9565, 2663, 12422,  29342, 16171, 19023,  3526, 17609, 14786,  \n29714, 29613, 29716,  10980, 10979, 3361,  19023, 29715, 29342,  \n5703, 17730, 8741,  19023, 21171, 29715,  14588, 21518, 29716,  \n7397, 18660, 621,  29717, 29715, 21171,  18660, 3388, 621,  \n13751, 14110, 13750,  1105, 12772, 578,  10876, 5921, 11945,  \n14940, 3870, 3872,  29615, 14588, 29614,  29614, 14588, 29716,  \n13539, 7287, 23103,  4967, 2596, 17515,  5897, 8492, 6145,  \n16541, 9244, 6223,  20103, 29615, 29718,  26695, 19758, 26260,  \n8980, 24686, 25122,  22600, 4027, 21039,  8963, 29708, 9751,  \n28014, 16704, 25529,  25262, 16792, 25263,  29708, 12545, 23282,  \n9204, 5553, 6425,  28811, 4077, 16714,  28811, 28067, 4077,  \n22062, 21999, 28822,  7982, 23001, 25467,  21866, 17976, 2743,  \n13061, 2354, 12584,  5637, 11170, 5636,  3153, 16063, 12286,  \n28824, 25698, 23450,  13866, 28680, 13865,  10874, 13409, 10882,  \n11409, 7574, 11952,  12163, 12162, 8079,  25017, 28211, 1843,  \n20113, 28400, 15760,  14572, 24833, 7136,  29148, 17937, 17975,  \n6557, 8222, 8221,  28769, 9428, 17948,  19031, 24654, 18606,  \n5884, 14379, 5882,  4433, 10911, 8748,  12745, 12746, 18430,  \n18632, 17481, 11316,  9183, 19654, 3245,  10795, 16951, 15627,  \n22370, 28302, 4342,  8963, 12545, 29708,  17013, 29655, 25529,  \n18466, 15508, 3899,  2078, 2077, 13803,  4034, 22822, 29719,  \n9559, 9875, 3742,  13695, 15281, 649,  13389, 9862, 13390,  \n24135, 11203, 2956,  10993, 13020, 20696,  28772, 29151, 1844,  \n17264, 21642, 21643,  1844, 29151, 29618,  11675, 3911, 19506,  \n13661, 7854, 6081,  8617, 12786, 1019,  10158, 5924, 5923,  \n13418, 1920, 1921,  16396, 16395, 5894,  12296, 10441, 19959,  \n26308, 27347, 24439,  17148, 7187, 14616,  9862, 17662, 13390,  \n6313, 29483, 8211,  10984, 11342, 2727,  18636, 21632, 12555,  \n11188, 22067, 20359,  12862, 8862, 8863,  12345, 3122, 926,  \n12935, 29485, 19829,  18506, 4060, 20118,  6313, 5140, 22711,  \n7417, 6800, 21829,  8165, 12277, 10940,  6244, 6245, 17418,  \n10485, 13566, 15182,  29153, 6313, 22711,  1216, 22447, 5455,  \n29484, 29486, 1843,  1843, 29486, 18720,  12936, 17464, 29485,  \n29347, 21830, 23806,  20359, 11189, 11188,  1650, 4097, 1651,  \n5549, 7372, 5548,  1966, 13689, 1621,  10072, 10073, 3174,  \n23997, 913, 912,  29347, 21216, 21830,  3280, 9650, 874,  \n13056, 29156, 19174,  21216, 13946, 13947,  6557, 13968, 8222,  \n16514, 16214, 16213,  23952, 13950, 24405,  18436, 4735, 957,  \n12547, 4948, 12548,  13071, 3599, 6291,  5175, 13027, 13643,  \n992, 991, 14012,  3781, 3780, 6675,  8430, 10525, 16084,  \n10973, 8215, 7419,  21458, 29157, 13056,  21404, 13176, 3666,  \n9131, 9115, 8598,  14632, 23051, 10979,  29491, 29783, 29784,  \n1861, 24586, 11281,  7470, 15234, 22309,  2106, 2105, 2240,  \n1727, 8090, 774,  8760, 21543, 18335,  29784, 20361, 29785,  \n19654, 13544, 16550,  16479, 13739, 5638,  20215, 8384, 10270,  \n17289, 11476, 3912,  29159, 14138, 10029,  20011, 14784, 16117,  \n9059, 6310, 13198,  20031, 18897, 4662,  1672, 4769, 12900,  \n29786, 29785, 27183,  27183, 29785, 20361,  14138, 28347, 4634,  \n7188, 2769, 7189,  5615, 7145, 3133,  22034, 22106, 5039,  \n19166, 22092, 20454,  5303, 12682, 13776,  18897, 6685, 20069,  \n7908, 7907, 17435,  29724, 29797, 29725,  11607, 28569, 19003,  \n29797, 29798, 29725,  29725, 29798, 29726,  12485, 17883, 5212,  \n9403, 9405, 12220,  11582, 7573, 11410,  18698, 5120, 15747,  \n11677, 3998, 3997,  8165, 10940, 8166,  28468, 29166, 29169,  \n1097, 17558, 8822,  29798, 22432, 29726,  16873, 21427, 29169,  \n7465, 11868, 11867,  13669, 11849, 13579,  23618, 22633, 6758,  \n6044, 13826, 14880,  11818, 3079, 1925,  13197, 21580, 7442,  \n7661, 7660, 9982,  8652, 5108, 5985,  19541, 19540, 29626,  \n9530, 10791, 19820,  20017, 20612, 21491,  13955, 15379, 4130,  \n29619, 25263, 16792,  15363, 7463, 7462,  7442, 18117, 18116,  \n16080, 4196, 14656,  19255, 28791, 10065,  17891, 29172, 15996,  \n10064, 29170, 7163,  19004, 8836, 15207,  6307, 19145, 16171,  \n12614, 21499, 12534,  7163, 29170, 17255,  13309, 3811, 3810,  \n3960, 3139, 3138,  1993, 20021, 20599,  10621, 14604, 16898,  \n29155, 28137, 11005,  13897, 8545, 21766,  15861, 23849, 24055,  \n28576, 28362, 3946,  13583, 29173, 553,  25205, 8469, 13018,  \n5255, 28997, 24272,  5726, 9878, 9879,  12274, 27779, 3113,  \n15886, 19235, 18280,  23138, 28798, 22391,  27160, 29174, 16268,  \n2390, 1644, 14370,  16506, 28365, 29503,  23146, 24932, 17493,  \n14037, 22082, 14038,  18170, 9508, 9509,  13069, 21892, 3970,  \n10655, 1170, 1169,  22713, 21017, 24931,  19456, 9954, 9955,  \n21598, 20199, 29503,  346, 10236, 18631,  28580, 14113, 14112,  \n4164, 20505, 20117,  24574, 28048, 19187,  10540, 18725, 663,  \n28179, 16515, 29362,  8122, 8123, 5419,  28799, 29176, 19672,  \n11660, 29361, 29627,  20443, 9780, 19495,  3475, 1377, 13916,  \n15928, 2672, 8520,  6634, 13111, 12780,  25422, 23339, 9356,  \n1595, 7022, 2670,  29177, 28805, 7637,  18411, 326, 10631,  \n16181, 2614, 17229,  3990, 18056, 2649,  19130, 8578, 10496,  \n29727, 29627, 29363,  29178, 29504, 20127,  6505, 8451, 8452,  \n19896, 18588, 18912,  5036, 8172, 21024,  14710, 1965, 18351,  \n934, 15030, 12004,  15485, 19615, 25434,  29365, 23223, 28583,  \n22231, 6769, 17337,  6030, 20267, 6031,  13257, 8009, 21485,  \n3411, 4408, 4928,  500, 12101, 10570,  3169, 3170, 18174,  \n29508, 20127, 7884,  3736, 14656, 4196,  9369, 9370, 11947,  \n14663, 13474, 817,  17679, 15068, 13353,  8237, 18094, 987,  \n14281, 15036, 16703,  29508, 29178, 20127,  24986, 29619, 26468,  \n17408, 15662, 15658,  15685, 25653, 24367,  18584, 20334, 15790,  \n7884, 23379, 29508,  9494, 25653, 15685,  812, 811, 21402,  \n22925, 8620, 22364,  18644, 18541, 12771,  18325, 3897, 13928,  \n29510, 13631, 29507,  12045, 13631, 29510,  12025, 12027, 14681,  \n11319, 23282, 19548,  23379, 29182, 29508,  29507, 27603, 29510,  \n4076, 14777, 10579,  2437, 6450, 16933,  16740, 4006, 14400,  \n16452, 20589, 12785,  29377, 20897, 9854,  11319, 29708, 23282,  \n10342, 1121, 19157,  29179, 25653, 25652,  10299, 15172, 889,  \n22376, 652, 16888,  16232, 7375, 7142,  5235, 3349, 2726,  \n19313, 3090, 18833,  22339, 18075, 5542,  11333, 14236, 3303,  \n15495, 13136, 23360,  29003, 21456, 16946,  9668, 1495, 17191,  \n1455, 3505, 8645,  8244, 21307, 11237,  29510, 28807, 29513,  \n5497, 17044, 5287,  29366, 29003, 16946,  7324, 1453, 1452,  \n5546, 17221, 5547,  12658, 12034, 21020,  11903, 6979, 14806,  \n1249, 650, 22862,  25086, 24304, 15322,  29183, 29512, 4389,  \n13554, 6705, 20388,  29183, 4389, 20504,  23694, 10533, 9039,  \n23661, 29184, 29367,  28590, 29366, 16947,  17843, 15236, 22137,  \n27991, 23099, 8394,  7682, 13153, 14052,  17263, 23347, 14340,  \n3409, 29004, 15060,  5222, 12813, 20231,  5814, 21649, 20305,  \n12245, 5379, 3785,  18748, 3597, 18747,  11782, 21065, 8245,  \n13962, 5430, 5429,  750, 5558, 3163,  18095, 18094, 8237,  \n8255, 9842, 15877,  20504, 10553, 29631,  23205, 14384, 8930,  \n7273, 7272, 11136,  11964, 20758, 29005,  14972, 718, 11583,  \n12081, 11073, 11886,  16747, 6585, 2518,  2814, 21293, 15448,  \n10555, 10542, 8778,  19218, 19365, 13478,  29729, 11964, 28380,  \n22349, 29633, 10384,  7715, 9052, 7716,  2680, 2679, 29516,  \n15296, 15717, 15297,  10751, 7372, 19298,  10625, 29633, 22349,  \n10625, 29634, 29633,  10624, 29634, 10625,  5639, 5106, 25443,  \n17498, 15907, 9638,  4542, 9763, 13524,  15098, 29731, 29799,  \n9374, 10581, 28329,  15863, 6768, 17571,  23622, 1190, 17346,  \n6178, 4607, 7674,  10624, 29728, 29634,  21558, 29730, 29728,  \n13836, 14058, 17420,  16200, 3440, 1284,  29799, 29731, 26198,  \n13238, 3007, 3008,  5367, 5269, 4064,  1973, 7982, 4942,  \n29370, 19837, 2680,  11347, 16310, 5003,  9888, 16524, 11266,  \n20455, 8488, 12758,  19649, 23626, 25158,  17361, 9562, 21185,  \n29637, 9651, 29732,  27794, 29192, 23407,  8935, 8818, 5055,  \n6118, 16246, 10695,  16177, 10097, 9228,  29519, 29788, 8067,  \n8511, 29374, 29734,  7767, 11445, 9848,  14142, 19964, 14638,  \n16354, 18384, 6637,  29519, 8067, 29733,  372, 371, 18006,  \n4287, 8584, 1559,  4230, 10704, 13748,  21883, 19479, 12139,  \n10391, 8103, 15226,  8493, 8841, 8842,  11905, 29739, 29738,  \n9161, 3461, 10107,  6058, 4823, 6217,  2495, 18889, 18769,  \n29737, 17290, 29736,  16779, 16780, 7758,  21122, 6831, 7601,  \n15965, 15796, 6977,  16866, 14425, 16867,  29639, 22899, 28142,  \n20485, 18523, 26143,  14842, 12762, 14420,  4949, 2242, 4947,  \n22338, 29742, 27631,  1284, 3440, 11291,  13209, 11655, 11085,  \n10132, 7110, 12663,  14233, 1461, 19281,  8751, 2263, 12399,  \n9588, 4757, 14645,  3779, 3778, 14448,  6690, 1927, 1926,  \n17625, 13633, 16173,  6907, 16738, 2433,  19890, 3663, 14502,  \n5134, 11846, 20376,  3400, 18257, 7769,  22151, 21912, 25148,  \n10415, 10345, 15864,  29641, 15976, 29737,  29640, 29518, 8904,  \n29741, 27631, 29742,  11079, 17649, 12429,  24252, 25125, 18301,  \n29641, 29740, 15976,  22388, 29789, 28142,  5823, 13533, 3668,  \n4365, 5327, 13782,  10888, 16267, 13584,  17094, 18039, 986,  \n3536, 29789, 22388,  833, 16645, 832,  16130, 13178, 6468,  \n11466, 2938, 15922,  29648, 29386, 29384,  2993, 23236, 21457,  \n11829, 3797, 9485,  11016, 6257, 22031,  12686, 6978, 20392,  \n24740, 29647, 972,  29790, 3536, 29646,  12395, 6257, 11016,  \n17725, 13706, 17726,  972, 29647, 29743,  10390, 29646, 3536,  \n8025, 10636, 10719,  11339, 17384, 11093,  3366, 16242, 3365,  \n9201, 4902, 8607,  19572, 9246, 9245,  20522, 21247, 3093,  \n29646, 10390, 27728,  27728, 29650, 29646,  26186, 17841, 29529,  \n26186, 13439, 17841,  2138, 8843, 11284,  8111, 5723, 16388,  \n13678, 10391, 15226,  10561, 16891, 10562,  14008, 13720, 14009,  \n11801, 28825, 2089,  18907, 17225, 10920,  9686, 4061, 13915,  \n972, 29743, 24343,  17650, 6495, 17649,  342, 1846, 13285,  \n7472, 12602, 853,  5945, 15052, 4628,  16846, 16849, 16882,  \n17084, 21675, 21839,  6517, 14590, 8447,  3036, 8494, 23326,  \n1120, 19465, 4445,  6682, 11292, 7114,  24343, 29743, 29654,  \n23408, 2125, 10745,  9206, 12455, 12454,  21724, 5076, 6452,  \n29656, 29651, 13500,  15999, 9946, 11325,  2973, 15640, 3357,  \n29744, 29653, 4136,  29744, 13933, 28852,  20113, 24921, 28400,  \n8245, 11781, 11782,  13933, 29744, 4135,  4135, 29744, 4136,  \n15991, 15266, 4550,  3102, 3103, 21887,  3353, 21178, 12087,  \n12753, 24877, 10267,  14183, 20046, 13912,  3480, 14902, 3481,  \n9678, 29657, 22246,  18367, 19903, 2032,  797, 2039, 796,  \n11694, 28852, 11695,  20113, 28419, 24921,  14454, 8749, 24384,  \n17439, 1335, 1334,  9678, 2426, 29657,  7860, 7862, 4718,  \n19264, 18901, 16697,  16692, 29745, 2426,  7441, 20082, 13197,  \n5799, 29659, 12078,  29746, 29745, 16692,  16692, 22253, 29746,  \n11781, 8245, 11693,  9794, 20055, 27874,  6277, 15882, 20540,  \n3427, 19629, 29037,  29037, 19629, 29042,  10207, 14226, 14229,  \n13485, 9742, 8123,  2824, 5497, 7399,  12523, 12797, 2802,  \n15033, 29746, 22253,  17013, 25529, 17530,  12078, 16022, 5799,  \n13740, 5639, 5638,  4375, 3552, 27874,  7352, 3907, 12769,  \n12493, 9143, 22230,  17903, 15797, 22061,  5569, 5568, 5854,  \n29393, 9624, 29535,  17424, 12714, 16469,  17005, 21671, 19007,  \n5401, 17791, 10464,  10722, 26468, 12934,  13655, 8219, 16621,  \n580, 14913, 22260,  15195, 11190, 29791,  5732, 18232, 18233,  \n1938, 23170, 5887,  21084, 8177, 6625,  12887, 1797, 16794,  \n3775, 5136, 9297,  10907, 7228, 4361,  11354, 29791, 11190,  \n2564, 3706, 9101,  27997, 16792, 25262,  19278, 20511, 20184,  \n20259, 29747, 3032,  22848, 29791, 11354,  8398, 970, 20465,  \n3831, 9867, 17002,  10037, 10038, 10029,  11542, 8395, 11541,  \n15503, 3037, 5482,  7687, 9947, 7686,  7367, 19095, 14222,  \n22514, 7111, 4089,  29398, 3001, 9624,  3032, 29539, 3033,  \n9998, 8808, 7343,  3407, 22848, 11354,  17385, 22750, 2930,  \n17976, 21866, 575,  10861, 5610, 16447,  3001, 29398, 29401,  \n11499, 3001, 29401,  20410, 15488, 23039,  22780, 14116, 22554,  \n23367, 22848, 3407,  6471, 7649, 21813,  2359, 14870, 13452,  \n9239, 11499, 29406,  11775, 7027, 15149,  13813, 23035, 8295,  \n7087, 11281, 6690,  1798, 16794, 1797,  341, 13320, 21911,  \n7785, 6971, 1015,  10617, 17732, 20424,  29406, 14516, 9239,  \n865, 14256, 866,  16109, 2528, 18861,  19986, 19166, 15974,  \n29670, 22144, 22938,  5000, 845, 846,  29238, 21320, 6630,  \n11047, 29409, 21385,  12371, 21631, 17110,  788, 9147, 9148,  \n29670, 22938, 29668,  3839, 3840, 15515,  20025, 21594, 482,  \n5467, 23378, 12040,  13534, 8238, 12818,  11047, 5577, 11411,  \n29542, 17110, 21631,  12977, 16091, 6906,  6274, 11299, 16632,  \n1911, 17110, 11652,  21564, 11826, 29749,  10196, 12964, 10872,  \n4264, 1123, 7664,  29675, 11411, 22052,  29750, 21201, 29749,  \n29749, 21201, 21564,  17616, 3121, 11190,  18400, 18540, 18644,  \n4543, 20261, 12426,  29750, 29752, 21201,  15666, 7339, 6614,  \n29315, 1912, 11652,  20046, 3373, 13912,  4225, 3424, 18751,  \n928, 21201, 29752,  12207, 29752, 29549,  29751, 18007, 17445,  \n29751, 17445, 29676,  19458, 13616, 7623,  12207, 928, 29752,  \n8980, 25122, 29687,  29676, 17445, 23689,  14455, 7275, 18341,  \n5026, 22520, 12710,  14470, 11058, 4086,  4147, 4146, 23689,  \n17528, 17529, 2644,  12207, 17037, 929,  17552, 15066, 1573,  \n8188, 2655, 8189,  22098, 1784, 3238,  22312, 29753, 2255,  \n22312, 22313, 29753,  29755, 2255, 29753,  4180, 15143, 2611,  \n13582, 8789, 9817,  27112, 8083, 29679,  15738, 15739, 7039,  \n5406, 20180, 18772,  19802, 13116, 19386,  4765, 9188, 17058,  \n6751, 1827, 10296,  22289, 15606, 21319,  8085, 29679, 8083,  \n29679, 8085, 21950,  14455, 10741, 2954,  21829, 1078, 441,  \n14576, 19065, 20038,  29619, 16792, 26468,  3356, 4831, 9686,  \n21354, 21741, 13513,  2255, 29755, 2059,  14958, 15466, 15917,  \n25537, 2059, 29755,  5902, 5901, 20238,  17541, 29759, 29554,  \n17541, 18896, 29759,  1450, 2807, 2808,  8085, 7456, 21950,  \n15057, 13502, 4209,  6227, 25126, 13024,  29759, 18896, 22019,  \n18709, 13604, 9924,  21518, 20255, 29714,  16112, 22547, 29289,  \n29757, 5901, 18905,  7723, 7483, 17418,  7480, 12921, 11403,  \n13113, 3761, 13030,  5901, 29757, 29792,  3517, 8145, 2326,  \n12456, 11252, 14879,  1488, 19026, 1489,  20238, 5901, 29792,  \n19219, 20409, 19220,  7156, 19026, 20014,  11970, 29550, 13383,  \n8518, 13965, 13723,  18542, 19352, 29758,  4760, 1371, 14467,  \n11969, 29550, 11970,  7694, 29758, 19352,  8639, 16406, 17621,  \n19054, 10941, 29070,  29421, 22640, 22473,  29792, 20237, 20238,  \n29762, 20237, 29792,  9933, 5962, 5963,  12809, 8657, 12810,  \n7759, 7250, 513,  2348, 18872, 17300,  27167, 20237, 29762,  \n15102, 25537, 26302,  18173, 2051, 19868,  22473, 29560, 29421,  \n3578, 11338, 11337,  1376, 2123, 1377,  12553, 12552, 20525,  \n22473, 22472, 29560,  2874, 12435, 5511,  11478, 11644, 4751,  \n15657, 22518, 7912,  5172, 13769, 4187,  1612, 12755, 10554,  \n20635, 29425, 10283,  6865, 4608, 5009,  22472, 29793, 29560,  \n29563, 29560, 29793,  29562, 4040, 29685,  4060, 9427, 3859,  \n8908, 15138, 4343,  3736, 4196, 3737,  5572, 20781, 18876,  \n4211, 7454, 4210,  9584, 11467, 24898,  25545, 19975, 19626,  \n29764, 29793, 22472,  15049, 6034, 6033,  17583, 10360, 2754,  \n20221, 16037, 8595,  29691, 19740, 28536,  28886, 26087, 7132,  \n26087, 16622, 7132,  19740, 23025, 28536,  5976, 13007, 16440,  \n8175, 17347, 6211,  17830, 23207, 20078,  7167, 7168, 5387,  \n13279, 7132, 5276,  12240, 3471, 12239,  13279, 22225, 29272,  \n1619, 20503, 29692,  12170, 14455, 18341,  3383, 6844, 1342,  \n1619, 29692, 29569,  16323, 5162, 9529,  23695, 25211, 23696,  \n11117, 3021, 3319,  9529, 5162, 11314,  29766, 15413, 20024,  \n12568, 12095, 9299,  4085, 23443, 10998,  13418, 5498, 11808,  \n20965, 8031, 12241,  29694, 4475, 16661,  5365, 3741, 16859,  \n11483, 23674, 29768,  20419, 9298, 19066,  29768, 6964, 11483,  \n29768, 23674, 29767,  10449, 16106, 3765,  13569, 9338, 322,  \n1061, 15963, 21168,  16788, 6964, 29695,  6964, 29768, 29695,  \n8129, 28689, 1724,  7266, 6645, 9606,  16297, 12145, 17570,  \n5270, 3224, 4946,  19977, 21912, 22151,  14133, 5989, 10691,  \n3074, 18438, 8169,  12778, 21364, 20325,  13637, 29439, 16661,  \n15663, 29769, 20834,  19185, 29769, 15663,  5241, 5806, 20600,  \n17658, 14211, 14214,  29085, 29091, 8338,  11540, 29697, 29439,  \n11540, 29439, 13637,  10869, 20300, 10783,  10382, 4864, 12647,  \n8629, 29282, 17683,  2920, 2132, 14886,  29769, 21080, 20834,  \n21354, 18923, 3995,  4351, 23390, 16391,  24297, 29500, 11540,  \n19824, 22658, 18274,  3699, 328, 3146,  29500, 29697, 11540,  \n17798, 17799, 17801,  29499, 24297, 29700,  20485, 26143, 21912,  \n10490, 14808, 21214,  13237, 13236, 15377,  5831, 16241, 16944,  \n711, 20090, 29091,  24297, 25545, 29700,  12286, 3127, 2140,  \n18620, 859, 858,  5094, 11384, 11922,  10497, 14042, 10498,  \n2759, 9444, 8597,  2079, 8944, 21220,  9215, 7881, 23475,  \n14011, 11452, 11409,  6211, 8174, 8175,  17838, 2760, 19295,  \n21566, 10498, 29794,  15548, 8275, 1257,  14838, 12387, 16198,  \n10498, 14042, 29794,  18345, 17061, 17088,  16360, 641, 698,  \n14042, 21080, 29698,  24985, 27995, 12601,  19467, 27990, 18523,  \n904, 3261, 19626,  4496, 23475, 13903,  15066, 17552, 4370,  \n28315, 16476, 12519,  3274, 3275, 10122,  15443, 15442, 12671,  \n3261, 904, 10717,  935, 1356, 946,  11260, 2128, 7969,  \n13903, 29773, 22325,  7478, 7480, 9748,  10337, 13648, 6639,  \n18975, 22266, 29581,  18975, 29581, 18976,  22325, 29587, 22981,  \n2307, 2306, 7404,  2264, 3356, 9686,  7007, 18976, 29771,  \n5647, 7978, 6521,  29587, 22997, 22981,  16929, 11811, 15112,  \n14700, 8604, 4966,  705, 3940, 12608,  11381, 11380, 549,  \n21728, 542, 18146,  6851, 5116, 5115,  9633, 808, 16362,  \n5800, 12540, 8442,  666, 29284, 29105,  1694, 2091, 1693,  \n20169, 22937, 23858,  4643, 12000, 22557,  5282, 14374, 20020,  \n22997, 20020, 20019,  10547, 3678, 10548,  571, 3937, 8554,  \n3620, 3621, 15197,  7646, 8007, 12393,  5719, 5636, 17991,  \n1914, 9209, 17296,  29456, 21244, 4002,  29705, 4002, 4003,  \n2040, 2344, 2345,  29706, 4003, 567,  20411, 17553, 15830,  \n6529, 28914, 6528,  2707, 1035, 5104,  7252, 29453, 9493,  \n1003, 2246, 6191,  21463, 28194, 6550,  11312, 28557, 2969,  \n9333, 9332, 4516,  4239, 11618, 2060,  3384, 14608, 5441,  \n13291, 21491, 16624,  8024, 8025, 20711,  15247, 11043, 15908,  \n23133, 17040, 28555,  14596, 9769, 9768,  2983, 13941, 2984,  \n29795, 28555, 29776,  29795, 29776, 29796,  2227, 8266, 13757,  \n5778, 24533, 21794,  1338, 7242, 16656,  24419, 28555, 29777,  \n28555, 29795, 29777,  28769, 21785, 4388,  29796, 6605, 12775,  \n29796, 20918, 6605,  20918, 28708, 29591,  19489, 22488, 12743,  \n28742, 17771, 24419,  4253, 3708, 28742,  28742, 29796, 4253,  \n29796, 12775, 4253,  7221, 10955, 18853,  12828, 12827, 22819,  \n2805, 19238, 2806,  16494, 28824, 16646,  18449, 5925, 3603,  \n3708, 4253, 4252,  10463, 2062, 8915,  4408, 15393, 15392,  \n4408, 29597, 29465,  8692, 924, 13824,  14232, 15486, 7870,  \n17258, 6519, 24997,  15487, 7870, 15486,  19094, 24738, 3411,  \n9976, 24870, 2844,  24738, 19094, 29778,  3583, 2665, 2664,  \n14182, 2307, 16659,  3921, 22688, 19094,  3738, 3992, 4866,  \n7431, 5354, 12182,  10241, 6925, 13865,  9957, 10973, 7419,  \n16221, 20480, 11972,  22017, 1601, 7120,  29322, 1251, 4357,  \n13315, 29321, 15427,  16168, 29600, 17574,  20647, 20648, 14938,  \n29600, 16168, 28938,  17631, 7226, 11810,  15498, 9919, 11176,  \n4987, 5627, 5508,  11604, 3150, 13141,  28938, 16168, 29710,  \n12462, 12461, 3355,  25680, 14177, 13792,  8952, 9370, 18003,  \n16971, 11840, 6638,  29710, 16168, 11216,  29655, 15376, 13522,  \n3056, 6695, 14532,  7996, 7997, 15778,  20683, 7596, 15047,  \n8111, 20420, 10161,  7615, 14996, 18119,  3740, 20420, 21195,  \n7479, 29602, 11216,  7479, 7478, 29602,  7478, 17531, 29602,  \n9241, 14443, 21316,  13915, 777, 14558,  14266, 15721, 22595,  \n15893, 3378, 5285,  24911, 11229, 11230,  13875, 25369, 17837,  \n1745, 6550, 28194,  915, 20072, 5244,  1471, 12524, 3918,  \n17572, 17375, 12302,  10533, 9203, 27358,  20831, 5549, 29328,  \n13680, 13681, 28135,  3973, 4744, 17004,  10000, 21442, 20888,  \n7487, 5825, 7427,  18290, 440, 439,  21526, 6999, 28943,  \n21298, 20831, 29779,  13602, 1918, 1919,  28751, 6999, 8449,  \n15097, 8449, 6999,  8449, 9094, 8448,  8448, 9105, 452,  \n447, 7854, 7259,  5060, 21069, 10287,  19605, 10518, 19604,  \n18800, 10931, 8956,  28038, 25266, 11365,  28156, 10250, 10249,  \n11347, 11016, 22031,  12314, 2445, 10249,  9242, 22285, 9241,  \n14005, 5870, 6913,  22459, 28811, 28640,  26541, 2445, 19190,  \n9917, 9918, 7294,  6979, 14475, 6548,  29333, 1390, 3722,  \n21953, 13398, 15185,  12859, 14579, 426,  22260, 29135, 9025,  \n9025, 29135, 19639,  12215, 23536, 3500,  7814, 2510, 13940,  \n26074, 14913, 9790,  29136, 26074, 9789,  3837, 3955, 11734,  \n10354, 21047, 19663,  2161, 11887, 22727,  29336, 14267, 6307,  \n3077, 7140, 5456,  20436, 21945, 21749,  12786, 29337, 5169,  \n6169, 15171, 18974,  18639, 3618, 14821,  18887, 14595, 15086,  \n5168, 5169, 29476,  16069, 16068, 19367,  10167, 16766, 16878,  \n5168, 29780, 20255,  5306, 23334, 15889,  29780, 29713, 20255,  \n1318, 5957, 12941,  5290, 18579, 5680,  29608, 6307, 16171,  \n22860, 25652, 9612,  29713, 29612, 29714,  15312, 15340, 15311,  \n10802, 1050, 12876,  16985, 16041, 15946,  7839, 7069, 10644,  \n13593, 13525, 1869,  1258, 10839, 4875,  3228, 7717, 3229,  \n29714, 29716, 21518,  23193, 21104, 2590,  11782, 5433, 21065,  \n12379, 16020, 12068,  13150, 3360, 10664,  7601, 5045, 4666,  \n4963, 2789, 18212,  14735, 20103, 29718,  29718, 29717, 14735,  \n10612, 9798, 9797,  8917, 21319, 8918,  11026, 18070, 19689,  \n7731, 19810, 4084,  15378, 29620, 12879,  16487, 22573, 22359,  \n22517, 19899, 22150,  28375, 26827, 10031,  3190, 28566, 22841,  \n9154, 4276, 1825,  5810, 2981, 9989,  7610, 14075, 14074,  \n28746, 7464, 10923,  25434, 19615, 19616,  10282, 14121, 3814,  \n15761, 14646, 17976,  3991, 2335, 14530,  11420, 22576, 21644,  \n5840, 14184, 28566,  13831, 6748, 13830,  6024, 9300, 1385,  \n4241, 12187, 21028,  3190, 3189, 28566,  5021, 8093, 15017,  \n10857, 13439, 13440,  6799, 11081, 1079,  17201, 17975, 9186,  \n4026, 22640, 21547,  5840, 22801, 14184,  8671, 17979, 20866,  \n11538, 18345, 9433,  6991, 9668, 17191,  22738, 28811, 22459,  \n15261, 3949, 21005,  16494, 29149, 17948,  17971, 13806, 13807,  \n16371, 10438, 4279,  28822, 25138, 19588,  4881, 6328, 3773,  \n11794, 8827, 6658,  18182, 14274, 14275,  12029, 22263, 28375,  \n24089, 20463, 23470,  1416, 16488, 2756,  13866, 6925, 29150,  \n15287, 5535, 15288,  19829, 26250, 25089,  5778, 16957, 23262,  \n2606, 9113, 12956,  29483, 2465, 8211,  22822, 2465, 29483,  \n2131, 2132, 7143,  21612, 22095, 19761,  10541, 7588, 7589,  \n11812, 13195, 14219,  21620, 25437, 25211,  15388, 10616, 8107,  \n17718, 19982, 4220,  22793, 8622, 15436,  14964, 455, 19368,  \n20143, 13074, 19069,  14902, 8227, 3704,  5140, 6313, 5141,  \n14948, 7470, 22309,  3112, 19387, 3110,  1843, 29618, 29484,  \n23851, 29026, 18991,  2568, 28026, 10340,  2955, 14936, 28545,  \n4880, 7998, 11175,  28548, 2955, 28545,  21719, 7666, 9507,  \n10042, 21842, 2244,  10184, 6898, 7944,  28548, 20123, 2955,  \n19174, 29156, 10240,  9822, 16483, 8315,  4831, 12171, 8230,  \n14156, 3158, 22418,  9041, 11996, 2773,  24405, 13950, 1112,  \n7177, 6971, 7785,  3087, 13056, 19174,  19184, 2263, 2262,  \n15190, 7368, 19815,  22363, 29721, 24405,  29721, 29489, 24405,  \n14780, 29782, 29721,  22363, 14780, 29721,  19963, 1105, 578,  \n13372, 10851, 9795,  17369, 5376, 20679,  29782, 17075, 29781,  \n29783, 29781, 12069,  20425, 28564, 11480,  19809, 1206, 5983,  \n5205, 6077, 11200,  26695, 24833, 20321,  20324, 7834, 9993,  \n12069, 29784, 29783,  19585, 22102, 5812,  6231, 17855, 7575,  \n10029, 13346, 29159,  5627, 633, 635,  14035, 7285, 2415,  \n12069, 12068, 29784,  5117, 17786, 9513,  12068, 20361, 29784,  \n1347, 2458, 11125,  14776, 444, 14775,  19003, 29492, 21930,  \n5870, 14005, 9488,  4258, 654, 656,  8760, 4192, 15469,  \n22549, 26299, 18988,  3930, 21546, 21980,  5256, 21046, 22565,  \n27183, 3463, 29724,  21911, 17128, 7468,  13625, 2327, 2326,  \n5864, 21394, 10438,  22549, 9553, 26299,  29724, 3463, 29797,  \n13538, 29168, 13433,  13066, 29797, 3463,  10332, 13918, 16713,  \n11480, 11481, 3385,  20525, 14757, 12553,  29797, 13066, 29798,  \n9288, 17710, 17709,  13066, 13065, 29798,  8459, 9495, 8460,  \n29798, 13065, 22432,  20092, 3610, 3611,  6047, 4045, 10742,  \n7465, 11867, 22615,  15180, 12398, 11450,  3397, 15352, 12468,  \n3586, 16102, 3585,  28990, 11608, 11607,  13533, 21580, 13197,  \n13329, 7038, 7040,  8169, 12597, 5267,  16648, 18477, 4904,  \n22801, 28557, 12863,  7441, 7442, 18116,  6382, 2420, 14050,  \n18117, 17891, 18116,  6127, 4149, 15009,  6409, 28945, 19271,  \n13571, 1417, 24596,  20097, 6606, 6294,  513, 514, 7759,  \n7550, 13162, 14412,  29171, 28945, 6409,  2187, 438, 8556,  \n2399, 5094, 10105,  18145, 19911, 19381,  20526, 15206, 19332,  \n14548, 14547, 8124,  6910, 16537, 1449,  6780, 6557, 8221,  \n19615, 4241, 21028,  11492, 12540, 5800,  15679, 18875, 15872,  \n9057, 16548, 19940,  15996, 28992, 7012,  11497, 1455, 8645,  \n18374, 14385, 13098,  10764, 2424, 11296,  1025, 459, 9033,  \n13583, 553, 559,  12361, 481, 16207,  1976, 987, 8710,  \n17608, 2247, 9024,  24116, 28576, 3946,  3367, 14517, 14518,  \n8469, 13583, 2762,  3244, 14511, 3243,  24116, 23807, 20653,  \n8469, 2762, 13018,  2470, 17140, 16534,  4524, 14253, 1239,  \n16683, 1339, 4943,  2760, 2108, 2107,  1330, 15249, 17556,  \n21681, 28364, 23138,  20513, 13607, 13608,  25205, 19439, 29502,  \n12301, 21681, 23138,  5255, 390, 19969,  3814, 3333, 5833,  \n9665, 9664, 5233,  4134, 22194, 6903,  16506, 29503, 18689,  \n17443, 16268, 17444,  23216, 19197, 20890,  20638, 17815, 10712,  \n11370, 16416, 12120,  29026, 18990, 18991,  17904, 12137, 19509,  \n19985, 1410, 28603,  16519, 3448, 6523,  21909, 29361, 14098,  \n17306, 10587, 10736,  3802, 19221, 21828,  4469, 12573, 12763,  \n11660, 14098, 29361,  4877, 5727, 8005,  19611, 3396, 3395,  \n2383, 18647, 6967,  6594, 7535, 7534,  13444, 11564, 13863,  \n9356, 20127, 25422,  3541, 537, 1821,  22263, 25466, 26827,  \n16461, 22834, 12949,  18739, 523, 11153,  19672, 29176, 1765,  \n20406, 10918, 1587,  6542, 4168, 8306,  21552, 22231, 29364,  \n8167, 5834, 10422,  1698, 1699, 9840,  5920, 17775, 17902,  \n13556, 7275, 7276,  3880, 15602, 10591,  12234, 21779, 11170,  \n7335, 6478, 15828,  12102, 10939, 20439,  1723, 1722, 4869,  \n1636, 17463, 6988,  3875, 19777, 17905,  4661, 11684, 4915,  \n15218, 8210, 14926,  28804, 12725, 1765,  20901, 18610, 15248,  \n2435, 2434, 13422,  6770, 18703, 6769,  17337, 6769, 18703,  \n7884, 20127, 7715,  15259, 15260, 16144,  17101, 5158, 29365,  \n3405, 29502, 19439,  20617, 11173, 21945,  17337, 18703, 17336,  \n9547, 21637, 17711,  9562, 2973, 3357,  29509, 13875, 29506,  \n13798, 17993, 5883,  4342, 17938, 21610,  7571, 5158, 17101,  \n16312, 12510, 21473,  399, 11900, 3184,  8493, 11084, 8710,  \n16243, 17190, 17189,  3692, 4236, 3693,  13299, 13823, 319,  \n17498, 11575, 15907,  2148, 18085, 12261,  13799, 2159, 10830,  \n8518, 5897, 5896,  8784, 21376, 12339,  20897, 29628, 17337,  \n10926, 20812, 19098,  2215, 10568, 19604,  11173, 8324, 19161,  \n6117, 11385, 10314,  12045, 13632, 13631,  17336, 20897, 17337,  \n16412, 11554, 10910,  14715, 7503, 15612,  16464, 11166, 17327,  \n14597, 15690, 9693,  17980, 20909, 13914,  29630, 17837, 29511,  \n14757, 5341, 12553,  29181, 15223, 17102,  9293, 13498, 5026,  \n29510, 10234, 12045,  26845, 21803, 8427,  21968, 21264, 13002,  \n1912, 17994, 1420,  9504, 10747, 680,  17275, 29377, 9854,  \n29181, 28810, 22919,  8174, 16946, 21456,  12661, 11991, 15098,  \n29512, 25652, 22860,  2912, 5868, 14216,  22330, 18820, 6007,  \n8251, 2005, 4320,  12210, 9340, 10273,  3321, 3322, 2879,  \n10233, 29787, 1388,  10234, 29787, 10233,  15792, 19007, 21671,  \n4389, 29512, 22860,  15455, 14120, 13451,  17650, 22836, 22837,  \n2817, 13666, 6070,  7754, 4032, 4033,  3164, 19421, 3163,  \n6126, 3199, 800,  9462, 398, 17437,  1052, 23407, 8511,  \n7100, 8467, 22919,  7100, 22919, 29184,  23661, 7100, 29184,  \n17132, 17131, 6454,  19943, 3295, 12837,  21081, 20874, 20873,  \n4115, 20711, 10719,  18422, 11080, 1863,  13235, 15848, 10392,  \n17157, 15442, 475,  12976, 14332, 14314,  874, 8719, 10887,  \n9583, 16947, 16946,  11057, 1212, 2887,  20081, 29514, 28816,  \n11890, 9548, 6677,  2806, 19238, 19390,  4249, 3808, 7217,  \n3451, 12914, 1562,  14124, 21474, 13229,  17668, 809, 16178,  \n7225, 1134, 17328,  20504, 3909, 10553,  4706, 6802, 12211,  \n16241, 16240, 17076,  22554, 14116, 16656,  29302, 5898, 18977,  \n1742, 15293, 14952,  21379, 11964, 29729,  29729, 21255, 13560,  \n10384, 15221, 22349,  9368, 3876, 10821,  16885, 16047, 4361,  \n7049, 9855, 9320,  2227, 2138, 8266,  5787, 10537, 12335,  \n12661, 15098, 29799,  23326, 8494, 15661,  29799, 26198, 12661,  \n8433, 20854, 18958,  6276, 9007, 18352,  10780, 20837, 23249,  \n29728, 10624, 21558,  9527, 16926, 2127,  23407, 1051, 27794,  \n16517, 21811, 13105,  12160, 4041, 15733,  1097, 13557, 13885,  \n22337, 8068, 8067,  11904, 29738, 3571,  3204, 16524, 9888,  \n12913, 2929, 20265,  12121, 2973, 15209,  11066, 6880, 20544,  \n14758, 20525, 13617,  29788, 22337, 8067,  29788, 22338, 22337,  \n3570, 25848, 16300,  1440, 7300, 1441,  1670, 20842, 4394,  \n12936, 12935, 18998,  2410, 18430, 2411,  7777, 12073, 7617,  \n25848, 29644, 16300,  29734, 8509, 8511,  8509, 29734, 29735,  \n21330, 13196, 23522,  29644, 20112, 3664,  14484, 5648, 22773,  \n29736, 16662, 29735,  2773, 15058, 824,  4520, 4429, 20224,  \n9559, 22585, 9875,  17018, 8112, 17019,  13904, 16681, 20516,  \n16083, 4221, 17888,  15977, 17290, 29737,  29640, 8905, 12843,  \n7128, 20617, 14506,  12042, 22338, 27631,  21725, 5183, 10292,  \n14139, 3074, 8169,  20112, 29644, 24252,  14475, 10409, 6548,  \n17630, 13273, 20298,  10688, 2749, 9739,  13330, 17276, 13155,  \n6940, 8393, 13199,  28142, 22899, 4356,  12042, 27631, 3649,  \n17361, 21185, 7608,  28142, 4356, 2657,  14306, 2487, 5855,  \n8400, 17664, 10126,  27631, 29739, 3649,  10088, 12076, 8907,  \n17854, 9375, 2049,  14839, 3202, 783,  29740, 15103, 15976,  \n29518, 3314, 8904,  18684, 21257, 15487,  25125, 10111, 18301,  \n15976, 15103, 15782,  2731, 10199, 11610,  11848, 9358, 9357,  \n22565, 24410, 5256,  3850, 3851, 12421,  13962, 11756, 5430,  \n2750, 14369, 2908,  6350, 13950, 20003,  15104, 15103, 29648,  \n15103, 29740, 29648,  24740, 15104, 29648,  6785, 1924, 1923,  \n1564, 7204, 6450,  14344, 7498, 14174,  19244, 20136, 20138,  \n29647, 24740, 29648,  3536, 29790, 29789,  4776, 17803, 4775,  \n11909, 17654, 6738,  18021, 973, 18020,  20743, 5902, 20237,  \n8145, 10539, 8705,  972, 19380, 24740,  11596, 18227, 12459,  \n15503, 5482, 9012,  28967, 28993, 17089,  16524, 3204, 5424,  \n973, 18021, 19380,  1042, 12105, 10195,  536, 988, 10716,  \n454, 18146, 10103,  3263, 14407, 4248,  17503, 10455, 26898,  \n972, 973, 19380,  9622, 10956, 3705,  6611, 11669, 6418,  \n2580, 6400, 12912,  11556, 14962, 19670,  27728, 10390, 10393,  \n6947, 13439, 26186,  6918, 12900, 14832,  18450, 6702, 11006,  \n3765, 16106, 16105,  2535, 23139, 10886,  29382, 19547, 2006,  \n20711, 18059, 12490,  6017, 15211, 20619,  14059, 4541, 4540,  \n21071, 6565, 20315,  2006, 19547, 5246,  3114, 4582, 6303,  \n27728, 13500, 29651,  12021, 13500, 27728,  16509, 13823, 11906,  \n17295, 14154, 7134,  22491, 13826, 14497,  3234, 17875, 3235,  \n6947, 26186, 29531,  29531, 21359, 6947,  3322, 18625, 25381,  \n6515, 6514, 11872,  269, 245, 172,  172, 5847, 286,  \n5847, 5848, 286,  286, 5848, 285,  8443, 12, 14512,  \n4, 8658, 9,  9, 8658, 10,  8658, 11368, 10,  \n28, 10, 11368,  11368, 18429, 28,  19253, 28, 18429,  \n19253, 12844, 15,  2, 15, 12844,  2, 12844, 1,  \n3, 1, 12844,  21885, 3, 5872,  21885, 8035, 8036,  \n32, 22, 18,  8036, 18, 22,  16458, 7579, 8036,  \n18, 8036, 7579,  18, 7579, 30,  2462, 7580, 7579,  \n7579, 7580, 30,  12063, 7580, 12062,  7580, 12063, 30,  \n12063, 18970, 30,  30, 18970, 0,  173, 20649, 17442,  \n20649, 14942, 17442,  17442, 1388, 155,  155, 1388, 29787,  \n29186, 105, 94,  105, 29186, 57,  29186, 27799, 57,  \n28593, 57, 27799,  57, 28593, 42,  28593, 27610, 42,  \n43, 36, 27807,  42, 27610, 36,  27610, 27019, 36,  \n27021, 37, 27807,  63, 28003, 27441,  39, 50, 49,  \n50, 39, 28409,  28409, 27826, 52,  52, 28021, 28424,  \n29673, 29545, 29749,  29749, 169, 29673,  170, 169, 189,  \n12692, 245, 244,  12692, 172, 245]\n}\n}"
  },
  {
    "path": "13_pbd_mesh/imgui.ini",
    "content": "[Window][Debug##Default]\nPos=60,60\nSize=400,400\nCollapsed=0\n\n[Window][Controls]\nPos=51,51\nSize=307,256\nCollapsed=0\n\n"
  },
  {
    "path": "13_pbd_mesh/main.py",
    "content": "\"\"\"\nMain Orchestrator - XPBD Mesh Simulation\n\nThis module ties everything together:\n- Allocates all Taichi fields (memory)\n- Sets simulation constants (time step, compliance, etc.)\n- Runs the substep() loop which calls functions from the modules\n- Handles the GUI window, camera, and user input\n- Manages USD export for animation\n\"\"\"\n\nimport taichi as ti\nimport numpy as np\nimport json\nimport time\nimport warp as wp\nimport warp.render\n\n# Import all modules\nfrom xpbd_base import init_physics, pre_solve, post_solve\nfrom constraints import solve_edges, solve_volumes\nfrom skinning import build_hash_grid, compute_skinning_info_hashed, update_vis_mesh\n\nti.init(arch=ti.cpu, default_fp=ti.f64)\n\n\ndef load_dual_mesh_from_json(filepath):\n    \"\"\"Load simulation and visual mesh data from JSON file.\"\"\"\n    try:\n        with open(filepath, 'r') as f:\n            data = json.load(f)\n    except Exception as e:\n        print(f\"Error loading or parsing {filepath}: {e}\")\n        exit()\n\n    sim_verts_np = np.array(data['verts'], dtype=np.float64).reshape((-1, 3))\n    tet_ids_np = np.array(data['tetIds'], dtype=np.int32).reshape((-1, 4))\n    edge_ids_np = np.array(data['edgeIds'], dtype=np.int32).reshape((-1, 2))\n\n    vis_data = data.get('dragonVis')\n    if not vis_data:\n        print(\"Error: JSON file must contain a 'dragonVis' object for the visual mesh.\")\n        exit()\n    vis_verts_np = np.array(vis_data['verts'], dtype=np.float64).reshape((-1, 3))\n    vis_tri_ids_np = np.array(vis_data['triIds'], dtype=np.int32)\n    \n    return {\n        \"sim_verts\": sim_verts_np, \"tet_ids\": tet_ids_np, \"edge_ids\": edge_ids_np,\n        \"vis_verts\": vis_verts_np, \"vis_tri_ids\": vis_tri_ids_np\n    }\n\n\nclass USDExporter:\n    \"\"\"USD animation exporter for Blender compatibility.\"\"\"\n    \n    def __init__(self, output_path=\"dragon_animation.usd\", fps=60, scale=1.0):\n        self.output_path = output_path\n        self.fps = fps\n        self.scale = scale\n        self.frame_dt = 1.0 / fps\n        self.sim_time = 0.0\n        self.frame_count = 0\n        \n        # Initialize Warp USD renderer with scaling\n        self.renderer = wp.render.UsdRenderer(output_path, scaling=scale)\n        self.renderer.render_ground()\n        \n        print(f\"USD exporter initialized: {output_path}\")\n        print(f\"FPS: {fps}\")\n        print(f\"Scale: {scale}x\")\n    \n    def export_frame(self, vertices, faces):\n        \"\"\"Export a single frame to the USD file.\"\"\"\n        self.renderer.begin_frame(self.sim_time)\n        self.renderer.render_mesh(\n            name=\"dragon_mesh\",\n            points=vertices,\n            indices=faces.flatten()\n        )\n        self.renderer.end_frame()\n        \n        self.frame_count += 1\n        self.sim_time += self.frame_dt\n        \n        # Print progress every 60 frames\n        if self.frame_count % 60 == 0:\n            print(f\"Exported frame {self.frame_count} at time {self.sim_time:.3f}s\")\n    \n    def save(self):\n        \"\"\"Finalize and save the USD file.\"\"\"\n        self.renderer.save()\n        print(f\"\\nUSD animation saved: {self.output_path}\")\n        print(f\"Total frames: {self.frame_count}\")\n        print(f\"Duration: {self.sim_time:.3f} seconds\")\n        print(f\"\\nTo import into Blender:\")\n        print(f\"1. File > Import > Universal Scene Description (.usd)\")\n        print(f\"2. Select '{self.output_path}'\")\n        print(f\"3. The animation will be imported as a single animated sequence!\")\n\n\n# ============================================================================\n# Load Mesh Data\n# ============================================================================\n\nmesh = load_dual_mesh_from_json(\"dragon_data.json\")\n\n# ============================================================================\n# Simulation Constants\n# ============================================================================\n\npaused = True\ngravity = ti.Vector([0.0, -9.8, 0.0])\ndt = 1.0 / 60.0\nnum_substeps = 10\nsolver_iterations = 5\nsdt = dt / num_substeps\n\nnum_particles = len(mesh[\"sim_verts\"])\nnum_tets = len(mesh[\"tet_ids\"])\nnum_edges = len(mesh[\"edge_ids\"])\nnum_vis_verts = len(mesh[\"vis_verts\"])\nnum_vis_tris = len(mesh[\"vis_tri_ids\"]) // 3\n\nedge_compliance = 0.0\nvol_compliance = 0.0\nedge_compliance_slider = 0.0\nvol_id_order_np = np.array([[1, 3, 2], [0, 2, 3], [0, 3, 1], [0, 1, 2]], dtype=np.int32)\nvol_id_order = ti.field(ti.i32, shape=(4, 3))\nvol_id_order.from_numpy(vol_id_order_np)\n\nexport_enabled = False\nexport_frame_count = 0\nusd_exporter = None\n\nCELL_SPACING = 0.05\ninv_cell_spacing = 1.0 / CELL_SPACING\nGRID_SIZE = 128\n\nBOX_SIZE = 5.0\nbox_min = ti.Vector([-BOX_SIZE/2, 0.0, -BOX_SIZE/2])\nbox_max = ti.Vector([BOX_SIZE/2, BOX_SIZE, BOX_SIZE/2])\n\n# ============================================================================\n# Taichi Field Allocations\n# ============================================================================\n\n# Simulation mesh fields\npos = ti.Vector.field(3, dtype=ti.f64, shape=num_particles)\nprev_pos = ti.Vector.field(3, dtype=ti.f64, shape=num_particles)\nvel = ti.Vector.field(3, dtype=ti.f64, shape=num_particles)\ninv_mass = ti.field(dtype=ti.f64, shape=num_particles)\nrest_vol = ti.field(dtype=ti.f64, shape=num_tets)\nedge_lengths = ti.field(dtype=ti.f64, shape=num_edges)\ntet_ids = ti.field(ti.i32, shape=(num_tets, 4))\nedge_ids = ti.field(ti.i32, shape=(num_edges, 2))\n\n# XPBD accumulated lambdas (one per constraint, reset each substep)\nedge_lambdas = ti.field(dtype=ti.f64, shape=num_edges)\nvol_lambdas = ti.field(dtype=ti.f64, shape=num_tets)\n\n# Visual mesh fields\nvis_mesh_rest_pos = ti.Vector.field(3, dtype=ti.f64, shape=num_vis_verts)\nvis_mesh_pos = ti.Vector.field(3, dtype=ti.f64, shape=num_vis_verts)\nvis_mesh_indices = ti.field(ti.i32, shape=num_vis_tris * 3)\nvis_mesh_colors = ti.Vector.field(3, dtype=ti.f32, shape=num_vis_verts)\n\n# Skinning fields\nskinning_info_tet_idx = ti.field(ti.i32, shape=num_vis_verts)\nskinning_info_bary_weights = ti.Vector.field(3, dtype=ti.f64, shape=num_vis_verts)\nmin_dist = ti.field(ti.f64, shape=num_vis_verts)\n\n# Spatial hash grid fields\ngrid_cell_counts = ti.field(ti.i32, shape=(GRID_SIZE, GRID_SIZE, GRID_SIZE))\ngrid_cell_starts = ti.field(ti.i32, shape=(GRID_SIZE, GRID_SIZE, GRID_SIZE))\nsorted_vis_vert_ids = ti.field(ti.i32, shape=num_vis_verts)\n\n# Ground plane fields\nground_vertices = ti.Vector.field(3, dtype=ti.f64, shape=4)\nground_indices = ti.field(ti.i32, shape=6)\nground_colors = ti.Vector.field(3, dtype=ti.f32, shape=4)\n\n# ============================================================================\n# Initialize Fields from Mesh Data\n# ============================================================================\n\npos.from_numpy(mesh[\"sim_verts\"])\ntet_ids.from_numpy(mesh[\"tet_ids\"])\nedge_ids.from_numpy(mesh[\"edge_ids\"])\nvis_mesh_rest_pos.from_numpy(mesh[\"vis_verts\"])\nvis_mesh_indices.from_numpy(mesh[\"vis_tri_ids\"])\nvis_mesh_colors.fill(ti.Vector([0.968, 0.541, 0.113], dt=ti.f32))\nground_vertices.from_numpy(np.array([[-BOX_SIZE/2,0,-BOX_SIZE/2],[BOX_SIZE/2,0,-BOX_SIZE/2],[BOX_SIZE/2,0,BOX_SIZE/2],[-BOX_SIZE/2,0,BOX_SIZE/2]], dtype=np.float64))\nground_indices.from_numpy(np.array([0,1,2,0,2,3], dtype=np.int32))\nground_colors.fill(ti.Vector([0.8, 0.8, 0.8], dt=ti.f32))\n\n\n# ============================================================================\n# Simulation Substep Function\n# ============================================================================\n\n@ti.kernel\ndef reset_constraint_lambdas(\n    num_e: ti.i32, num_v: ti.i32,\n    e_lambdas: ti.template(), v_lambdas: ti.template()\n):\n    for i in range(num_e):\n        e_lambdas[i] = 0.0\n    for i in range(num_v):\n        v_lambdas[i] = 0.0\n\n\ndef substep():\n    pre_solve(sdt, 1, num_particles, gravity, box_min, box_max, pos, prev_pos, vel, inv_mass)\n    # XPBD: reset lambdas once per substep (they accumulate across solver iterations)\n    reset_constraint_lambdas(num_edges, num_tets, edge_lambdas, vol_lambdas)\n    for _ in range(solver_iterations):\n        solve_edges(edge_compliance, sdt, num_edges, pos, edge_ids, edge_lengths, inv_mass, edge_lambdas)\n        solve_volumes(vol_compliance, sdt, num_tets, pos, tet_ids, rest_vol, inv_mass, vol_id_order, vol_lambdas)\n    post_solve(sdt, num_particles, pos, prev_pos, vel, inv_mass)\n\n\n# ============================================================================\n# Initialize Simulation\n# ============================================================================\n\nprint(\"Building spatial hash grid for skinning...\")\nstart_time = time.time()\nbuild_hash_grid(num_vis_verts, GRID_SIZE, inv_cell_spacing, vis_mesh_rest_pos, grid_cell_counts, grid_cell_starts, sorted_vis_vert_ids)\nend_time = time.time()\nprint(f\"Hash grid built in {end_time - start_time:.4f} seconds.\")\n\nprint(\"Computing skinning information with hash grid...\")\nstart_time = time.time()\ncompute_skinning_info_hashed(num_tets, num_vis_verts, CELL_SPACING, inv_cell_spacing, GRID_SIZE, pos, tet_ids, vis_mesh_rest_pos, grid_cell_counts, grid_cell_starts, sorted_vis_vert_ids, min_dist, skinning_info_tet_idx, skinning_info_bary_weights)\nend_time = time.time()\nprint(f\"Skinning computation finished in {end_time - start_time:.4f} seconds.\")\n\ninit_physics(num_edges, num_tets, num_particles, edge_ids, edge_lengths, pos, tet_ids, rest_vol, inv_mass, prev_pos, vel)\n\n# ============================================================================\n# Setup UI and Camera\n# ============================================================================\n\nwindow = ti.ui.Window(\"Taichi XPBD - Dragon Simulation\", (1024, 1024), vsync=True)\ncanvas = window.get_canvas()\nscene = window.get_scene()\ncamera = ti.ui.Camera()\ncamera.position(0, 1.5, 4.5)\ncamera.lookat(0, 0.5, 0)\n\n# ============================================================================\n# Main Simulation and Rendering Loop\n# ============================================================================\n\nwhile window.running:\n    gui = window.GUI\n    with gui.sub_window(\"Controls\", 0.05, 0.05, 0.3, 0.25):\n        paused = gui.checkbox(\"Paused\", paused)\n        \n        gui.text(\"Animation Export:\")\n        export_enabled = gui.checkbox(\"Export Animation\", export_enabled)\n        \n        if export_enabled and usd_exporter is None:\n            usd_exporter = USDExporter(\"dragon_animation.usd\", fps=60, scale=1.0)\n            print(\"USD exporter initialized!\")\n        \n        edge_compliance_slider = gui.slider_float(\"Edge Compliance\", edge_compliance_slider, 0.0, 50.0)\n        edge_compliance = edge_compliance_slider\n        vol_compliance = gui.slider_float(\"Volume Compliance\", vol_compliance, 0.0, 10.0)\n        \n        gui.text(f\"Exported Frames: {export_frame_count}\")\n        if usd_exporter:\n            gui.text(f\"USD File: {usd_exporter.output_path}\")\n        \n        if gui.button(\"Reset\"):\n            pos.from_numpy(mesh[\"sim_verts\"])\n            init_physics(num_edges, num_tets, num_particles, edge_ids, edge_lengths, pos, tet_ids, rest_vol, inv_mass, prev_pos, vel)\n            export_frame_count = 0\n            if usd_exporter:\n                usd_exporter = None\n\n    if not paused:\n        for _ in range(num_substeps):\n            substep()\n\n    # Update visual mesh before rendering\n    update_vis_mesh(num_vis_verts, pos, tet_ids, vis_mesh_rest_pos, vis_mesh_pos, skinning_info_tet_idx, skinning_info_bary_weights)\n    \n    # Export mesh frame if enabled\n    if export_enabled and not paused and usd_exporter:\n        vertices = vis_mesh_pos.to_numpy()\n        faces = vis_mesh_indices.to_numpy().reshape((-1, 3))\n        usd_exporter.export_frame(vertices, faces)\n        export_frame_count += 1\n\n    # Rendering\n    camera.track_user_inputs(window, movement_speed=0.03, hold_key=ti.ui.RMB)\n    scene.set_camera(camera)\n    scene.ambient_light((0.5, 0.5, 0.5))\n    scene.point_light(pos=(2, 3, 4), color=(1, 1, 1))\n    \n    scene.mesh(vis_mesh_pos, indices=vis_mesh_indices, per_vertex_color=vis_mesh_colors)\n    scene.mesh(ground_vertices, indices=ground_indices, per_vertex_color=ground_colors)\n    canvas.set_background_color((1.0, 1.0, 1.0))  # white\n\n    canvas.scene(scene)\n    window.show()\n\n# Save USD file when simulation ends\nif usd_exporter and export_frame_count > 0:\n    usd_exporter.save()\n    print(f\"\\nAnimation export complete!\")\n    print(f\"Total frames exported: {export_frame_count}\")\n    print(f\"USD file: {usd_exporter.output_path}\")\n    print(f\"\\nTo import into Blender:\")\n    print(f\"1. File > Import > Universal Scene Description (.usd)\")\n    print(f\"2. Select '{usd_exporter.output_path}'\")\n    print(f\"3. The animation will be imported as a single animated sequence!\")\n"
  },
  {
    "path": "13_pbd_mesh/skinning/__init__.py",
    "content": "from .hash_grid import build_hash_grid\nfrom .skinning import compute_skinning_info_hashed, update_vis_mesh\n\n__all__ = [\n    'build_hash_grid',\n    'compute_skinning_info_hashed',\n    'update_vis_mesh',\n]\n"
  },
  {
    "path": "13_pbd_mesh/skinning/hash_grid.py",
    "content": "\"\"\"\nThis module builds a spatial hash grid for efficient nearest-neighbor queries used in the skinning computation.\n\"\"\"\n\nimport taichi as ti\nimport numpy as np\nimport sys\nimport os\n_parent_dir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nif _parent_dir not in sys.path:\n    sys.path.insert(0, _parent_dir)\nfrom xpbd_base import get_grid_cell\n\n\ndef build_hash_grid(\n    num_vis_verts: int, grid_size: int, inv_cell_spacing: float,\n    vis_mesh_rest_pos: ti.template(), grid_cell_counts: ti.template(),\n    grid_cell_starts: ti.template(), sorted_vis_vert_ids: ti.template()\n):\n    \"\"\"\n    Build a spatial hash grid for efficient skinning queries.\n    \n    1. Count how many visual vertices fall into each grid cell\n    2. Compute prefix sums to determine starting indices for each cell\n    3. Sort visual vertex IDs by their grid cell locations\n    \"\"\"\n    grid_cell_counts.fill(0)\n    \n    @ti.kernel\n    def count_verts_in_cells(\n        num_vis_verts: ti.i32, inv_cell_spacing: ti.f64, grid_size: ti.i32,\n        vis_mesh_rest_pos: ti.template(), grid_cell_counts: ti.template()\n    ):\n        for i in range(num_vis_verts):\n            cell = get_grid_cell(vis_mesh_rest_pos[i], inv_cell_spacing, grid_size)\n            ti.atomic_add(grid_cell_counts[cell], 1)\n    \n    count_verts_in_cells(num_vis_verts, inv_cell_spacing, grid_size, vis_mesh_rest_pos, grid_cell_counts)\n\n    total_verts = 0\n    counts_np = grid_cell_counts.to_numpy()\n    starts_np = np.zeros_like(counts_np)\n    # This prefix sum must be done serially on the CPU.\n    for i in range(grid_size):\n        for j in range(grid_size):\n            for k in range(grid_size):\n                starts_np[i, j, k] = total_verts\n                total_verts += counts_np[i, j, k]\n    grid_cell_starts.from_numpy(starts_np)\n\n    write_offsets = ti.field(ti.i32, shape=(grid_size, grid_size, grid_size))\n    write_offsets.copy_from(grid_cell_starts)\n\n    @ti.kernel\n    def fill_sorted_ids(\n        num_vis_verts: ti.i32, inv_cell_spacing: ti.f64, grid_size: ti.i32,\n        vis_mesh_rest_pos: ti.template(), write_offsets: ti.template(),\n        sorted_vis_vert_ids: ti.template()\n    ):\n        for i in range(num_vis_verts):\n            cell = get_grid_cell(vis_mesh_rest_pos[i], inv_cell_spacing, grid_size)\n            write_idx = ti.atomic_add(write_offsets[cell], 1)\n            sorted_vis_vert_ids[write_idx] = i\n\n    fill_sorted_ids(num_vis_verts, inv_cell_spacing, grid_size, vis_mesh_rest_pos, write_offsets, sorted_vis_vert_ids)\n"
  },
  {
    "path": "13_pbd_mesh/skinning/skinning.py",
    "content": "\"\"\"\nThis module handles the computation of skinning weights and updates the visual mesh.\nSkinning maps visual mesh vertices to simulation tetrahedra using barycentric coordinates,\nallowing the visual mesh to deform smoothly with the simulation mesh.\n\"\"\"\n\nimport taichi as ti\nimport sys\nimport os\n# Add parent directory to path to import xpbd_base\n_parent_dir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nif _parent_dir not in sys.path:\n    sys.path.insert(0, _parent_dir)\nfrom xpbd_base import get_barycentric_coords, get_grid_cell\n\n\n@ti.kernel\ndef compute_skinning_info_hashed(\n    num_tets: ti.i32, num_vis_verts: ti.i32, cell_spacing: ti.f64,\n    inv_cell_spacing: ti.f64, grid_size: ti.i32,\n    pos: ti.template(), tet_ids: ti.template(), vis_mesh_rest_pos: ti.template(),\n    grid_cell_counts: ti.template(), grid_cell_starts: ti.template(),\n    sorted_vis_vert_ids: ti.template(), min_dist: ti.template(),\n    skinning_info_tet_idx: ti.template(), skinning_info_bary_weights: ti.template()\n):\n    \"\"\"\n    For each simulation tetrahedron, this kernel:\n    1. Determines which grid cells the tetrahedron overlaps\n    2. Queries the hash grid to find nearby visual vertices\n    3. Computes barycentric coordinates for each visual vertex\n    4. Stores the closest tetrahedron and barycentric weights for each visual vertex\n    \"\"\"\n    min_dist.fill(1e9)\n    skinning_info_tet_idx.fill(-1)\n\n    for tet_idx in range(num_tets):\n        p_indices = ti.Vector([tet_ids[tet_idx, 0], tet_ids[tet_idx, 1], tet_ids[tet_idx, 2], tet_ids[tet_idx, 3]])\n        p0, p1, p2, p3 = pos[p_indices[0]], pos[p_indices[1]], pos[p_indices[2]], pos[p_indices[3]]\n        \n        min_coord = min(p0, p1, p2, p3) - cell_spacing\n        max_coord = max(p0, p1, p2, p3) + cell_spacing\n        min_cell = get_grid_cell(min_coord, inv_cell_spacing, grid_size)\n        max_cell = get_grid_cell(max_coord, inv_cell_spacing, grid_size)\n\n        for i, j, k in ti.ndrange(\n            (min_cell[0], max_cell[0] + 1), (min_cell[1], max_cell[1] + 1), (min_cell[2], max_cell[2] + 1)):\n            \n            start, end = grid_cell_starts[i, j, k], grid_cell_starts[i, j, k] + grid_cell_counts[i, j, k]\n            \n            for vert_offset in range(start, end):\n                vis_vert_idx = sorted_vis_vert_ids[vert_offset]\n                p_vis = vis_mesh_rest_pos[vis_vert_idx]\n                \n                bary = get_barycentric_coords(p_vis, p0, p1, p2, p3)\n                dist = 0.0\n                for c in ti.static(range(4)): dist = max(dist, -bary[c])\n                \n                if dist < ti.atomic_min(min_dist[vis_vert_idx], dist):\n                    skinning_info_tet_idx[vis_vert_idx] = tet_idx\n                    skinning_info_bary_weights[vis_vert_idx] = ti.Vector([bary[0], bary[1], bary[2]])\n\n\n@ti.kernel\ndef update_vis_mesh(\n    num_vis_verts: ti.i32,\n    pos: ti.template(), tet_ids: ti.template(),\n    vis_mesh_rest_pos: ti.template(), vis_mesh_pos: ti.template(),\n    skinning_info_tet_idx: ti.template(), skinning_info_bary_weights: ti.template()\n):\n    \"\"\"\n    For each visual vertex, this kernel:\n    1. Looks up the associated simulation tetrahedron\n    2. Retrieves the barycentric weights\n    3. Interpolates the visual vertex position from the tetrahedron vertices\n    \"\"\"\n    for i in range(num_vis_verts):\n        tet_idx = skinning_info_tet_idx[i]\n        if tet_idx < 0:\n            vis_mesh_pos[i] = vis_mesh_rest_pos[i]\n            continue\n        p_indices = ti.Vector([tet_ids[tet_idx, 0], tet_ids[tet_idx, 1], tet_ids[tet_idx, 2], tet_ids[tet_idx, 3]])\n        p0, p1, p2, p3 = pos[p_indices[0]], pos[p_indices[1]], pos[p_indices[2]], pos[p_indices[3]]\n        b = skinning_info_bary_weights[i]\n        b3 = 1.0 - b.sum()\n        vis_mesh_pos[i] = b[0] * p0 + b[1] * p1 + b[2] * p2 + b3 * p3\n"
  },
  {
    "path": "13_pbd_mesh/xpbd_base.py",
    "content": "\"\"\"\nThis module contains:\n- Helper functions (tet volume, barycentric coords, grid cell, box clamping)\n- Time integration (pre_solve, post_solve)\n- Physics initialization (init_physics)\n\"\"\"\n\nimport taichi as ti\n\n\n@ti.func\ndef get_tet_volume(p_indices, pos):\n    \"\"\"Calculate the volume of a tetrahedron given vertex indices and positions.\"\"\"\n    p0, p1, p2, p3 = pos[p_indices[0]], pos[p_indices[1]], pos[p_indices[2]], pos[p_indices[3]]\n    return (p1 - p0).cross(p2 - p0).dot(p3 - p0) / 6.0\n\n\n@ti.func\ndef get_barycentric_coords(p, a, b, c, d):\n    \"\"\"Compute barycentric coordinates of point p relative to tetrahedron (a, b, c, d).\"\"\"\n    mat = ti.Matrix.cols([a - d, b - d, c - d])\n    weights = ti.Vector([0.0, 0.0, 0.0])\n    if abs(mat.determinant()) > 1e-9:\n        weights = mat.inverse() @ (p - d)\n    w4 = 1.0 - weights.sum()\n    return ti.Vector([weights[0], weights[1], weights[2], w4])\n\n\n@ti.func\ndef get_grid_cell(p, inv_cell_spacing, grid_size):\n    \"\"\"Convert world position to grid cell coordinates.\"\"\"\n    return ti.max(0, ti.min(grid_size - 1, ti.floor(p * inv_cell_spacing, ti.i32)))\n\n\n@ti.func\ndef clamp_to_box(p, box_min, box_max):\n    \"\"\"Clamp a position to stay within the collision box bounds.\"\"\"\n    return ti.Vector([\n        ti.max(box_min[0], ti.min(box_max[0], p[0])),\n        ti.max(box_min[1], ti.min(box_max[1], p[1])),\n        ti.max(box_min[2], ti.min(box_max[2], p[2]))\n    ])\n\n\n@ti.kernel\ndef init_physics(\n    num_edges: ti.i32, num_tets: ti.i32, num_particles: ti.i32,\n    edge_ids: ti.template(), edge_lengths: ti.template(),\n    pos: ti.template(), tet_ids: ti.template(), rest_vol: ti.template(),\n    inv_mass: ti.template(), prev_pos: ti.template(), vel: ti.template()\n):\n    \"\"\"\n    1. Compute rest lengths for all edges\n    2. Compute rest volumes and inverse masses for all tetrahedra\n    3. Initialize positions, previous positions, and velocities\n    \"\"\"\n    for i in range(num_edges):\n        id0, id1 = edge_ids[i, 0], edge_ids[i, 1]\n        edge_lengths[i] = (pos[id0] - pos[id1]).norm()\n\n    inv_mass.fill(0.0)\n    for i in range(num_tets):\n        p_indices = ti.Vector([tet_ids[i, 0], tet_ids[i, 1], tet_ids[i, 2], tet_ids[i, 3]])\n        vol = get_tet_volume(p_indices, pos)\n        rest_vol[i] = vol\n        if vol > 0.0:\n            p_inv_mass = 1.0 / (vol / 4.0)\n            for j in ti.static(range(4)):\n                inv_mass[p_indices[j]] += p_inv_mass\n\n    for i in range(num_particles):\n        pos[i] += ti.Vector([0.0, 1.0, 0.0])\n        prev_pos[i] = pos[i]\n        vel[i] = ti.Vector([0.0, 0.0, 0.0])\n\n\n@ti.kernel\ndef pre_solve(\n    dt: ti.f64, use_gravity: ti.i32, num_particles: ti.i32,\n    gravity: ti.template(), box_min: ti.template(), box_max: ti.template(),\n    pos: ti.template(), prev_pos: ti.template(), vel: ti.template(), inv_mass: ti.template()\n):\n    \"\"\"\n    1. Apply gravity to velocities\n    2. Save current positions\n    3. Integrate positions forward\n    4. Clamp positions to box bounds\n    \"\"\"\n    for i in range(num_particles):\n        if inv_mass[i] == 0.0: continue\n        if use_gravity != 0:\n            vel[i] += gravity * dt\n        prev_pos[i] = pos[i]\n        pos[i] += vel[i] * dt\n        \n        # Box collision - clamp position to box bounds\n        pos[i] = clamp_to_box(pos[i], box_min, box_max)\n\n\n@ti.kernel\ndef post_solve(\n    dt: ti.f64, num_particles: ti.i32,\n    pos: ti.template(), prev_pos: ti.template(), vel: ti.template(), inv_mass: ti.template()\n):\n    for i in range(num_particles):\n        if inv_mass[i] == 0.0: continue\n        vel[i] = (pos[i] - prev_pos[i]) / dt\n"
  },
  {
    "path": "14_pbf/constraints/__init__.py",
    "content": "from .density import solve_density_constraints\nfrom .vorticity import calculate_vorticity, apply_vorticity_confinement\nfrom .viscosity import apply_xsph_viscosity\n\n__all__ = [\n    'solve_density_constraints',\n    'calculate_vorticity',\n    'apply_vorticity_confinement',\n    'apply_xsph_viscosity',\n]\n"
  },
  {
    "path": "14_pbf/constraints/density.py",
    "content": "import taichi as ti\nimport sys\nimport os\n_parent_dir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nif _parent_dir not in sys.path:\n    sys.path.insert(0, _parent_dir)\nfrom sph_base import poly6_value, spiky_gradient\n\n\n@ti.func\ndef compute_scorr(pos_ji, h_, poly6_factor_, corr_deltaQ_coeff_, corrK_):\n    x = poly6_value(pos_ji.norm(), h_, poly6_factor_) / poly6_value(corr_deltaQ_coeff_ * h_, h_, poly6_factor_)\n    x = x * x; x = x * x\n    return -corrK_ * x\n\n\n@ti.kernel\ndef solve_density_constraints(\n    positions: ti.template(),\n    particle_num_neighbors: ti.template(),\n    particle_neighbors: ti.template(),\n    lambdas: ti.template(),\n    position_deltas: ti.template(),\n    h_: float,\n    poly6_factor_: float,\n    spiky_grad_factor_: float,\n    mass_: float,\n    rho0_: float,\n    lambda_epsilon_: float,\n    epsilon_: float,\n    corr_deltaQ_coeff_: float,\n    corrK_: float\n):\n\n    # Pass 1: Calculate lambda values (constraint multipliers)\n    for p_i in positions:\n        pos_i = positions[p_i]\n        grad_i, sum_gradient_sqr, density_constraint = ti.Vector([0.0, 0.0, 0.0]), 0.0, 0.0\n\n        for j in range(particle_num_neighbors[p_i]):\n            p_j = particle_neighbors[p_i, j]\n            pos_ji = pos_i - positions[p_j]\n            grad_j = spiky_gradient(pos_ji, h_, spiky_grad_factor_)\n            grad_i += grad_j\n            sum_gradient_sqr += grad_j.dot(grad_j)\n            density_constraint += poly6_value(pos_ji.norm(), h_, poly6_factor_)\n\n        density_constraint = (mass_ * density_constraint / rho0_) - 1.0\n        sum_gradient_sqr += grad_i.dot(grad_i)\n        \n        denominator = (1.0 / mass_) * sum_gradient_sqr + lambda_epsilon_\n        lambdas[p_i] = -density_constraint / denominator if denominator > epsilon_ else 0.0\n\n    # Pass 2: Calculate position corrections\n    for p_i in positions:\n        pos_i = positions[p_i]\n        lambda_i = lambdas[p_i]\n        pos_delta_i = ti.Vector([0.0, 0.0, 0.0])\n\n        for j in range(particle_num_neighbors[p_i]):\n            p_j = particle_neighbors[p_i, j]\n            lambda_j = lambdas[p_j]\n            pos_ji = pos_i - positions[p_j]\n            scorr_ij = compute_scorr(pos_ji, h_, poly6_factor_, corr_deltaQ_coeff_, corrK_)\n            pos_delta_i += (lambda_i + lambda_j + scorr_ij) * spiky_gradient(pos_ji, h_, spiky_grad_factor_)\n        \n        position_deltas[p_i] = pos_delta_i / rho0_\n\n    # Pass 3: Apply position corrections\n    for i in positions:\n        positions[i] += position_deltas[i]\n"
  },
  {
    "path": "14_pbf/constraints/viscosity.py",
    "content": "\"\"\"\nViscosity Module - XSPH Viscosity\n\nThis module implements XSPH (eXtended Smoothed Particle Hydrodynamics) viscosity,\nwhich smooths particle velocities by making neighboring particles move more coherently.\nThis reduces numerical noise and creates more stable, visually pleasing simulations.\n\"\"\"\n\nimport taichi as ti\nimport sys\nimport os\n_parent_dir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nif _parent_dir not in sys.path:\n    sys.path.insert(0, _parent_dir)\nfrom sph_base import poly6_value\n\n\n@ti.kernel\ndef apply_xsph_viscosity(\n    positions: ti.template(),\n    velocities: ti.template(),\n    particle_num_neighbors: ti.template(),\n    particle_neighbors: ti.template(),\n    velocity_deltas_xsph: ti.template(),\n    h_: float,\n    poly6_factor_: float,\n    xsph_viscosity_c_: float\n):\n    # Step 1: Calculate velocity corrections in parallel\n    for i in positions:\n        vel_i = velocities[i]\n        delta_v = ti.Vector([0.0, 0.0, 0.0])\n        for j in range(particle_num_neighbors[i]):\n            p_j = particle_neighbors[i, j]\n            pos_ji = positions[i] - positions[p_j]\n            vel_ij = velocities[p_j] - vel_i\n            w_ij = poly6_value(pos_ji.norm(), h_, poly6_factor_)\n            delta_v += vel_ij * w_ij\n        velocity_deltas_xsph[i] = xsph_viscosity_c_ * delta_v\n\n    # Step 2: Apply corrections\n    for i in positions:\n        velocities[i] += velocity_deltas_xsph[i]\n"
  },
  {
    "path": "14_pbf/constraints/vorticity.py",
    "content": "\"\"\"\nVorticity Confinement Module\n\nThis module restores energy lost to numerical damping by detecting and amplifying\nvorticity (rotational motion) in the fluid. This keeps the simulation visually\ninteresting and physically plausible.\n\"\"\"\n\nimport taichi as ti\nimport sys\nimport os\n_parent_dir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nif _parent_dir not in sys.path:\n    sys.path.insert(0, _parent_dir)\nfrom sph_base import spiky_gradient\n\n\n@ti.kernel\ndef calculate_vorticity(\n    positions: ti.template(),\n    velocities: ti.template(),\n    particle_num_neighbors: ti.template(),\n    particle_neighbors: ti.template(),\n    vorticity: ti.template(),\n    h_: float,\n    spiky_grad_factor_: float\n):\n\n    for i in positions:\n        vort_i = ti.Vector([0.0, 0.0, 0.0])\n        for j in range(particle_num_neighbors[i]):\n            p_j = particle_neighbors[i, j]\n            pos_ji = positions[i] - positions[p_j]\n            \n            # Relative velocity: v_ij = v_j - v_i\n            vel_ij = velocities[p_j] - velocities[i]\n            \n            # Cross product of relative velocity and spiky gradient\n            vort_i += vel_ij.cross(spiky_gradient(pos_ji, h_, spiky_grad_factor_))\n            \n        vorticity[i] = vort_i\n\n\n@ti.kernel\ndef apply_vorticity_confinement(\n    positions: ti.template(),\n    velocities: ti.template(),\n    particle_num_neighbors: ti.template(),\n    particle_neighbors: ti.template(),\n    vorticity: ti.template(),\n    vorticity_force: ti.template(),\n    h_: float,\n    spiky_grad_factor_: float,\n    epsilon_: float,\n    vorticity_epsilon_: float,\n    time_delta_: float\n):\n\n    # Step 1: Calculate the corrective force `f_vorticity` for each particle\n    for i in positions:\n        # First, calculate eta = \\nabla|\\omega|\n        # This is the gradient of the magnitude of the vorticity field.\n        eta = ti.Vector([0.0, 0.0, 0.0])\n        vort_i_norm = vorticity[i].norm()\n\n        for j in range(particle_num_neighbors[i]):\n            p_j = particle_neighbors[i, j]\n            pos_ji = positions[i] - positions[p_j]\n            \n            vort_j_norm = vorticity[p_j].norm()\n            \n            # Difference in vorticity magnitude multiplied by the kernel gradient\n            eta += (vort_j_norm - vort_i_norm) * spiky_gradient(pos_ji, h_, spiky_grad_factor_)\n        \n        # Calculate the direction vector N = eta / |eta|\n        eta_norm = eta.norm()\n        if eta_norm > epsilon_: # Avoid division by zero\n            N = eta / eta_norm\n            # Calculate the final force: f_vorticity = epsilon * (N x omega_i)\n            vorticity_force[i] = vorticity_epsilon_ * N.cross(vorticity[i])\n        else:\n            vorticity_force[i] = ti.Vector([0.0, 0.0, 0.0])\n\n    # Step 2: Apply the calculated force to the velocities\n    for i in velocities:\n        # The paper applies a force, so we integrate it over the timestep\n        velocities[i] += vorticity_force[i] * time_delta_\n"
  },
  {
    "path": "14_pbf/main.py",
    "content": "import math\nimport numpy as np\nimport taichi as ti\n\n# Import all modules\nfrom sph_base import pre_solve, post_solve\nfrom constraints import solve_density_constraints, calculate_vorticity, apply_vorticity_confinement, apply_xsph_viscosity\nfrom scene import init_particles, move_wall, update_particle_colors, create_box_edges, create_original_box_edges\n\nti.init(arch=ti.gpu, default_fp=ti.f32)\n\n# ============================================================================\n# Simulation Constants\n# ============================================================================\n\nSUBSTEPS_PER_FRAME = 2\n\ndim = 3\nscreen_res = (800, 800)\nscreen_to_world_ratio = 20.0\nboundary = (screen_res[0] / screen_to_world_ratio * 2.2,\n            screen_res[1] / screen_to_world_ratio * 1.0,\n            screen_res[0] / screen_to_world_ratio * 1.0)\n\ncell_size = 1.8\ncell_recpr = 1.0 / cell_size\n\ndef round_up(f, s):\n    return (math.floor(f * cell_recpr / s) + 1) * s\n\ngrid_size = (round_up(boundary[0], 1), round_up(boundary[1], 1), round_up(boundary[2], 1))\n\nnum_particles = 100000\nmax_num_particles_per_cell = 100\nmax_num_neighbors = 100\ntime_delta = 1.0 / 30.0\nepsilon = 1e-5\n\nparticle_radius = 4.0\nparticle_radius_in_world = particle_radius / screen_to_world_ratio\n\nparticle_color = (0.4, 0.7, 1.0)\nboundary_color = (0.9, 0.7, 0.6)\n\n# SPH parameters\nh = 1.1\nmass = 1.0\nrho0 = 1.0\nlambda_epsilon = 50.0\npbf_num_iters = 7\ncorr_deltaQ_coeff = 0.3\ncorrK = 0.001\nneighbor_radius = h * 1.05\nxsph_viscosity_c = 0.01\nvorticity_epsilon = 0.01\n\npoly6_factor = 315.0 / (64.0 * math.pi)\nspiky_grad_factor = -45.0 / math.pi\n\n# ============================================================================\n# Taichi Field Allocations\n# ============================================================================\n\nold_positions = ti.Vector.field(dim, float, shape=num_particles)\npositions = ti.Vector.field(dim, float, shape=num_particles)\nvelocities = ti.Vector.field(dim, float, shape=num_particles)\ngrid_num_particles = ti.field(int, shape=grid_size)\ngrid2particles = ti.field(int, shape=(*grid_size, max_num_particles_per_cell))\nparticle_num_neighbors = ti.field(int, shape=num_particles)\nparticle_neighbors = ti.field(int, shape=(num_particles, max_num_neighbors))\nlambdas = ti.field(float, shape=num_particles)\nposition_deltas = ti.Vector.field(dim, float, shape=num_particles)\nvelocity_deltas_xsph = ti.Vector.field(dim, float, shape=num_particles)\nwall_states = ti.Vector.field(3, float, shape=())\nparticle_colors = ti.Vector.field(3, float, shape=num_particles)\nvorticity = ti.Vector.field(dim, float, shape=num_particles)\nvorticity_force = ti.Vector.field(dim, float, shape=num_particles)\nwall_moving = ti.field(bool, shape=())\nsimulation_running = ti.field(bool, shape=())\n\n\n# ============================================================================\n# Simulation Loop\n# ============================================================================\n\ndef substep():\n    if simulation_running[None]:\n        # Pre-solve: time integration and neighbor search\n        pre_solve(\n            old_positions, positions, velocities, grid_num_particles, grid2particles,\n            particle_num_neighbors, particle_neighbors,\n            time_delta, cell_recpr, grid_size[0], grid_size[1], grid_size[2],\n            max_num_particles_per_cell, max_num_neighbors, neighbor_radius\n        )\n        \n        # Solve density constraints (iterated for stability)\n        for _ in range(pbf_num_iters):\n            solve_density_constraints(\n                positions, particle_num_neighbors, particle_neighbors, lambdas, position_deltas,\n                h, poly6_factor, spiky_grad_factor, mass, rho0, lambda_epsilon, epsilon,\n                corr_deltaQ_coeff, corrK\n            )\n        \n        # Post-solve: boundary collision and velocity update\n        post_solve(\n            positions, old_positions, velocities, wall_states,\n            boundary[0], boundary[1], boundary[2],\n            particle_radius_in_world, epsilon, time_delta\n        )\n        \n        # Vorticity confinement: restore lost rotational energy\n        calculate_vorticity(\n            positions, velocities, particle_num_neighbors, particle_neighbors, vorticity,\n            h, spiky_grad_factor\n        )\n        apply_vorticity_confinement(\n            positions, velocities, particle_num_neighbors, particle_neighbors,\n            vorticity, vorticity_force, h, spiky_grad_factor, epsilon, vorticity_epsilon, time_delta\n        )\n        \n        # XSPH viscosity: smooth velocities\n        apply_xsph_viscosity(\n            positions, velocities, particle_num_neighbors, particle_neighbors, velocity_deltas_xsph,\n            h, poly6_factor, xsph_viscosity_c\n        )\n\n\n# ============================================================================\n# Main Application\n# ============================================================================\n\ndef main():\n    global SUBSTEPS_PER_FRAME\n    \n    wall_moving[None] = False\n    simulation_running[None] = False\n    \n    fps_counter = 0\n    fps_timer = 0.0\n    current_fps = 0.0\n    \n    # Initialize particles and visualization\n    init_particles(positions, velocities, wall_states, num_particles, particle_radius_in_world, boundary[0], boundary[1], boundary[2], epsilon)\n    update_particle_colors(positions, velocities, particle_colors)\n    \n    # Setup window and rendering\n    window = ti.ui.Window(\"PBF3D with XSPH Viscosity\", screen_res, vsync=True)\n    canvas = window.get_canvas()\n    scene = window.get_scene()\n    camera = ti.ui.Camera()\n    gui = window.get_gui()\n    \n    # Camera setup\n    cam_pos = ti.Vector([20.0, 25.0, 120.0])\n    cam_yaw = 0.0\n    cam_pitch = 0.0\n    cam_move_speed = 1.5\n    cam_rot_speed = 0.02\n    \n    def get_forward():\n        cy = math.cos(cam_yaw); sy = math.sin(cam_yaw)\n        cp = math.cos(cam_pitch); sp = math.sin(cam_pitch)\n        return ti.Vector([sy * cp, -sp, -cy * cp])\n    \n    def get_right():\n        f = get_forward()\n        up = ti.Vector([0.0, 1.0, 0.0])\n        r = f.cross(up)\n        n = r.norm()\n        return r / (n if n > 1e-8 else 1.0)\n    \n    def get_up():\n        r = get_right()\n        f = get_forward()\n        return r.cross(f) * -1.0\n\n    # Main loop\n    while window.running:\n        fps_counter += 1\n        fps_timer += time_delta\n        if fps_timer >= 1.0:\n            current_fps = fps_counter / fps_timer\n            fps_counter = 0\n            fps_timer = 0.0\n        \n        # GUI\n        gui.begin(\"Simulation Controls\", 0.05, 0.05, 0.3, 0.2)\n        \n        gui.text(f\"FPS: {current_fps:.1f}\")\n        gui.text(f\"Substeps per frame: {SUBSTEPS_PER_FRAME}\")\n        gui.text(f\"Effective simulation speed: {SUBSTEPS_PER_FRAME}x\")\n        gui.text(f\"Wall movement: Synchronized\")\n        \n        gui.text(\"Performance:\")\n        if gui.button(\"1x Speed (1 substep)\"):\n            SUBSTEPS_PER_FRAME = 1\n        if gui.button(\"2x Speed (2 substeps)\"):\n            SUBSTEPS_PER_FRAME = 2\n        if gui.button(\"3x Speed (3 substeps)\"):\n            SUBSTEPS_PER_FRAME = 3\n        if gui.button(\"4x Speed (4 substeps)\"):\n            SUBSTEPS_PER_FRAME = 4\n        \n        if gui.button(\"Run Simulation\"):\n            simulation_running[None] = True\n            wall_moving[None] = True\n            \n        gui.end()\n        \n        # Simulation step\n        if simulation_running[None]:\n            move_wall(wall_states, wall_moving, simulation_running, SUBSTEPS_PER_FRAME, time_delta, boundary[0], epsilon)\n            \n            for _ in range(SUBSTEPS_PER_FRAME):\n                substep()\n            \n            update_particle_colors(positions, velocities, particle_colors)\n\n        # Camera controls\n        if window.is_pressed(ti.ui.LEFT):\n            cam_yaw -= cam_rot_speed\n        if window.is_pressed(ti.ui.RIGHT):\n            cam_yaw += cam_rot_speed\n        if window.is_pressed(ti.ui.UP):\n            cam_pitch = max(cam_pitch - cam_rot_speed, -1.4)\n        if window.is_pressed(ti.ui.DOWN):\n            cam_pitch = min(cam_pitch + cam_rot_speed, 1.4)\n        \n        move = ti.Vector([0.0, 0.0, 0.0])\n        if window.is_pressed('w'):\n            move += get_forward()\n        if window.is_pressed('s'):\n            move -= get_forward()\n        if window.is_pressed('a'):\n            move -= get_right()\n        if window.is_pressed('d'):\n            move += get_right()\n        if window.is_pressed('q'):\n            move -= ti.Vector([0.0, 1.0, 0.0])\n        if window.is_pressed('e'):\n            move += ti.Vector([0.0, 1.0, 0.0])\n        if move.norm() > 1e-8:\n            move = move / move.norm()\n        cam_pos += move * cam_move_speed\n        \n        # Update camera\n        cam_forward = get_forward()\n        cam_target = cam_pos + cam_forward\n        camera.position(cam_pos[0], cam_pos[1], cam_pos[2])\n        camera.lookat(cam_target[0], cam_target[1], cam_target[2])\n        \n        # Render scene\n        scene.set_camera(camera)\n        scene.ambient_light((0.5, 0.5, 0.5))\n        scene.point_light(pos=(30, 30, 30), color=(1, 1, 1))\n\n        scene.particles(positions, radius=particle_radius_in_world, per_vertex_color=particle_colors)\n        \n        # Render bounding boxes\n        orig_corners, orig_edges = create_original_box_edges(boundary, epsilon)\n        for i in range(12):\n            start_corner = np.array(orig_corners[orig_edges[i][0]], dtype=np.float32)\n            end_corner = np.array(orig_corners[orig_edges[i][1]], dtype=np.float32)\n            scene.lines(np.array([start_corner, end_corner], dtype=np.float32), color=(0.6, 0.6, 0.6), width=1)\n\n        corners, edges = create_box_edges(wall_states, boundary)\n        for i in range(12):\n            start_corner = np.array(corners[edges[i][0]], dtype=np.float32)\n            end_corner = np.array(corners[edges[i][1]], dtype=np.float32)\n            scene.lines(np.array([start_corner, end_corner], dtype=np.float32), color=(0.85, 0.85, 0.85), width=2)\n        \n        canvas.scene(scene)\n        window.show()\n\n\nif __name__ == \"__main__\":\n    main()\n"
  },
  {
    "path": "14_pbf/scene.py",
    "content": "import taichi as ti\n\n\n@ti.kernel\ndef init_particles(\n    positions: ti.template(),\n    velocities: ti.template(),\n    wall_states: ti.template(),\n    num_particles_: int,\n    particle_radius_in_world_: float,\n    boundary_x: float,\n    boundary_y: float,\n    boundary_z: float,\n    epsilon_: float\n):\n    padding = particle_radius_in_world_\n    \n    for i in range(num_particles_):\n        x = padding + ti.random() * (boundary_x - 2 * padding)\n        y = padding + ti.random() * (boundary_y - 2 * padding)\n        z = padding + ti.random() * (boundary_z - 2 * padding)\n        \n        positions[i] = ti.Vector([x, y, z])\n        velocities[i] = ti.Vector([0.0, 0.0, 0.0])\n    \n    # Initialize wall states: [left_wall_x, right_wall_x, movement_time]\n    wall_states[None] = ti.Vector([epsilon_, boundary_x - epsilon_, 0.0])\n\n\n@ti.kernel\ndef move_wall(\n    wall_states: ti.template(),\n    wall_moving: ti.template(),\n    simulation_running: ti.template(),\n    speed_multiplier: float,\n    time_delta_: float,\n    boundary_x: float,\n    epsilon_: float\n):\n    w = wall_states[None]\n    \n    if wall_moving[None] and simulation_running[None]:\n        w[2] += speed_multiplier\n        period = 90\n        vel_strength = 5.0\n        movement_time = w[2]\n        if movement_time >= 2 * period:\n            w[2] = 0\n            movement_time = 0\n        \n        movement_offset = ti.sin(movement_time * 3.14159 / period) * vel_strength * time_delta_ * speed_multiplier\n        \n        w[0] += movement_offset\n        w[1] -= movement_offset\n        \n        w[0] = ti.max(w[0], epsilon_)\n        w[1] = ti.min(w[1], boundary_x - epsilon_)\n    else:\n        w[0] = epsilon_\n        w[1] = boundary_x - epsilon_\n        w[2] = 0\n    \n    wall_states[None] = w\n\n\n@ti.kernel\ndef update_particle_colors(\n    positions: ti.template(),\n    velocities: ti.template(),\n    particle_colors: ti.template()\n):\n    max_velocity = 10.0\n\n    blue = ti.Vector([0.0941, 0.2784, 0.6314])\n    teal = ti.Vector([0.1392, 0.7226, 0.5441])\n    yellow = ti.Vector([0.9922, 0.9216, 0.0431])\n    red = ti.Vector([0.9804, 0.1961, 0.0196])\n\n    for i in positions:\n        vel_magnitude = velocities[i].norm()\n        normalized_vel = ti.min(vel_magnitude / max_velocity, 1.0)\n\n        if normalized_vel < 0.35:\n            t = normalized_vel / 0.35\n            particle_colors[i] = blue + t * (teal - blue)\n        elif normalized_vel < 0.65:\n            t = (normalized_vel - 0.35) / 0.30\n            particle_colors[i] = teal + t * (yellow - teal)\n        elif normalized_vel < 0.85:\n            t = (normalized_vel - 0.65) / 0.20\n            particle_colors[i] = yellow + t * (red - yellow)\n        else:\n            particle_colors[i] = red\n\n\ndef create_box_edges(wall_states, boundary):\n    left_wall_x = wall_states[None][0]\n    right_wall_x = wall_states[None][1]\n    \n    corners = [\n        [left_wall_x, 0.0, 0.0],\n        [right_wall_x, 0.0, 0.0],\n        [right_wall_x, boundary[1], 0.0],\n        [left_wall_x, boundary[1], 0.0],\n        [left_wall_x, 0.0, boundary[2]],\n        [right_wall_x, 0.0, boundary[2]],\n        [right_wall_x, boundary[1], boundary[2]],\n        [left_wall_x, boundary[1], boundary[2]]\n    ]\n    \n    edges = [\n        [0, 1], [1, 2], [2, 3], [3, 0],\n        [4, 5], [5, 6], [6, 7], [7, 4],\n        [0, 4], [1, 5], [2, 6], [3, 7]\n    ]\n    \n    return corners, edges\n\n\ndef create_original_box_edges(boundary, epsilon):\n    left_wall_x = epsilon\n    right_wall_x = boundary[0] - epsilon\n    \n    corners = [\n        [left_wall_x, 0.0, 0.0],\n        [right_wall_x, 0.0, 0.0],\n        [right_wall_x, boundary[1], 0.0],\n        [left_wall_x, boundary[1], 0.0],\n        [left_wall_x, 0.0, boundary[2]],\n        [right_wall_x, 0.0, boundary[2]],\n        [right_wall_x, boundary[1], boundary[2]],\n        [left_wall_x, boundary[1], boundary[2]]\n    ]\n    edges = [\n        [0, 1], [1, 2], [2, 3], [3, 0],\n        [4, 5], [5, 6], [6, 7], [7, 4],\n        [0, 4], [1, 5], [2, 6], [3, 7]\n    ]\n    return corners, edges\n"
  },
  {
    "path": "14_pbf/sph_base.py",
    "content": "\"\"\"\nThis module contains:\n- Smoothing kernels (poly6, spiky_gradient)\n- Grid hashing and neighbor search\n- Boundary collision handling\n- Time integration (pre_solve, post_solve)\n\"\"\"\n\nimport taichi as ti\n\n\n@ti.func\ndef poly6_value(s, h_, poly6_factor_):\n    \"\"\"Poly6 smoothing kernel for density estimation.\"\"\"\n    result = 0.0\n    if 0 < s and s < h_:\n        x = (h_ * h_ - s * s) / (h_ * h_ * h_)\n        result = poly6_factor_ * x * x * x\n    return result\n\n\n@ti.func\ndef spiky_gradient(r, h_, spiky_grad_factor_):\n    \"\"\"Spiky gradient kernel for pressure forces.\"\"\"\n    result = ti.Vector([0.0, 0.0, 0.0])\n    r_len = r.norm()\n    if 0 < r_len and r_len < h_:\n        x = (h_ - r_len) / (h_ * h_ * h_)\n        g_factor = spiky_grad_factor_ * x * x\n        result = r * g_factor / r_len\n    return result\n\n\n@ti.func\ndef get_cell(pos, cell_recpr_):\n    \"\"\"Convert world position to grid cell coordinates.\"\"\"\n    return int(pos * cell_recpr_)\n\n\n@ti.func\ndef is_in_grid(c, grid_size_x: int, grid_size_y: int, grid_size_z: int):\n    \"\"\"Check if a grid cell coordinate is within bounds.\"\"\"\n    return 0 <= c[0] < grid_size_x and 0 <= c[1] < grid_size_y and 0 <= c[2] < grid_size_z\n\n\n@ti.func\ndef confine_position_to_boundary(p, wall_states_, boundary_x: float, boundary_y: float, boundary_z: float, particle_radius_in_world_, epsilon_):\n    \"\"\"Confine particle position to simulation boundary with moving walls.\"\"\"\n    left_wall_x = wall_states_[None][0]\n    right_wall_x = wall_states_[None][1]\n    bmax = ti.Vector([right_wall_x, boundary_y, boundary_z]) - particle_radius_in_world_\n    bmin = ti.Vector([left_wall_x, 0.0, 0.0]) + particle_radius_in_world_\n    for i in ti.static(range(3)):\n        if p[i] <= bmin[i]:\n            p[i] = bmin[i] + epsilon_ * ti.random()\n        elif p[i] >= bmax[i]:\n            p[i] = bmax[i] - epsilon_ * ti.random()\n    return p\n\n\n@ti.kernel\ndef pre_solve(\n    old_positions: ti.template(),\n    positions: ti.template(),\n    velocities: ti.template(),\n    grid_num_particles: ti.template(),\n    grid2particles: ti.template(),\n    particle_num_neighbors: ti.template(),\n    particle_neighbors: ti.template(),\n    time_delta_: float,\n    cell_recpr_: float,\n    grid_size_x: int,\n    grid_size_y: int,\n    grid_size_z: int,\n    max_num_particles_per_cell_: int,\n    max_num_neighbors_: int,\n    neighbor_radius_: float\n):\n    \"\"\"\n    Pre-solve step: time integration and neighbor search.\n    \n    Steps:\n    1. Save old positions\n    2. Apply gravity and update positions/velocities\n    3. Build spatial hash grid\n    4. Find neighbors for each particle\n    \"\"\"\n    # Save old positions\n    for i in positions:\n        old_positions[i] = positions[i]\n\n    # Apply gravity and integrate\n    for i in positions:\n        g = ti.Vector([0.0, -9.8, 0.0])\n        vel = velocities[i] + g * time_delta_\n        velocities[i] = vel\n        positions[i] = positions[i] + vel * time_delta_\n\n    # Clear and rebuild spatial hash grid\n    grid_num_particles.fill(0)\n    \n    for p_i in positions:\n        cell = get_cell(positions[p_i], cell_recpr_)\n        offs = ti.atomic_add(grid_num_particles[cell], 1)\n        if offs < max_num_particles_per_cell_:\n            grid2particles[cell, offs] = p_i\n            \n    # Find neighbors for each particle\n    for p_i in positions:\n        pos_i = positions[p_i]\n        cell = get_cell(pos_i, cell_recpr_)\n        nb_i = 0\n        for offs in ti.static(ti.grouped(ti.ndrange((-1, 2), (-1, 2), (-1, 2)))):\n            cell_to_check = cell + offs\n            if is_in_grid(cell_to_check, grid_size_x, grid_size_y, grid_size_z):\n                for j in range(grid_num_particles[cell_to_check]):\n                    p_j = grid2particles[cell_to_check, j]\n                    if nb_i < max_num_neighbors_ and p_j != p_i and (pos_i - positions[p_j]).norm() < neighbor_radius_:\n                        particle_neighbors[p_i, nb_i] = p_j\n                        nb_i += 1\n        particle_num_neighbors[p_i] = nb_i\n\n\n@ti.kernel\ndef post_solve(\n    positions: ti.template(),\n    old_positions: ti.template(),\n    velocities: ti.template(),\n    wall_states: ti.template(),\n    boundary_x: float,\n    boundary_y: float,\n    boundary_z: float,\n    particle_radius_in_world_: float,\n    epsilon_: float,\n    time_delta_: float\n):\n    \"\"\"\n    Post-solve step: boundary collision and velocity update.\n    \n    Steps:\n    1. Confine particles to boundary\n    2. Update velocities based on position changes\n    \"\"\"\n    for i in positions:\n        positions[i] = confine_position_to_boundary(positions[i], wall_states, boundary_x, boundary_y, boundary_z, particle_radius_in_world_, epsilon_)\n        \n    for i in positions:\n        velocities[i] = (positions[i] - old_positions[i]) / time_delta_\n"
  },
  {
    "path": "1_mass_spring/InertiaEnergy.py",
    "content": "import numpy as np\n\ndef val(x, x_tilde, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        diff = x[i] - x_tilde[i]\n        sum += 0.5 * m[i] * diff.dot(diff)\n    return sum\n\ndef grad(x, x_tilde, m):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(x)):\n        g[i] = m[i] * (x[i] - x_tilde[i])\n    return g\n\ndef hess(x, x_tilde, m):\n    IJV = [[0] * (len(x) * 2), [0] * (len(x) * 2), np.array([0.0] * (len(x) * 2))]\n    for i in range(0, len(x)):\n        for d in range(0, 2):\n            IJV[0][i * 2 + d] = i * 2 + d\n            IJV[1][i * 2 + d] = i * 2 + d\n            IJV[2][i * 2 + d] = m[i]\n    return IJV"
  },
  {
    "path": "1_mass_spring/MassSpringEnergy.py",
    "content": "import numpy as np\nimport utils\n\ndef val(x, e, l2, k):\n    sum = 0.0\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        sum += l2[i] * 0.5 * k[i] * (diff.dot(diff) / l2[i] - 1) ** 2\n    return sum\n\ndef grad(x, e, l2, k):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        g_diff = 2 * k[i] * (diff.dot(diff) / l2[i] - 1) * diff\n        g[e[i][0]] += g_diff\n        g[e[i][1]] -= g_diff\n    return g\n\ndef hess(x, e, l2, k):\n    IJV = [[0] * (len(e) * 16), [0] * (len(e) * 16), np.array([0.0] * (len(e) * 16))]\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        H_diff = 2 * k[i] / l2[i] * (2 * np.outer(diff, diff) + (diff.dot(diff) - l2[i]) * np.identity(2))\n        H_local = utils.make_PSD(np.block([[H_diff, -H_diff], [-H_diff, H_diff]]))\n        # add to global matrix\n        for nI in range(0, 2):\n            for nJ in range(0, 2):\n                indStart = i * 16 + (nI * 2 + nJ) * 4\n                for r in range(0, 2):\n                    for c in range(0, 2):\n                        IJV[0][indStart + r * 2 + c] = e[i][nI] * 2 + r\n                        IJV[1][indStart + r * 2 + c] = e[i][nJ] * 2 + c\n                        IJV[2][indStart + r * 2 + c] = H_local[nI * 2 + r, nJ * 2 + c]\n    return IJV"
  },
  {
    "path": "1_mass_spring/readme.md",
    "content": "# Mass-Spring Solids Simulation\n\nAn initially stretched square is simulated with mass-spring elasticity potential and implicit Euler time integration.\nEach time step is solved by minimizing the Incremental Potential with the projected Newton method.\n\n## Dependencies\n```\npip install numpy scipy pygame\n```\n\n## Run\n```\npython simulator.py\n```"
  },
  {
    "path": "1_mass_spring/simulator.py",
    "content": "# Mass-Spring Solids Simulation\n\nimport numpy as np  # numpy for linear algebra\nimport pygame       # pygame for visualization\npygame.init()\n\nimport square_mesh   # square mesh\nimport time_integrator\n\n# simulation setup\nside_len = 1\nrho = 1000  # density of square\nk = 1e5     # spring stiffness\ninitial_stretch = 1.4\nn_seg = 4   # num of segments per side of the square\nh = 0.004   # time step size in s\n\n# initialize simulation\n[x, e] = square_mesh.generate(side_len, n_seg)  # node positions and edge node indices\nv = np.array([[0.0, 0.0]] * len(x))             # velocity\nm = [rho * side_len * side_len / ((n_seg + 1) * (n_seg + 1))] * len(x)  # calculate node mass evenly\n# rest length squared\nl2 = []\nfor i in range(0, len(e)):\n    diff = x[e[i][0]] - x[e[i][1]]\n    l2.append(diff.dot(diff))\nk = [k] * len(e)    # spring stiffness\n# apply initial stretch horizontally\nfor i in range(0, len(x)):\n    x[i][0] *= initial_stretch\n\n# simulation with visualization\nresolution = np.array([900, 900])\noffset = resolution / 2\nscale = 200\ndef screen_projection(x):\n    return [offset[0] + scale * x[0], resolution[1] - (offset[1] + scale * x[1])]\n\ntime_step = 0\nsquare_mesh.write_to_file(time_step, x, n_seg)\nscreen = pygame.display.set_mode(resolution)\nrunning = True\nwhile running:\n    # run until the user asks to quit\n    for event in pygame.event.get():\n        if event.type == pygame.QUIT:\n            running = False\n    \n    print('### Time step', time_step, '###')\n\n    # fill the background and draw the square\n    screen.fill((255, 255, 255))\n    for eI in e:\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[0]]), screen_projection(x[eI[1]]))\n    for xI in x:\n        pygame.draw.circle(screen, (0, 0, 255), screen_projection(xI), 0.1 * side_len / n_seg * scale)\n\n    pygame.display.flip()   # flip the display\n\n    # step forward simulation and wait for screen refresh\n    [x, v] = time_integrator.step_forward(x, e, v, m, l2, k, h, 1e-2)\n    time_step += 1\n    pygame.time.wait(int(h * 1000))\n    square_mesh.write_to_file(time_step, x, n_seg)\n\npygame.quit()"
  },
  {
    "path": "1_mass_spring/square_mesh.py",
    "content": "# ANCHOR: generate\nimport numpy as np\nimport os\n\ndef generate(side_length, n_seg):\n    # sample nodes uniformly on a square\n    x = np.array([[0.0, 0.0]] * ((n_seg + 1) ** 2))\n    step = side_length / n_seg\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg + 1):\n            x[i * (n_seg + 1) + j] = [-side_length / 2 + i * step, -side_length / 2 + j * step]\n    \n    # connect the nodes with edges\n    e = []\n    # horizontal edges\n    for i in range(0, n_seg):\n        for j in range(0, n_seg + 1):\n            e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j])\n    # vertical edges\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg):\n            e.append([i * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n    # diagonals\n    for i in range(0, n_seg):\n        for j in range(0, n_seg):\n            e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1])\n            e.append([(i + 1) * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n\n    return [x, e]\n# ANCHOR_END: generate\n\n# ANCHOR: write_to_file\ndef write_to_file(frameNum, x, n_seg):\n    # Check if 'output' directory exists; if not, create it\n    if not os.path.exists('output'):\n        os.makedirs('output')\n\n    # create obj file\n    filename = f\"output/{frameNum}.obj\"\n    with open(filename, 'w') as f:\n        # write vertex coordinates\n        for row in x:\n            f.write(f\"v {float(row[0]):.6f} {float(row[1]):.6f} 0.0\\n\") \n        # write vertex indices for each triangle\n        for i in range(0, n_seg):\n            for j in range(0, n_seg):\n                #NOTE: each cell is exported as 2 triangles for rendering\n                f.write(f\"f {i * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j+1 + 1}\\n\")\n                f.write(f\"f {i * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j+1 + 1} {i * (n_seg+1) + j+1 + 1}\\n\")\n# ANCHOR_END: write_to_file"
  },
  {
    "path": "1_mass_spring/time_integrator.py",
    "content": "import copy\nfrom cmath import inf\n\nimport numpy as np\nimport numpy.linalg as LA\nimport scipy.sparse as sparse\nfrom scipy.sparse.linalg import spsolve\n\nimport InertiaEnergy\nimport MassSpringEnergy\n\ndef step_forward(x, e, v, m, l2, k, h, tol):\n    x_tilde = x + v * h     # implicit Euler predictive position\n    x_n = copy.deepcopy(x)\n\n    # Newton loop\n    iter = 0\n    E_last = IP_val(x, e, x_tilde, m, l2, k, h)\n    p = search_dir(x, e, x_tilde, m, l2, k, h)\n    while LA.norm(p, inf) / h > tol:\n        print('Iteration', iter, ':')\n        print('residual =', LA.norm(p, inf) / h)\n\n        # line search\n        alpha = 1\n        while IP_val(x + alpha * p, e, x_tilde, m, l2, k, h) > E_last:\n            alpha /= 2\n        print('step size =', alpha)\n\n        x += alpha * p\n        E_last = IP_val(x, e, x_tilde, m, l2, k, h)\n        p = search_dir(x, e, x_tilde, m, l2, k, h)\n        iter += 1\n\n    v = (x - x_n) / h   # implicit Euler velocity update\n    return [x, v]\n\ndef IP_val(x, e, x_tilde, m, l2, k, h):\n    return InertiaEnergy.val(x, x_tilde, m) + h * h * MassSpringEnergy.val(x, e, l2, k)     # implicit Euler\n\ndef IP_grad(x, e, x_tilde, m, l2, k, h):\n    return InertiaEnergy.grad(x, x_tilde, m) + h * h * MassSpringEnergy.grad(x, e, l2, k)   # implicit Euler\n\ndef IP_hess(x, e, x_tilde, m, l2, k, h):\n    IJV_In = InertiaEnergy.hess(x, x_tilde, m)\n    IJV_MS = MassSpringEnergy.hess(x, e, l2, k)\n    IJV_MS[2] *= h * h    # implicit Euler\n    IJV = np.append(IJV_In, IJV_MS, axis=1)\n    H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()\n    return H\n\ndef search_dir(x, e, x_tilde, m, l2, k, h):\n    projected_hess = IP_hess(x, e, x_tilde, m, l2, k, h)\n    reshaped_grad = IP_grad(x, e, x_tilde, m, l2, k, h).reshape(len(x) * 2, 1)\n    return spsolve(projected_hess, -reshaped_grad).reshape(len(x), 2)"
  },
  {
    "path": "1_mass_spring/utils.py",
    "content": "import numpy as np\nimport numpy.linalg as LA\n\ndef make_PSD(hess):\n    [lam, V] = LA.eigh(hess)    # Eigen decomposition on symmetric matrix\n    # set all negative Eigenvalues to 0\n    for i in range(0, len(lam)):\n        lam[i] = max(0, lam[i])\n    return np.matmul(np.matmul(V, np.diag(lam)), np.transpose(V))"
  },
  {
    "path": "2_dirichlet/GravityEnergy.py",
    "content": "import numpy as np\n\ngravity = [0.0, -9.81]\n\ndef val(x, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        sum += -m[i] * x[i].dot(gravity)\n    return sum\n\ndef grad(x, m):\n    g = np.array([gravity] * len(x))\n    for i in range(0, len(x)):\n        g[i] *= -m[i]\n    return g\n\n# Hessian is 0"
  },
  {
    "path": "2_dirichlet/InertiaEnergy.py",
    "content": "import numpy as np\n\ndef val(x, x_tilde, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        diff = x[i] - x_tilde[i]\n        sum += 0.5 * m[i] * diff.dot(diff)\n    return sum\n\ndef grad(x, x_tilde, m):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(x)):\n        g[i] = m[i] * (x[i] - x_tilde[i])\n    return g\n\ndef hess(x, x_tilde, m):\n    IJV = [[0] * (len(x) * 2), [0] * (len(x) * 2), np.array([0.0] * (len(x) * 2))]\n    for i in range(0, len(x)):\n        for d in range(0, 2):\n            IJV[0][i * 2 + d] = i * 2 + d\n            IJV[1][i * 2 + d] = i * 2 + d\n            IJV[2][i * 2 + d] = m[i]\n    return IJV"
  },
  {
    "path": "2_dirichlet/MassSpringEnergy.py",
    "content": "import numpy as np\nimport utils\n\ndef val(x, e, l2, k):\n    sum = 0.0\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        sum += l2[i] * 0.5 * k[i] * (diff.dot(diff) / l2[i] - 1) ** 2\n    return sum\n\ndef grad(x, e, l2, k):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        g_diff = 2 * k[i] * (diff.dot(diff) / l2[i] - 1) * diff\n        g[e[i][0]] += g_diff\n        g[e[i][1]] -= g_diff\n    return g\n\ndef hess(x, e, l2, k):\n    IJV = [[0] * (len(e) * 16), [0] * (len(e) * 16), np.array([0.0] * (len(e) * 16))]\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        H_diff = 2 * k[i] / l2[i] * (2 * np.outer(diff, diff) + (diff.dot(diff) - l2[i]) * np.identity(2))\n        H_local = utils.make_PSD(np.block([[H_diff, -H_diff], [-H_diff, H_diff]]))\n        # add to global matrix\n        for nI in range(0, 2):\n            for nJ in range(0, 2):\n                indStart = i * 16 + (nI * 2 + nJ) * 4\n                for r in range(0, 2):\n                    for c in range(0, 2):\n                        IJV[0][indStart + r * 2 + c] = e[i][nI] * 2 + r\n                        IJV[1][indStart + r * 2 + c] = e[i][nJ] * 2 + c\n                        IJV[2][indStart + r * 2 + c] = H_local[nI * 2 + r, nJ * 2 + c]\n    return IJV"
  },
  {
    "path": "2_dirichlet/readme.md",
    "content": "# Mass-Spring Solids Simulation\n\nA square hanging under gravity with its right and left top nodes fixed is simulated with mass-spring elasticity potential and implicit Euler time integration.\nEach time step is solved by minimizing the Incremental Potential with the projected Newton method.\n\n## Dependencies\n```\npip install numpy scipy pygame\n```\n\n## Run\n```\npython simulator.py\n```"
  },
  {
    "path": "2_dirichlet/simulator.py",
    "content": "# Mass-Spring Solids Simulation\n\nimport numpy as np  # numpy for linear algebra\nimport pygame       # pygame for visualization\npygame.init()\n\nimport square_mesh   # square mesh\nimport time_integrator\n\n# simulation setup\nside_len = 1\nrho = 1000  # density of square\nk = 1e3     # spring stiffness\nn_seg = 4   # num of segments per side of the square\nh = 0.02    # time step size in s\n# ANCHOR: DBC_def\nDBC = [n_seg, (n_seg + 1) * (n_seg + 1) - 1]  # fix the left and right top nodes\n# ANCHOR_END: DBC_def\n\n# initialize simulation\n[x, e] = square_mesh.generate(side_len, n_seg)  # node positions and edge node indices\nv = np.array([[0.0, 0.0]] * len(x))             # velocity\nm = [rho * side_len * side_len / ((n_seg + 1) * (n_seg + 1))] * len(x)  # calculate node mass evenly\n# rest length squared\nl2 = []\nfor i in range(0, len(e)):\n    diff = x[e[i][0]] - x[e[i][1]]\n    l2.append(diff.dot(diff))\nk = [k] * len(e)    # spring stiffness\n# ANCHOR: DBC_mask\n# identify whether a node is Dirichlet\nis_DBC = [False] * len(x)\nfor i in DBC:\n    is_DBC[i] = True\n# ANCHOR_END: DBC_mask\n# simulation with visualization\nresolution = np.array([900, 900])\noffset = resolution / 2\nscale = 200\ndef screen_projection(x):\n    return [offset[0] + scale * x[0], resolution[1] - (offset[1] + scale * x[1])]\n\ntime_step = 0\nsquare_mesh.write_to_file(time_step, x, n_seg)\nscreen = pygame.display.set_mode(resolution)\nrunning = True\nwhile running:\n    # run until the user asks to quit\n    for event in pygame.event.get():\n        if event.type == pygame.QUIT:\n            running = False\n    \n    print('### Time step', time_step, '###')\n\n    # fill the background and draw the square\n    screen.fill((255, 255, 255))\n    for eI in e:\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[0]]), screen_projection(x[eI[1]]))\n    for xI in x:\n        pygame.draw.circle(screen, (0, 0, 255), screen_projection(xI), 0.1 * side_len / n_seg * scale)\n\n    pygame.display.flip()   # flip the display\n\n    # step forward simulation and wait for screen refresh\n    [x, v] = time_integrator.step_forward(x, e, v, m, l2, k, is_DBC, h, 1e-2)\n    time_step += 1\n    pygame.time.wait(int(h * 1000))\n    square_mesh.write_to_file(time_step, x, n_seg)\n\npygame.quit()"
  },
  {
    "path": "2_dirichlet/square_mesh.py",
    "content": "import numpy as np\nimport os\n\ndef generate(side_length, n_seg):\n    # sample nodes uniformly on a square\n    x = np.array([[0.0, 0.0]] * ((n_seg + 1) ** 2))\n    step = side_length / n_seg\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg + 1):\n            x[i * (n_seg + 1) + j] = [-side_length / 2 + i * step, -side_length / 2 + j * step]\n    \n    # connect the nodes with edges\n    e = []\n    # horizontal edges\n    for i in range(0, n_seg):\n        for j in range(0, n_seg + 1):\n            e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j])\n    # vertical edges\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg):\n            e.append([i * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n    # diagonals\n    for i in range(0, n_seg):\n        for j in range(0, n_seg):\n            e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1])\n            e.append([(i + 1) * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n\n    return [x, e]\n\ndef write_to_file(frameNum, x, n_seg):\n    # Check if 'output' directory exists; if not, create it\n    if not os.path.exists('output'):\n        os.makedirs('output')\n\n    # create obj file\n    filename = f\"output/{frameNum}.obj\"\n    with open(filename, 'w') as f:\n        # write vertex coordinates\n        for row in x:\n            f.write(f\"v {float(row[0]):.6f} {float(row[1]):.6f} 0.0\\n\") \n        # write vertex indices for each triangle\n        for i in range(0, n_seg):\n            for j in range(0, n_seg):\n                #NOTE: each cell is exported as 2 triangles for rendering\n                f.write(f\"f {i * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j+1 + 1}\\n\")\n                f.write(f\"f {i * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j+1 + 1} {i * (n_seg+1) + j+1 + 1}\\n\")"
  },
  {
    "path": "2_dirichlet/time_integrator.py",
    "content": "import copy\nfrom cmath import inf\n\nimport numpy as np\nimport numpy.linalg as LA\nimport scipy.sparse as sparse\nfrom scipy.sparse.linalg import spsolve\n\nimport InertiaEnergy\nimport MassSpringEnergy\nimport GravityEnergy\n\ndef step_forward(x, e, v, m, l2, k, is_DBC, h, tol):\n    x_tilde = x + v * h     # implicit Euler predictive position\n    x_n = copy.deepcopy(x)\n\n    # Newton loop\n    iter = 0\n    E_last = IP_val(x, e, x_tilde, m, l2, k, h)\n    p = search_dir(x, e, x_tilde, m, l2, k, is_DBC, h)\n    while LA.norm(p, inf) / h > tol:\n        print('Iteration', iter, ':')\n        print('residual =', LA.norm(p, inf) / h)\n\n        # line search\n        alpha = 1\n        while IP_val(x + alpha * p, e, x_tilde, m, l2, k, h) > E_last:\n            alpha /= 2\n        print('step size =', alpha)\n\n        x += alpha * p\n        E_last = IP_val(x, e, x_tilde, m, l2, k, h)\n        p = search_dir(x, e, x_tilde, m, l2, k, is_DBC, h)\n        iter += 1\n\n    v = (x - x_n) / h   # implicit Euler velocity update\n    return [x, v]\n\n# ANCHOR: ADDING_GRAVITY\ndef IP_val(x, e, x_tilde, m, l2, k, h):\n    return InertiaEnergy.val(x, x_tilde, m) + h * h * (MassSpringEnergy.val(x, e, l2, k) + GravityEnergy.val(x, m))     # implicit Euler\n\ndef IP_grad(x, e, x_tilde, m, l2, k, h):\n    return InertiaEnergy.grad(x, x_tilde, m) + h * h * (MassSpringEnergy.grad(x, e, l2, k) + GravityEnergy.grad(x, m))   # implicit Euler\n# ANCHOR_END: ADDING_GRAVITY\n\ndef IP_hess(x, e, x_tilde, m, l2, k, h):\n    IJV_In = InertiaEnergy.hess(x, x_tilde, m)\n    IJV_MS = MassSpringEnergy.hess(x, e, l2, k)\n    IJV_MS[2] *= h * h    # implicit Euler\n    IJV = np.append(IJV_In, IJV_MS, axis=1)\n    H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()\n    return H\n\n# ANCHOR: search_dir\ndef search_dir(x, e, x_tilde, m, l2, k, is_DBC, h):\n    projected_hess = IP_hess(x, e, x_tilde, m, l2, k, h)\n    reshaped_grad = IP_grad(x, e, x_tilde, m, l2, k, h).reshape(len(x) * 2, 1)\n    # eliminate DOF by modifying gradient and Hessian for DBC:\n    for i, j in zip(*projected_hess.nonzero()):\n        if is_DBC[int(i / 2)] | is_DBC[int(j / 2)]: \n            projected_hess[i, j] = (i == j)\n    for i in range(0, len(x)):\n        if is_DBC[i]:\n            reshaped_grad[i * 2] = reshaped_grad[i * 2 + 1] = 0.0\n    return spsolve(projected_hess, -reshaped_grad).reshape(len(x), 2)\n#ANCHOR_END: search_dir"
  },
  {
    "path": "2_dirichlet/utils.py",
    "content": "import numpy as np\nimport numpy.linalg as LA\n\ndef make_PSD(hess):\n    [lam, V] = LA.eigh(hess)    # Eigen decomposition on symmetric matrix\n    # set all negative Eigenvalues to 0\n    for i in range(0, len(lam)):\n        lam[i] = max(0, lam[i])\n    return np.matmul(np.matmul(V, np.diag(lam)), np.transpose(V))"
  },
  {
    "path": "3_contact/BarrierEnergy.py",
    "content": "# ANCHOR: val_grad_hess\nimport math\nimport numpy as np\n\ndhat = 0.01\nkappa = 1e5\n\ndef val(x, y_ground, contact_area):\n    sum = 0.0\n    for i in range(0, len(x)):\n        d = x[i][1] - y_ground\n        if d < dhat:\n            s = d / dhat\n            sum += contact_area[i] * dhat * kappa / 2 * (s - 1) * math.log(s)\n    return sum\n\ndef grad(x, y_ground, contact_area):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(x)):\n        d = x[i][1] - y_ground\n        if d < dhat:\n            s = d / dhat\n            g[i][1] = contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d))\n    return g\n\ndef hess(x, y_ground, contact_area):\n    IJV = [[0] * len(x), [0] * len(x), np.array([0.0] * len(x))]\n    for i in range(0, len(x)):\n        IJV[0][i] = i * 2 + 1\n        IJV[1][i] = i * 2 + 1\n        d = x[i][1] - y_ground\n        if d < dhat:\n            IJV[2][i] = contact_area[i] * dhat * kappa / (2 * d * d * dhat) * (d + dhat)\n        else:\n            IJV[2][i] = 0.0\n    return IJV\n# ANCHOR_END: val_grad_hess\n\n# ANCHOR: init_step_size\ndef init_step_size(x, y_ground, p):\n    alpha = 1\n    for i in range(0, len(x)):\n        if p[i][1] < 0:\n            alpha = min(alpha, 0.9 * (y_ground - x[i][1]) / p[i][1])\n    return alpha\n# ANCHOR_END: init_step_size"
  },
  {
    "path": "3_contact/GravityEnergy.py",
    "content": "import numpy as np\n\ngravity = [0.0, -9.81]\n\ndef val(x, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        sum += -m[i] * x[i].dot(gravity)\n    return sum\n\ndef grad(x, m):\n    g = np.array([gravity] * len(x))\n    for i in range(0, len(x)):\n        g[i] *= -m[i]\n    return g\n\n# Hessian is 0"
  },
  {
    "path": "3_contact/InertiaEnergy.py",
    "content": "import numpy as np\n\ndef val(x, x_tilde, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        diff = x[i] - x_tilde[i]\n        sum += 0.5 * m[i] * diff.dot(diff)\n    return sum\n\ndef grad(x, x_tilde, m):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(x)):\n        g[i] = m[i] * (x[i] - x_tilde[i])\n    return g\n\ndef hess(x, x_tilde, m):\n    IJV = [[0] * (len(x) * 2), [0] * (len(x) * 2), np.array([0.0] * (len(x) * 2))]\n    for i in range(0, len(x)):\n        for d in range(0, 2):\n            IJV[0][i * 2 + d] = i * 2 + d\n            IJV[1][i * 2 + d] = i * 2 + d\n            IJV[2][i * 2 + d] = m[i]\n    return IJV"
  },
  {
    "path": "3_contact/MassSpringEnergy.py",
    "content": "import numpy as np\nimport utils\n\ndef val(x, e, l2, k):\n    sum = 0.0\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        sum += l2[i] * 0.5 * k[i] * (diff.dot(diff) / l2[i] - 1) ** 2\n    return sum\n\ndef grad(x, e, l2, k):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        g_diff = 2 * k[i] * (diff.dot(diff) / l2[i] - 1) * diff\n        g[e[i][0]] += g_diff\n        g[e[i][1]] -= g_diff\n    return g\n\ndef hess(x, e, l2, k):\n    IJV = [[0] * (len(e) * 16), [0] * (len(e) * 16), np.array([0.0] * (len(e) * 16))]\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        H_diff = 2 * k[i] / l2[i] * (2 * np.outer(diff, diff) + (diff.dot(diff) - l2[i]) * np.identity(2))\n        H_local = utils.make_PSD(np.block([[H_diff, -H_diff], [-H_diff, H_diff]]))\n        # add to global matrix\n        for nI in range(0, 2):\n            for nJ in range(0, 2):\n                indStart = i * 16 + (nI * 2 + nJ) * 4\n                for r in range(0, 2):\n                    for c in range(0, 2):\n                        IJV[0][indStart + r * 2 + c] = e[i][nI] * 2 + r\n                        IJV[1][indStart + r * 2 + c] = e[i][nJ] * 2 + c\n                        IJV[2][indStart + r * 2 + c] = H_local[nI * 2 + r, nJ * 2 + c]\n    return IJV"
  },
  {
    "path": "3_contact/readme.md",
    "content": "# Mass-Spring Solids Simulation\n\nA square falling onto the ground under gravity is simulated with mass-spring elasticity potential and implicit Euler time integration.\nEach time step is solved by minimizing the Incremental Potential with the projected Newton method.\n\n## Dependencies\n```\npip install numpy scipy pygame\n```\n\n## Run\n```\npython simulator.py\n```"
  },
  {
    "path": "3_contact/simulator.py",
    "content": "# Mass-Spring Solids Simulation\n\nimport numpy as np  # numpy for linear algebra\nimport pygame       # pygame for visualization\npygame.init()\n\nimport square_mesh   # square mesh\nimport time_integrator\n\n# simulation setup\nside_len = 1\nrho = 1000      # density of square\nk = 2e4         # spring stiffness\nn_seg = 4       # num of segments per side of the square\nh = 0.01        # time step size in s\nDBC = []        # no nodes need to be fixed\ny_ground = -1   # height of the planar ground\n\n# initialize simulation\n[x, e] = square_mesh.generate(side_len, n_seg)  # node positions and edge node indices\nv = np.array([[0.0, 0.0]] * len(x))             # velocity\nm = [rho * side_len * side_len / ((n_seg + 1) * (n_seg + 1))] * len(x)  # calculate node mass evenly\n# rest length squared\nl2 = []\nfor i in range(0, len(e)):\n    diff = x[e[i][0]] - x[e[i][1]]\n    l2.append(diff.dot(diff))\nk = [k] * len(e)    # spring stiffness\n# identify whether a node is Dirichlet\nis_DBC = [False] * len(x)\nfor i in DBC:\n    is_DBC[i] = True\n# ANCHOR: contact_area\ncontact_area = [side_len / n_seg] * len(x)     # perimeter split to each node\n# ANCHOR_END: contact_area\n\n# simulation with visualization\nresolution = np.array([900, 900])\noffset = resolution / 2\nscale = 200\ndef screen_projection(x):\n    return [offset[0] + scale * x[0], resolution[1] - (offset[1] + scale * x[1])]\n\ntime_step = 0\nsquare_mesh.write_to_file(time_step, x, n_seg)\nscreen = pygame.display.set_mode(resolution)\nrunning = True\nwhile running:\n    # run until the user asks to quit\n    for event in pygame.event.get():\n        if event.type == pygame.QUIT:\n            running = False\n    \n    print('### Time step', time_step, '###')\n\n    # fill the background and draw the square\n    screen.fill((255, 255, 255))\n    pygame.draw.aaline(screen, (0, 0, 255), screen_projection([-2, y_ground]), screen_projection([2, y_ground]))   # ground\n    for eI in e:\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[0]]), screen_projection(x[eI[1]]))\n    for xI in x:\n        pygame.draw.circle(screen, (0, 0, 255), screen_projection(xI), 0.1 * side_len / n_seg * scale)\n\n    pygame.display.flip()   # flip the display\n\n    # step forward simulation and wait for screen refresh\n    [x, v] = time_integrator.step_forward(x, e, v, m, l2, k, y_ground, contact_area, is_DBC, h, 1e-2)\n    time_step += 1\n    pygame.time.wait(int(h * 1000))\n    square_mesh.write_to_file(time_step, x, n_seg)\n\npygame.quit()"
  },
  {
    "path": "3_contact/square_mesh.py",
    "content": "import numpy as np\nimport os\n\ndef generate(side_length, n_seg):\n    # sample nodes uniformly on a square\n    x = np.array([[0.0, 0.0]] * ((n_seg + 1) ** 2))\n    step = side_length / n_seg\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg + 1):\n            x[i * (n_seg + 1) + j] = [-side_length / 2 + i * step, -side_length / 2 + j * step]\n    \n    # connect the nodes with edges\n    e = []\n    # horizontal edges\n    for i in range(0, n_seg):\n        for j in range(0, n_seg + 1):\n            e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j])\n    # vertical edges\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg):\n            e.append([i * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n    # diagonals\n    for i in range(0, n_seg):\n        for j in range(0, n_seg):\n            e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1])\n            e.append([(i + 1) * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n\n    return [x, e]\n\ndef write_to_file(frameNum, x, n_seg):\n    # Check if 'output' directory exists; if not, create it\n    if not os.path.exists('output'):\n        os.makedirs('output')\n\n    # create obj file\n    filename = f\"output/{frameNum}.obj\"\n    with open(filename, 'w') as f:\n        # write vertex coordinates\n        for row in x:\n            f.write(f\"v {float(row[0]):.6f} {float(row[1]):.6f} 0.0\\n\") \n        # write vertex indices for each triangle\n        for i in range(0, n_seg):\n            for j in range(0, n_seg):\n                #NOTE: each cell is exported as 2 triangles for rendering\n                f.write(f\"f {i * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j+1 + 1}\\n\")\n                f.write(f\"f {i * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j+1 + 1} {i * (n_seg+1) + j+1 + 1}\\n\")"
  },
  {
    "path": "3_contact/time_integrator.py",
    "content": "import copy\nfrom cmath import inf\n\nimport numpy as np\nimport numpy.linalg as LA\nimport scipy.sparse as sparse\nfrom scipy.sparse.linalg import spsolve\n\nimport InertiaEnergy\nimport MassSpringEnergy\nimport GravityEnergy\nimport BarrierEnergy\n\ndef step_forward(x, e, v, m, l2, k, y_ground, contact_area, is_DBC, h, tol):\n    x_tilde = x + v * h     # implicit Euler predictive position\n    x_n = copy.deepcopy(x)\n\n    # Newton loop\n    iter = 0\n    E_last = IP_val(x, e, x_tilde, m, l2, k, y_ground, contact_area, h)\n    p = search_dir(x, e, x_tilde, m, l2, k, y_ground, contact_area, is_DBC, h)\n    while LA.norm(p, inf) / h > tol:\n        print('Iteration', iter, ':')\n        print('residual =', LA.norm(p, inf) / h)\n\n        # ANCHOR: filter_ls\n        # filter line search\n        alpha = BarrierEnergy.init_step_size(x, y_ground, p)  # avoid interpenetration and tunneling\n        while IP_val(x + alpha * p, e, x_tilde, m, l2, k, y_ground, contact_area, h) > E_last:\n            alpha /= 2\n        # ANCHOR_END: filter_ls\n        print('step size =', alpha)\n\n        x += alpha * p\n        E_last = IP_val(x, e, x_tilde, m, l2, k, y_ground, contact_area, h)\n        p = search_dir(x, e, x_tilde, m, l2, k, y_ground, contact_area, is_DBC, h)\n        iter += 1\n\n    v = (x - x_n) / h   # implicit Euler velocity update\n    return [x, v]\n\ndef IP_val(x, e, x_tilde, m, l2, k, y_ground, contact_area, h):\n    return InertiaEnergy.val(x, x_tilde, m) + h * h * (MassSpringEnergy.val(x, e, l2, k) + GravityEnergy.val(x, m) + BarrierEnergy.val(x, y_ground, contact_area))     # implicit Euler\n\ndef IP_grad(x, e, x_tilde, m, l2, k, y_ground, contact_area, h):\n    return InertiaEnergy.grad(x, x_tilde, m) + h * h * (MassSpringEnergy.grad(x, e, l2, k) + GravityEnergy.grad(x, m) + BarrierEnergy.grad(x, y_ground, contact_area))   # implicit Euler\n\ndef IP_hess(x, e, x_tilde, m, l2, k, y_ground, contact_area, h):\n    IJV_In = InertiaEnergy.hess(x, x_tilde, m)\n    IJV_MS = MassSpringEnergy.hess(x, e, l2, k)\n    IJV_B = BarrierEnergy.hess(x, y_ground, contact_area)\n    IJV_MS[2] *= h * h    # implicit Euler\n    IJV_B[2] *= h * h     # implicit Euler\n    IJV_In_MS = np.append(IJV_In, IJV_MS, axis=1)\n    IJV = np.append(IJV_In_MS, IJV_B, axis=1)\n    H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()\n    return H\n\ndef search_dir(x, e, x_tilde, m, l2, k, y_ground, contact_area, is_DBC, h):\n    projected_hess = IP_hess(x, e, x_tilde, m, l2, k, y_ground, contact_area, h)\n    reshaped_grad = IP_grad(x, e, x_tilde, m, l2, k, y_ground, contact_area, h).reshape(len(x) * 2, 1)\n    # eliminate DOF by modifying gradient and Hessian for DBC:\n    for i, j in zip(*projected_hess.nonzero()):\n        if is_DBC[int(i / 2)] | is_DBC[int(j / 2)]: \n            projected_hess[i, j] = (i == j)\n    for i in range(0, len(x)):\n        if is_DBC[i]:\n            reshaped_grad[i * 2] = reshaped_grad[i * 2 + 1] = 0.0\n    return spsolve(projected_hess, -reshaped_grad).reshape(len(x), 2)"
  },
  {
    "path": "3_contact/utils.py",
    "content": "import numpy as np\nimport numpy.linalg as LA\n\ndef make_PSD(hess):\n    [lam, V] = LA.eigh(hess)    # Eigen decomposition on symmetric matrix\n    # set all negative Eigenvalues to 0\n    for i in range(0, len(lam)):\n        lam[i] = max(0, lam[i])\n    return np.matmul(np.matmul(V, np.diag(lam)), np.transpose(V))"
  },
  {
    "path": "4_friction/BarrierEnergy.py",
    "content": "# ANCHOR: slope_barrier\nimport math\nimport numpy as np\n\ndhat = 0.01\nkappa = 1e5\n\ndef val(x, n, o, contact_area):\n    sum = 0.0\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            sum += contact_area[i] * dhat * kappa / 2 * (s - 1) * math.log(s)\n    return sum\n\ndef grad(x, n, o, contact_area):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            g[i] = contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d)) * n\n    return g\n\ndef hess(x, n, o, contact_area):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            local_hess = contact_area[i] * dhat * kappa / (2 * d * d * dhat) * (d + dhat) * np.outer(n, n)\n            for c in range(0, 2):\n                for r in range(0, 2):\n                    IJV[0].append(i * 2 + r)\n                    IJV[1].append(i * 2 + c)\n                    IJV[2] = np.append(IJV[2], local_hess[r, c])\n    return IJV\n# ANCHOR_END: slope_barrier\n\n# ANCHOR: init_step_size\ndef init_step_size(x, n, o, p):\n    alpha = 1\n    for i in range(0, len(x)):\n        p_n = p[i].dot(n)\n        if p_n < 0:\n            alpha = min(alpha, 0.9 * n.dot(x[i] - o) / -p_n)\n    return alpha\n# ANCHOR_END: init_step_size\n\n# ANCHOR: compute_mu_lambda\ndef compute_mu_lambda(x, n, o, contact_area, mu):\n    mu_lambda = np.array([0.0] * len(x))\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            mu_lambda[i] = mu * -contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d))\n    return mu_lambda\n# ANCHOR_END: compute_mu_lambda"
  },
  {
    "path": "4_friction/FrictionEnergy.py",
    "content": "# ANCHOR: f_terms\nimport numpy as np\nimport utils\n\nepsv = 1e-3\n\ndef f0(vbarnorm, epsv, hhat):\n    if vbarnorm >= epsv:\n        return vbarnorm * hhat\n    else:\n        vbarnormhhat = vbarnorm * hhat\n        epsvhhat = epsv * hhat\n        return vbarnormhhat * vbarnormhhat * (-vbarnormhhat / 3.0 + epsvhhat) / (epsvhhat * epsvhhat) + epsvhhat / 3.0\n\ndef f1_div_vbarnorm(vbarnorm, epsv):\n    if vbarnorm >= epsv:\n        return 1.0 / vbarnorm\n    else:\n        return (-vbarnorm + 2.0 * epsv) / (epsv * epsv)\n\ndef f_hess_term(vbarnorm, epsv):\n    if vbarnorm >= epsv:\n        return -1.0 / (vbarnorm * vbarnorm)\n    else:\n        return -1.0 / (epsv * epsv)\n# ANCHOR_END: f_terms\n\n# ANCHOR: val_grad_hess\ndef val(v, mu_lambda, hhat, n):\n    sum = 0.0\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            sum += mu_lambda[i] * f0(np.linalg.norm(vbar), epsv, hhat)\n    return sum\n\ndef grad(v, mu_lambda, hhat, n):\n    g = np.array([[0.0, 0.0]] * len(v))\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            g[i] = mu_lambda[i] * f1_div_vbarnorm(np.linalg.norm(vbar), epsv) * T.dot(vbar)\n    return g\n\ndef hess(v, mu_lambda, hhat, n):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            vbarnorm = np.linalg.norm(vbar)\n            inner_term = f1_div_vbarnorm(vbarnorm, epsv) * np.identity(2)\n            if vbarnorm != 0:\n                inner_term += f_hess_term(vbarnorm, epsv) / vbarnorm * np.outer(vbar, vbar)\n            local_hess = mu_lambda[i] * T.dot(utils.make_PSD(inner_term)).dot(np.transpose(T)) / hhat\n            for c in range(0, 2):\n                for r in range(0, 2):\n                    IJV[0].append(i * 2 + r)\n                    IJV[1].append(i * 2 + c)\n                    IJV[2] = np.append(IJV[2], local_hess[r, c])\n    return IJV\n# ANCHOR_END: val_grad_hess"
  },
  {
    "path": "4_friction/GravityEnergy.py",
    "content": "import numpy as np\n\ngravity = [0.0, -9.81]\n\ndef val(x, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        sum += -m[i] * x[i].dot(gravity)\n    return sum\n\ndef grad(x, m):\n    g = np.array([gravity] * len(x))\n    for i in range(0, len(x)):\n        g[i] *= -m[i]\n    return g\n\n# Hessian is 0"
  },
  {
    "path": "4_friction/InertiaEnergy.py",
    "content": "import numpy as np\n\ndef val(x, x_tilde, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        diff = x[i] - x_tilde[i]\n        sum += 0.5 * m[i] * diff.dot(diff)\n    return sum\n\ndef grad(x, x_tilde, m):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(x)):\n        g[i] = m[i] * (x[i] - x_tilde[i])\n    return g\n\ndef hess(x, x_tilde, m):\n    IJV = [[0] * (len(x) * 2), [0] * (len(x) * 2), np.array([0.0] * (len(x) * 2))]\n    for i in range(0, len(x)):\n        for d in range(0, 2):\n            IJV[0][i * 2 + d] = i * 2 + d\n            IJV[1][i * 2 + d] = i * 2 + d\n            IJV[2][i * 2 + d] = m[i]\n    return IJV"
  },
  {
    "path": "4_friction/MassSpringEnergy.py",
    "content": "import numpy as np\nimport utils\n\ndef val(x, e, l2, k):\n    sum = 0.0\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        sum += l2[i] * 0.5 * k[i] * (diff.dot(diff) / l2[i] - 1) ** 2\n    return sum\n\ndef grad(x, e, l2, k):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        g_diff = 2 * k[i] * (diff.dot(diff) / l2[i] - 1) * diff\n        g[e[i][0]] += g_diff\n        g[e[i][1]] -= g_diff\n    return g\n\ndef hess(x, e, l2, k):\n    IJV = [[0] * (len(e) * 16), [0] * (len(e) * 16), np.array([0.0] * (len(e) * 16))]\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        H_diff = 2 * k[i] / l2[i] * (2 * np.outer(diff, diff) + (diff.dot(diff) - l2[i]) * np.identity(2))\n        H_local = utils.make_PSD(np.block([[H_diff, -H_diff], [-H_diff, H_diff]]))\n        # add to global matrix\n        for nI in range(0, 2):\n            for nJ in range(0, 2):\n                indStart = i * 16 + (nI * 2 + nJ) * 4\n                for r in range(0, 2):\n                    for c in range(0, 2):\n                        IJV[0][indStart + r * 2 + c] = e[i][nI] * 2 + r\n                        IJV[1][indStart + r * 2 + c] = e[i][nJ] * 2 + c\n                        IJV[2][indStart + r * 2 + c] = H_local[nI * 2 + r, nJ * 2 + c]\n    return IJV"
  },
  {
    "path": "4_friction/readme.md",
    "content": "# Mass-Spring Solids Simulation\n\nA square sliding/residing on a slope under gravity is simulated with mass-spring elasticity potential and implicit Euler time integration.\nEach time step is solved by minimizing the Incremental Potential with the projected Newton method.\n\n## Dependencies\n```\npip install numpy scipy pygame\n```\n\n## Run\n```\npython simulator.py\n```"
  },
  {
    "path": "4_friction/simulator.py",
    "content": "# Mass-Spring Solids Simulation\n\nimport numpy as np  # numpy for linear algebra\nimport pygame       # pygame for visualization\npygame.init()\n\nimport square_mesh   # square mesh\nimport time_integrator\n\n# simulation setup\nside_len = 1\nrho = 1000      # density of square\nk = 2e4         # spring stiffness\nn_seg = 4       # num of segments per side of the square\nh = 0.01        # time step size in s\nDBC = []        # no nodes need to be fixed\n# ANCHOR: slope_setup\nground_n = np.array([0.1, 1.0])     # normal of the slope\nground_n /= np.linalg.norm(ground_n)    # normalize ground normal vector just in case\nground_o = np.array([0.0, -1.0])    # a point on the slope  \n# ANCHOR_END: slope_setup\n# ANCHOR: set_mu\nmu = 0.11        # friction coefficient of the slope\n# ANCHOR_END: set_mu\n\n# initialize simulation\n[x, e] = square_mesh.generate(side_len, n_seg)  # node positions and edge node indices\nv = np.array([[0.0, 0.0]] * len(x))             # velocity\nm = [rho * side_len * side_len / ((n_seg + 1) * (n_seg + 1))] * len(x)  # calculate node mass evenly\n# rest length squared\nl2 = []\nfor i in range(0, len(e)):\n    diff = x[e[i][0]] - x[e[i][1]]\n    l2.append(diff.dot(diff))\nk = [k] * len(e)    # spring stiffness\n# identify whether a node is Dirichlet\nis_DBC = [False] * len(x)\nfor i in DBC:\n    is_DBC[i] = True\ncontact_area = [side_len / n_seg] * len(x)     # perimeter split to each node\n\n# simulation with visualization\nresolution = np.array([900, 900])\noffset = resolution / 2\nscale = 200\ndef screen_projection(x):\n    return [offset[0] + scale * x[0], resolution[1] - (offset[1] + scale * x[1])]\n\ntime_step = 0\nsquare_mesh.write_to_file(time_step, x, n_seg)\nscreen = pygame.display.set_mode(resolution)\nrunning = True\nwhile running:\n    # run until the user asks to quit\n    for event in pygame.event.get():\n        if event.type == pygame.QUIT:\n            running = False\n    \n    print('### Time step', time_step, '###')\n\n    # fill the background and draw the square\n    screen.fill((255, 255, 255))\n    # ANCHOR: slope_vis\n    pygame.draw.aaline(screen, (0, 0, 255), screen_projection([ground_o[0] - 3.0 * ground_n[1], ground_o[1] + 3.0 * ground_n[0]]), \n        screen_projection([ground_o[0] + 3.0 * ground_n[1], ground_o[1] - 3.0 * ground_n[0]]))   # slope\n    # ANCHOR_END: slope_vis\n    for eI in e:\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[0]]), screen_projection(x[eI[1]]))\n    for xI in x:\n        pygame.draw.circle(screen, (0, 0, 255), screen_projection(xI), 0.1 * side_len / n_seg * scale)\n\n    pygame.display.flip()   # flip the display\n\n    # step forward simulation and wait for screen refresh\n    [x, v] = time_integrator.step_forward(x, e, v, m, l2, k, ground_n, ground_o, contact_area, mu, is_DBC, h, 1e-2)\n    time_step += 1\n    pygame.time.wait(int(h * 1000))\n    square_mesh.write_to_file(time_step, x, n_seg)\n\npygame.quit()"
  },
  {
    "path": "4_friction/square_mesh.py",
    "content": "import numpy as np\nimport os\n\ndef generate(side_length, n_seg):\n    # sample nodes uniformly on a square\n    x = np.array([[0.0, 0.0]] * ((n_seg + 1) ** 2))\n    step = side_length / n_seg\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg + 1):\n            x[i * (n_seg + 1) + j] = [-side_length / 2 + i * step, -side_length / 2 + j * step]\n    \n    # connect the nodes with edges\n    e = []\n    # horizontal edges\n    for i in range(0, n_seg):\n        for j in range(0, n_seg + 1):\n            e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j])\n    # vertical edges\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg):\n            e.append([i * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n    # diagonals\n    for i in range(0, n_seg):\n        for j in range(0, n_seg):\n            e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1])\n            e.append([(i + 1) * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n\n    return [x, e]\n\ndef write_to_file(frameNum, x, n_seg):\n    # Check if 'output' directory exists; if not, create it\n    if not os.path.exists('output'):\n        os.makedirs('output')\n\n    # create obj file\n    filename = f\"output/{frameNum}.obj\"\n    with open(filename, 'w') as f:\n        # write vertex coordinates\n        for row in x:\n            f.write(f\"v {float(row[0]):.6f} {float(row[1]):.6f} 0.0\\n\") \n        # write vertex indices for each triangle\n        for i in range(0, n_seg):\n            for j in range(0, n_seg):\n                #NOTE: each cell is exported as 2 triangles for rendering\n                f.write(f\"f {i * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j+1 + 1}\\n\")\n                f.write(f\"f {i * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j+1 + 1} {i * (n_seg+1) + j+1 + 1}\\n\")"
  },
  {
    "path": "4_friction/time_integrator.py",
    "content": "import copy\nfrom cmath import inf\n\nimport numpy as np\nimport numpy.linalg as LA\nimport scipy.sparse as sparse\nfrom scipy.sparse.linalg import spsolve\n\nimport InertiaEnergy\nimport MassSpringEnergy\nimport GravityEnergy\nimport BarrierEnergy\nimport FrictionEnergy\n\n# ANCHOR: mu_lambda\ndef step_forward(x, e, v, m, l2, k, n, o, contact_area, mu, is_DBC, h, tol):\n    x_tilde = x + v * h     # implicit Euler predictive position\n    x_n = copy.deepcopy(x)\n    mu_lambda = BarrierEnergy.compute_mu_lambda(x, n, o, contact_area, mu)  # compute mu * lambda for each node using x^n\n\n    # Newton loop\n# ANCHOR_END: mu_lambda\n    iter = 0\n    E_last = IP_val(x, e, x_tilde, m, l2, k, n, o, contact_area, (x - x_n) / h, mu_lambda, h)\n    p = search_dir(x, e, x_tilde, m, l2, k, n, o, contact_area, (x - x_n) / h, mu_lambda, is_DBC, h)\n    while LA.norm(p, inf) / h > tol:\n        print('Iteration', iter, ':')\n        print('residual =', LA.norm(p, inf) / h)\n\n        # filter line search\n        alpha = BarrierEnergy.init_step_size(x, n, o, p)  # avoid interpenetration and tunneling\n        while IP_val(x + alpha * p, e, x_tilde, m, l2, k, n, o, contact_area, (x + alpha * p - x_n) / h, mu_lambda, h) > E_last:\n            alpha /= 2\n        print('step size =', alpha)\n\n        x += alpha * p\n        E_last = IP_val(x, e, x_tilde, m, l2, k, n, o, contact_area, (x - x_n) / h, mu_lambda, h)\n        p = search_dir(x, e, x_tilde, m, l2, k, n, o, contact_area, (x - x_n) / h, mu_lambda, is_DBC, h)\n        iter += 1\n\n    v = (x - x_n) / h   # implicit Euler velocity update\n    return [x, v]\n\ndef IP_val(x, e, x_tilde, m, l2, k, n, o, contact_area, v, mu_lambda, h):\n    return InertiaEnergy.val(x, x_tilde, m) + h * h * (MassSpringEnergy.val(x, e, l2, k) + GravityEnergy.val(x, m) + BarrierEnergy.val(x, n, o, contact_area) + FrictionEnergy.val(v, mu_lambda, h, n))     # implicit Euler\n\ndef IP_grad(x, e, x_tilde, m, l2, k, n, o, contact_area, v, mu_lambda, h):\n    return InertiaEnergy.grad(x, x_tilde, m) + h * h * (MassSpringEnergy.grad(x, e, l2, k) + GravityEnergy.grad(x, m) + BarrierEnergy.grad(x, n, o, contact_area) + FrictionEnergy.grad(v, mu_lambda, h, n))   # implicit Euler\n\ndef IP_hess(x, e, x_tilde, m, l2, k, n, o, contact_area, v, mu_lambda, h):\n    IJV_In = InertiaEnergy.hess(x, x_tilde, m)\n    IJV_MS = MassSpringEnergy.hess(x, e, l2, k)\n    IJV_B = BarrierEnergy.hess(x, n, o, contact_area)\n    IJV_F = FrictionEnergy.hess(v, mu_lambda, h, n)\n    IJV_MS[2] *= h * h    # implicit Euler\n    IJV_B[2] *= h * h     # implicit Euler\n    IJV_F[2] *= h * h     # implicit Euler\n    IJV_In_MS = np.append(IJV_In, IJV_MS, axis=1)\n    IJV_In_MS_B = np.append(IJV_In_MS, IJV_B, axis=1)\n    IJV = np.append(IJV_In_MS_B, IJV_F, axis=1)\n    H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()\n    return H\n\ndef search_dir(x, e, x_tilde, m, l2, k, n, o, contact_area, v, mu_lambda, is_DBC, h):\n    projected_hess = IP_hess(x, e, x_tilde, m, l2, k, n, o, contact_area, v, mu_lambda, h)\n    reshaped_grad = IP_grad(x, e, x_tilde, m, l2, k, n, o, contact_area, v, mu_lambda, h).reshape(len(x) * 2, 1)\n    # eliminate DOF by modifying gradient and Hessian for DBC:\n    for i, j in zip(*projected_hess.nonzero()):\n        if is_DBC[int(i / 2)] | is_DBC[int(j / 2)]: \n            projected_hess[i, j] = (i == j)\n    for i in range(0, len(x)):\n        if is_DBC[i]:\n            reshaped_grad[i * 2] = reshaped_grad[i * 2 + 1] = 0.0\n    return spsolve(projected_hess, -reshaped_grad).reshape(len(x), 2)"
  },
  {
    "path": "4_friction/utils.py",
    "content": "import numpy as np\nimport numpy.linalg as LA\n\ndef make_PSD(hess):\n    [lam, V] = LA.eigh(hess)    # Eigen decomposition on symmetric matrix\n    # set all negative Eigenvalues to 0\n    for i in range(0, len(lam)):\n        lam[i] = max(0, lam[i])\n    return np.matmul(np.matmul(V, np.diag(lam)), np.transpose(V))"
  },
  {
    "path": "5_mov_dirichlet/BarrierEnergy.py",
    "content": "import math\nimport numpy as np\n\ndhat = 0.01\nkappa = 1e5\n\ndef val(x, n, o, contact_area):\n    sum = 0.0\n    # floor:\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            sum += contact_area[i] * dhat * kappa / 2 * (s - 1) * math.log(s)\n    # ANCHOR: ceiling_val\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        d = n.dot(x[i] - x[-1])\n        if d < dhat:\n            s = d / dhat\n            sum += contact_area[i] * dhat * kappa / 2 * (s - 1) * math.log(s)\n    # ANCHOR_END: ceiling_val\n    return sum\n\ndef grad(x, n, o, contact_area):\n    g = np.array([[0.0, 0.0]] * len(x))\n    # floor:\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            g[i] = contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d)) * n\n    # ANCHOR: ceiling_grad\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        d = n.dot(x[i] - x[-1])\n        if d < dhat:\n            s = d / dhat\n            local_grad = contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d)) * n\n            g[i] += local_grad\n            g[-1] -= local_grad\n    # ANCHOR_END: ceiling_grad\n    return g\n\ndef hess(x, n, o, contact_area):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    # floor:\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            local_hess = contact_area[i] * dhat * kappa / (2 * d * d * dhat) * (d + dhat) * np.outer(n, n)\n            for c in range(0, 2):\n                for r in range(0, 2):\n                    IJV[0].append(i * 2 + r)\n                    IJV[1].append(i * 2 + c)\n                    IJV[2] = np.append(IJV[2], local_hess[r, c])\n    # ANCHOR: ceiling_hess\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        d = n.dot(x[i] - x[-1])\n        if d < dhat:\n            local_hess = contact_area[i] * dhat * kappa / (2 * d * d * dhat) * (d + dhat) * np.outer(n, n)\n            index = [i, len(x) - 1]\n            for nI in range(0, 2):\n                for nJ in range(0, 2):\n                    for c in range(0, 2):\n                        for r in range(0, 2):\n                            IJV[0].append(index[nI] * 2 + r)\n                            IJV[1].append(index[nJ] * 2 + c)\n                            IJV[2] = np.append(IJV[2], ((-1) ** (nI != nJ)) * local_hess[r, c])\n    # ANCHOR_END: ceiling_hess\n    return IJV\n\ndef init_step_size(x, n, o, p):\n    alpha = 1\n    # floor:\n    for i in range(0, len(x)):\n        p_n = p[i].dot(n)\n        if p_n < 0:\n            alpha = min(alpha, 0.9 * n.dot(x[i] - o) / -p_n)\n    # ANCHOR: ceiling_ccd\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        p_n = (p[i] - p[-1]).dot(n)\n        if p_n < 0:\n            alpha = min(alpha, 0.9 * n.dot(x[i] - x[-1]) / -p_n)\n    # ANCHOR_END: ceiling_ccd\n    return alpha\n\ndef compute_mu_lambda(x, n, o, contact_area, mu):\n    mu_lambda = np.array([0.0] * len(x))\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            mu_lambda[i] = mu * -contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d))\n    return mu_lambda"
  },
  {
    "path": "5_mov_dirichlet/FrictionEnergy.py",
    "content": "import numpy as np\nimport utils\n\nepsv = 1e-3\n\ndef f0(vbarnorm, epsv, hhat):\n    if vbarnorm >= epsv:\n        return vbarnorm * hhat\n    else:\n        vbarnormhhat = vbarnorm * hhat\n        epsvhhat = epsv * hhat\n        return vbarnormhhat * vbarnormhhat * (-vbarnormhhat / 3.0 + epsvhhat) / (epsvhhat * epsvhhat) + epsvhhat / 3.0\n\ndef f1_div_vbarnorm(vbarnorm, epsv):\n    if vbarnorm >= epsv:\n        return 1.0 / vbarnorm\n    else:\n        return (-vbarnorm + 2.0 * epsv) / (epsv * epsv)\n\ndef f_hess_term(vbarnorm, epsv):\n    if vbarnorm >= epsv:\n        return -1.0 / (vbarnorm * vbarnorm)\n    else:\n        return -1.0 / (epsv * epsv)\n\ndef val(v, mu_lambda, hhat, n):\n    sum = 0.0\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            sum += mu_lambda[i] * f0(np.linalg.norm(vbar), epsv, hhat)\n    return sum\n\ndef grad(v, mu_lambda, hhat, n):\n    g = np.array([[0.0, 0.0]] * len(v))\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            g[i] = mu_lambda[i] * f1_div_vbarnorm(np.linalg.norm(vbar), epsv) * T.dot(vbar)\n    return g\n\ndef hess(v, mu_lambda, hhat, n):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            vbarnorm = np.linalg.norm(vbar)\n            inner_term = f1_div_vbarnorm(vbarnorm, epsv) * np.identity(2)\n            if vbarnorm != 0:\n                inner_term += f_hess_term(vbarnorm, epsv) / vbarnorm * np.outer(vbar, vbar)\n            local_hess = mu_lambda[i] * T.dot(utils.make_PSD(inner_term)).dot(np.transpose(T)) / hhat\n            for c in range(0, 2):\n                for r in range(0, 2):\n                    IJV[0].append(i * 2 + r)\n                    IJV[1].append(i * 2 + c)\n                    IJV[2] = np.append(IJV[2], local_hess[r, c])\n    return IJV"
  },
  {
    "path": "5_mov_dirichlet/GravityEnergy.py",
    "content": "import numpy as np\n\ngravity = [0.0, -9.81]\n\ndef val(x, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        sum += -m[i] * x[i].dot(gravity)\n    return sum\n\ndef grad(x, m):\n    g = np.array([gravity] * len(x))\n    for i in range(0, len(x)):\n        g[i] *= -m[i]\n    return g\n\n# Hessian is 0"
  },
  {
    "path": "5_mov_dirichlet/InertiaEnergy.py",
    "content": "import numpy as np\n\ndef val(x, x_tilde, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        diff = x[i] - x_tilde[i]\n        sum += 0.5 * m[i] * diff.dot(diff)\n    return sum\n\ndef grad(x, x_tilde, m):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(x)):\n        g[i] = m[i] * (x[i] - x_tilde[i])\n    return g\n\ndef hess(x, x_tilde, m):\n    IJV = [[0] * (len(x) * 2), [0] * (len(x) * 2), np.array([0.0] * (len(x) * 2))]\n    for i in range(0, len(x)):\n        for d in range(0, 2):\n            IJV[0][i * 2 + d] = i * 2 + d\n            IJV[1][i * 2 + d] = i * 2 + d\n            IJV[2][i * 2 + d] = m[i]\n    return IJV"
  },
  {
    "path": "5_mov_dirichlet/MassSpringEnergy.py",
    "content": "import numpy as np\nimport utils\n\ndef val(x, e, l2, k):\n    sum = 0.0\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        sum += l2[i] * 0.5 * k[i] * (diff.dot(diff) / l2[i] - 1) ** 2\n    return sum\n\ndef grad(x, e, l2, k):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        g_diff = 2 * k[i] * (diff.dot(diff) / l2[i] - 1) * diff\n        g[e[i][0]] += g_diff\n        g[e[i][1]] -= g_diff\n    return g\n\ndef hess(x, e, l2, k):\n    IJV = [[0] * (len(e) * 16), [0] * (len(e) * 16), np.array([0.0] * (len(e) * 16))]\n    for i in range(0, len(e)):\n        diff = x[e[i][0]] - x[e[i][1]]\n        H_diff = 2 * k[i] / l2[i] * (2 * np.outer(diff, diff) + (diff.dot(diff) - l2[i]) * np.identity(2))\n        H_local = utils.make_PSD(np.block([[H_diff, -H_diff], [-H_diff, H_diff]]))\n        # add to global matrix\n        for nI in range(0, 2):\n            for nJ in range(0, 2):\n                indStart = i * 16 + (nI * 2 + nJ) * 4\n                for r in range(0, 2):\n                    for c in range(0, 2):\n                        IJV[0][indStart + r * 2 + c] = e[i][nI] * 2 + r\n                        IJV[1][indStart + r * 2 + c] = e[i][nJ] * 2 + c\n                        IJV[2][indStart + r * 2 + c] = H_local[nI * 2 + r, nJ * 2 + c]\n    return IJV"
  },
  {
    "path": "5_mov_dirichlet/SpringEnergy.py",
    "content": "import numpy as np\n\ndef val(x, m, DBC, DBC_target, k):\n    sum = 0.0\n    for i in range(0, len(DBC)):\n        diff = x[DBC[i]] - DBC_target[i]\n        sum += 0.5 * k * m[DBC[i]] * diff.dot(diff)\n    return sum\n\ndef grad(x, m, DBC, DBC_target, k):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(DBC)):\n        g[DBC[i]] = k * m[DBC[i]] * (x[DBC[i]] - DBC_target[i])\n    return g\n\ndef hess(x, m, DBC, DBC_target, k):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    for i in range(0, len(DBC)):\n        for d in range(0, 2):\n            IJV[0].append(DBC[i] * 2 + d)\n            IJV[1].append(DBC[i] * 2 + d)\n            IJV[2] = np.append(IJV[2], k * m[DBC[i]])\n    return IJV"
  },
  {
    "path": "5_mov_dirichlet/readme.md",
    "content": "# Mass-Spring Solids Simulation\n\nA square falling onto a ground under gravity and then compressed by a ceiling is simulated with mass-spring elasticity potential and implicit Euler time integration.\nEach time step is solved by minimizing the Incremental Potential with the projected Newton method.\n\n## Dependencies\n```\npip install numpy scipy pygame\n```\n\n## Run\n```\npython simulator.py\n```"
  },
  {
    "path": "5_mov_dirichlet/simulator.py",
    "content": "# Mass-Spring Solids Simulation\n\nimport numpy as np  # numpy for linear algebra\nimport pygame       # pygame for visualization\npygame.init()\n\nimport square_mesh   # square mesh\nimport time_integrator\n\n# simulation setup\nside_len = 1\nrho = 1000      # density of square\nk = 2e4         # spring stiffness\nn_seg = 4       # num of segments per side of the square\nh = 0.01        # time step size in s\n# ANCHOR: ceiling_dbc_setup\nDBC = [(n_seg + 1) * (n_seg + 1)]       # dirichlet node index\nDBC_v = [np.array([0.0, -0.5])]         # dirichlet node velocity\nDBC_limit = [np.array([0.0, -0.6])]     # dirichlet node limit position\n# ANCHOR_END: ceiling_dbc_setup\nground_n = np.array([0.0, 1.0])         # normal of the slope\nground_n /= np.linalg.norm(ground_n)    # normalize ground normal vector just in case\nground_o = np.array([0.0, -1.0])        # a point on the slope  \nmu = 0.11        # friction coefficient of the slope\n\n# initialize simulation\n# ANCHOR: ceiling_dof\n[x, e] = square_mesh.generate(side_len, n_seg)      # node positions and edge node indices\nx = np.append(x, [[0.0, side_len * 0.6]], axis=0)   # ceil origin (with normal [0.0, -1.0])\n# ANCHOR_END: ceiling_dof\nv = np.array([[0.0, 0.0]] * len(x))                 # velocity\nm = [rho * side_len * side_len / ((n_seg + 1) * (n_seg + 1))] * len(x)  # calculate node mass evenly\n# rest length squared\nl2 = []\nfor i in range(0, len(e)):\n    diff = x[e[i][0]] - x[e[i][1]]\n    l2.append(diff.dot(diff))\nk = [k] * len(e)    # spring stiffness\n# identify whether a node is Dirichlet\nis_DBC = [False] * len(x)\nfor i in DBC:\n    is_DBC[i] = True\nDBC_stiff = [1000]  # DBC stiffness, adjusted and warm-started across time steps\ncontact_area = [side_len / n_seg] * len(x)     # perimeter split to each node\n\n# simulation with visualization\nresolution = np.array([900, 900])\noffset = resolution / 2\nscale = 200\ndef screen_projection(x):\n    return [offset[0] + scale * x[0], resolution[1] - (offset[1] + scale * x[1])]\n\ntime_step = 0\nsquare_mesh.write_to_file(time_step, x, n_seg)\nscreen = pygame.display.set_mode(resolution)\nrunning = True\nwhile running:\n    # run until the user asks to quit\n    for event in pygame.event.get():\n        if event.type == pygame.QUIT:\n            running = False\n    \n    print('### Time step', time_step, '###')\n\n    # fill the background and draw the square\n    screen.fill((255, 255, 255))\n    pygame.draw.aaline(screen, (0, 0, 255), screen_projection([ground_o[0] - 3.0 * ground_n[1], ground_o[1] + 3.0 * ground_n[0]]), \n        screen_projection([ground_o[0] + 3.0 * ground_n[1], ground_o[1] - 3.0 * ground_n[0]]))   # ground\n    pygame.draw.aaline(screen, (0, 0, 255), screen_projection([x[-1][0] + 3.0, x[-1][1]]), \n        screen_projection([x[-1][0] - 3.0, x[-1][1]]))   # ceil\n    for eI in e:\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[0]]), screen_projection(x[eI[1]]))\n    for xId in range(0, len(x) - 1):\n        xI = x[xId]\n        pygame.draw.circle(screen, (0, 0, 255), screen_projection(xI), 0.1 * side_len / n_seg * scale)\n\n    pygame.display.flip()   # flip the display\n\n    # step forward simulation and wait for screen refresh\n    [x, v] = time_integrator.step_forward(x, e, v, m, l2, k, ground_n, ground_o, contact_area, mu, is_DBC, DBC, DBC_v, DBC_limit, DBC_stiff, h, 1e-2)\n    time_step += 1\n    pygame.time.wait(int(h * 1000))\n    square_mesh.write_to_file(time_step, x, n_seg)\n\npygame.quit()"
  },
  {
    "path": "5_mov_dirichlet/square_mesh.py",
    "content": "import numpy as np\nimport os\n\ndef generate(side_length, n_seg):\n    # sample nodes uniformly on a square\n    x = np.array([[0.0, 0.0]] * ((n_seg + 1) ** 2))\n    step = side_length / n_seg\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg + 1):\n            x[i * (n_seg + 1) + j] = [-side_length / 2 + i * step, -side_length / 2 + j * step]\n    \n    # connect the nodes with edges\n    e = []\n    # horizontal edges\n    for i in range(0, n_seg):\n        for j in range(0, n_seg + 1):\n            e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j])\n    # vertical edges\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg):\n            e.append([i * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n    # diagonals\n    for i in range(0, n_seg):\n        for j in range(0, n_seg):\n            e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1])\n            e.append([(i + 1) * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n\n    return [x, e]\n\ndef write_to_file(frameNum, x, n_seg):\n    # Check if 'output' directory exists; if not, create it\n    if not os.path.exists('output'):\n        os.makedirs('output')\n\n    # create obj file\n    filename = f\"output/{frameNum}.obj\"\n    with open(filename, 'w') as f:\n        # write vertex coordinates\n        for row in x:\n            f.write(f\"v {float(row[0]):.6f} {float(row[1]):.6f} 0.0\\n\") \n        # write vertex indices for each triangle\n        for i in range(0, n_seg):\n            for j in range(0, n_seg):\n                #NOTE: each cell is exported as 2 triangles for rendering\n                f.write(f\"f {i * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j+1 + 1}\\n\")\n                f.write(f\"f {i * (n_seg+1) + j + 1} {(i+1) * (n_seg+1) + j+1 + 1} {i * (n_seg+1) + j+1 + 1}\\n\")"
  },
  {
    "path": "5_mov_dirichlet/time_integrator.py",
    "content": "import copy\nfrom cmath import inf\n\nimport numpy as np\nimport numpy.linalg as LA\nimport scipy.sparse as sparse\nfrom scipy.sparse.linalg import spsolve\n\nimport InertiaEnergy\nimport MassSpringEnergy\nimport GravityEnergy\nimport BarrierEnergy\nimport FrictionEnergy\nimport SpringEnergy\n\ndef step_forward(x, e, v, m, l2, k, n, o, contact_area, mu, is_DBC, DBC, DBC_v, DBC_limit, DBC_stiff, h, tol):\n    x_tilde = x + v * h     # implicit Euler predictive position\n    x_n = copy.deepcopy(x)\n    mu_lambda = BarrierEnergy.compute_mu_lambda(x, n, o, contact_area, mu)  # compute mu * lambda for each node using x^n\n    # ANCHOR: dbc_initialization\n    DBC_target = [] # target position of each DBC in the current time step\n    for i in range(0, len(DBC)):\n        if (DBC_limit[i] - x_n[DBC[i]]).dot(DBC_v[i]) > 0:\n            DBC_target.append(x_n[DBC[i]] + h * DBC_v[i])\n        else:\n            DBC_target.append(x_n[DBC[i]])\n    # ANCHOR_END: dbc_initialization\n\n    # Newton loop\n    iter = 0\n    E_last = IP_val(x, e, x_tilde, m, l2, k, n, o, contact_area, (x - x_n) / h, mu_lambda, DBC, DBC_target, DBC_stiff[0], h)\n    # ANCHOR: convergence_criteria\n    [p, DBC_satisfied] = search_dir(x, e, x_tilde, m, l2, k, n, o, contact_area, (x - x_n) / h, mu_lambda, is_DBC, DBC, DBC_target, DBC_stiff[0], tol, h)\n    while (LA.norm(p, inf) / h > tol) | (sum(DBC_satisfied) != len(DBC)):   # also check whether all DBCs are satisfied\n        print('Iteration', iter, ':')\n        print('residual =', LA.norm(p, inf) / h)\n\n        if (LA.norm(p, inf) / h <= tol) & (sum(DBC_satisfied) != len(DBC)):\n            # increase DBC stiffness and recompute energy value record\n            DBC_stiff[0] *= 2\n            E_last = IP_val(x, e, x_tilde, m, l2, k, n, o, contact_area, (x - x_n) / h, mu_lambda, DBC, DBC_target, DBC_stiff[0], h)\n        # ANCHOR_END: convergence_criteria\n\n        # filter line search\n        alpha = BarrierEnergy.init_step_size(x, n, o, p)  # avoid interpenetration and tunneling\n        while IP_val(x + alpha * p, e, x_tilde, m, l2, k, n, o, contact_area, (x + alpha * p - x_n) / h, mu_lambda, DBC, DBC_target, DBC_stiff[0], h) > E_last:\n            alpha /= 2\n        print('step size =', alpha)\n\n        x += alpha * p\n        E_last = IP_val(x, e, x_tilde, m, l2, k, n, o, contact_area, (x - x_n) / h, mu_lambda, DBC, DBC_target, DBC_stiff[0], h)\n        [p, DBC_satisfied] = search_dir(x, e, x_tilde, m, l2, k, n, o, contact_area, (x - x_n) / h, mu_lambda, is_DBC, DBC, DBC_target, DBC_stiff[0], tol, h)\n        iter += 1\n\n    v = (x - x_n) / h   # implicit Euler velocity update\n    return [x, v]\n\ndef IP_val(x, e, x_tilde, m, l2, k, n, o, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h):\n    return InertiaEnergy.val(x, x_tilde, m) + h * h * (     # implicit Euler\n        MassSpringEnergy.val(x, e, l2, k) + \n        GravityEnergy.val(x, m) + \n        BarrierEnergy.val(x, n, o, contact_area) + \n        FrictionEnergy.val(v, mu_lambda, h, n)\n    ) + SpringEnergy.val(x, m, DBC, DBC_target, DBC_stiff)\n\ndef IP_grad(x, e, x_tilde, m, l2, k, n, o, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h):\n    return InertiaEnergy.grad(x, x_tilde, m) + h * h * (    # implicit Euler\n        MassSpringEnergy.grad(x, e, l2, k) + \n        GravityEnergy.grad(x, m) + \n        BarrierEnergy.grad(x, n, o, contact_area) + \n        FrictionEnergy.grad(v, mu_lambda, h, n)\n    ) + SpringEnergy.grad(x, m, DBC, DBC_target, DBC_stiff)\n\ndef IP_hess(x, e, x_tilde, m, l2, k, n, o, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h):\n    IJV_In = InertiaEnergy.hess(x, x_tilde, m)\n    IJV_MS = MassSpringEnergy.hess(x, e, l2, k)\n    IJV_B = BarrierEnergy.hess(x, n, o, contact_area)\n    IJV_F = FrictionEnergy.hess(v, mu_lambda, h, n)\n    IJV_S = SpringEnergy.hess(x, m, DBC, DBC_target, DBC_stiff)\n    IJV_MS[2] *= h * h    # implicit Euler\n    IJV_B[2] *= h * h     # implicit Euler\n    IJV_F[2] *= h * h     # implicit Euler\n    IJV_In_MS = np.append(IJV_In, IJV_MS, axis=1)\n    IJV_In_MS_B = np.append(IJV_In_MS, IJV_B, axis=1)\n    IJV_In_MS_B_F = np.append(IJV_In_MS_B, IJV_F, axis=1)\n    IJV = np.append(IJV_In_MS_B_F, IJV_S, axis=1)\n    H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()\n    return H\n\ndef search_dir(x, e, x_tilde, m, l2, k, n, o, contact_area, v, mu_lambda, is_DBC, DBC, DBC_target, DBC_stiff, tol, h):\n    projected_hess = IP_hess(x, e, x_tilde, m, l2, k, n, o, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h)\n    reshaped_grad = IP_grad(x, e, x_tilde, m, l2, k, n, o, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h).reshape(len(x) * 2, 1)\n    # ANCHOR: dbc_check\n    # check whether each DBC is satisfied\n    DBC_satisfied = [False] * len(x)\n    for i in range(0, len(DBC)):\n        if LA.norm(x[DBC[i]] - DBC_target[i]) / h < tol:\n            DBC_satisfied[DBC[i]] = True\n    # ANCHOR_END: dbc_check\n    # ANCHOR: dof_elimination\n    # eliminate DOF if it's a satisfied DBC by modifying gradient and Hessian for DBC:\n    for i, j in zip(*projected_hess.nonzero()):\n        if (is_DBC[int(i / 2)] & DBC_satisfied[int(i / 2)]) | (is_DBC[int(j / 2)] & DBC_satisfied[int(j / 2)]): \n            projected_hess[i, j] = (i == j)\n    for i in range(0, len(x)):\n        if is_DBC[i] & DBC_satisfied[i]:\n            reshaped_grad[i * 2] = reshaped_grad[i * 2 + 1] = 0.0\n    return [spsolve(projected_hess, -reshaped_grad).reshape(len(x), 2), DBC_satisfied]\n    # ANCHOR_END: dof_elimination"
  },
  {
    "path": "5_mov_dirichlet/utils.py",
    "content": "import numpy as np\nimport numpy.linalg as LA\n\ndef make_PSD(hess):\n    [lam, V] = LA.eigh(hess)    # Eigen decomposition on symmetric matrix\n    # set all negative Eigenvalues to 0\n    for i in range(0, len(lam)):\n        lam[i] = max(0, lam[i])\n    return np.matmul(np.matmul(V, np.diag(lam)), np.transpose(V))"
  },
  {
    "path": "6_inv_free/BarrierEnergy.py",
    "content": "import math\nimport numpy as np\n\ndhat = 0.01\nkappa = 1e5\n\ndef val(x, n, o, contact_area):\n    sum = 0.0\n    # floor:\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            sum += contact_area[i] * dhat * kappa / 2 * (s - 1) * math.log(s)\n    # ceil:\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        d = n.dot(x[i] - x[-1])\n        if d < dhat:\n            s = d / dhat\n            sum += contact_area[i] * dhat * kappa / 2 * (s - 1) * math.log(s)\n    return sum\n\ndef grad(x, n, o, contact_area):\n    g = np.array([[0.0, 0.0]] * len(x))\n    # floor:\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            g[i] = contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d)) * n\n    # ceil:\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        d = n.dot(x[i] - x[-1])\n        if d < dhat:\n            s = d / dhat\n            local_grad = contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d)) * n\n            g[i] += local_grad\n            g[-1] -= local_grad\n    return g\n\ndef hess(x, n, o, contact_area):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    # floor:\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            local_hess = contact_area[i] * dhat * kappa / (2 * d * d * dhat) * (d + dhat) * np.outer(n, n)\n            for c in range(0, 2):\n                for r in range(0, 2):\n                    IJV[0].append(i * 2 + r)\n                    IJV[1].append(i * 2 + c)\n                    IJV[2] = np.append(IJV[2], local_hess[r, c])\n    # ceil:\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        d = n.dot(x[i] - x[-1])\n        if d < dhat:\n            local_hess = contact_area[i] * dhat * kappa / (2 * d * d * dhat) * (d + dhat) * np.outer(n, n)\n            index = [i, len(x) - 1]\n            for nI in range(0, 2):\n                for nJ in range(0, 2):\n                    for c in range(0, 2):\n                        for r in range(0, 2):\n                            IJV[0].append(index[nI] * 2 + r)\n                            IJV[1].append(index[nJ] * 2 + c)\n                            IJV[2] = np.append(IJV[2], ((-1) ** (nI != nJ)) * local_hess[r, c])\n    return IJV\n\ndef init_step_size(x, n, o, p):\n    alpha = 1\n    # floor:\n    for i in range(0, len(x)):\n        p_n = p[i].dot(n)\n        if p_n < 0:\n            alpha = min(alpha, 0.9 * n.dot(x[i] - o) / -p_n)\n    # ceil:\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        p_n = (p[i] - p[-1]).dot(n)\n        if p_n < 0:\n            alpha = min(alpha, 0.9 * n.dot(x[i] - x[-1]) / -p_n)\n    return alpha\n\ndef compute_mu_lambda(x, n, o, contact_area, mu):\n    mu_lambda = np.array([0.0] * len(x))\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            mu_lambda[i] = mu * -contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d))\n    return mu_lambda"
  },
  {
    "path": "6_inv_free/FrictionEnergy.py",
    "content": "import numpy as np\nimport utils\n\nepsv = 1e-3\n\ndef f0(vbarnorm, epsv, hhat):\n    if vbarnorm >= epsv:\n        return vbarnorm * hhat\n    else:\n        vbarnormhhat = vbarnorm * hhat\n        epsvhhat = epsv * hhat\n        return vbarnormhhat * vbarnormhhat * (-vbarnormhhat / 3.0 + epsvhhat) / (epsvhhat * epsvhhat) + epsvhhat / 3.0\n\ndef f1_div_vbarnorm(vbarnorm, epsv):\n    if vbarnorm >= epsv:\n        return 1.0 / vbarnorm\n    else:\n        return (-vbarnorm + 2.0 * epsv) / (epsv * epsv)\n\ndef f_hess_term(vbarnorm, epsv):\n    if vbarnorm >= epsv:\n        return -1.0 / (vbarnorm * vbarnorm)\n    else:\n        return -1.0 / (epsv * epsv)\n\ndef val(v, mu_lambda, hhat, n):\n    sum = 0.0\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            sum += mu_lambda[i] * f0(np.linalg.norm(vbar), epsv, hhat)\n    return sum\n\ndef grad(v, mu_lambda, hhat, n):\n    g = np.array([[0.0, 0.0]] * len(v))\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            g[i] = mu_lambda[i] * f1_div_vbarnorm(np.linalg.norm(vbar), epsv) * T.dot(vbar)\n    return g\n\ndef hess(v, mu_lambda, hhat, n):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            vbarnorm = np.linalg.norm(vbar)\n            inner_term = f1_div_vbarnorm(vbarnorm, epsv) * np.identity(2)\n            if vbarnorm != 0:\n                inner_term += f_hess_term(vbarnorm, epsv) / vbarnorm * np.outer(vbar, vbar)\n            local_hess = mu_lambda[i] * T.dot(utils.make_PSD(inner_term)).dot(np.transpose(T)) / hhat\n            for c in range(0, 2):\n                for r in range(0, 2):\n                    IJV[0].append(i * 2 + r)\n                    IJV[1].append(i * 2 + c)\n                    IJV[2] = np.append(IJV[2], local_hess[r, c])\n    return IJV"
  },
  {
    "path": "6_inv_free/GravityEnergy.py",
    "content": "import numpy as np\n\ngravity = [0.0, -9.81]\n\ndef val(x, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        sum += -m[i] * x[i].dot(gravity)\n    return sum\n\ndef grad(x, m):\n    g = np.array([gravity] * len(x))\n    for i in range(0, len(x)):\n        g[i] *= -m[i]\n    return g\n\n# Hessian is 0"
  },
  {
    "path": "6_inv_free/InertiaEnergy.py",
    "content": "import numpy as np\n\ndef val(x, x_tilde, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        diff = x[i] - x_tilde[i]\n        sum += 0.5 * m[i] * diff.dot(diff)\n    return sum\n\ndef grad(x, x_tilde, m):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(x)):\n        g[i] = m[i] * (x[i] - x_tilde[i])\n    return g\n\ndef hess(x, x_tilde, m):\n    IJV = [[0] * (len(x) * 2), [0] * (len(x) * 2), np.array([0.0] * (len(x) * 2))]\n    for i in range(0, len(x)):\n        for d in range(0, 2):\n            IJV[0][i * 2 + d] = i * 2 + d\n            IJV[1][i * 2 + d] = i * 2 + d\n            IJV[2][i * 2 + d] = m[i]\n    return IJV"
  },
  {
    "path": "6_inv_free/NeoHookeanEnergy.py",
    "content": "# ANCHOR: helper_func\nimport utils\nimport numpy as np\nimport math\n\ndef polar_svd(F):\n    [U, s, VT] = np.linalg.svd(F)\n    if np.linalg.det(U) < 0:\n        U[:, 1] = -U[:, 1]\n        s[1] = -s[1]\n    if np.linalg.det(VT) < 0:\n        VT[1, :] = -VT[1, :]\n        s[1] = -s[1]\n    return [U, s, VT]\n\ndef dPsi_div_dsigma(s, mu, lam):\n    ln_sigma_prod = math.log(s[0] * s[1])\n    inv0 = 1.0 / s[0]\n    dPsi_dsigma_0 = mu * (s[0] - inv0) + lam * inv0 * ln_sigma_prod\n    inv1 = 1.0 / s[1]\n    dPsi_dsigma_1 = mu * (s[1] - inv1) + lam * inv1 * ln_sigma_prod\n    return [dPsi_dsigma_0, dPsi_dsigma_1]\n\ndef d2Psi_div_dsigma2(s, mu, lam):\n    ln_sigma_prod = math.log(s[0] * s[1])\n    inv2_0 = 1 / (s[0] * s[0])\n    d2Psi_dsigma2_00 = mu * (1 + inv2_0) - lam * inv2_0 * (ln_sigma_prod - 1)\n    inv2_1 = 1 / (s[1] * s[1])\n    d2Psi_dsigma2_11 = mu * (1 + inv2_1) - lam * inv2_1 * (ln_sigma_prod - 1)\n    d2Psi_dsigma2_01 = lam / (s[0] * s[1])\n    return [[d2Psi_dsigma2_00, d2Psi_dsigma2_01], [d2Psi_dsigma2_01, d2Psi_dsigma2_11]]\n\ndef B_left_coef(s, mu, lam):\n    sigma_prod = s[0] * s[1]\n    return (mu + (mu - lam * math.log(sigma_prod)) / sigma_prod) / 2\n\ndef Psi(F, mu, lam):\n    J = np.linalg.det(F)\n    lnJ = math.log(J)\n    return mu / 2 * (np.trace(np.transpose(F).dot(F)) - 2) - mu * lnJ + lam / 2 * lnJ * lnJ\n\ndef dPsi_div_dF(F, mu, lam):\n    FinvT = np.transpose(np.linalg.inv(F))\n    return mu * (F - FinvT) + lam * math.log(np.linalg.det(F)) * FinvT\n\ndef d2Psi_div_dF2(F, mu, lam):\n    [U, sigma, VT] = polar_svd(F)\n\n    Psi_sigma_sigma = utils.make_PSD(d2Psi_div_dsigma2(sigma, mu, lam))\n\n    B_left = B_left_coef(sigma, mu, lam)\n    Psi_sigma = dPsi_div_dsigma(sigma, mu, lam)\n    B_right = (Psi_sigma[0] + Psi_sigma[1]) / (2 * max(sigma[0] + sigma[1], 1e-6))\n    B = utils.make_PSD([[B_left + B_right, B_left - B_right], [B_left - B_right, B_left + B_right]])\n\n    M = np.array([[0, 0, 0, 0]] * 4)\n    M[0, 0] = Psi_sigma_sigma[0, 0]\n    M[0, 3] = Psi_sigma_sigma[0, 1]\n    M[1, 1] = B[0, 0]\n    M[1, 2] = B[0, 1]\n    M[2, 1] = B[1, 0]\n    M[2, 2] = B[1, 1]\n    M[3, 0] = Psi_sigma_sigma[1, 0]\n    M[3, 3] = Psi_sigma_sigma[1, 1]\n\n    dP_div_dF = np.array([[0, 0, 0, 0]] * 4)\n    for j in range(0, 2):\n        for i in range(0, 2):\n            ij = j * 2 + i\n            for s in range(0, 2):\n                for r in range(0, 2):\n                    rs = s * 2 + r\n                    dP_div_dF[ij, rs] = M[0, 0] * U[i, 0] * VT[0, j] * U[r, 0] * VT[0, s] \\\n                        + M[0, 3] * U[i, 0] * VT[0, j] * U[r, 1] * VT[1, s] \\\n                        + M[1, 1] * U[i, 1] * VT[0, j] * U[r, 1] * VT[0, s] \\\n                        + M[1, 2] * U[i, 1] * VT[0, j] * U[r, 0] * VT[1, s] \\\n                        + M[2, 1] * U[i, 0] * VT[1, j] * U[r, 1] * VT[0, s] \\\n                        + M[2, 2] * U[i, 0] * VT[1, j] * U[r, 0] * VT[1, s] \\\n                        + M[3, 0] * U[i, 1] * VT[1, j] * U[r, 0] * VT[0, s] \\\n                        + M[3, 3] * U[i, 1] * VT[1, j] * U[r, 1] * VT[1, s]\n    return dP_div_dF\n# ANCHOR_END: helper_func\n\n# ANCHOR: stress_deriv\ndef deformation_grad(x, elemVInd, IB):\n    F = [x[elemVInd[1]] - x[elemVInd[0]], x[elemVInd[2]] - x[elemVInd[0]]]\n    return np.transpose(F).dot(IB)\n\ndef dPsi_div_dx(P, IB):  # applying chain-rule, dPsi_div_dx = dPsi_div_dF * dF_div_dx\n    dPsi_dx_2 = P[0, 0] * IB[0, 0] + P[0, 1] * IB[0, 1]\n    dPsi_dx_3 = P[1, 0] * IB[0, 0] + P[1, 1] * IB[0, 1]\n    dPsi_dx_4 = P[0, 0] * IB[1, 0] + P[0, 1] * IB[1, 1]\n    dPsi_dx_5 = P[1, 0] * IB[1, 0] + P[1, 1] * IB[1, 1]\n    return [np.array([-dPsi_dx_2 - dPsi_dx_4, -dPsi_dx_3 - dPsi_dx_5]), np.array([dPsi_dx_2, dPsi_dx_3]), np.array([dPsi_dx_4, dPsi_dx_5])]\n\ndef d2Psi_div_dx2(dP_div_dF, IB):  # applying chain-rule, d2Psi_div_dx2 = dF_div_dx^T * d2Psi_div_dF2 * dF_div_dx (note that d2F_div_dx2 = 0)\n    intermediate = np.array([[0.0, 0.0, 0.0, 0.0]] * 6)\n    for colI in range(0, 4):\n        _000 = dP_div_dF[0, colI] * IB[0, 0]\n        _010 = dP_div_dF[0, colI] * IB[1, 0]\n        _101 = dP_div_dF[2, colI] * IB[0, 1]\n        _111 = dP_div_dF[2, colI] * IB[1, 1]\n        _200 = dP_div_dF[1, colI] * IB[0, 0]\n        _210 = dP_div_dF[1, colI] * IB[1, 0]\n        _301 = dP_div_dF[3, colI] * IB[0, 1]\n        _311 = dP_div_dF[3, colI] * IB[1, 1]\n        intermediate[2, colI] = _000 + _101\n        intermediate[3, colI] = _200 + _301\n        intermediate[4, colI] = _010 + _111\n        intermediate[5, colI] = _210 + _311\n        intermediate[0, colI] = -intermediate[2, colI] - intermediate[4, colI]\n        intermediate[1, colI] = -intermediate[3, colI] - intermediate[5, colI]\n    result = np.array([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]] * 6)\n    for colI in range(0, 6):\n        _000 = intermediate[colI, 0] * IB[0, 0]\n        _010 = intermediate[colI, 0] * IB[1, 0]\n        _101 = intermediate[colI, 2] * IB[0, 1]\n        _111 = intermediate[colI, 2] * IB[1, 1]\n        _200 = intermediate[colI, 1] * IB[0, 0]\n        _210 = intermediate[colI, 1] * IB[1, 0]\n        _301 = intermediate[colI, 3] * IB[0, 1]\n        _311 = intermediate[colI, 3] * IB[1, 1]\n        result[2, colI] = _000 + _101\n        result[3, colI] = _200 + _301\n        result[4, colI] = _010 + _111\n        result[5, colI] = _210 + _311\n        result[0, colI] = -_000 - _101 - _010 - _111\n        result[1, colI] = -_200 - _301 - _210 - _311\n    return result\n# ANCHOR_END: stress_deriv\n\n# ANCHOR: val_grad_hess\ndef val(x, e, vol, IB, mu, lam):\n    sum = 0.0\n    for i in range(0, len(e)):\n        F = deformation_grad(x, e[i], IB[i])\n        sum += vol[i] * Psi(F, mu[i], lam[i])\n    return sum\n\ndef grad(x, e, vol, IB, mu, lam):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(e)):\n        F = deformation_grad(x, e[i], IB[i])\n        P = vol[i] * dPsi_div_dF(F, mu[i], lam[i])\n        g_local = dPsi_div_dx(P, IB[i])\n        for j in range(0, 3):\n            g[e[i][j]] += g_local[j]\n    return g\n\ndef hess(x, e, vol, IB, mu, lam):\n    IJV = [[0] * (len(e) * 36), [0] * (len(e) * 36), np.array([0.0] * (len(e) * 36))]\n    for i in range(0, len(e)):\n        F = deformation_grad(x, e[i], IB[i])\n        dP_div_dF = vol[i] * d2Psi_div_dF2(F, mu[i], lam[i])\n        local_hess = d2Psi_div_dx2(dP_div_dF, IB[i])\n        for xI in range(0, 3):\n            for xJ in range(0, 3):\n                for dI in range(0, 2):\n                    for dJ in range(0, 2):\n                        ind = i * 36 + (xI * 3 + xJ) * 4 + dI * 2 + dJ\n                        IJV[0][ind] = e[i][xI] * 2 + dI\n                        IJV[1][ind] = e[i][xJ] * 2 + dJ\n                        IJV[2][ind] = local_hess[xI * 2 + dI, xJ * 2 + dJ]\n    return IJV\n# ANCHOR_END: val_grad_hess\n\n# ANCHOR: filter_line_search\ndef init_step_size(x, e, p):\n    alpha = 1\n    for i in range(0, len(e)):\n        x21 = x[e[i][1]] - x[e[i][0]]\n        x31 = x[e[i][2]] - x[e[i][0]]\n        p21 = p[e[i][1]] - p[e[i][0]]\n        p31 = p[e[i][2]] - p[e[i][0]]\n        detT = np.linalg.det(np.transpose([x21, x31]))\n        a = np.linalg.det(np.transpose([p21, p31])) / detT\n        b = (np.linalg.det(np.transpose([x21, p31])) + np.linalg.det(np.transpose([p21, x31]))) / detT\n        c = 0.9  # solve for alpha that first brings the new volume to 0.1x the old volume for slackness\n        critical_alpha = utils.smallest_positive_real_root_quad(a, b, c)\n        if critical_alpha > 0:\n            alpha = min(alpha, critical_alpha)\n    return alpha\n# ANCHOR_END: filter_line_search"
  },
  {
    "path": "6_inv_free/SpringEnergy.py",
    "content": "import numpy as np\n\ndef val(x, m, DBC, DBC_target, k):\n    sum = 0.0\n    for i in range(0, len(DBC)):\n        diff = x[DBC[i]] - DBC_target[i]\n        sum += 0.5 * k * m[DBC[i]] * diff.dot(diff)\n    return sum\n\ndef grad(x, m, DBC, DBC_target, k):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(DBC)):\n        g[DBC[i]] = k * m[DBC[i]] * (x[DBC[i]] - DBC_target[i])\n    return g\n\ndef hess(x, m, DBC, DBC_target, k):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    for i in range(0, len(DBC)):\n        for d in range(0, 2):\n            IJV[0].append(DBC[i] * 2 + d)\n            IJV[1].append(DBC[i] * 2 + d)\n            IJV[2] = np.append(IJV[2], k * m[DBC[i]])\n    return IJV"
  },
  {
    "path": "6_inv_free/readme.md",
    "content": "# Inversion-free Hyperelastic Solids Simulation\n\nA square falling onto a ground under gravity and then compressed by a ceiling is simulated with an inversion-free hyperelastic potential and implicit Euler time integration.\nEach time step is solved by minimizing the Incremental Potential with the projected Newton method.\n\n## Dependencies\n```\npip install numpy scipy pygame\n```\n\n## Run\n```\npython simulator.py\n```"
  },
  {
    "path": "6_inv_free/simulator.py",
    "content": "# FEM Solids Simulation\n\nimport numpy as np  # numpy for linear algebra\nimport pygame       # pygame for visualization\npygame.init()\n\nimport square_mesh   # square mesh\nimport time_integrator\n\n# simulation setup\nside_len = 1\nrho = 1000      # density of square\n# ANCHOR: lame_param\nE = 1e5         # Young's modulus\nnu = 0.4        # Poisson's ratio\n# ANCHOR_END: lame_param\nn_seg = 4      # num of segments per side of the square\nh = 0.01        # time step size in s\nDBC = [(n_seg + 1) * (n_seg + 1)]       # dirichlet node index\nDBC_v = [np.array([0.0, -0.5])]         # dirichlet node velocity\nDBC_limit = [np.array([0.0, -0.7])]     # dirichlet node limit position\nground_n = np.array([0.0, 1.0])         # normal of the slope\nground_n /= np.linalg.norm(ground_n)    # normalize ground normal vector just in case\nground_o = np.array([0.0, -1.0])        # a point on the slope  \nmu = 0.11        # friction coefficient of the slope\n\n# initialize simulation\n[x, e] = square_mesh.generate(side_len, n_seg)      # node positions and triangle node indices\nx = np.append(x, [[0.0, side_len * 0.6]], axis=0)   # ceil origin (with normal [0.0, -1.0])\nv = np.array([[0.0, 0.0]] * len(x))                 # velocity\nm = [rho * side_len * side_len / ((n_seg + 1) * (n_seg + 1))] * len(x)  # calculate node mass evenly\n# ANCHOR: elem_precomp\n# rest shape basis, volume, and lame parameters\nvol = [0.0] * len(e)\nIB = [np.array([[0.0, 0.0]] * 2)] * len(e)\nfor i in range(0, len(e)):\n    TB = [x[e[i][1]] - x[e[i][0]], x[e[i][2]] - x[e[i][0]]]\n    vol[i] = np.linalg.det(np.transpose(TB)) / 2\n    IB[i] = np.linalg.inv(np.transpose(TB))\nmu_lame = [0.5 * E / (1 + nu)] * len(e)\nlam = [E * nu / ((1 + nu) * (1 - 2 * nu))] * len(e)\n# ANCHOR_END: elem_precomp\n# identify whether a node is Dirichlet\nis_DBC = [False] * len(x)\nfor i in DBC:\n    is_DBC[i] = True\nDBC_stiff = [1000]  # DBC stiffness, adjusted and warm-started across time steps\ncontact_area = [side_len / n_seg] * len(x)     # perimeter split to each node\n\n# simulation with visualization\nresolution = np.array([900, 900])\noffset = resolution / 2\nscale = 200\ndef screen_projection(x):\n    return [offset[0] + scale * x[0], resolution[1] - (offset[1] + scale * x[1])]\n\ntime_step = 0\nsquare_mesh.write_to_file(time_step, x, e)\nscreen = pygame.display.set_mode(resolution)\nrunning = True\nwhile running:\n    # run until the user asks to quit\n    for event in pygame.event.get():\n        if event.type == pygame.QUIT:\n            running = False\n    \n    print('### Time step', time_step, '###')\n\n    # fill the background and draw the square\n    screen.fill((255, 255, 255))\n    pygame.draw.aaline(screen, (0, 0, 255), screen_projection([ground_o[0] - 3.0 * ground_n[1], ground_o[1] + 3.0 * ground_n[0]]), \n        screen_projection([ground_o[0] + 3.0 * ground_n[1], ground_o[1] - 3.0 * ground_n[0]]))   # ground\n    pygame.draw.aaline(screen, (0, 0, 255), screen_projection([x[-1][0] + 3.0, x[-1][1]]), \n        screen_projection([x[-1][0] - 3.0, x[-1][1]]))   # ceil\n    for eI in e:\n        # ANCHOR: draw_tri\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[0]]), screen_projection(x[eI[1]]))\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[1]]), screen_projection(x[eI[2]]))\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[2]]), screen_projection(x[eI[0]]))\n        # ANCHOR_END: draw_tri\n    for xId in range(0, len(x) - 1):\n        xI = x[xId]\n        pygame.draw.circle(screen, (0, 0, 255), screen_projection(xI), 0.1 * side_len / n_seg * scale)\n\n    pygame.display.flip()   # flip the display\n\n    # step forward simulation and wait for screen refresh\n    [x, v] = time_integrator.step_forward(x, e, v, m, vol, IB, mu_lame, lam, ground_n, ground_o, contact_area, mu, is_DBC, DBC, DBC_v, DBC_limit,DBC_stiff, h, 1e-2)\n    time_step += 1\n    pygame.time.wait(int(h * 1000))\n    square_mesh.write_to_file(time_step, x, e)\n\npygame.quit()"
  },
  {
    "path": "6_inv_free/square_mesh.py",
    "content": "import numpy as np\nimport os\n\ndef generate(side_length, n_seg):\n    # sample nodes uniformly on a square\n    x = np.array([[0.0, 0.0]] * ((n_seg + 1) ** 2))\n    step = side_length / n_seg\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg + 1):\n            x[i * (n_seg + 1) + j] = [-side_length / 2 + i * step, -side_length / 2 + j * step]\n    \n    # ANCHOR: tri_vert_ind\n    # connect the nodes with triangle elements\n    e = []\n    for i in range(0, n_seg):\n        for j in range(0, n_seg):\n            # triangulate each cell following a symmetric pattern:\n            if (i % 2)^(j % 2):\n                e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n                e.append([(i + 1) * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1, i * (n_seg + 1) + j + 1])\n            else:\n                e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1])\n                e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1, i * (n_seg + 1) + j + 1])\n    # ANCHOR_END: tri_vert_ind\n\n    return [x, e]\n\ndef write_to_file(frameNum, x, e):\n    # Check if 'output' directory exists; if not, create it\n    if not os.path.exists('output'):\n        os.makedirs('output')\n\n    # create obj file\n    filename = f\"output/{frameNum}.obj\"\n    with open(filename, 'w') as f:\n        # write vertex coordinates\n        for row in x:\n            f.write(f\"v {float(row[0]):.6f} {float(row[1]):.6f} 0.0\\n\") \n        # write vertex indices for each triangle\n        for row in e:\n            #NOTE: vertex indices start from 1 in obj file format\n            f.write(f\"f {row[0] + 1} {row[1] + 1} {row[2] + 1}\\n\")"
  },
  {
    "path": "6_inv_free/time_integrator.py",
    "content": "import copy\nfrom cmath import inf\n\nimport numpy as np\nimport numpy.linalg as LA\nimport scipy.sparse as sparse\nfrom scipy.sparse.linalg import spsolve\n\nimport InertiaEnergy\nimport NeoHookeanEnergy\nimport GravityEnergy\nimport BarrierEnergy\nimport FrictionEnergy\nimport SpringEnergy\n\n\n\n\ndef step_forward(x, e, v, m, vol, IB, mu_lame, lam, n, o, contact_area, mu, is_DBC, DBC, DBC_v, DBC_limit, DBC_stiff, h, tol):\n    x_tilde = x + v * h     # implicit Euler predictive position\n    x_n = copy.deepcopy(x)\n    mu_lambda = BarrierEnergy.compute_mu_lambda(x, n, o, contact_area, mu)  # compute mu * lambda for each node using x^n\n    DBC_target = [] # target position of each DBC in the current time step\n    for i in range(0, len(DBC)):\n        if (DBC_limit[i] - x_n[DBC[i]]).dot(DBC_v[i]) > 0:\n            DBC_target.append(x_n[DBC[i]] + h * DBC_v[i])\n        else:\n            DBC_target.append(x_n[DBC[i]])\n\n    # Newton loop\n    iter = 0\n    E_last = IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, contact_area, (x - x_n) / h, mu_lambda, DBC, DBC_target, DBC_stiff[0], h)\n    [p, DBC_satisfied] = search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, contact_area, (x - x_n) / h, mu_lambda, is_DBC, DBC, DBC_target, DBC_stiff[0], tol, h)\n    while (LA.norm(p, inf) / h > tol) | (sum(DBC_satisfied) != len(DBC)):   # also check whether all DBCs are satisfied\n        print('Iteration', iter, ':')\n        print('residual =', LA.norm(p, inf) / h)\n\n        if (LA.norm(p, inf) / h <= tol) & (sum(DBC_satisfied) != len(DBC)):\n            # increase DBC stiffness and recompute energy value record\n            DBC_stiff[0] *= 2\n            E_last = IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, contact_area, (x - x_n) / h, mu_lambda, DBC, DBC_target, DBC_stiff[0], h)\n\n        # filter line search\n        # ANCHOR: apply_filter\n        alpha = min(BarrierEnergy.init_step_size(x, n, o, p), NeoHookeanEnergy.init_step_size(x, e, p))  # avoid interpenetration, tunneling, and inversion\n        # ANCHOR_END: apply_filter\n        while IP_val(x + alpha * p, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, contact_area, (x + alpha * p - x_n) / h, mu_lambda, DBC, DBC_target, DBC_stiff[0], h) > E_last:\n            alpha /= 2\n        print('step size =', alpha)\n\n        x += alpha * p\n        E_last = IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, contact_area, (x - x_n) / h, mu_lambda, DBC, DBC_target, DBC_stiff[0], h)\n        [p, DBC_satisfied] = search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, contact_area, (x - x_n) / h, mu_lambda, is_DBC, DBC, DBC_target, DBC_stiff[0], tol, h)\n        iter += 1\n\n    v = (x - x_n) / h   # implicit Euler velocity update\n    return [x, v]\n\ndef IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h):\n    return InertiaEnergy.val(x, x_tilde, m) + h * h * (     # implicit Euler\n        NeoHookeanEnergy.val(x, e, vol, IB, mu_lame, lam) + \n        GravityEnergy.val(x, m) + \n        BarrierEnergy.val(x, n, o, contact_area) + \n        FrictionEnergy.val(v, mu_lambda, h, n)\n    ) + SpringEnergy.val(x, m, DBC, DBC_target, DBC_stiff)\n\ndef IP_grad(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h):\n    return InertiaEnergy.grad(x, x_tilde, m) + h * h * (    # implicit Euler\n        NeoHookeanEnergy.grad(x, e, vol, IB, mu_lame, lam) + \n        GravityEnergy.grad(x, m) + \n        BarrierEnergy.grad(x, n, o, contact_area) + \n        FrictionEnergy.grad(v, mu_lambda, h, n)\n    ) + SpringEnergy.grad(x, m, DBC, DBC_target, DBC_stiff)\n\ndef IP_hess(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h):\n    IJV_In = InertiaEnergy.hess(x, x_tilde, m)\n    IJV_MS = NeoHookeanEnergy.hess(x, e, vol, IB, mu_lame, lam)\n    IJV_B = BarrierEnergy.hess(x, n, o, contact_area)\n    IJV_F = FrictionEnergy.hess(v, mu_lambda, h, n)\n    IJV_S = SpringEnergy.hess(x, m, DBC, DBC_target, DBC_stiff)\n    IJV_MS[2] *= h * h    # implicit Euler\n    IJV_B[2] *= h * h     # implicit Euler\n    IJV_F[2] *= h * h     # implicit Euler\n    IJV_In_MS = np.append(IJV_In, IJV_MS, axis=1)\n    IJV_In_MS_B = np.append(IJV_In_MS, IJV_B, axis=1)\n    IJV_In_MS_B_F = np.append(IJV_In_MS_B, IJV_F, axis=1)\n    IJV = np.append(IJV_In_MS_B_F, IJV_S, axis=1)\n    H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()\n    return H\n\ndef search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, contact_area, v, mu_lambda, is_DBC, DBC, DBC_target, DBC_stiff, tol, h):\n    projected_hess = IP_hess(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h)\n    reshaped_grad = IP_grad(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h).reshape(len(x) * 2, 1)\n    # check whether each DBC is satisfied\n    DBC_satisfied = [False] * len(x)\n    for i in range(0, len(DBC)):\n        if LA.norm(x[DBC[i]] - DBC_target[i]) / h < tol:\n            DBC_satisfied[DBC[i]] = True\n    # eliminate DOF if it's a satisfied DBC by modifying gradient and Hessian for DBC:\n    for i, j in zip(*projected_hess.nonzero()):\n        if (is_DBC[int(i / 2)] & DBC_satisfied[int(i / 2)]) | (is_DBC[int(j / 2)] & DBC_satisfied[int(j / 2)]): \n            projected_hess[i, j] = (i == j)\n    for i in range(0, len(x)):\n        if is_DBC[i] & DBC_satisfied[i]:\n            reshaped_grad[i * 2] = reshaped_grad[i * 2 + 1] = 0.0\n    return [spsolve(projected_hess, -reshaped_grad).reshape(len(x), 2), DBC_satisfied]"
  },
  {
    "path": "6_inv_free/utils.py",
    "content": "import numpy as np\nimport numpy.linalg as LA\nimport math\n\ndef make_PSD(hess):\n    [lam, V] = LA.eigh(hess)    # Eigen decomposition on symmetric matrix\n    # set all negative Eigenvalues to 0\n    for i in range(0, len(lam)):\n        lam[i] = max(0, lam[i])\n    return np.matmul(np.matmul(V, np.diag(lam)), np.transpose(V))\n\n# ANCHOR: find_positive_real_root\ndef smallest_positive_real_root_quad(a, b, c, tol = 1e-6):\n    # return negative value if no positive real root is found\n    t = 0\n    if abs(a) <= tol:\n        if abs(b) <= tol: # f(x) = c > 0 for all x\n            t = -1\n        else:\n            t = -c / b\n    else:\n        desc = b * b - 4 * a * c\n        if desc > 0:\n            t = (-b - math.sqrt(desc)) / (2 * a) # if a > 0, this is either the smaller positive root, or both roots are negative; \n            # if a < 0, there are 1 negative and 1 positive real roots, and we just need the positive one.\n            if t < 0:\n                t = (-b + math.sqrt(desc)) / (2 * a)\n        else: # desv<0 ==> imag, f(x) > 0 for all x > 0\n            t = -1\n    return t\n# ANCHOR_END: find_positive_real_root"
  },
  {
    "path": "7_self_contact/BarrierEnergy.py",
    "content": "import math\nimport numpy as np\n\nimport distance.PointEdgeDistance as PE\nimport distance.CCD as CCD\n\nimport utils\n\ndhat = 0.01\nkappa = 1e5\n\ndef val(x, n, o, bp, be, contact_area):\n    sum = 0.0\n    # floor:\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            sum += contact_area[i] * dhat * kappa / 2 * (s - 1) * math.log(s)\n    # ceil:\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        d = n.dot(x[i] - x[-1])\n        if d < dhat:\n            s = d / dhat\n            sum += contact_area[i] * dhat * kappa / 2 * (s - 1) * math.log(s)\n    # ANCHOR: value\n    # self-contact\n    dhat_sqr = dhat * dhat\n    for xI in bp:\n        for eI in be:\n            if xI != eI[0] and xI != eI[1]: # do not consider a point and its incident edge\n                d_sqr = PE.val(x[xI], x[eI[0]], x[eI[1]])\n                if d_sqr < dhat_sqr:\n                    s = d_sqr / dhat_sqr\n                    # since d_sqr is used, need to divide by 8 not 2 here for consistency to linear elasticity:\n                    sum += 0.5 * contact_area[xI] * dhat * kappa / 8 * (s - 1) * math.log(s)\n    # ANCHOR_END: value\n    return sum\n\ndef grad(x, n, o, bp, be, contact_area):\n    g = np.array([[0.0, 0.0]] * len(x))\n    # floor:\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            g[i] = contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d)) * n\n    # ceil:\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        d = n.dot(x[i] - x[-1])\n        if d < dhat:\n            s = d / dhat\n            local_grad = contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d)) * n\n            g[i] += local_grad\n            g[-1] -= local_grad\n    # ANCHOR: gradient\n    # self-contact\n    dhat_sqr = dhat * dhat\n    for xI in bp:\n        for eI in be:\n            if xI != eI[0] and xI != eI[1]: # do not consider a point and its incident edge\n                d_sqr = PE.val(x[xI], x[eI[0]], x[eI[1]])\n                if d_sqr < dhat_sqr:\n                    s = d_sqr / dhat_sqr\n                    # since d_sqr is used, need to divide by 8 not 2 here for consistency to linear elasticity:\n                    local_grad = 0.5 * contact_area[xI] * dhat * (kappa / 8 * (math.log(s) / dhat_sqr + (s - 1) / d_sqr)) * PE.grad(x[xI], x[eI[0]], x[eI[1]])\n                    g[xI] += local_grad[0:2]\n                    g[eI[0]] += local_grad[2:4]\n                    g[eI[1]] += local_grad[4:6]\n    # ANCHOR_END: gradient\n    return g\n\ndef hess(x, n, o, bp, be, contact_area):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    # floor:\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            local_hess = contact_area[i] * dhat * kappa / (2 * d * d * dhat) * (d + dhat) * np.outer(n, n)\n            for c in range(0, 2):\n                for r in range(0, 2):\n                    IJV[0].append(i * 2 + r)\n                    IJV[1].append(i * 2 + c)\n                    IJV[2] = np.append(IJV[2], local_hess[r, c])\n    # ceil:\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        d = n.dot(x[i] - x[-1])\n        if d < dhat:\n            local_hess = contact_area[i] * dhat * kappa / (2 * d * d * dhat) * (d + dhat) * np.outer(n, n)\n            index = [i, len(x) - 1]\n            for nI in range(0, 2):\n                for nJ in range(0, 2):\n                    for c in range(0, 2):\n                        for r in range(0, 2):\n                            IJV[0].append(index[nI] * 2 + r)\n                            IJV[1].append(index[nJ] * 2 + c)\n                            IJV[2] = np.append(IJV[2], ((-1) ** (nI != nJ)) * local_hess[r, c])\n    # ANCHOR: Hessian\n    # self-contact\n    dhat_sqr = dhat * dhat\n    for xI in bp:\n        for eI in be:\n            if xI != eI[0] and xI != eI[1]: # do not consider a point and its incident edge\n                d_sqr = PE.val(x[xI], x[eI[0]], x[eI[1]])\n                if d_sqr < dhat_sqr:\n                    d_sqr_grad = PE.grad(x[xI], x[eI[0]], x[eI[1]])\n                    s = d_sqr / dhat_sqr\n                    # since d_sqr is used, need to divide by 8 not 2 here for consistency to linear elasticity:\n                    local_hess = 0.5 * contact_area[xI] * dhat * utils.make_PSD(kappa / (8 * d_sqr * d_sqr * dhat_sqr) * (d_sqr + dhat_sqr) * np.outer(d_sqr_grad, d_sqr_grad) \\\n                        + (kappa / 8 * (math.log(s) / dhat_sqr + (s - 1) / d_sqr)) * PE.hess(x[xI], x[eI[0]], x[eI[1]]))\n                    index = [xI, eI[0], eI[1]]\n                    for nI in range(0, 3):\n                        for nJ in range(0, 3):\n                            for c in range(0, 2):\n                                for r in range(0, 2):\n                                    IJV[0].append(index[nI] * 2 + r)\n                                    IJV[1].append(index[nJ] * 2 + c)\n                                    IJV[2] = np.append(IJV[2], local_hess[nI * 2 + r, nJ * 2 + c])\n    # ANCHOR_END: Hessian\n    return IJV\n\ndef init_step_size(x, n, o, bp, be, p):\n    alpha = 1\n    # floor:\n    for i in range(0, len(x)):\n        p_n = p[i].dot(n)\n        if p_n < 0:\n            alpha = min(alpha, 0.9 * n.dot(x[i] - o) / -p_n)\n    # ceil:\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        p_n = (p[i] - p[-1]).dot(n)\n        if p_n < 0:\n            alpha = min(alpha, 0.9 * n.dot(x[i] - x[-1]) / -p_n)\n    # ANCHOR: line_search_filtering\n    # self-contact\n    for xI in bp:\n        for eI in be:\n            if xI != eI[0] and xI != eI[1]: # do not consider a point and its incident edge\n                if CCD.bbox_overlap(x[xI], x[eI[0]], x[eI[1]], p[xI], p[eI[0]], p[eI[1]], alpha):\n                    toc = CCD.narrow_phase_CCD(x[xI], x[eI[0]], x[eI[1]], p[xI], p[eI[0]], p[eI[1]], alpha)\n                    if alpha > toc:\n                        alpha = toc\n    # ANCHOR_END: line_search_filtering\n    return alpha\n\ndef compute_mu_lambda(x, n, o, bp, be, contact_area, mu):\n    # floor:\n    mu_lambda = np.array([0.0] * len(x))\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            mu_lambda[i] = mu * -contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d))\n    return mu_lambda"
  },
  {
    "path": "7_self_contact/FrictionEnergy.py",
    "content": "import numpy as np\nimport utils\n\nepsv = 1e-3\n\ndef f0(vbarnorm, epsv, hhat):\n    if vbarnorm >= epsv:\n        return vbarnorm * hhat\n    else:\n        vbarnormhhat = vbarnorm * hhat\n        epsvhhat = epsv * hhat\n        return vbarnormhhat * vbarnormhhat * (-vbarnormhhat / 3.0 + epsvhhat) / (epsvhhat * epsvhhat) + epsvhhat / 3.0\n\ndef f1_div_vbarnorm(vbarnorm, epsv):\n    if vbarnorm >= epsv:\n        return 1.0 / vbarnorm\n    else:\n        return (-vbarnorm + 2.0 * epsv) / (epsv * epsv)\n\ndef f_hess_term(vbarnorm, epsv):\n    if vbarnorm >= epsv:\n        return -1.0 / (vbarnorm * vbarnorm)\n    else:\n        return -1.0 / (epsv * epsv)\n\ndef val(v, mu_lambda, hhat, n):\n    sum = 0.0\n    # floor:\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            sum += mu_lambda[i] * f0(np.linalg.norm(vbar), epsv, hhat)\n    return sum\n\ndef grad(v, mu_lambda, hhat, n):\n    g = np.array([[0.0, 0.0]] * len(v))\n    # floor:\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            g[i] = mu_lambda[i] * f1_div_vbarnorm(np.linalg.norm(vbar), epsv) * T.dot(vbar)\n    return g\n\ndef hess(v, mu_lambda, hhat, n):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    # floor:\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            vbarnorm = np.linalg.norm(vbar)\n            inner_term = f1_div_vbarnorm(vbarnorm, epsv) * np.identity(2)\n            if vbarnorm != 0:\n                inner_term += f_hess_term(vbarnorm, epsv) / vbarnorm * np.outer(vbar, vbar)\n            local_hess = mu_lambda[i] * T.dot(utils.make_PSD(inner_term)).dot(np.transpose(T)) / hhat\n            for c in range(0, 2):\n                for r in range(0, 2):\n                    IJV[0].append(i * 2 + r)\n                    IJV[1].append(i * 2 + c)\n                    IJV[2] = np.append(IJV[2], local_hess[r, c])\n    return IJV"
  },
  {
    "path": "7_self_contact/GravityEnergy.py",
    "content": "import numpy as np\n\ngravity = [0.0, -9.81]\n\ndef val(x, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        sum += -m[i] * x[i].dot(gravity)\n    return sum\n\ndef grad(x, m):\n    g = np.array([gravity] * len(x))\n    for i in range(0, len(x)):\n        g[i] *= -m[i]\n    return g\n\n# Hessian is 0"
  },
  {
    "path": "7_self_contact/InertiaEnergy.py",
    "content": "import numpy as np\n\ndef val(x, x_tilde, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        diff = x[i] - x_tilde[i]\n        sum += 0.5 * m[i] * diff.dot(diff)\n    return sum\n\ndef grad(x, x_tilde, m):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(x)):\n        g[i] = m[i] * (x[i] - x_tilde[i])\n    return g\n\ndef hess(x, x_tilde, m):\n    IJV = [[0] * (len(x) * 2), [0] * (len(x) * 2), np.array([0.0] * (len(x) * 2))]\n    for i in range(0, len(x)):\n        for d in range(0, 2):\n            IJV[0][i * 2 + d] = i * 2 + d\n            IJV[1][i * 2 + d] = i * 2 + d\n            IJV[2][i * 2 + d] = m[i]\n    return IJV"
  },
  {
    "path": "7_self_contact/NeoHookeanEnergy.py",
    "content": "import utils\nimport numpy as np\nimport math\n\ndef polar_svd(F):\n    [U, s, VT] = np.linalg.svd(F)\n    if np.linalg.det(U) < 0:\n        U[:, 1] = -U[:, 1]\n        s[1] = -s[1]\n    if np.linalg.det(VT) < 0:\n        VT[1, :] = -VT[1, :]\n        s[1] = -s[1]\n    return [U, s, VT]\n\ndef dPsi_div_dsigma(s, mu, lam):\n    ln_sigma_prod = math.log(s[0] * s[1])\n    inv0 = 1.0 / s[0]\n    dPsi_dsigma_0 = mu * (s[0] - inv0) + lam * inv0 * ln_sigma_prod\n    inv1 = 1.0 / s[1]\n    dPsi_dsigma_1 = mu * (s[1] - inv1) + lam * inv1 * ln_sigma_prod\n    return [dPsi_dsigma_0, dPsi_dsigma_1]\n\ndef d2Psi_div_dsigma2(s, mu, lam):\n    ln_sigma_prod = math.log(s[0] * s[1])\n    inv2_0 = 1 / (s[0] * s[0])\n    d2Psi_dsigma2_00 = mu * (1 + inv2_0) - lam * inv2_0 * (ln_sigma_prod - 1)\n    inv2_1 = 1 / (s[1] * s[1])\n    d2Psi_dsigma2_11 = mu * (1 + inv2_1) - lam * inv2_1 * (ln_sigma_prod - 1)\n    d2Psi_dsigma2_01 = lam / (s[0] * s[1])\n    return [[d2Psi_dsigma2_00, d2Psi_dsigma2_01], [d2Psi_dsigma2_01, d2Psi_dsigma2_11]]\n\ndef B_left_coef(s, mu, lam):\n    sigma_prod = s[0] * s[1]\n    return (mu + (mu - lam * math.log(sigma_prod)) / sigma_prod) / 2\n\ndef Psi(F, mu, lam):\n    J = np.linalg.det(F)\n    lnJ = math.log(J)\n    return mu / 2 * (np.trace(np.transpose(F).dot(F)) - 2) - mu * lnJ + lam / 2 * lnJ * lnJ\n\ndef dPsi_div_dF(F, mu, lam):\n    FinvT = np.transpose(np.linalg.inv(F))\n    return mu * (F - FinvT) + lam * math.log(np.linalg.det(F)) * FinvT\n\ndef d2Psi_div_dF2(F, mu, lam):\n    [U, sigma, VT] = polar_svd(F)\n\n    Psi_sigma_sigma = utils.make_PSD(d2Psi_div_dsigma2(sigma, mu, lam))\n\n    B_left = B_left_coef(sigma, mu, lam)\n    Psi_sigma = dPsi_div_dsigma(sigma, mu, lam)\n    B_right = (Psi_sigma[0] + Psi_sigma[1]) / (2 * max(sigma[0] + sigma[1], 1e-6))\n    B = utils.make_PSD([[B_left + B_right, B_left - B_right], [B_left - B_right, B_left + B_right]])\n\n    M = np.array([[0, 0, 0, 0]] * 4)\n    M[0, 0] = Psi_sigma_sigma[0, 0]\n    M[0, 3] = Psi_sigma_sigma[0, 1]\n    M[1, 1] = B[0, 0]\n    M[1, 2] = B[0, 1]\n    M[2, 1] = B[1, 0]\n    M[2, 2] = B[1, 1]\n    M[3, 0] = Psi_sigma_sigma[1, 0]\n    M[3, 3] = Psi_sigma_sigma[1, 1]\n\n    dP_div_dF = np.array([[0, 0, 0, 0]] * 4)\n    for j in range(0, 2):\n        for i in range(0, 2):\n            ij = j * 2 + i\n            for s in range(0, 2):\n                for r in range(0, 2):\n                    rs = s * 2 + r\n                    dP_div_dF[ij, rs] = M[0, 0] * U[i, 0] * VT[0, j] * U[r, 0] * VT[0, s] \\\n                        + M[0, 3] * U[i, 0] * VT[0, j] * U[r, 1] * VT[1, s] \\\n                        + M[1, 1] * U[i, 1] * VT[0, j] * U[r, 1] * VT[0, s] \\\n                        + M[1, 2] * U[i, 1] * VT[0, j] * U[r, 0] * VT[1, s] \\\n                        + M[2, 1] * U[i, 0] * VT[1, j] * U[r, 1] * VT[0, s] \\\n                        + M[2, 2] * U[i, 0] * VT[1, j] * U[r, 0] * VT[1, s] \\\n                        + M[3, 0] * U[i, 1] * VT[1, j] * U[r, 0] * VT[0, s] \\\n                        + M[3, 3] * U[i, 1] * VT[1, j] * U[r, 1] * VT[1, s]\n    return dP_div_dF\n\ndef deformation_grad(x, elemVInd, IB):\n    F = [x[elemVInd[1]] - x[elemVInd[0]], x[elemVInd[2]] - x[elemVInd[0]]]\n    return np.transpose(F).dot(IB)\n\ndef dPsi_div_dx(P, IB):  # applying chain-rule, dPsi_div_dx = dPsi_div_dF * dF_div_dx\n    dPsi_dx_2 = P[0, 0] * IB[0, 0] + P[0, 1] * IB[0, 1]\n    dPsi_dx_3 = P[1, 0] * IB[0, 0] + P[1, 1] * IB[0, 1]\n    dPsi_dx_4 = P[0, 0] * IB[1, 0] + P[0, 1] * IB[1, 1]\n    dPsi_dx_5 = P[1, 0] * IB[1, 0] + P[1, 1] * IB[1, 1]\n    return [np.array([-dPsi_dx_2 - dPsi_dx_4, -dPsi_dx_3 - dPsi_dx_5]), np.array([dPsi_dx_2, dPsi_dx_3]), np.array([dPsi_dx_4, dPsi_dx_5])]\n\ndef d2Psi_div_dx2(dP_div_dF, IB):  # applying chain-rule, d2Psi_div_dx2 = dF_div_dx^T * d2Psi_div_dF2 * dF_div_dx (note that d2F_div_dx2 = 0)\n    intermediate = np.array([[0.0, 0.0, 0.0, 0.0]] * 6)\n    for colI in range(0, 4):\n        _000 = dP_div_dF[0, colI] * IB[0, 0]\n        _010 = dP_div_dF[0, colI] * IB[1, 0]\n        _101 = dP_div_dF[2, colI] * IB[0, 1]\n        _111 = dP_div_dF[2, colI] * IB[1, 1]\n        _200 = dP_div_dF[1, colI] * IB[0, 0]\n        _210 = dP_div_dF[1, colI] * IB[1, 0]\n        _301 = dP_div_dF[3, colI] * IB[0, 1]\n        _311 = dP_div_dF[3, colI] * IB[1, 1]\n        intermediate[2, colI] = _000 + _101\n        intermediate[3, colI] = _200 + _301\n        intermediate[4, colI] = _010 + _111\n        intermediate[5, colI] = _210 + _311\n        intermediate[0, colI] = -intermediate[2, colI] - intermediate[4, colI]\n        intermediate[1, colI] = -intermediate[3, colI] - intermediate[5, colI]\n    result = np.array([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]] * 6)\n    for colI in range(0, 6):\n        _000 = intermediate[colI, 0] * IB[0, 0]\n        _010 = intermediate[colI, 0] * IB[1, 0]\n        _101 = intermediate[colI, 2] * IB[0, 1]\n        _111 = intermediate[colI, 2] * IB[1, 1]\n        _200 = intermediate[colI, 1] * IB[0, 0]\n        _210 = intermediate[colI, 1] * IB[1, 0]\n        _301 = intermediate[colI, 3] * IB[0, 1]\n        _311 = intermediate[colI, 3] * IB[1, 1]\n        result[2, colI] = _000 + _101\n        result[3, colI] = _200 + _301\n        result[4, colI] = _010 + _111\n        result[5, colI] = _210 + _311\n        result[0, colI] = -_000 - _101 - _010 - _111\n        result[1, colI] = -_200 - _301 - _210 - _311\n    return result\n\ndef val(x, e, vol, IB, mu, lam):\n    sum = 0.0\n    for i in range(0, len(e)):\n        F = deformation_grad(x, e[i], IB[i])\n        sum += vol[i] * Psi(F, mu[i], lam[i])\n    return sum\n\ndef grad(x, e, vol, IB, mu, lam):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(e)):\n        F = deformation_grad(x, e[i], IB[i])\n        P = vol[i] * dPsi_div_dF(F, mu[i], lam[i])\n        g_local = dPsi_div_dx(P, IB[i])\n        for j in range(0, 3):\n            g[e[i][j]] += g_local[j]\n    return g\n\ndef hess(x, e, vol, IB, mu, lam):\n    IJV = [[0] * (len(e) * 36), [0] * (len(e) * 36), np.array([0.0] * (len(e) * 36))]\n    for i in range(0, len(e)):\n        F = deformation_grad(x, e[i], IB[i])\n        dP_div_dF = vol[i] * d2Psi_div_dF2(F, mu[i], lam[i])\n        local_hess = d2Psi_div_dx2(dP_div_dF, IB[i])\n        for xI in range(0, 3):\n            for xJ in range(0, 3):\n                for dI in range(0, 2):\n                    for dJ in range(0, 2):\n                        ind = i * 36 + (xI * 3 + xJ) * 4 + dI * 2 + dJ\n                        IJV[0][ind] = e[i][xI] * 2 + dI\n                        IJV[1][ind] = e[i][xJ] * 2 + dJ\n                        IJV[2][ind] = local_hess[xI * 2 + dI, xJ * 2 + dJ]\n    return IJV\n\ndef init_step_size(x, e, p):\n    alpha = 1\n    for i in range(0, len(e)):\n        x21 = x[e[i][1]] - x[e[i][0]]\n        x31 = x[e[i][2]] - x[e[i][0]]\n        p21 = p[e[i][1]] - p[e[i][0]]\n        p31 = p[e[i][2]] - p[e[i][0]]\n        detT = np.linalg.det(np.transpose([x21, x31]))\n        a = np.linalg.det(np.transpose([p21, p31])) / detT\n        b = (np.linalg.det(np.transpose([x21, p31])) + np.linalg.det(np.transpose([p21, x31]))) / detT\n        c = 0.9  # solve for alpha that first brings the new volume to 0.1x the old volume for slackness\n        critical_alpha = utils.smallest_positive_real_root_quad(a, b, c)\n        if critical_alpha > 0:\n            alpha = min(alpha, critical_alpha)\n    return alpha"
  },
  {
    "path": "7_self_contact/SpringEnergy.py",
    "content": "import numpy as np\n\ndef val(x, m, DBC, DBC_target, k):\n    sum = 0.0\n    for i in range(0, len(DBC)):\n        diff = x[DBC[i]] - DBC_target[i]\n        sum += 0.5 * k * m[DBC[i]] * diff.dot(diff)\n    return sum\n\ndef grad(x, m, DBC, DBC_target, k):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(DBC)):\n        g[DBC[i]] = k * m[DBC[i]] * (x[DBC[i]] - DBC_target[i])\n    return g\n\ndef hess(x, m, DBC, DBC_target, k):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    for i in range(0, len(DBC)):\n        for d in range(0, 2):\n            IJV[0].append(DBC[i] * 2 + d)\n            IJV[1].append(DBC[i] * 2 + d)\n            IJV[2] = np.append(IJV[2], k * m[DBC[i]])\n    return IJV"
  },
  {
    "path": "7_self_contact/distance/CCD.py",
    "content": "# ANCHOR: broad_phase\nfrom copy import deepcopy\nimport numpy as np\nimport math\n\nimport distance.PointEdgeDistance as PE\n\n# check whether the bounding box of the trajectory of the point and the edge overlap\ndef bbox_overlap(p, e0, e1, dp, de0, de1, toc_upperbound):\n    max_p = np.maximum(p, p + toc_upperbound * dp) # point trajectory bbox top-right\n    min_p = np.minimum(p, p + toc_upperbound * dp) # point trajectory bbox bottom-left\n    max_e = np.maximum(np.maximum(e0, e0 + toc_upperbound * de0), np.maximum(e1, e1 + toc_upperbound * de1)) # edge trajectory bbox top-right\n    min_e = np.minimum(np.minimum(e0, e0 + toc_upperbound * de0), np.minimum(e1, e1 + toc_upperbound * de1)) # edge trajectory bbox bottom-left\n    if np.any(np.greater(min_p, max_e)) or np.any(np.greater(min_e, max_p)):\n        return False\n    else:\n        return True\n# ANCHOR_END: broad_phase\n\n# ANCHOR: accd\n# compute the first \"time\" of contact, or toc,\n# return the computed toc only if it is smaller than the previously computed toc_upperbound\ndef narrow_phase_CCD(_p, _e0, _e1, _dp, _de0, _de1, toc_upperbound):\n    p = deepcopy(_p)\n    e0 = deepcopy(_e0)\n    e1 = deepcopy(_e1)\n    dp = deepcopy(_dp)\n    de0 = deepcopy(_de0)\n    de1 = deepcopy(_de1)\n\n    # use relative displacement for faster convergence\n    mov = (dp + de0 + de1) / 3 \n    de0 -= mov\n    de1 -= mov\n    dp -= mov\n    maxDispMag = np.linalg.norm(dp) + math.sqrt(max(np.dot(de0, de0), np.dot(de1, de1)))\n    if maxDispMag == 0:\n        return toc_upperbound\n\n    eta = 0.1 # calculate the toc that first brings the distance to 0.1x the current distance\n    dist2_cur = PE.val(p, e0, e1)\n    dist_cur = math.sqrt(dist2_cur)\n    gap = eta * dist_cur\n    # iteratively move the point and edge towards each other and\n    # grow the toc estimate without numerical errors\n    toc = 0\n    while True:\n        tocLowerBound = (1 - eta) * dist_cur / maxDispMag\n\n        p += tocLowerBound * dp\n        e0 += tocLowerBound * de0\n        e1 += tocLowerBound * de1\n        dist2_cur = PE.val(p, e0, e1)\n        dist_cur = math.sqrt(dist2_cur)\n        if toc != 0 and dist_cur < gap:\n            break\n\n        toc += tocLowerBound\n        if toc > toc_upperbound:\n            return toc_upperbound\n\n    return toc\n# ANCHOR_END: accd"
  },
  {
    "path": "7_self_contact/distance/PointEdgeDistance.py",
    "content": "# ANCHOR: PE_val_grad\nimport numpy as np\n\nimport distance.PointPointDistance as PP\nimport distance.PointLineDistance as PL\n\ndef val(p, e0, e1):\n    e = e1 - e0\n    ratio = np.dot(e, p - e0) / np.dot(e, e)\n    if ratio < 0:    # point(p)-point(e0) expression\n        return PP.val(p, e0)\n    elif ratio > 1:  # point(p)-point(e1) expression\n        return PP.val(p, e1)\n    else:            # point(p)-line(e0e1) expression\n        return PL.val(p, e0, e1)\n\ndef grad(p, e0, e1):\n    e = e1 - e0\n    ratio = np.dot(e, p - e0) / np.dot(e, e)\n    if ratio < 0:    # point(p)-point(e0) expression\n        g_PP = PP.grad(p, e0)\n        return np.reshape([g_PP[0:2], g_PP[2:4], np.array([0.0, 0.0])], (1, 6))[0]\n    elif ratio > 1:  # point(p)-point(e1) expression\n        g_PP = PP.grad(p, e1)\n        return np.reshape([g_PP[0:2], np.array([0.0, 0.0]), g_PP[2:4]], (1, 6))[0]\n    else:            # point(p)-line(e0e1) expression\n        return PL.grad(p, e0, e1)\n# ANCHOR_END: PE_val_grad\n\ndef hess(p, e0, e1):\n    e = e1 - e0\n    ratio = np.dot(e, p - e0) / np.dot(e, e)\n    if ratio < 0:    # point(p)-point(e0) expression\n        H_PP =  PP.hess(p, e0)\n        return np.array([np.reshape([H_PP[0, 0:2], H_PP[0, 2:4], np.array([0.0, 0.0])], (1, 6))[0], \\\n            np.reshape([H_PP[1, 0:2], H_PP[1, 2:4], np.array([0.0, 0.0])], (1, 6))[0], \\\n            np.reshape([H_PP[2, 0:2], H_PP[2, 2:4], np.array([0.0, 0.0])], (1, 6))[0], \\\n            np.reshape([H_PP[3, 0:2], H_PP[3, 2:4], np.array([0.0, 0.0])], (1, 6))[0], \\\n            np.array([0.0] * 6), \\\n            np.array([0.0] * 6)])\n    elif ratio > 1:  # point(p)-point(e1) expression\n        H_PP = PP.hess(p, e1)\n        return np.array([np.reshape([H_PP[0, 0:2], np.array([0.0, 0.0]), H_PP[0, 2:4]], (1, 6))[0], \\\n            np.reshape([H_PP[1, 0:2], np.array([0.0, 0.0]), H_PP[1, 2:4]], (1, 6))[0], \\\n            np.array([0.0] * 6), \\\n            np.array([0.0] * 6), \\\n            np.reshape([H_PP[2, 0:2], np.array([0.0, 0.0]), H_PP[2, 2:4]], (1, 6))[0], \\\n            np.reshape([H_PP[3, 0:2], np.array([0.0, 0.0]), H_PP[3, 2:4]], (1, 6))[0]])\n    else:            # point(p)-line(e0e1) expression\n        return PL.hess(p, e0, e1)"
  },
  {
    "path": "7_self_contact/distance/PointLineDistance.py",
    "content": "# ANCHOR: PL_val_grad\nimport numpy as np\n\ndef val(p, e0, e1):\n    e = e1 - e0\n    numerator = e[1] * p[0] - e[0] * p[1] + e1[0] * e0[1] - e1[1] * e0[0]\n    return numerator * numerator / np.dot(e, e)\n\ndef grad(p, e0, e1):\n    g = np.array([0.0] * 6)\n    t13 = -e1[0] + e0[0]\n    t14 = -e1[1] + e0[1]\n    t23 = 1.0 / (t13 * t13 + t14 * t14)\n    t25 = ((e0[0] * e1[1] + -(e0[1] * e1[0])) + t14 * p[0]) + -(t13 * p[1])\n    t24 = t23 * t23\n    t26 = t25 * t25\n    t27 = (e0[0] * 2.0 + -(e1[0] * 2.0)) * t24 * t26\n    t26 *= (e0[1] * 2.0 + -(e1[1] * 2.0)) * t24\n    g[0] = t14 * t23 * t25 * 2.0\n    g[1] = t13 * t23 * t25 * -2.0\n    t24 = t23 * t25\n    g[2] = -t27 - t24 * (-e1[1] + p[1]) * 2.0\n    g[3] = -t26 + t24 * (-e1[0] + p[0]) * 2.0\n    g[4] = t27 + t24 * (p[1] - e0[1]) * 2.0\n    g[5] = t26 - t24 * (p[0] - e0[0]) * 2.0\n    return g\n# ANCHOR_END: PL_val_grad\n\ndef hess(p, e0, e1):\n    H = np.array([0.0] * 36)\n    t15 = -e0[0] + p[0]\n    t16 = -e0[1] + p[1]\n    t17 = -e1[0] + p[0]\n    t18 = -e1[1] + p[1]\n    t19 = -e1[0] + e0[0]\n    t20 = -e1[1] + e0[1]\n    t21 = e0[0] * 2.0 + -(e1[0] * 2.0)\n    t22 = e0[1] * 2.0 + -(e1[1] * 2.0)\n    t23 = t19 * t19\n    t24 = t20 * t20\n    t31 = 1.0 / (t23 + t24)\n    t34 = ((e0[0] * e1[1] + -(e0[1] * e1[0])) + t20 * p[0]) + -(t19 * p[1])\n    t32 = t31 * t31\n    t33 = t32 * t31\n    t35 = t34 * t34\n    t60 = t31 * t34 * 2.0\n    t59 = -(t19 * t20 * t31 * 2.0)\n    t62 = t32 * t35 * 2.0\n    t64 = t21 * t21 * t33 * t35 * 2.0\n    t65 = t22 * t22 * t33 * t35 * 2.0\n    t68 = t15 * t21 * t32 * t34 * 2.0\n    t71 = t16 * t22 * t32 * t34 * 2.0\n    t72 = t17 * t21 * t32 * t34 * 2.0\n    t75 = t18 * t22 * t32 * t34 * 2.0\n    t76 = t19 * t21 * t32 * t34 * 2.0\n    t77 = t20 * t21 * t32 * t34 * 2.0\n    t78 = t19 * t22 * t32 * t34 * 2.0\n    t79 = t20 * t22 * t32 * t34 * 2.0\n    t90 = t21 * t22 * t33 * t35 * 2.0\n    t92 = t16 * t20 * t31 * 2.0 + t77\n    t94 = -(t17 * t19 * t31 * 2.0) + t78\n    t96 = (t18 * t19 * t31 * 2.0 + -t60) + t76\n    t99 = (-(t15 * t20 * t31 * 2.0) + -t60) + t79\n    t93 = t15 * t19 * t31 * 2.0 + -t78\n    t35 = -(t18 * t20 * t31 * 2.0) + -t77\n    t97 = (t17 * t20 * t31 * 2.0 + t60) + -t79\n    t98 = (-(t16 * t19 * t31 * 2.0) + t60) + -t76\n    t100 = ((-(t15 * t16 * t31 * 2.0) + t71) + -t68) + t90\n    t19 = ((-(t17 * t18 * t31 * 2.0) + t75) + -t72) + t90\n    t102_tmp = t17 * t22 * t32 * t34\n    t76 = t15 * t22 * t32 * t34\n    t22 = (((-(t15 * t17 * t31 * 2.0) + t62) + -t65) + t76 * 2.0) + t102_tmp * 2.0\n    t33 = t18 * t21 * t32 * t34\n    t20 = t16 * t21 * t32 * t34\n    t79 = (((-(t16 * t18 * t31 * 2.0) + t62) + -t64) + -(t20 * 2.0)) + -(t33 * 2.0)\n    t77 = (((t15 * t18 * t31 * 2.0 + t60) + t68) + -t75) + -t90\n    t78 = (((t16 * t17 * t31 * 2.0 + -t60) + t72) + -t71) + -t90\n    H[0] = t24 * t31 * 2.0\n    H[1] = t59\n    H[2] = t35\n    H[3] = t97\n    H[4] = t92\n    H[5] = t99\n    H[6] = t59\n    H[7] = t23 * t31 * 2.0\n    H[8] = t96\n    H[9] = t94\n    H[10] = t98\n    H[11] = t93\n    H[12] = t35\n    H[13] = t96\n    t35 = -t62 + t64\n    H[14] = (t35 + t18 * t18 * t31 * 2.0) + t33 * 4.0\n    H[15] = t19\n    H[16] = t79\n    H[17] = t77\n    H[18] = t97\n    H[19] = t94\n    H[20] = t19\n    t33 = -t62 + t65\n    H[21] = (t33 + t17 * t17 * t31 * 2.0) - t102_tmp * 4.0\n    H[22] = t78\n    H[23] = t22\n    H[24] = t92\n    H[25] = t98\n    H[26] = t79\n    H[27] = t78\n    H[28] = (t35 + t16 * t16 * t31 * 2.0) + t20 * 4.0\n    H[29] = t100\n    H[30] = t99\n    H[31] = t93\n    H[32] = t77\n    H[33] = t22\n    H[34] = t100\n    H[35] = (t33 + t15 * t15 * t31 * 2.0) - t76 * 4.0\n    return np.reshape(H, (6, 6))"
  },
  {
    "path": "7_self_contact/distance/PointPointDistance.py",
    "content": "import numpy as np\n\ndef val(p0, p1):\n    e = p0 - p1\n    return np.dot(e, e)\n\ndef grad(p0, p1):\n    e = p0 - p1\n    return np.reshape([2 * e, -2 * e], (1, 4))[0]\n\ndef hess(p0, p1):\n    H = np.array([[0.0] * 4] * 4)\n    H[0, 0] = H[1, 1] = H[2, 2] = H[3, 3] = 2\n    H[0, 2] = H[1, 3] = H[2, 0] = H[3, 1] = -2\n    return H"
  },
  {
    "path": "7_self_contact/readme.md",
    "content": "# Inversion-free Hyperelastic Solids Simulation\n\nTwo squares falling onto the ground under gravity, contacting with each other, and then compressed by a ceiling is simulated with an inversion-free hyperelastic potential and IPC with implicit Euler time integration.\nEach time step is solved by minimizing the Incremental Potential with the projected Newton method.\n\n## Dependencies\n```\npip install numpy scipy pygame\n```\n\n## Run\n```\npython simulator.py\n```"
  },
  {
    "path": "7_self_contact/simulator.py",
    "content": "# FEM Solids Simulation\n\nimport numpy as np  # numpy for linear algebra\nimport pygame       # pygame for visualization\npygame.init()\n\nimport square_mesh   # square mesh\nimport time_integrator\n\n# ANCHOR: sim_setup\n# simulation setup\nside_len = 0.45\nrho = 1000      # density of square\nE = 1e5         # Young's modulus\nnu = 0.4        # Poisson's ratio\nn_seg = 2       # num of segments per side of the square\nh = 0.01        # time step size in s\nDBC = [(n_seg + 1) * (n_seg + 1) * 2]   # dirichlet node index\nDBC_v = [np.array([0.0, -0.5])]         # dirichlet node velocity\nDBC_limit = [np.array([0.0, -0.7])]     # dirichlet node limit position\nground_n = np.array([0.0, 1.0])         # normal of the slope\nground_n /= np.linalg.norm(ground_n)    # normalize ground normal vector just in case\nground_o = np.array([0.0, -1.0])        # a point on the slope  \nmu = 0.4        # friction coefficient of the slope\n\n# initialize simulation\n[x, e] = square_mesh.generate(side_len, n_seg)       # node positions and triangle node indices of the top square\ne = np.append(e, np.array(e) + [len(x)] * 3, axis=0) # add triangle node indices of the bottom square\nx = np.append(x, x + [side_len * 0.1, -side_len * 1.1], axis=0) # add node positions of the bottom square\n# ANCHOR_END: sim_setup\n[bp, be] = square_mesh.find_boundary(e)             # find boundary points and edges for self-contact\nx = np.append(x, [[0.0, side_len * 0.6]], axis=0)   # ceil origin (with normal [0.0, -1.0])\nv = np.array([[0.0, 0.0]] * len(x))                 # velocity\nm = [rho * side_len * side_len / ((n_seg + 1) * (n_seg + 1))] * len(x)  # calculate node mass evenly\n# rest shape basis, volume, and lame parameters\nvol = [0.0] * len(e)\nIB = [np.array([[0.0, 0.0]] * 2)] * len(e)\nfor i in range(0, len(e)):\n    TB = [x[e[i][1]] - x[e[i][0]], x[e[i][2]] - x[e[i][0]]]\n    vol[i] = np.linalg.det(np.transpose(TB)) / 2\n    IB[i] = np.linalg.inv(np.transpose(TB))\nmu_lame = [0.5 * E / (1 + nu)] * len(e)\nlam = [E * nu / ((1 + nu) * (1 - 2 * nu))] * len(e)\n# identify whether a node is Dirichlet\nis_DBC = [False] * len(x)\nfor i in DBC:\n    is_DBC[i] = True\nDBC_stiff = [1000]  # DBC stiffness, adjusted and warm-started across time steps\ncontact_area = [side_len / n_seg] * len(x)     # perimeter split to each node\n\n# simulation with visualization\nresolution = np.array([900, 900])\noffset = resolution / 2\nscale = 200\ndef screen_projection(x):\n    return [offset[0] + scale * x[0], resolution[1] - (offset[1] + scale * x[1])]\n\ntime_step = 0\nsquare_mesh.write_to_file(time_step, x, e)\nscreen = pygame.display.set_mode(resolution)\nrunning = True\nwhile running:\n    # run until the user asks to quit\n    for event in pygame.event.get():\n        if event.type == pygame.QUIT:\n            running = False\n    \n    print('### Time step', time_step, '###')\n\n    # fill the background and draw the square\n    screen.fill((255, 255, 255))\n    pygame.draw.aaline(screen, (0, 0, 255), screen_projection([ground_o[0] - 3.0 * ground_n[1], ground_o[1] + 3.0 * ground_n[0]]), \n        screen_projection([ground_o[0] + 3.0 * ground_n[1], ground_o[1] - 3.0 * ground_n[0]]))   # ground\n    pygame.draw.aaline(screen, (0, 0, 255), screen_projection([x[-1][0] + 3.0, x[-1][1]]), \n        screen_projection([x[-1][0] - 3.0, x[-1][1]]))   # ceil\n    for eI in e:\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[0]]), screen_projection(x[eI[1]]))\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[1]]), screen_projection(x[eI[2]]))\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[2]]), screen_projection(x[eI[0]]))\n    for xId in range(0, len(x) - 1):\n        xI = x[xId]\n        pygame.draw.circle(screen, (0, 0, 255), screen_projection(xI), 0.1 * side_len / n_seg * scale)\n\n    pygame.display.flip()   # flip the display\n\n    # step forward simulation and wait for screen refresh\n    [x, v] = time_integrator.step_forward(x, e, v, m, vol, IB, mu_lame, lam, ground_n, ground_o, bp, be, contact_area, mu, is_DBC, DBC, DBC_v, DBC_limit, DBC_stiff, h, 1e-2)\n    time_step += 1\n    pygame.time.wait(int(h * 1000))\n    square_mesh.write_to_file(time_step, x, e)\n\npygame.quit()"
  },
  {
    "path": "7_self_contact/square_mesh.py",
    "content": "import numpy as np\nimport os\n\ndef generate(side_length, n_seg):\n    # sample nodes uniformly on a square\n    x = np.array([[0.0, 0.0]] * ((n_seg + 1) ** 2))\n    step = side_length / n_seg\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg + 1):\n            x[i * (n_seg + 1) + j] = [-side_length / 2 + i * step, -side_length / 2 + j * step]\n    \n    # connect the nodes with triangle elements\n    e = []\n    for i in range(0, n_seg):\n        for j in range(0, n_seg):\n            # triangulate each cell following a symmetric pattern:\n            if (i % 2)^(j % 2):\n                e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n                e.append([(i + 1) * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1, i * (n_seg + 1) + j + 1])\n            else:\n                e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1])\n                e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1, i * (n_seg + 1) + j + 1])\n\n    return [x, e]\n\n# ANCHOR: find_boundary\ndef find_boundary(e):\n    # index all half-edges for fast query\n    edge_set = set()\n    for i in range(0, len(e)):\n        for j in range(0, 3):\n            edge_set.add((e[i][j], e[i][(j + 1) % 3]))\n\n    # find boundary points and edges\n    bp_set = set()\n    be = []\n    for eI in edge_set:\n        if (eI[1], eI[0]) not in edge_set:\n            # if the inverse edge of a half-edge does not exist,\n            # then it is a boundary edge\n            be.append([eI[0], eI[1]])\n            bp_set.add(eI[0])\n            bp_set.add(eI[1])\n    return [list(bp_set), be]\n# ANCHOR_END: find_boundary\n\ndef write_to_file(frameNum, x, e):\n    # Check if 'output' directory exists; if not, create it\n    if not os.path.exists('output'):\n        os.makedirs('output')\n\n    # create obj file\n    filename = f\"output/{frameNum}.obj\"\n    with open(filename, 'w') as f:\n        # write vertex coordinates\n        for row in x:\n            f.write(f\"v {float(row[0]):.6f} {float(row[1]):.6f} 0.0\\n\") \n        # write vertex indices for each triangle\n        for row in e:\n            #NOTE: vertex indices start from 1 in obj file format\n            f.write(f\"f {row[0] + 1} {row[1] + 1} {row[2] + 1}\\n\")"
  },
  {
    "path": "7_self_contact/time_integrator.py",
    "content": "import copy\nfrom cmath import inf\n\nimport numpy as np\nimport numpy.linalg as LA\nimport scipy.sparse as sparse\nfrom scipy.sparse.linalg import spsolve\n\nimport InertiaEnergy\nimport NeoHookeanEnergy\nimport GravityEnergy\nimport BarrierEnergy\nimport FrictionEnergy\nimport SpringEnergy\n\ndef step_forward(x, e, v, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, mu, is_DBC, DBC, DBC_v, DBC_limit, DBC_stiff, h, tol):\n    x_tilde = x + v * h     # implicit Euler predictive position\n    x_n = copy.deepcopy(x)\n    mu_lambda = BarrierEnergy.compute_mu_lambda(x, n, o, bp, be, contact_area, mu)  # compute mu * lambda for each node using x^n\n    DBC_target = [] # target position of each DBC in the current time step\n    for i in range(0, len(DBC)):\n        if (DBC_limit[i] - x_n[DBC[i]]).dot(DBC_v[i]) > 0:\n            DBC_target.append(x_n[DBC[i]] + h * DBC_v[i])\n        else:\n            DBC_target.append(x_n[DBC[i]])\n\n    # Newton loop\n    iter = 0\n    E_last = IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, (x - x_n) / h, mu_lambda, DBC, DBC_target, DBC_stiff[0], h)\n    [p, DBC_satisfied] = search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, (x - x_n) / h, mu_lambda, is_DBC, DBC, DBC_target, DBC_stiff[0], tol, h)\n    while (LA.norm(p, inf) / h > tol) | (sum(DBC_satisfied) != len(DBC)):   # also check whether all DBCs are satisfied\n        print('Iteration', iter, ':')\n        print('residual =', LA.norm(p, inf) / h)\n\n        if (LA.norm(p, inf) / h <= tol) & (sum(DBC_satisfied) != len(DBC)):\n            # increase DBC stiffness and recompute energy value record\n            DBC_stiff[0] *= 2\n            E_last = IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, (x - x_n) / h, mu_lambda, DBC, DBC_target, DBC_stiff[0], h)\n\n        # filter line search\n        alpha = min(BarrierEnergy.init_step_size(x, n, o, bp, be, p), NeoHookeanEnergy.init_step_size(x, e, p))  # avoid interpenetration, tunneling, and inversion\n        while IP_val(x + alpha * p, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, (x + alpha * p - x_n) / h, mu_lambda, DBC, DBC_target, DBC_stiff[0], h) > E_last:\n            alpha /= 2\n        print('step size =', alpha)\n\n        x += alpha * p\n        E_last = IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, (x - x_n) / h, mu_lambda, DBC, DBC_target, DBC_stiff[0], h)\n        [p, DBC_satisfied] = search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, (x - x_n) / h, mu_lambda, is_DBC, DBC, DBC_target, DBC_stiff[0], tol, h)\n        iter += 1\n\n    v = (x - x_n) / h   # implicit Euler velocity update\n    return [x, v]\n\ndef IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h):\n    return InertiaEnergy.val(x, x_tilde, m) + h * h * (     # implicit Euler\n        NeoHookeanEnergy.val(x, e, vol, IB, mu_lame, lam) + \n        GravityEnergy.val(x, m) + \n        BarrierEnergy.val(x, n, o, bp, be, contact_area) + \n        FrictionEnergy.val(v, mu_lambda, h, n)\n    ) + SpringEnergy.val(x, m, DBC, DBC_target, DBC_stiff)\n\ndef IP_grad(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h):\n    return InertiaEnergy.grad(x, x_tilde, m) + h * h * (    # implicit Euler\n        NeoHookeanEnergy.grad(x, e, vol, IB, mu_lame, lam) + \n        GravityEnergy.grad(x, m) + \n        BarrierEnergy.grad(x, n, o, bp, be, contact_area) + \n        FrictionEnergy.grad(v, mu_lambda, h, n)\n    ) + SpringEnergy.grad(x, m, DBC, DBC_target, DBC_stiff)\n\ndef IP_hess(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h):\n    IJV_In = InertiaEnergy.hess(x, x_tilde, m)\n    IJV_MS = NeoHookeanEnergy.hess(x, e, vol, IB, mu_lame, lam)\n    IJV_B = BarrierEnergy.hess(x, n, o, bp, be, contact_area)\n    IJV_F = FrictionEnergy.hess(v, mu_lambda, h, n)\n    IJV_S = SpringEnergy.hess(x, m, DBC, DBC_target, DBC_stiff)\n    IJV_MS[2] *= h * h    # implicit Euler\n    IJV_B[2] *= h * h     # implicit Euler\n    IJV_F[2] *= h * h     # implicit Euler\n    IJV_In_MS = np.append(IJV_In, IJV_MS, axis=1)\n    IJV_In_MS_B = np.append(IJV_In_MS, IJV_B, axis=1)\n    IJV_In_MS_B_F = np.append(IJV_In_MS_B, IJV_F, axis=1)\n    IJV = np.append(IJV_In_MS_B_F, IJV_S, axis=1)\n    H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()\n    return H\n\ndef search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, v, mu_lambda, is_DBC, DBC, DBC_target, DBC_stiff, tol, h):\n    projected_hess = IP_hess(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h)\n    reshaped_grad = IP_grad(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, v, mu_lambda, DBC, DBC_target, DBC_stiff, h).reshape(len(x) * 2, 1)\n    # check whether each DBC is satisfied\n    DBC_satisfied = [False] * len(x)\n    for i in range(0, len(DBC)):\n        if LA.norm(x[DBC[i]] - DBC_target[i]) / h < tol:\n            DBC_satisfied[DBC[i]] = True\n    # eliminate DOF if it's a satisfied DBC by modifying gradient and Hessian for DBC:\n    for i, j in zip(*projected_hess.nonzero()):\n        if (is_DBC[int(i / 2)] & DBC_satisfied[int(i / 2)]) | (is_DBC[int(j / 2)] & DBC_satisfied[int(j / 2)]): \n            projected_hess[i, j] = (i == j)\n    for i in range(0, len(x)):\n        if is_DBC[i] & DBC_satisfied[i]:\n            reshaped_grad[i * 2] = reshaped_grad[i * 2 + 1] = 0.0\n    return [spsolve(projected_hess, -reshaped_grad).reshape(len(x), 2), DBC_satisfied]"
  },
  {
    "path": "7_self_contact/utils.py",
    "content": "import numpy as np\nimport numpy.linalg as LA\nimport math\n\ndef make_PSD(hess):\n    [lam, V] = LA.eigh(hess)    # Eigen decomposition on symmetric matrix\n    # set all negative Eigenvalues to 0\n    for i in range(0, len(lam)):\n        lam[i] = max(0, lam[i])\n    return np.matmul(np.matmul(V, np.diag(lam)), np.transpose(V))\n\ndef smallest_positive_real_root_quad(a, b, c, tol = 1e-6):\n    # return negative value if no positive real root is found\n    t = 0\n    if abs(a) <= tol:\n        if abs(b) <= tol: # f(x) = c > 0 for all x\n            t = -1\n        else:\n            t = -c / b\n    else:\n        desc = b * b - 4 * a * c\n        if desc > 0:\n            t = (-b - math.sqrt(desc)) / (2 * a) # if a > 0, this is either the smaller positive root, or both roots are negative; \n            # if a < 0, there are 1 negative and 1 positive real roots, and we just need the positive one.\n            if t < 0:\n                t = (-b + math.sqrt(desc)) / (2 * a)\n        else: # desv<0 ==> imag, f(x) > 0 for all x > 0\n            t = -1\n    return t"
  },
  {
    "path": "8_self_friction/BarrierEnergy.py",
    "content": "import math\nimport numpy as np\n\nimport distance.PointEdgeDistance as PE\nimport distance.CCD as CCD\n\nimport utils\n\ndhat = 0.01\nkappa = 1e5\n\ndef val(x, n, o, bp, be, contact_area):\n    sum = 0.0\n    # floor:\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            sum += contact_area[i] * dhat * kappa / 2 * (s - 1) * math.log(s)\n    # ceil:\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        d = n.dot(x[i] - x[-1])\n        if d < dhat:\n            s = d / dhat\n            sum += contact_area[i] * dhat * kappa / 2 * (s - 1) * math.log(s)\n    # self-contact\n    dhat_sqr = dhat * dhat\n    for xI in bp:\n        for eI in be:\n            if xI != eI[0] and xI != eI[1]: # do not consider a point and its incident edge\n                d_sqr = PE.val(x[xI], x[eI[0]], x[eI[1]])\n                if d_sqr < dhat_sqr:\n                    s = d_sqr / dhat_sqr\n                    # since d_sqr is used, need to divide by 8 not 2 here for consistency to linear elasticity:\n                    sum += 0.5 * contact_area[xI] * dhat * kappa / 8 * (s - 1) * math.log(s)\n    return sum\n\ndef grad(x, n, o, bp, be, contact_area):\n    g = np.array([[0.0, 0.0]] * len(x))\n    # floor:\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            g[i] = contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d)) * n\n    # ceil:\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        d = n.dot(x[i] - x[-1])\n        if d < dhat:\n            s = d / dhat\n            local_grad = contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d)) * n\n            g[i] += local_grad\n            g[-1] -= local_grad\n    # self-contact\n    dhat_sqr = dhat * dhat\n    for xI in bp:\n        for eI in be:\n            if xI != eI[0] and xI != eI[1]: # do not consider a point and its incident edge\n                d_sqr = PE.val(x[xI], x[eI[0]], x[eI[1]])\n                if d_sqr < dhat_sqr:\n                    s = d_sqr / dhat_sqr\n                    # since d_sqr is used, need to divide by 8 not 2 here for consistency to linear elasticity:\n                    local_grad = 0.5 * contact_area[xI] * dhat * (kappa / 8 * (math.log(s) / dhat_sqr + (s - 1) / d_sqr)) * PE.grad(x[xI], x[eI[0]], x[eI[1]])\n                    g[xI] += local_grad[0:2]\n                    g[eI[0]] += local_grad[2:4]\n                    g[eI[1]] += local_grad[4:6]\n    return g\n\ndef hess(x, n, o, bp, be, contact_area):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    # floor:\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            local_hess = contact_area[i] * dhat * kappa / (2 * d * d * dhat) * (d + dhat) * np.outer(n, n)\n            for c in range(0, 2):\n                for r in range(0, 2):\n                    IJV[0].append(i * 2 + r)\n                    IJV[1].append(i * 2 + c)\n                    IJV[2] = np.append(IJV[2], local_hess[r, c])\n    # ceil:\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        d = n.dot(x[i] - x[-1])\n        if d < dhat:\n            local_hess = contact_area[i] * dhat * kappa / (2 * d * d * dhat) * (d + dhat) * np.outer(n, n)\n            index = [i, len(x) - 1]\n            for nI in range(0, 2):\n                for nJ in range(0, 2):\n                    for c in range(0, 2):\n                        for r in range(0, 2):\n                            IJV[0].append(index[nI] * 2 + r)\n                            IJV[1].append(index[nJ] * 2 + c)\n                            IJV[2] = np.append(IJV[2], ((-1) ** (nI != nJ)) * local_hess[r, c])\n    # self-contact\n    dhat_sqr = dhat * dhat\n    for xI in bp:\n        for eI in be:\n            if xI != eI[0] and xI != eI[1]: # do not consider a point and its incident edge\n                d_sqr = PE.val(x[xI], x[eI[0]], x[eI[1]])\n                if d_sqr < dhat_sqr:\n                    d_sqr_grad = PE.grad(x[xI], x[eI[0]], x[eI[1]])\n                    s = d_sqr / dhat_sqr\n                    # since d_sqr is used, need to divide by 8 not 2 here for consistency to linear elasticity:\n                    local_hess = 0.5 * contact_area[xI] * dhat * utils.make_PSD(kappa / (8 * d_sqr * d_sqr * dhat_sqr) * (d_sqr + dhat_sqr) * np.outer(d_sqr_grad, d_sqr_grad) \\\n                        + (kappa / 8 * (math.log(s) / dhat_sqr + (s - 1) / d_sqr)) * PE.hess(x[xI], x[eI[0]], x[eI[1]]))\n                    index = [xI, eI[0], eI[1]]\n                    for nI in range(0, 3):\n                        for nJ in range(0, 3):\n                            for c in range(0, 2):\n                                for r in range(0, 2):\n                                    IJV[0].append(index[nI] * 2 + r)\n                                    IJV[1].append(index[nJ] * 2 + c)\n                                    IJV[2] = np.append(IJV[2], local_hess[nI * 2 + r, nJ * 2 + c])\n    return IJV\n\ndef init_step_size(x, n, o, bp, be, p):\n    alpha = 1\n    # floor:\n    for i in range(0, len(x)):\n        p_n = p[i].dot(n)\n        if p_n < 0:\n            alpha = min(alpha, 0.9 * n.dot(x[i] - o) / -p_n)\n    # ceil:\n    n = np.array([0.0, -1.0])\n    for i in range(0, len(x) - 1):\n        p_n = (p[i] - p[-1]).dot(n)\n        if p_n < 0:\n            alpha = min(alpha, 0.9 * n.dot(x[i] - x[-1]) / -p_n)\n    # self-contact\n    for xI in bp:\n        for eI in be:\n            if xI != eI[0] and xI != eI[1]: # do not consider a point and its incident edge\n                if CCD.bbox_overlap(x[xI], x[eI[0]], x[eI[1]], p[xI], p[eI[0]], p[eI[1]], alpha):\n                    toc = CCD.narrow_phase_CCD(x[xI], x[eI[0]], x[eI[1]], p[xI], p[eI[0]], p[eI[1]], alpha)\n                    if alpha > toc:\n                        alpha = toc\n    return alpha\n\ndef compute_mu_lambda(x, n, o, bp, be, contact_area, mu):\n    # floor:\n    mu_lambda = np.array([0.0] * len(x))\n    for i in range(0, len(x)):\n        d = n.dot(x[i] - o)\n        if d < dhat:\n            s = d / dhat\n            mu_lambda[i] = mu * -contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d))\n    # ANCHOR: fric_precomp\n    # self-contact\n    mu_lambda_self = []\n    dhat_sqr = dhat * dhat\n    for xI in bp:\n        for eI in be:\n            if xI != eI[0] and xI != eI[1]: # do not consider a point and its incident edge\n                d_sqr = PE.val(x[xI], x[eI[0]], x[eI[1]])\n                if d_sqr < dhat_sqr:\n                    s = d_sqr / dhat_sqr\n                    # since d_sqr is used, need to divide by 8 not 2 here for consistency to linear elasticity\n                    # also, lambda = -\\partial b / \\partial d = -(\\partial b / \\partial d^2) * (\\partial d^2 / \\partial d)\n                    mu_lam = mu * -0.5 * contact_area[xI] * dhat * (kappa / 8 * (math.log(s) / dhat_sqr + (s - 1) / d_sqr)) * 2 * math.sqrt(d_sqr)\n                    [n, r] = PE.tangent(x[xI], x[eI[0]], x[eI[1]]) # normal and closest point parameterization on the edge\n                    mu_lambda_self.append([xI, eI[0], eI[1], mu_lam, n, r])\n    # ANCHOR_END: fric_precomp\n    return [mu_lambda, mu_lambda_self]"
  },
  {
    "path": "8_self_friction/FrictionEnergy.py",
    "content": "import numpy as np\nimport utils\n\nepsv = 1e-3\n\ndef f0(vbarnorm, epsv, hhat):\n    if vbarnorm >= epsv:\n        return vbarnorm * hhat\n    else:\n        vbarnormhhat = vbarnorm * hhat\n        epsvhhat = epsv * hhat\n        return vbarnormhhat * vbarnormhhat * (-vbarnormhhat / 3.0 + epsvhhat) / (epsvhhat * epsvhhat) + epsvhhat / 3.0\n\ndef f1_div_vbarnorm(vbarnorm, epsv):\n    if vbarnorm >= epsv:\n        return 1.0 / vbarnorm\n    else:\n        return (-vbarnorm + 2.0 * epsv) / (epsv * epsv)\n\ndef f_hess_term(vbarnorm, epsv):\n    if vbarnorm >= epsv:\n        return -1.0 / (vbarnorm * vbarnorm)\n    else:\n        return -1.0 / (epsv * epsv)\n\ndef val(v, mu_lambda, mu_lambda_self, hhat, n):\n    sum = 0.0\n    # floor:\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            sum += mu_lambda[i] * f0(np.linalg.norm(vbar), epsv, hhat)\n    # ANCHOR: val\n    # self-contact:\n    for i in range(0, len(mu_lambda_self)):\n        [xI, eI0, eI1, mu_lam, n, r] = mu_lambda_self[i]\n        T = np.identity(2) - np.outer(n, n)\n        rel_v = v[xI] - ((1 - r) * v[eI0] + r * v[eI1])\n        vbar = np.transpose(T).dot(rel_v)\n        sum += mu_lam * f0(np.linalg.norm(vbar), epsv, hhat)\n    # ANCHOR_END: val\n    return sum\n\ndef grad(v, mu_lambda, mu_lambda_self, hhat, n):\n    g = np.array([[0.0, 0.0]] * len(v))\n    # floor:\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            g[i] = mu_lambda[i] * f1_div_vbarnorm(np.linalg.norm(vbar), epsv) * T.dot(vbar)\n    # ANCHOR: grad\n    # self-contact:\n    for i in range(0, len(mu_lambda_self)):\n        [xI, eI0, eI1, mu_lam, n, r] = mu_lambda_self[i]\n        T = np.identity(2) - np.outer(n, n)\n        rel_v = v[xI] - ((1 - r) * v[eI0] + r * v[eI1])\n        vbar = np.transpose(T).dot(rel_v)\n        g_rel_v = mu_lam * f1_div_vbarnorm(np.linalg.norm(vbar), epsv) * T.dot(vbar)\n        g[xI] += g_rel_v\n        g[eI0] += g_rel_v * -(1 - r)\n        g[eI1] += g_rel_v * -r\n    # ANCHOR_END: grad\n    return g\n\ndef hess(v, mu_lambda, mu_lambda_self, hhat, n):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    # floor:\n    T = np.identity(2) - np.outer(n, n) # tangent of slope is constant\n    for i in range(0, len(v)):\n        if mu_lambda[i] > 0:\n            vbar = np.transpose(T).dot(v[i])\n            vbarnorm = np.linalg.norm(vbar)\n            inner_term = f1_div_vbarnorm(vbarnorm, epsv) * np.identity(2)\n            if vbarnorm != 0:\n                inner_term += f_hess_term(vbarnorm, epsv) / vbarnorm * np.outer(vbar, vbar)\n            local_hess = mu_lambda[i] * T.dot(utils.make_PSD(inner_term)).dot(np.transpose(T)) / hhat\n            for c in range(0, 2):\n                for r in range(0, 2):\n                    IJV[0].append(i * 2 + r)\n                    IJV[1].append(i * 2 + c)\n                    IJV[2] = np.append(IJV[2], local_hess[r, c])\n    # ANCHOR: hess\n    # self-contact:\n    for i in range(0, len(mu_lambda_self)):\n        [xI, eI0, eI1, mu_lam, n, r] = mu_lambda_self[i]\n        T = np.identity(2) - np.outer(n, n)\n        rel_v = v[xI] - ((1 - r) * v[eI0] + r * v[eI1])\n        vbar = np.transpose(T).dot(rel_v)\n        vbarnorm = np.linalg.norm(vbar)\n        inner_term = f1_div_vbarnorm(vbarnorm, epsv) * np.identity(2)\n        if vbarnorm != 0:\n            inner_term += f_hess_term(vbarnorm, epsv) / vbarnorm * np.outer(vbar, vbar)\n        hess_rel_v = mu_lam * T.dot(utils.make_PSD(inner_term)).dot(np.transpose(T)) / hhat\n        index = [xI, eI0, eI1]\n        d_rel_v_dv = [1, -(1 - r), -r]\n        for nI in range(0, 3):\n            for nJ in range(0, 3):\n                for c in range(0, 2):\n                    for r in range(0, 2):\n                        IJV[0].append(index[nI] * 2 + r)\n                        IJV[1].append(index[nJ] * 2 + c)\n                        IJV[2] = np.append(IJV[2], d_rel_v_dv[nI] * d_rel_v_dv[nJ] * hess_rel_v[r, c])\n    # ANCHOR_END: hess\n    return IJV"
  },
  {
    "path": "8_self_friction/GravityEnergy.py",
    "content": "import numpy as np\n\ngravity = [0.0, -9.81]\n\ndef val(x, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        sum += -m[i] * x[i].dot(gravity)\n    return sum\n\ndef grad(x, m):\n    g = np.array([gravity] * len(x))\n    for i in range(0, len(x)):\n        g[i] *= -m[i]\n    return g\n\n# Hessian is 0"
  },
  {
    "path": "8_self_friction/InertiaEnergy.py",
    "content": "import numpy as np\n\ndef val(x, x_tilde, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        diff = x[i] - x_tilde[i]\n        sum += 0.5 * m[i] * diff.dot(diff)\n    return sum\n\ndef grad(x, x_tilde, m):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(x)):\n        g[i] = m[i] * (x[i] - x_tilde[i])\n    return g\n\ndef hess(x, x_tilde, m):\n    IJV = [[0] * (len(x) * 2), [0] * (len(x) * 2), np.array([0.0] * (len(x) * 2))]\n    for i in range(0, len(x)):\n        for d in range(0, 2):\n            IJV[0][i * 2 + d] = i * 2 + d\n            IJV[1][i * 2 + d] = i * 2 + d\n            IJV[2][i * 2 + d] = m[i]\n    return IJV"
  },
  {
    "path": "8_self_friction/NeoHookeanEnergy.py",
    "content": "import utils\nimport numpy as np\nimport math\n\ndef polar_svd(F):\n    [U, s, VT] = np.linalg.svd(F)\n    if np.linalg.det(U) < 0:\n        U[:, 1] = -U[:, 1]\n        s[1] = -s[1]\n    if np.linalg.det(VT) < 0:\n        VT[1, :] = -VT[1, :]\n        s[1] = -s[1]\n    return [U, s, VT]\n\ndef dPsi_div_dsigma(s, mu, lam):\n    ln_sigma_prod = math.log(s[0] * s[1])\n    inv0 = 1.0 / s[0]\n    dPsi_dsigma_0 = mu * (s[0] - inv0) + lam * inv0 * ln_sigma_prod\n    inv1 = 1.0 / s[1]\n    dPsi_dsigma_1 = mu * (s[1] - inv1) + lam * inv1 * ln_sigma_prod\n    return [dPsi_dsigma_0, dPsi_dsigma_1]\n\ndef d2Psi_div_dsigma2(s, mu, lam):\n    ln_sigma_prod = math.log(s[0] * s[1])\n    inv2_0 = 1 / (s[0] * s[0])\n    d2Psi_dsigma2_00 = mu * (1 + inv2_0) - lam * inv2_0 * (ln_sigma_prod - 1)\n    inv2_1 = 1 / (s[1] * s[1])\n    d2Psi_dsigma2_11 = mu * (1 + inv2_1) - lam * inv2_1 * (ln_sigma_prod - 1)\n    d2Psi_dsigma2_01 = lam / (s[0] * s[1])\n    return [[d2Psi_dsigma2_00, d2Psi_dsigma2_01], [d2Psi_dsigma2_01, d2Psi_dsigma2_11]]\n\ndef B_left_coef(s, mu, lam):\n    sigma_prod = s[0] * s[1]\n    return (mu + (mu - lam * math.log(sigma_prod)) / sigma_prod) / 2\n\ndef Psi(F, mu, lam):\n    J = np.linalg.det(F)\n    lnJ = math.log(J)\n    return mu / 2 * (np.trace(np.transpose(F).dot(F)) - 2) - mu * lnJ + lam / 2 * lnJ * lnJ\n\ndef dPsi_div_dF(F, mu, lam):\n    FinvT = np.transpose(np.linalg.inv(F))\n    return mu * (F - FinvT) + lam * math.log(np.linalg.det(F)) * FinvT\n\ndef d2Psi_div_dF2(F, mu, lam):\n    [U, sigma, VT] = polar_svd(F)\n\n    Psi_sigma_sigma = utils.make_PSD(d2Psi_div_dsigma2(sigma, mu, lam))\n\n    B_left = B_left_coef(sigma, mu, lam)\n    Psi_sigma = dPsi_div_dsigma(sigma, mu, lam)\n    B_right = (Psi_sigma[0] + Psi_sigma[1]) / (2 * max(sigma[0] + sigma[1], 1e-6))\n    B = utils.make_PSD([[B_left + B_right, B_left - B_right], [B_left - B_right, B_left + B_right]])\n\n    M = np.array([[0, 0, 0, 0]] * 4)\n    M[0, 0] = Psi_sigma_sigma[0, 0]\n    M[0, 3] = Psi_sigma_sigma[0, 1]\n    M[1, 1] = B[0, 0]\n    M[1, 2] = B[0, 1]\n    M[2, 1] = B[1, 0]\n    M[2, 2] = B[1, 1]\n    M[3, 0] = Psi_sigma_sigma[1, 0]\n    M[3, 3] = Psi_sigma_sigma[1, 1]\n\n    dP_div_dF = np.array([[0, 0, 0, 0]] * 4)\n    for j in range(0, 2):\n        for i in range(0, 2):\n            ij = j * 2 + i\n            for s in range(0, 2):\n                for r in range(0, 2):\n                    rs = s * 2 + r\n                    dP_div_dF[ij, rs] = M[0, 0] * U[i, 0] * VT[0, j] * U[r, 0] * VT[0, s] \\\n                        + M[0, 3] * U[i, 0] * VT[0, j] * U[r, 1] * VT[1, s] \\\n                        + M[1, 1] * U[i, 1] * VT[0, j] * U[r, 1] * VT[0, s] \\\n                        + M[1, 2] * U[i, 1] * VT[0, j] * U[r, 0] * VT[1, s] \\\n                        + M[2, 1] * U[i, 0] * VT[1, j] * U[r, 1] * VT[0, s] \\\n                        + M[2, 2] * U[i, 0] * VT[1, j] * U[r, 0] * VT[1, s] \\\n                        + M[3, 0] * U[i, 1] * VT[1, j] * U[r, 0] * VT[0, s] \\\n                        + M[3, 3] * U[i, 1] * VT[1, j] * U[r, 1] * VT[1, s]\n    return dP_div_dF\n\ndef deformation_grad(x, elemVInd, IB):\n    F = [x[elemVInd[1]] - x[elemVInd[0]], x[elemVInd[2]] - x[elemVInd[0]]]\n    return np.transpose(F).dot(IB)\n\ndef dPsi_div_dx(P, IB):  # applying chain-rule, dPsi_div_dx = dPsi_div_dF * dF_div_dx\n    dPsi_dx_2 = P[0, 0] * IB[0, 0] + P[0, 1] * IB[0, 1]\n    dPsi_dx_3 = P[1, 0] * IB[0, 0] + P[1, 1] * IB[0, 1]\n    dPsi_dx_4 = P[0, 0] * IB[1, 0] + P[0, 1] * IB[1, 1]\n    dPsi_dx_5 = P[1, 0] * IB[1, 0] + P[1, 1] * IB[1, 1]\n    return [np.array([-dPsi_dx_2 - dPsi_dx_4, -dPsi_dx_3 - dPsi_dx_5]), np.array([dPsi_dx_2, dPsi_dx_3]), np.array([dPsi_dx_4, dPsi_dx_5])]\n\ndef d2Psi_div_dx2(dP_div_dF, IB):  # applying chain-rule, d2Psi_div_dx2 = dF_div_dx^T * d2Psi_div_dF2 * dF_div_dx (note that d2F_div_dx2 = 0)\n    intermediate = np.array([[0.0, 0.0, 0.0, 0.0]] * 6)\n    for colI in range(0, 4):\n        _000 = dP_div_dF[0, colI] * IB[0, 0]\n        _010 = dP_div_dF[0, colI] * IB[1, 0]\n        _101 = dP_div_dF[2, colI] * IB[0, 1]\n        _111 = dP_div_dF[2, colI] * IB[1, 1]\n        _200 = dP_div_dF[1, colI] * IB[0, 0]\n        _210 = dP_div_dF[1, colI] * IB[1, 0]\n        _301 = dP_div_dF[3, colI] * IB[0, 1]\n        _311 = dP_div_dF[3, colI] * IB[1, 1]\n        intermediate[2, colI] = _000 + _101\n        intermediate[3, colI] = _200 + _301\n        intermediate[4, colI] = _010 + _111\n        intermediate[5, colI] = _210 + _311\n        intermediate[0, colI] = -intermediate[2, colI] - intermediate[4, colI]\n        intermediate[1, colI] = -intermediate[3, colI] - intermediate[5, colI]\n    result = np.array([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]] * 6)\n    for colI in range(0, 6):\n        _000 = intermediate[colI, 0] * IB[0, 0]\n        _010 = intermediate[colI, 0] * IB[1, 0]\n        _101 = intermediate[colI, 2] * IB[0, 1]\n        _111 = intermediate[colI, 2] * IB[1, 1]\n        _200 = intermediate[colI, 1] * IB[0, 0]\n        _210 = intermediate[colI, 1] * IB[1, 0]\n        _301 = intermediate[colI, 3] * IB[0, 1]\n        _311 = intermediate[colI, 3] * IB[1, 1]\n        result[2, colI] = _000 + _101\n        result[3, colI] = _200 + _301\n        result[4, colI] = _010 + _111\n        result[5, colI] = _210 + _311\n        result[0, colI] = -_000 - _101 - _010 - _111\n        result[1, colI] = -_200 - _301 - _210 - _311\n    return result\n\ndef val(x, e, vol, IB, mu, lam):\n    sum = 0.0\n    for i in range(0, len(e)):\n        F = deformation_grad(x, e[i], IB[i])\n        sum += vol[i] * Psi(F, mu[i], lam[i])\n    return sum\n\ndef grad(x, e, vol, IB, mu, lam):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(e)):\n        F = deformation_grad(x, e[i], IB[i])\n        P = vol[i] * dPsi_div_dF(F, mu[i], lam[i])\n        g_local = dPsi_div_dx(P, IB[i])\n        for j in range(0, 3):\n            g[e[i][j]] += g_local[j]\n    return g\n\ndef hess(x, e, vol, IB, mu, lam):\n    IJV = [[0] * (len(e) * 36), [0] * (len(e) * 36), np.array([0.0] * (len(e) * 36))]\n    for i in range(0, len(e)):\n        F = deformation_grad(x, e[i], IB[i])\n        dP_div_dF = vol[i] * d2Psi_div_dF2(F, mu[i], lam[i])\n        local_hess = d2Psi_div_dx2(dP_div_dF, IB[i])\n        for xI in range(0, 3):\n            for xJ in range(0, 3):\n                for dI in range(0, 2):\n                    for dJ in range(0, 2):\n                        ind = i * 36 + (xI * 3 + xJ) * 4 + dI * 2 + dJ\n                        IJV[0][ind] = e[i][xI] * 2 + dI\n                        IJV[1][ind] = e[i][xJ] * 2 + dJ\n                        IJV[2][ind] = local_hess[xI * 2 + dI, xJ * 2 + dJ]\n    return IJV\n\ndef init_step_size(x, e, p):\n    alpha = 1\n    for i in range(0, len(e)):\n        x21 = x[e[i][1]] - x[e[i][0]]\n        x31 = x[e[i][2]] - x[e[i][0]]\n        p21 = p[e[i][1]] - p[e[i][0]]\n        p31 = p[e[i][2]] - p[e[i][0]]\n        detT = np.linalg.det(np.transpose([x21, x31]))\n        a = np.linalg.det(np.transpose([p21, p31])) / detT\n        b = (np.linalg.det(np.transpose([x21, p31])) + np.linalg.det(np.transpose([p21, x31]))) / detT\n        c = 0.9  # solve for alpha that first brings the new volume to 0.1x the old volume for slackness\n        critical_alpha = utils.smallest_positive_real_root_quad(a, b, c)\n        if critical_alpha > 0:\n            alpha = min(alpha, critical_alpha)\n    return alpha"
  },
  {
    "path": "8_self_friction/SpringEnergy.py",
    "content": "import numpy as np\n\ndef val(x, m, DBC, DBC_target, k):\n    sum = 0.0\n    for i in range(0, len(DBC)):\n        diff = x[DBC[i]] - DBC_target[i]\n        sum += 0.5 * k * m[DBC[i]] * diff.dot(diff)\n    return sum\n\ndef grad(x, m, DBC, DBC_target, k):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(DBC)):\n        g[DBC[i]] = k * m[DBC[i]] * (x[DBC[i]] - DBC_target[i])\n    return g\n\ndef hess(x, m, DBC, DBC_target, k):\n    IJV = [[0] * 0, [0] * 0, np.array([0.0] * 0)]\n    for i in range(0, len(DBC)):\n        for d in range(0, 2):\n            IJV[0].append(DBC[i] * 2 + d)\n            IJV[1].append(DBC[i] * 2 + d)\n            IJV[2] = np.append(IJV[2], k * m[DBC[i]])\n    return IJV"
  },
  {
    "path": "8_self_friction/distance/CCD.py",
    "content": "from copy import deepcopy\nimport numpy as np\nimport math\n\nimport distance.PointEdgeDistance as PE\n\n# check whether the bounding box of the trajectory of the point and the edge overlap\ndef bbox_overlap(p, e0, e1, dp, de0, de1, toc_upperbound):\n    max_p = np.maximum(p, p + toc_upperbound * dp) # point trajectory bbox top-right\n    min_p = np.minimum(p, p + toc_upperbound * dp) # point trajectory bbox bottom-left\n    max_e = np.maximum(np.maximum(e0, e0 + toc_upperbound * de0), np.maximum(e1, e1 + toc_upperbound * de1)) # edge trajectory bbox top-right\n    min_e = np.minimum(np.minimum(e0, e0 + toc_upperbound * de0), np.minimum(e1, e1 + toc_upperbound * de1)) # edge trajectory bbox bottom-left\n    if np.any(np.greater(min_p, max_e)) or np.any(np.greater(min_e, max_p)):\n        return False\n    else:\n        return True\n\n# compute the first \"time\" of contact, or toc,\n# return the computed toc only if it is smaller than the previously computed toc_upperbound\ndef narrow_phase_CCD(_p, _e0, _e1, _dp, _de0, _de1, toc_upperbound):\n    p = deepcopy(_p)\n    e0 = deepcopy(_e0)\n    e1 = deepcopy(_e1)\n    dp = deepcopy(_dp)\n    de0 = deepcopy(_de0)\n    de1 = deepcopy(_de1)\n\n    # use relative displacement for faster convergence\n    mov = (dp + de0 + de1) / 3 \n    de0 -= mov\n    de1 -= mov\n    dp -= mov\n    maxDispMag = np.linalg.norm(dp) + math.sqrt(max(np.dot(de0, de0), np.dot(de1, de1)))\n    if maxDispMag == 0:\n        return toc_upperbound\n\n    eta = 0.1 # calculate the toc that first brings the distance to 0.1x the current distance\n    dist2_cur = PE.val(p, e0, e1)\n    dist_cur = math.sqrt(dist2_cur)\n    gap = eta * dist_cur\n    # iteratively move the point and edge towards each other and\n    # grow the toc estimate without numerical errors\n    toc = 0\n    while True:\n        tocLowerBound = (1 - eta) * dist_cur / maxDispMag\n\n        p += tocLowerBound * dp\n        e0 += tocLowerBound * de0\n        e1 += tocLowerBound * de1\n        dist2_cur = PE.val(p, e0, e1)\n        dist_cur = math.sqrt(dist2_cur)\n        if toc != 0 and dist_cur < gap:\n            break\n\n        toc += tocLowerBound\n        if toc > toc_upperbound:\n            return toc_upperbound\n\n    return toc"
  },
  {
    "path": "8_self_friction/distance/PointEdgeDistance.py",
    "content": "import numpy as np\n\nimport distance.PointPointDistance as PP\nimport distance.PointLineDistance as PL\n\ndef val(p, e0, e1):\n    e = e1 - e0\n    ratio = np.dot(e, p - e0) / np.dot(e, e)\n    if ratio < 0:    # point(p)-point(e0) expression\n        return PP.val(p, e0)\n    elif ratio > 1:  # point(p)-point(e1) expression\n        return PP.val(p, e1)\n    else:            # point(p)-line(e0e1) expression\n        return PL.val(p, e0, e1)\n\ndef grad(p, e0, e1):\n    e = e1 - e0\n    ratio = np.dot(e, p - e0) / np.dot(e, e)\n    if ratio < 0:    # point(p)-point(e0) expression\n        g_PP = PP.grad(p, e0)\n        return np.reshape([g_PP[0:2], g_PP[2:4], np.array([0.0, 0.0])], (1, 6))[0]\n    elif ratio > 1:  # point(p)-point(e1) expression\n        g_PP = PP.grad(p, e1)\n        return np.reshape([g_PP[0:2], np.array([0.0, 0.0]), g_PP[2:4]], (1, 6))[0]\n    else:            # point(p)-line(e0e1) expression\n        return PL.grad(p, e0, e1)\n\ndef hess(p, e0, e1):\n    e = e1 - e0\n    ratio = np.dot(e, p - e0) / np.dot(e, e)\n    if ratio < 0:    # point(p)-point(e0) expression\n        H_PP =  PP.hess(p, e0)\n        return np.array([np.reshape([H_PP[0, 0:2], H_PP[0, 2:4], np.array([0.0, 0.0])], (1, 6))[0], \\\n            np.reshape([H_PP[1, 0:2], H_PP[1, 2:4], np.array([0.0, 0.0])], (1, 6))[0], \\\n            np.reshape([H_PP[2, 0:2], H_PP[2, 2:4], np.array([0.0, 0.0])], (1, 6))[0], \\\n            np.reshape([H_PP[3, 0:2], H_PP[3, 2:4], np.array([0.0, 0.0])], (1, 6))[0], \\\n            np.array([0.0] * 6), \\\n            np.array([0.0] * 6)])\n    elif ratio > 1:  # point(p)-point(e1) expression\n        H_PP = PP.hess(p, e1)\n        return np.array([np.reshape([H_PP[0, 0:2], np.array([0.0, 0.0]), H_PP[0, 2:4]], (1, 6))[0], \\\n            np.reshape([H_PP[1, 0:2], np.array([0.0, 0.0]), H_PP[1, 2:4]], (1, 6))[0], \\\n            np.array([0.0] * 6), \\\n            np.array([0.0] * 6), \\\n            np.reshape([H_PP[2, 0:2], np.array([0.0, 0.0]), H_PP[2, 2:4]], (1, 6))[0], \\\n            np.reshape([H_PP[3, 0:2], np.array([0.0, 0.0]), H_PP[3, 2:4]], (1, 6))[0]])\n    else:            # point(p)-line(e0e1) expression\n        return PL.hess(p, e0, e1)\n\n# ANCHOR: tangent\n# compute normal and the parameterization of the closest point on the edge\ndef tangent(p, e0, e1):\n    e = e1 - e0\n    ratio = np.dot(e, p - e0) / np.dot(e, e)\n    if ratio < 0:    # point(p)-point(e0) expression\n        n = p - e0\n    elif ratio > 1:  # point(p)-point(e1) expression\n        n = p - e1\n    else:            # point(p)-line(e0e1) expression\n        n = p - ((1 - ratio) * e0 + ratio * e1)\n    return [n / np.linalg.norm(n), ratio]\n# ANCHOR_END: tangent"
  },
  {
    "path": "8_self_friction/distance/PointLineDistance.py",
    "content": "import numpy as np\n\ndef val(p, e0, e1):\n    e = e1 - e0\n    numerator = e[1] * p[0] - e[0] * p[1] + e1[0] * e0[1] - e1[1] * e0[0]\n    return numerator * numerator / np.dot(e, e)\n\ndef grad(p, e0, e1):\n    g = np.array([0.0] * 6)\n    t13 = -e1[0] + e0[0]\n    t14 = -e1[1] + e0[1]\n    t23 = 1.0 / (t13 * t13 + t14 * t14)\n    t25 = ((e0[0] * e1[1] + -(e0[1] * e1[0])) + t14 * p[0]) + -(t13 * p[1])\n    t24 = t23 * t23\n    t26 = t25 * t25\n    t27 = (e0[0] * 2.0 + -(e1[0] * 2.0)) * t24 * t26\n    t26 *= (e0[1] * 2.0 + -(e1[1] * 2.0)) * t24\n    g[0] = t14 * t23 * t25 * 2.0\n    g[1] = t13 * t23 * t25 * -2.0\n    t24 = t23 * t25\n    g[2] = -t27 - t24 * (-e1[1] + p[1]) * 2.0\n    g[3] = -t26 + t24 * (-e1[0] + p[0]) * 2.0\n    g[4] = t27 + t24 * (p[1] - e0[1]) * 2.0\n    g[5] = t26 - t24 * (p[0] - e0[0]) * 2.0\n    return g\n\ndef hess(p, e0, e1):\n    H = np.array([0.0] * 36)\n    t15 = -e0[0] + p[0]\n    t16 = -e0[1] + p[1]\n    t17 = -e1[0] + p[0]\n    t18 = -e1[1] + p[1]\n    t19 = -e1[0] + e0[0]\n    t20 = -e1[1] + e0[1]\n    t21 = e0[0] * 2.0 + -(e1[0] * 2.0)\n    t22 = e0[1] * 2.0 + -(e1[1] * 2.0)\n    t23 = t19 * t19\n    t24 = t20 * t20\n    t31 = 1.0 / (t23 + t24)\n    t34 = ((e0[0] * e1[1] + -(e0[1] * e1[0])) + t20 * p[0]) + -(t19 * p[1])\n    t32 = t31 * t31\n    t33 = t32 * t31\n    t35 = t34 * t34\n    t60 = t31 * t34 * 2.0\n    t59 = -(t19 * t20 * t31 * 2.0)\n    t62 = t32 * t35 * 2.0\n    t64 = t21 * t21 * t33 * t35 * 2.0\n    t65 = t22 * t22 * t33 * t35 * 2.0\n    t68 = t15 * t21 * t32 * t34 * 2.0\n    t71 = t16 * t22 * t32 * t34 * 2.0\n    t72 = t17 * t21 * t32 * t34 * 2.0\n    t75 = t18 * t22 * t32 * t34 * 2.0\n    t76 = t19 * t21 * t32 * t34 * 2.0\n    t77 = t20 * t21 * t32 * t34 * 2.0\n    t78 = t19 * t22 * t32 * t34 * 2.0\n    t79 = t20 * t22 * t32 * t34 * 2.0\n    t90 = t21 * t22 * t33 * t35 * 2.0\n    t92 = t16 * t20 * t31 * 2.0 + t77\n    t94 = -(t17 * t19 * t31 * 2.0) + t78\n    t96 = (t18 * t19 * t31 * 2.0 + -t60) + t76\n    t99 = (-(t15 * t20 * t31 * 2.0) + -t60) + t79\n    t93 = t15 * t19 * t31 * 2.0 + -t78\n    t35 = -(t18 * t20 * t31 * 2.0) + -t77\n    t97 = (t17 * t20 * t31 * 2.0 + t60) + -t79\n    t98 = (-(t16 * t19 * t31 * 2.0) + t60) + -t76\n    t100 = ((-(t15 * t16 * t31 * 2.0) + t71) + -t68) + t90\n    t19 = ((-(t17 * t18 * t31 * 2.0) + t75) + -t72) + t90\n    t102_tmp = t17 * t22 * t32 * t34\n    t76 = t15 * t22 * t32 * t34\n    t22 = (((-(t15 * t17 * t31 * 2.0) + t62) + -t65) + t76 * 2.0) + t102_tmp * 2.0\n    t33 = t18 * t21 * t32 * t34\n    t20 = t16 * t21 * t32 * t34\n    t79 = (((-(t16 * t18 * t31 * 2.0) + t62) + -t64) + -(t20 * 2.0)) + -(t33 * 2.0)\n    t77 = (((t15 * t18 * t31 * 2.0 + t60) + t68) + -t75) + -t90\n    t78 = (((t16 * t17 * t31 * 2.0 + -t60) + t72) + -t71) + -t90\n    H[0] = t24 * t31 * 2.0\n    H[1] = t59\n    H[2] = t35\n    H[3] = t97\n    H[4] = t92\n    H[5] = t99\n    H[6] = t59\n    H[7] = t23 * t31 * 2.0\n    H[8] = t96\n    H[9] = t94\n    H[10] = t98\n    H[11] = t93\n    H[12] = t35\n    H[13] = t96\n    t35 = -t62 + t64\n    H[14] = (t35 + t18 * t18 * t31 * 2.0) + t33 * 4.0\n    H[15] = t19\n    H[16] = t79\n    H[17] = t77\n    H[18] = t97\n    H[19] = t94\n    H[20] = t19\n    t33 = -t62 + t65\n    H[21] = (t33 + t17 * t17 * t31 * 2.0) - t102_tmp * 4.0\n    H[22] = t78\n    H[23] = t22\n    H[24] = t92\n    H[25] = t98\n    H[26] = t79\n    H[27] = t78\n    H[28] = (t35 + t16 * t16 * t31 * 2.0) + t20 * 4.0\n    H[29] = t100\n    H[30] = t99\n    H[31] = t93\n    H[32] = t77\n    H[33] = t22\n    H[34] = t100\n    H[35] = (t33 + t15 * t15 * t31 * 2.0) - t76 * 4.0\n    return np.reshape(H, (6, 6))"
  },
  {
    "path": "8_self_friction/distance/PointPointDistance.py",
    "content": "import numpy as np\n\ndef val(p0, p1):\n    e = p0 - p1\n    return np.dot(e, e)\n\ndef grad(p0, p1):\n    e = p0 - p1\n    return np.reshape([2 * e, -2 * e], (1, 4))[0]\n\ndef hess(p0, p1):\n    H = np.array([[0.0] * 4] * 4)\n    H[0, 0] = H[1, 1] = H[2, 2] = H[3, 3] = 2\n    H[0, 2] = H[1, 3] = H[2, 0] = H[3, 1] = -2\n    return H"
  },
  {
    "path": "8_self_friction/readme.md",
    "content": "# Inversion-free Hyperelastic Solids Simulation\n\nTwo squares falling onto the ground under gravity, contacting with each other, and then compressed by a ceiling is simulated with an inversion-free hyperelastic potential and IPC with implicit Euler time integration.\nEach time step is solved by minimizing the Incremental Potential with the projected Newton method.\n\n## Dependencies\n```\npip install numpy scipy pygame\n```\n\n## Run\n```\npython simulator.py\n```"
  },
  {
    "path": "8_self_friction/simulator.py",
    "content": "# FEM Solids Simulation\n\nimport numpy as np  # numpy for linear algebra\nimport pygame       # pygame for visualization\npygame.init()\n\nimport square_mesh   # square mesh\nimport time_integrator\n\n# simulation setup\nside_len = 0.45\nrho = 1000      # density of square\nE = 1e5         # Young's modulus\nnu = 0.4        # Poisson's ratio\nn_seg = 2       # num of segments per side of the square\nh = 0.01        # time step size in s\nDBC = [(n_seg + 1) * (n_seg + 1) * 2]   # dirichlet node index\nDBC_v = [np.array([0.0, -0.5])]         # dirichlet node velocity\nDBC_limit = [np.array([0.0, -0.7])]     # dirichlet node limit position\nground_n = np.array([0.0, 1.0])         # normal of the slope\nground_n /= np.linalg.norm(ground_n)    # normalize ground normal vector just in case\nground_o = np.array([0.0, -1.0])        # a point on the slope  \nmu = 0.4        # friction coefficient of the slope\n\n# initialize simulation\n[x, e] = square_mesh.generate(side_len, n_seg)       # node positions and triangle node indices of the top square\ne = np.append(e, np.array(e) + [len(x)] * 3, axis=0) # add triangle node indices of the bottom square\nx = np.append(x, x + [side_len * 0.1, -side_len * 1.1], axis=0) # add node positions of the bottom square\n[bp, be] = square_mesh.find_boundary(e)             # find boundary points and edges for self-contact\nx = np.append(x, [[0.0, side_len * 0.6]], axis=0)   # ceil origin (with normal [0.0, -1.0])\nv = np.array([[0.0, 0.0]] * len(x))                 # velocity\nm = [rho * side_len * side_len / ((n_seg + 1) * (n_seg + 1))] * len(x)  # calculate node mass evenly\n# rest shape basis, volume, and lame parameters\nvol = [0.0] * len(e)\nIB = [np.array([[0.0, 0.0]] * 2)] * len(e)\nfor i in range(0, len(e)):\n    TB = [x[e[i][1]] - x[e[i][0]], x[e[i][2]] - x[e[i][0]]]\n    vol[i] = np.linalg.det(np.transpose(TB)) / 2\n    IB[i] = np.linalg.inv(np.transpose(TB))\nmu_lame = [0.5 * E / (1 + nu)] * len(e)\nlam = [E * nu / ((1 + nu) * (1 - 2 * nu))] * len(e)\n# identify whether a node is Dirichlet\nis_DBC = [False] * len(x)\nfor i in DBC:\n    is_DBC[i] = True\nDBC_stiff = [1000]  # DBC stiffness, adjusted and warm-started across time steps\ncontact_area = [side_len / n_seg] * len(x)     # perimeter split to each node\n\n# simulation with visualization\nresolution = np.array([900, 900])\noffset = resolution / 2\nscale = 200\ndef screen_projection(x):\n    return [offset[0] + scale * x[0], resolution[1] - (offset[1] + scale * x[1])]\n\ntime_step = 0\nsquare_mesh.write_to_file(time_step, x, e)\nscreen = pygame.display.set_mode(resolution)\nrunning = True\nwhile running:\n    # run until the user asks to quit\n    for event in pygame.event.get():\n        if event.type == pygame.QUIT:\n            running = False\n    \n    print('### Time step', time_step, '###')\n\n    # fill the background and draw the square\n    screen.fill((255, 255, 255))\n    pygame.draw.aaline(screen, (0, 0, 255), screen_projection([ground_o[0] - 3.0 * ground_n[1], ground_o[1] + 3.0 * ground_n[0]]), \n        screen_projection([ground_o[0] + 3.0 * ground_n[1], ground_o[1] - 3.0 * ground_n[0]]))   # ground\n    pygame.draw.aaline(screen, (0, 0, 255), screen_projection([x[-1][0] + 3.0, x[-1][1]]), \n        screen_projection([x[-1][0] - 3.0, x[-1][1]]))   # ceil\n    for eI in e:\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[0]]), screen_projection(x[eI[1]]))\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[1]]), screen_projection(x[eI[2]]))\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[2]]), screen_projection(x[eI[0]]))\n    for xId in range(0, len(x) - 1):\n        xI = x[xId]\n        pygame.draw.circle(screen, (0, 0, 255), screen_projection(xI), 0.1 * side_len / n_seg * scale)\n\n    pygame.display.flip()   # flip the display\n\n    # step forward simulation and wait for screen refresh\n    [x, v] = time_integrator.step_forward(x, e, v, m, vol, IB, mu_lame, lam, ground_n, ground_o, bp, be, contact_area, mu, is_DBC, DBC, DBC_v, DBC_limit, DBC_stiff, h, 1e-2)\n    time_step += 1\n    pygame.time.wait(int(h * 1000))\n    square_mesh.write_to_file(time_step, x, e)\n\npygame.quit()"
  },
  {
    "path": "8_self_friction/square_mesh.py",
    "content": "import numpy as np\nimport os\n\ndef generate(side_length, n_seg):\n    # sample nodes uniformly on a square\n    x = np.array([[0.0, 0.0]] * ((n_seg + 1) ** 2))\n    step = side_length / n_seg\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg + 1):\n            x[i * (n_seg + 1) + j] = [-side_length / 2 + i * step, -side_length / 2 + j * step]\n    \n    # connect the nodes with triangle elements\n    e = []\n    for i in range(0, n_seg):\n        for j in range(0, n_seg):\n            # triangulate each cell following a symmetric pattern:\n            if (i % 2)^(j % 2):\n                e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n                e.append([(i + 1) * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1, i * (n_seg + 1) + j + 1])\n            else:\n                e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1])\n                e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1, i * (n_seg + 1) + j + 1])\n\n    return [x, e]\n\ndef find_boundary(e):\n    # index all half-edges for fast query\n    edge_set = set()\n    for i in range(0, len(e)):\n        for j in range(0, 3):\n            edge_set.add((e[i][j], e[i][(j + 1) % 3]))\n\n    # find boundary points and edges\n    bp_set = set()\n    be = []\n    for eI in edge_set:\n        if (eI[1], eI[0]) not in edge_set:\n            # if the inverse edge of a half-edge does not exist,\n            # then it is a boundary edge\n            be.append([eI[0], eI[1]])\n            bp_set.add(eI[0])\n            bp_set.add(eI[1])\n    return [list(bp_set), be]\n\ndef write_to_file(frameNum, x, e):\n    # Check if 'output' directory exists; if not, create it\n    if not os.path.exists('output'):\n        os.makedirs('output')\n\n    # create obj file\n    filename = f\"output/{frameNum}.obj\"\n    with open(filename, 'w') as f:\n        # write vertex coordinates\n        for row in x:\n            f.write(f\"v {float(row[0]):.6f} {float(row[1]):.6f} 0.0\\n\") \n        # write vertex indices for each triangle\n        for row in e:\n            #NOTE: vertex indices start from 1 in obj file format\n            f.write(f\"f {row[0] + 1} {row[1] + 1} {row[2] + 1}\\n\")"
  },
  {
    "path": "8_self_friction/time_integrator.py",
    "content": "import copy\nfrom cmath import inf\n\nimport numpy as np\nimport numpy.linalg as LA\nimport scipy.sparse as sparse\nfrom scipy.sparse.linalg import spsolve\n\nimport InertiaEnergy\nimport NeoHookeanEnergy\nimport GravityEnergy\nimport BarrierEnergy\nimport FrictionEnergy\nimport SpringEnergy\n\ndef step_forward(x, e, v, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, mu, is_DBC, DBC, DBC_v, DBC_limit, DBC_stiff, h, tol):\n    x_tilde = x + v * h     # implicit Euler predictive position\n    x_n = copy.deepcopy(x)\n    [mu_lambda, mu_lambda_self] = BarrierEnergy.compute_mu_lambda(x, n, o, bp, be, contact_area, mu)  # compute mu * lambda for each node using x^n\n    DBC_target = [] # target position of each DBC in the current time step\n    for i in range(0, len(DBC)):\n        if (DBC_limit[i] - x_n[DBC[i]]).dot(DBC_v[i]) > 0:\n            DBC_target.append(x_n[DBC[i]] + h * DBC_v[i])\n        else:\n            DBC_target.append(x_n[DBC[i]])\n\n    # Newton loop\n    iter = 0\n    E_last = IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, (x - x_n) / h, mu_lambda, mu_lambda_self, DBC, DBC_target, DBC_stiff[0], h)\n    [p, DBC_satisfied] = search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, (x - x_n) / h, mu_lambda, mu_lambda_self, is_DBC, DBC, DBC_target, DBC_stiff[0], tol, h)\n    while (LA.norm(p, inf) / h > tol) | (sum(DBC_satisfied) != len(DBC)):   # also check whether all DBCs are satisfied\n        print('Iteration', iter, ':')\n        print('residual =', LA.norm(p, inf) / h)\n\n        if (LA.norm(p, inf) / h <= tol) & (sum(DBC_satisfied) != len(DBC)):\n            # increase DBC stiffness and recompute energy value record\n            DBC_stiff[0] *= 2\n            E_last = IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, (x - x_n) / h, mu_lambda, mu_lambda_self, DBC, DBC_target, DBC_stiff[0], h)\n\n        # filter line search\n        alpha = min(BarrierEnergy.init_step_size(x, n, o, bp, be, p), NeoHookeanEnergy.init_step_size(x, e, p))  # avoid interpenetration, tunneling, and inversion\n        while IP_val(x + alpha * p, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, (x + alpha * p - x_n) / h, mu_lambda, mu_lambda_self, DBC, DBC_target, DBC_stiff[0], h) > E_last:\n            alpha /= 2\n        print('step size =', alpha)\n\n        x += alpha * p\n        E_last = IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, (x - x_n) / h, mu_lambda, mu_lambda_self, DBC, DBC_target, DBC_stiff[0], h)\n        [p, DBC_satisfied] = search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, (x - x_n) / h, mu_lambda, mu_lambda_self, is_DBC, DBC, DBC_target, DBC_stiff[0], tol, h)\n        iter += 1\n\n    v = (x - x_n) / h   # implicit Euler velocity update\n    return [x, v]\n\ndef IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, v, mu_lambda, mu_lambda_self, DBC, DBC_target, DBC_stiff, h):\n    return InertiaEnergy.val(x, x_tilde, m) + h * h * (     # implicit Euler\n        NeoHookeanEnergy.val(x, e, vol, IB, mu_lame, lam) + \n        GravityEnergy.val(x, m) + \n        BarrierEnergy.val(x, n, o, bp, be, contact_area) + \n        FrictionEnergy.val(v, mu_lambda, mu_lambda_self, h, n)\n    ) + SpringEnergy.val(x, m, DBC, DBC_target, DBC_stiff)\n\ndef IP_grad(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, v, mu_lambda, mu_lambda_self, DBC, DBC_target, DBC_stiff, h):\n    return InertiaEnergy.grad(x, x_tilde, m) + h * h * (    # implicit Euler\n        NeoHookeanEnergy.grad(x, e, vol, IB, mu_lame, lam) + \n        GravityEnergy.grad(x, m) + \n        BarrierEnergy.grad(x, n, o, bp, be, contact_area) + \n        FrictionEnergy.grad(v, mu_lambda, mu_lambda_self, h, n)\n    ) + SpringEnergy.grad(x, m, DBC, DBC_target, DBC_stiff)\n\ndef IP_hess(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, v, mu_lambda, mu_lambda_self, DBC, DBC_target, DBC_stiff, h):\n    IJV_In = InertiaEnergy.hess(x, x_tilde, m)\n    IJV_MS = NeoHookeanEnergy.hess(x, e, vol, IB, mu_lame, lam)\n    IJV_B = BarrierEnergy.hess(x, n, o, bp, be, contact_area)\n    IJV_F = FrictionEnergy.hess(v, mu_lambda, mu_lambda_self, h, n)\n    IJV_S = SpringEnergy.hess(x, m, DBC, DBC_target, DBC_stiff)\n    IJV_MS[2] *= h * h    # implicit Euler\n    IJV_B[2] *= h * h     # implicit Euler\n    IJV_F[2] *= h * h     # implicit Euler\n    IJV_In_MS = np.append(IJV_In, IJV_MS, axis=1)\n    IJV_In_MS_B = np.append(IJV_In_MS, IJV_B, axis=1)\n    IJV_In_MS_B_F = np.append(IJV_In_MS_B, IJV_F, axis=1)\n    IJV = np.append(IJV_In_MS_B_F, IJV_S, axis=1)\n    H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()\n    return H\n\ndef search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, v, mu_lambda, mu_lambda_self, is_DBC, DBC, DBC_target, DBC_stiff, tol, h):\n    projected_hess = IP_hess(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, v, mu_lambda, mu_lambda_self, DBC, DBC_target, DBC_stiff, h)\n    reshaped_grad = IP_grad(x, e, x_tilde, m, vol, IB, mu_lame, lam, n, o, bp, be, contact_area, v, mu_lambda, mu_lambda_self, DBC, DBC_target, DBC_stiff, h).reshape(len(x) * 2, 1)\n    # check whether each DBC is satisfied\n    DBC_satisfied = [False] * len(x)\n    for i in range(0, len(DBC)):\n        if LA.norm(x[DBC[i]] - DBC_target[i]) / h < tol:\n            DBC_satisfied[DBC[i]] = True\n    # eliminate DOF if it's a satisfied DBC by modifying gradient and Hessian for DBC:\n    for i, j in zip(*projected_hess.nonzero()):\n        if (is_DBC[int(i / 2)] & DBC_satisfied[int(i / 2)]) | (is_DBC[int(j / 2)] & DBC_satisfied[int(j / 2)]): \n            projected_hess[i, j] = (i == j)\n    for i in range(0, len(x)):\n        if is_DBC[i] & DBC_satisfied[i]:\n            reshaped_grad[i * 2] = reshaped_grad[i * 2 + 1] = 0.0\n    return [spsolve(projected_hess, -reshaped_grad).reshape(len(x), 2), DBC_satisfied]"
  },
  {
    "path": "8_self_friction/utils.py",
    "content": "import numpy as np\nimport numpy.linalg as LA\nimport math\n\ndef make_PSD(hess):\n    [lam, V] = LA.eigh(hess)    # Eigen decomposition on symmetric matrix\n    # set all negative Eigenvalues to 0\n    for i in range(0, len(lam)):\n        lam[i] = max(0, lam[i])\n    return np.matmul(np.matmul(V, np.diag(lam)), np.transpose(V))\n\ndef smallest_positive_real_root_quad(a, b, c, tol = 1e-6):\n    # return negative value if no positive real root is found\n    t = 0\n    if abs(a) <= tol:\n        if abs(b) <= tol: # f(x) = c > 0 for all x\n            t = -1\n        else:\n            t = -c / b\n    else:\n        desc = b * b - 4 * a * c\n        if desc > 0:\n            t = (-b - math.sqrt(desc)) / (2 * a) # if a > 0, this is either the smaller positive root, or both roots are negative; \n            # if a < 0, there are 1 negative and 1 positive real roots, and we just need the positive one.\n            if t < 0:\n                t = (-b + math.sqrt(desc)) / (2 * a)\n        else: # desv<0 ==> imag, f(x) > 0 for all x > 0\n            t = -1\n    return t"
  },
  {
    "path": "9_reduced_DOF/BarrierEnergy.py",
    "content": "# ANCHOR: val_grad_hess\nimport math\nimport numpy as np\n\ndhat = 0.01\nkappa = 1e5\n\ndef val(x, y_ground, contact_area):\n    sum = 0.0\n    for i in range(0, len(x)):\n        d = x[i][1] - y_ground\n        if d < dhat:\n            s = d / dhat\n            sum += contact_area[i] * dhat * kappa / 2 * (s - 1) * math.log(s)\n    return sum\n\ndef grad(x, y_ground, contact_area):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(x)):\n        d = x[i][1] - y_ground\n        if d < dhat:\n            s = d / dhat\n            g[i][1] = contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d))\n    return g\n\ndef hess(x, y_ground, contact_area):\n    IJV = [[0] * len(x), [0] * len(x), np.array([0.0] * len(x))]\n    for i in range(0, len(x)):\n        IJV[0][i] = i * 2 + 1\n        IJV[1][i] = i * 2 + 1\n        d = x[i][1] - y_ground\n        if d < dhat:\n            IJV[2][i] = contact_area[i] * dhat * kappa / (2 * d * d * dhat) * (d + dhat)\n        else:\n            IJV[2][i] = 0.0\n    return IJV\n# ANCHOR_END: val_grad_hess\n\n# ANCHOR: init_step_size\ndef init_step_size(x, y_ground, p):\n    alpha = 1\n    for i in range(0, len(x)):\n        if p[i][1] < 0:\n            alpha = min(alpha, 0.9 * (y_ground - x[i][1]) / p[i][1])\n    return alpha\n# ANCHOR_END: init_step_size"
  },
  {
    "path": "9_reduced_DOF/GravityEnergy.py",
    "content": "import numpy as np\n\ngravity = [0.0, -9.81]\n\ndef val(x, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        sum += -m[i] * x[i].dot(gravity)\n    return sum\n\ndef grad(x, m):\n    g = np.array([gravity] * len(x))\n    for i in range(0, len(x)):\n        g[i] *= -m[i]\n    return g\n\n# Hessian is 0"
  },
  {
    "path": "9_reduced_DOF/InertiaEnergy.py",
    "content": "import numpy as np\n\ndef val(x, x_tilde, m):\n    sum = 0.0\n    for i in range(0, len(x)):\n        diff = x[i] - x_tilde[i]\n        sum += 0.5 * m[i] * diff.dot(diff)\n    return sum\n\ndef grad(x, x_tilde, m):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(x)):\n        g[i] = m[i] * (x[i] - x_tilde[i])\n    return g\n\ndef hess(x, x_tilde, m):\n    IJV = [[0] * (len(x) * 2), [0] * (len(x) * 2), np.array([0.0] * (len(x) * 2))]\n    for i in range(0, len(x)):\n        for d in range(0, 2):\n            IJV[0][i * 2 + d] = i * 2 + d\n            IJV[1][i * 2 + d] = i * 2 + d\n            IJV[2][i * 2 + d] = m[i]\n    return IJV"
  },
  {
    "path": "9_reduced_DOF/NeoHookeanEnergy.py",
    "content": "# ANCHOR: helper_func\nimport utils\nimport numpy as np\nimport math\n\ndef polar_svd(F):\n    [U, s, VT] = np.linalg.svd(F)\n    if np.linalg.det(U) < 0:\n        U[:, 1] = -U[:, 1]\n        s[1] = -s[1]\n    if np.linalg.det(VT) < 0:\n        VT[1, :] = -VT[1, :]\n        s[1] = -s[1]\n    return [U, s, VT]\n\ndef dPsi_div_dsigma(s, mu, lam):\n    ln_sigma_prod = math.log(s[0] * s[1])\n    inv0 = 1.0 / s[0]\n    dPsi_dsigma_0 = mu * (s[0] - inv0) + lam * inv0 * ln_sigma_prod\n    inv1 = 1.0 / s[1]\n    dPsi_dsigma_1 = mu * (s[1] - inv1) + lam * inv1 * ln_sigma_prod\n    return [dPsi_dsigma_0, dPsi_dsigma_1]\n\ndef d2Psi_div_dsigma2(s, mu, lam):\n    ln_sigma_prod = math.log(s[0] * s[1])\n    inv2_0 = 1 / (s[0] * s[0])\n    d2Psi_dsigma2_00 = mu * (1 + inv2_0) - lam * inv2_0 * (ln_sigma_prod - 1)\n    inv2_1 = 1 / (s[1] * s[1])\n    d2Psi_dsigma2_11 = mu * (1 + inv2_1) - lam * inv2_1 * (ln_sigma_prod - 1)\n    d2Psi_dsigma2_01 = lam / (s[0] * s[1])\n    return [[d2Psi_dsigma2_00, d2Psi_dsigma2_01], [d2Psi_dsigma2_01, d2Psi_dsigma2_11]]\n\ndef B_left_coef(s, mu, lam):\n    sigma_prod = s[0] * s[1]\n    return (mu + (mu - lam * math.log(sigma_prod)) / sigma_prod) / 2\n\ndef Psi(F, mu, lam):\n    J = np.linalg.det(F)\n    lnJ = math.log(J)\n    return mu / 2 * (np.trace(np.transpose(F).dot(F)) - 2) - mu * lnJ + lam / 2 * lnJ * lnJ\n\ndef dPsi_div_dF(F, mu, lam):\n    FinvT = np.transpose(np.linalg.inv(F))\n    return mu * (F - FinvT) + lam * math.log(np.linalg.det(F)) * FinvT\n\ndef d2Psi_div_dF2(F, mu, lam, project_PSD = True):\n    [U, sigma, VT] = polar_svd(F)\n\n    Psi_sigma_sigma = np.array(d2Psi_div_dsigma2(sigma, mu, lam))\n    if project_PSD:\n        Psi_sigma_sigma = utils.make_PSD(Psi_sigma_sigma)\n\n    B_left = B_left_coef(sigma, mu, lam)\n    Psi_sigma = dPsi_div_dsigma(sigma, mu, lam)\n    B_right = (Psi_sigma[0] + Psi_sigma[1]) / (2 * max(sigma[0] + sigma[1], 1e-6))\n    B = np.array([[B_left + B_right, B_left - B_right], [B_left - B_right, B_left + B_right]])\n    if project_PSD:\n        B = utils.make_PSD(B)\n\n    M = np.array([[0, 0, 0, 0]] * 4)\n    M[0, 0] = Psi_sigma_sigma[0, 0]\n    M[0, 3] = Psi_sigma_sigma[0, 1]\n    M[1, 1] = B[0, 0]\n    M[1, 2] = B[0, 1]\n    M[2, 1] = B[1, 0]\n    M[2, 2] = B[1, 1]\n    M[3, 0] = Psi_sigma_sigma[1, 0]\n    M[3, 3] = Psi_sigma_sigma[1, 1]\n\n    dP_div_dF = np.array([[0, 0, 0, 0]] * 4)\n    for j in range(0, 2):\n        for i in range(0, 2):\n            ij = j * 2 + i\n            for s in range(0, 2):\n                for r in range(0, 2):\n                    rs = s * 2 + r\n                    dP_div_dF[ij, rs] = M[0, 0] * U[i, 0] * VT[0, j] * U[r, 0] * VT[0, s] \\\n                        + M[0, 3] * U[i, 0] * VT[0, j] * U[r, 1] * VT[1, s] \\\n                        + M[1, 1] * U[i, 1] * VT[0, j] * U[r, 1] * VT[0, s] \\\n                        + M[1, 2] * U[i, 1] * VT[0, j] * U[r, 0] * VT[1, s] \\\n                        + M[2, 1] * U[i, 0] * VT[1, j] * U[r, 1] * VT[0, s] \\\n                        + M[2, 2] * U[i, 0] * VT[1, j] * U[r, 0] * VT[1, s] \\\n                        + M[3, 0] * U[i, 1] * VT[1, j] * U[r, 0] * VT[0, s] \\\n                        + M[3, 3] * U[i, 1] * VT[1, j] * U[r, 1] * VT[1, s]\n    return dP_div_dF\n# ANCHOR_END: helper_func\n\n# ANCHOR: stress_deriv\ndef deformation_grad(x, elemVInd, IB):\n    F = [x[elemVInd[1]] - x[elemVInd[0]], x[elemVInd[2]] - x[elemVInd[0]]]\n    return np.transpose(F).dot(IB)\n\ndef dPsi_div_dx(P, IB):  # applying chain-rule, dPsi_div_dx = dPsi_div_dF * dF_div_dx\n    dPsi_dx_2 = P[0, 0] * IB[0, 0] + P[0, 1] * IB[0, 1]\n    dPsi_dx_3 = P[1, 0] * IB[0, 0] + P[1, 1] * IB[0, 1]\n    dPsi_dx_4 = P[0, 0] * IB[1, 0] + P[0, 1] * IB[1, 1]\n    dPsi_dx_5 = P[1, 0] * IB[1, 0] + P[1, 1] * IB[1, 1]\n    return [np.array([-dPsi_dx_2 - dPsi_dx_4, -dPsi_dx_3 - dPsi_dx_5]), np.array([dPsi_dx_2, dPsi_dx_3]), np.array([dPsi_dx_4, dPsi_dx_5])]\n\ndef d2Psi_div_dx2(dP_div_dF, IB):  # applying chain-rule, d2Psi_div_dx2 = dF_div_dx^T * d2Psi_div_dF2 * dF_div_dx (note that d2F_div_dx2 = 0)\n    intermediate = np.array([[0.0, 0.0, 0.0, 0.0]] * 6)\n    for colI in range(0, 4):\n        _000 = dP_div_dF[0, colI] * IB[0, 0]\n        _010 = dP_div_dF[0, colI] * IB[1, 0]\n        _101 = dP_div_dF[2, colI] * IB[0, 1]\n        _111 = dP_div_dF[2, colI] * IB[1, 1]\n        _200 = dP_div_dF[1, colI] * IB[0, 0]\n        _210 = dP_div_dF[1, colI] * IB[1, 0]\n        _301 = dP_div_dF[3, colI] * IB[0, 1]\n        _311 = dP_div_dF[3, colI] * IB[1, 1]\n        intermediate[2, colI] = _000 + _101\n        intermediate[3, colI] = _200 + _301\n        intermediate[4, colI] = _010 + _111\n        intermediate[5, colI] = _210 + _311\n        intermediate[0, colI] = -intermediate[2, colI] - intermediate[4, colI]\n        intermediate[1, colI] = -intermediate[3, colI] - intermediate[5, colI]\n    result = np.array([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]] * 6)\n    for colI in range(0, 6):\n        _000 = intermediate[colI, 0] * IB[0, 0]\n        _010 = intermediate[colI, 0] * IB[1, 0]\n        _101 = intermediate[colI, 2] * IB[0, 1]\n        _111 = intermediate[colI, 2] * IB[1, 1]\n        _200 = intermediate[colI, 1] * IB[0, 0]\n        _210 = intermediate[colI, 1] * IB[1, 0]\n        _301 = intermediate[colI, 3] * IB[0, 1]\n        _311 = intermediate[colI, 3] * IB[1, 1]\n        result[2, colI] = _000 + _101\n        result[3, colI] = _200 + _301\n        result[4, colI] = _010 + _111\n        result[5, colI] = _210 + _311\n        result[0, colI] = -_000 - _101 - _010 - _111\n        result[1, colI] = -_200 - _301 - _210 - _311\n    return result\n# ANCHOR_END: stress_deriv\n\n# ANCHOR: val_grad_hess\ndef val(x, e, vol, IB, mu, lam):\n    sum = 0.0\n    for i in range(0, len(e)):\n        F = deformation_grad(x, e[i], IB[i])\n        sum += vol[i] * Psi(F, mu[i], lam[i])\n    return sum\n\ndef grad(x, e, vol, IB, mu, lam):\n    g = np.array([[0.0, 0.0]] * len(x))\n    for i in range(0, len(e)):\n        F = deformation_grad(x, e[i], IB[i])\n        P = vol[i] * dPsi_div_dF(F, mu[i], lam[i])\n        g_local = dPsi_div_dx(P, IB[i])\n        for j in range(0, 3):\n            g[e[i][j]] += g_local[j]\n    return g\n\ndef hess(x, e, vol, IB, mu, lam, project_PSD = True):\n    IJV = [[0] * (len(e) * 36), [0] * (len(e) * 36), np.array([0.0] * (len(e) * 36))]\n    for i in range(0, len(e)):\n        F = deformation_grad(x, e[i], IB[i])\n        dP_div_dF = vol[i] * d2Psi_div_dF2(F, mu[i], lam[i], project_PSD)\n        local_hess = d2Psi_div_dx2(dP_div_dF, IB[i])\n        for xI in range(0, 3):\n            for xJ in range(0, 3):\n                for dI in range(0, 2):\n                    for dJ in range(0, 2):\n                        ind = i * 36 + (xI * 3 + xJ) * 4 + dI * 2 + dJ\n                        IJV[0][ind] = e[i][xI] * 2 + dI\n                        IJV[1][ind] = e[i][xJ] * 2 + dJ\n                        IJV[2][ind] = local_hess[xI * 2 + dI, xJ * 2 + dJ]\n    return IJV\n# ANCHOR_END: val_grad_hess\n\n# ANCHOR: filter_line_search\ndef init_step_size(x, e, p):\n    alpha = 1\n    for i in range(0, len(e)):\n        x21 = x[e[i][1]] - x[e[i][0]]\n        x31 = x[e[i][2]] - x[e[i][0]]\n        p21 = p[e[i][1]] - p[e[i][0]]\n        p31 = p[e[i][2]] - p[e[i][0]]\n        detT = np.linalg.det(np.transpose([x21, x31]))\n        a = np.linalg.det(np.transpose([p21, p31])) / detT\n        b = (np.linalg.det(np.transpose([x21, p31])) + np.linalg.det(np.transpose([p21, x31]))) / detT\n        c = 0.9  # solve for alpha that first brings the new volume to 0.1x the old volume for slackness\n        critical_alpha = utils.smallest_positive_real_root_quad(a, b, c)\n        if critical_alpha > 0:\n            alpha = min(alpha, critical_alpha)\n    return alpha\n# ANCHOR_END: filter_line_search"
  },
  {
    "path": "9_reduced_DOF/linear.py",
    "content": "\n\"\"\"\n2D Modal Analysis with Combined Animation of Mode Shapes\n\nThis program performs a dynamic modal analysis of a 2D vertical cantilever beam\nusing 4-node quadrilateral finite elements under a plane stress assumption.\nThe first 6 eigenmodes are computed and visualized side-by-side in a single\nanimated GIF, showing the harmonic motion of each mode over time.\n\nAuthor: Žiga Kovačič\nDate: 2025-06-22\n\"\"\"\n\nimport numpy as np\nfrom scipy.sparse import lil_matrix\nfrom scipy.sparse.linalg import eigsh\nimport matplotlib.pyplot as plt\nimport matplotlib.tri as tri\nimport matplotlib.animation as animation\nimport time\n\n# Problem parameters\nL = 15.0  # Length (now vertical)\nH = 1.0   # Height (now horizontal width)\nt = 0.1   # Thickness\n\n# Material properties\nE = 5e7   # Young's modulus\nnu = 0.3  # Poisson's ratio\nrho = 500 # Density\n\n# Mesh discretization\nNel_L = 30 # Elements along the length\nNel_H = 5  # Elements along the height\n\nprint(f\"Solving with a 2D mesh: {Nel_H}x{Nel_L} elements for a vertical beam.\")\n\ndef generate_2d_mesh(L_mesh, H_mesh, Nx_mesh, Ny_mesh):\n    \"\"\"Generate structured grid of nodes and quadrilateral elements.\"\"\"\n    x_coords = np.linspace(0, L_mesh, Nx_mesh + 1)\n    y_coords = np.linspace(0, H_mesh, Ny_mesh + 1)\n    nodes_x, nodes_y = np.meshgrid(x_coords, y_coords)\n    nodes = np.vstack([nodes_x.ravel(), nodes_y.ravel()]).T\n\n    elements = []\n    for j in range(Ny_mesh):\n        for i in range(Nx_mesh):\n            n0, n1 = j * (Nx_mesh + 1) + i, j * (Nx_mesh + 1) + (i + 1)\n            n2, n3 = (j + 1) * (Nx_mesh + 1) + i, (j + 1) * (Nx_mesh + 1) + (i + 1)\n            elements.append([n0, n1, n3, n2])\n    return nodes, np.array(elements)\n\ndef get_element_matrices(element_nodes, D, rho, t):\n    r\"\"\"\n    Compute stiffness (K) and mass (M) matrices for a 4-node quad element.\n    This function computes the building blocks for the global M and K matrices\n    required by the PDF's Equation (2): $M \\ddot{u} + D \\dot{u} + K u = f$.\n    \"\"\"\n    \n    # The integrals for k_e and m_e are computed numerically using Gaussian Quadrature.\n    # The method approximates an integral over the standard interval [-1, 1] as:\n    # $\\int_{-1}^{1} g(x) dx \\approx \\sum_{i=1}^{n} w_i g(x_i)$\n    # We use the 2-point Gauss-Legendre rule (n=2), which is exact for polynomials up to degree 2n-1=3.\n\n    # Gauss point coordinate $\\xi_i, \\eta_i = \\pm 1/\\sqrt{3}$ for 2x2 numerical integration.\n    gp = 1.0 / np.sqrt(3) \n\n    gauss_points = np.array([[-gp, -gp], [gp, -gp], [gp, gp], [-gp, gp]])\n\n    # Initialize element stiffness $k_e$ and mass $m_e$ matrices\n    k_e, m_e = np.zeros((8, 8)), np.zeros((8, 8))\n\n    # loop over the 4 Gauss points to perform numerical integration.\n    for i in range(4):\n        xi, eta = gauss_points[i]\n\n        # derivatives of shape functions w.r.t. natural coords $(\\xi,\\eta)$:\n        # dN_dxi_eta corresponds to the matrix $[\\partial N / \\partial \\xi, \\partial N / \\partial \\eta]^T$\n        dN_dxi_eta = 0.25 * np.array([\n            [-(1 - eta), (1 - eta), (1 + eta), -(1 + eta)],\n            [-(1 - xi), -(1 + xi), (1 + xi), (1 - xi)]\n        ])\n\n        # Jacobian matrix: $J = \\frac{\\partial(x,y)}{\\partial(\\xi,\\eta)}$\n        J = dN_dxi_eta @ element_nodes\n        # $dA = \\det(J) d\\xi d\\eta$\n        detJ = np.linalg.det(J)\n        # derivatives of shape functions w.r.t. real coords $(x,y)$: $[\\partial N / \\partial x, \\partial N / \\partial y]^T = J^{-1} [\\partial N / \\partial \\xi, \\partial N / \\partial \\eta]^T$\n        dN_dxy = np.linalg.inv(J) @ dN_dxi_eta\n\n        # Form the strain-displacement matrix $B$, which defines strain: $\\varepsilon = B d$\n        B = np.zeros((3, 8))\n        for j in range(4):\n            B[0, 2*j], B[1, 2*j + 1] = dN_dxy[0, j], dN_dxy[1, j]\n            B[2, 2*j], B[2, 2*j + 1] = dN_dxy[1, j], dN_dxy[0, j]\n\n        # Approximate the stiffness matrix integral: $k_e = \\int_A (B^T D B) t \\, dA$\n        # by calculating one term in the Gauss quadrature sum: $(B^T D B) \\cdot (t \\cdot \\det(J)) \\cdot w_i$, where again $w_i=1$.\n        k_e += B.T @ D @ B * detJ * t\n\n        # Shape function matrix $N$, for interpolating displacement: $u(x,y) = N d$\n        N_shape = 0.25 * (1 + np.array([-1, 1, 1, -1])*xi) * (1 + np.array([-1, -1, 1, 1])*eta)\n        N_mat = np.zeros((2, 8))\n        for j in range(4):\n            N_mat[0, 2*j] = N_mat[1, 2*j+1] = N_shape[j]\n        \n        # Approximate the mass matrix integral: $m_e = \\int_A (\\rho N^T N) t \\, dA$\n        # by calculating one term in the sum: $(\\rho N^T N) \\cdot (t \\cdot \\det(J)) \\cdot w_i$, where again $w_i=1$.\n        m_e += rho * t * N_mat.T @ N_mat * detJ\n\n    return k_e, m_e\n\nstart_time = time.time()\n\n# Generate mesh for a vertical beam (width H, length L)\nnodes, elements = generate_2d_mesh(H, L, Nel_H, Nel_L)\nn_nodes, n_dof = nodes.shape[0], 2 * nodes.shape[0]\n\n# Plane stress constitutive matrix, defines stress-strain relationship\nD = (E / (1 - nu**2)) * np.array([[1, nu, 0], [nu, 1, 0], [0, 0, (1 - nu) / 2]])\n\nK_global = lil_matrix((n_dof, n_dof))\nM_global = lil_matrix((n_dof, n_dof))\n\nprint(\"Assembling global matrices...\")\nfor el_nodes_indices in elements:\n    k_e, m_e = get_element_matrices(nodes[el_nodes_indices], D, rho, t)\n    dof_indices = np.ravel([[2*n, 2*n+1] for n in el_nodes_indices])\n    K_global[np.ix_(dof_indices, dof_indices)] += k_e\n    M_global[np.ix_(dof_indices, dof_indices)] += m_e\n \nK_global, M_global = K_global.tocsr(), M_global.tocsr() # Convert to CSR format for efficient operations\n\n# Apply boundary conditions \n# Vertical beam fixed at the bottom (y=0)\nclamped_nodes = np.where(nodes[:, 1] < 1e-9)[0]\nclamped_dofs = np.ravel([[2*n, 2*n+1] for n in clamped_nodes])\nfree_dofs = np.setdiff1d(np.arange(n_dof), clamped_dofs)\n\n# Compute reduced matrices\nK_reduced = K_global[np.ix_(free_dofs, free_dofs)]\nM_reduced = M_global[np.ix_(free_dofs, free_dofs)]\n\n# Solve eigenvalue problem\n# Equation: K_reduced * psi = lambda * M_reduced * psi\nN_eig = 8\nprint(f\"Solving eigenvalue problem for {N_eig} modes...\")\n\neigenvalues, eigenvectors_reduced = eigsh(K_reduced, k=N_eig, M=M_reduced, sigma=0, which='LM')\nangular_freq = np.sqrt(np.abs(eigenvalues))\nfrequencies = angular_freq / (2 * np.pi) \n\n# Reconstruct full eigenvectors, zero out fixed DOFs\neigenvectors = np.zeros((n_dof, N_eig)) \neigenvectors[free_dofs, :] = eigenvectors_reduced\n\nassembly_time = time.time() - start_time\nprint(f\"Assembly and solution took {assembly_time:.2f} seconds.\")\n\nprint(\"\\nComputed Frequencies (Hz):\")\nfor i in range(N_eig):\n    print(f\"Mode {i+1}: {frequencies[i]:.2f} Hz\")\n\n\n# ---------------------\n# --- Visualization ---\n# ---------------------\nprint(\"\\nGenerating combined mode animation...\")\n\nnum_modes_to_animate = 6\nanimation_duration = 4.0\nfps = 20\nnum_frames = int(animation_duration * fps)\ndisplacement_scale = L * 0.15 # Scale displacements for better visibility\n\nfig, axes = plt.subplots(1, num_modes_to_animate, figsize=(7.5, 4))\n\ntriangles = []\nfor el in elements:\n    triangles.append([el[0], el[1], el[3]])\n    triangles.append([el[1], el[2], el[3]])\ntriang = tri.Triangulation(nodes[:, 0], nodes[:, 1], triangles)\n\nall_deformed_nodes = []\nfor i in range(num_modes_to_animate):\n    if i >= N_eig: break\n    psi = eigenvectors[:, i]\n    max_disp_shape = (psi.reshape(-1, 2) / np.max(np.abs(psi))) * displacement_scale\n    all_deformed_nodes.append(nodes + max_disp_shape)\n    all_deformed_nodes.append(nodes - max_disp_shape)\n\nall_deformed_nodes = np.vstack(all_deformed_nodes)\nx_min, y_min = all_deformed_nodes.min(axis=0)\nx_max, y_max = all_deformed_nodes.max(axis=0)\nx_range, y_range = x_max - x_min, y_max - y_min\nfixed_xlim = [x_min - 0.1 * x_range, x_max + 0.1 * x_range]\nfixed_ylim = [y_min - 0.1 * y_range, y_max + 0.1 * y_range]\n\nvmax_values = []\nfor i in range(num_modes_to_animate):\n    psi = eigenvectors[:, i]\n    psi_normalized = psi / np.max(np.abs(psi))\n    disp_mag_static = np.sqrt(psi_normalized.reshape(-1, 2)[:, 0]**2 + psi_normalized.reshape(-1, 2)[:, 1]**2)\n    vmax_values.append(np.max(disp_mag_static) * displacement_scale)\n\ndef animate(frame):\n    t_current = frame / fps\n    for i, ax in enumerate(axes):\n        if i >= N_eig: \n            ax.axis('off')\n            continue\n\n        ax.clear()\n        ax.set_xlim(fixed_xlim)\n        ax.set_ylim(fixed_ylim)\n        ax.set_aspect('equal')\n        \n        ax.triplot(triang, '--', color='gray', linewidth=0.25)\n        \n        psi = eigenvectors[:, i]\n        omega = angular_freq[i]\n        \n        # Normalize eigenvector so max displacement is displacement_scale\n        psi_normalized = psi / np.max(np.abs(psi))\n        \n        scale_factor = np.sin(omega * t_current)\n        current_disp = psi_normalized.reshape(-1, 2) * scale_factor * displacement_scale\n        deformed_nodes = nodes + current_disp\n        \n        disp_mag_instant = np.sqrt(current_disp[:, 0]**2 + current_disp[:, 1]**2)\n        \n        tpc = ax.tripcolor(deformed_nodes[:, 0], deformed_nodes[:, 1], triang.triangles,\n                          facecolors=disp_mag_instant[triang.triangles].mean(axis=1),\n                          edgecolors='k', cmap='viridis', linewidth=0.5,\n                          vmin=0, vmax=vmax_values[i])\n                          \n        ax.set_title(f'Mode {i+1}\\n{frequencies[i]:.2f} Hz', fontsize=7.5)\n        ax.set_xticks([])\n        ax.set_yticks([])\n\n    if axes[0]:\n        axes[0].set_ylabel('Y-Position (m)')\n    fig.supxlabel('Mode Shapes', y=0.05)\n    \n    return [artist for ax in axes for artist in ax.get_children() if isinstance(artist, plt.Artist)]\n\nani = animation.FuncAnimation(fig, animate, frames=num_frames, interval=1000/fps, blit=False)\nfig.tight_layout(rect=[0, 0.05, 1, 1]) \n\nfilename = f\"modes_1-{num_modes_to_animate}_combined_animation.gif\"\nprint(f\"Saving combined animation for Modes 1-{num_modes_to_animate} to '{filename}'...\")\nani.save(filename, writer='pillow', fps=fps)\nplt.close(fig)\n\nprint(\"All animations generated.\")"
  },
  {
    "path": "9_reduced_DOF/readme.md",
    "content": "# Reduced Simulation of Neo-Hookean Solids \n\nA square falling onto the ground under gravity is simulated using neo-Hookean elasticity and implicit Euler time integration in the reduced solution space constructed via polynomial functions or modal-order reduction.\nEach time step is solved by minimizing the Incremental Potential with the projected Newton method.\n\n![results](results.gif)\n\n## Dependencies\n```\npip install numpy scipy pygame\n```\n\n## Run\n```\npython simulator.py\n```"
  },
  {
    "path": "9_reduced_DOF/simulator.py",
    "content": "# Mass-Spring Solids Simulation\n\nimport numpy as np  # numpy for linear algebra\nimport pygame       # pygame for visualization\npygame.init()\n\nimport math \nimport utils\nimport square_mesh   # square mesh\nimport time_integrator\n\n# simulation setup\nside_len = 1\nrho = 1000          # density of square\nE = 2e4             # Young's modulus\nnu = 0.4            # Poisson's ratio\nn_seg = 10          # num of segments per side of the square\nh = 0.01            # time step size in s\nDBC = []            # no nodes need to be fixed\ny_ground = -1       # height of the planar ground\ndraw_abd = True     # whether to draw the embedding mesh for ABD \n\n# initialize simulation\n[x, e] = square_mesh.generate(side_len, n_seg)  # node positions and edge node indices\nv = np.array([[0.0, 0.0]] * len(x))             # velocity\nm = [rho * side_len * side_len / ((n_seg + 1) * (n_seg + 1))] * len(x)  # calculate node mass evenly\n# ANCHOR: elem_precomp\n# rest shape basis, volume, and lame parameters\nvol = [0.0] * len(e)\nIB = [np.array([[0.0, 0.0]] * 2)] * len(e)\nfor i in range(0, len(e)):\n    TB = [x[e[i][1]] - x[e[i][0]], x[e[i][2]] - x[e[i][0]]]\n    vol[i] = np.linalg.det(np.transpose(TB)) / 2\n    IB[i] = np.linalg.inv(np.transpose(TB))\nmu_lame = [0.5 * E / (1 + nu)] * len(e)\nlam = [E * nu / ((1 + nu) * (1 - 2 * nu))] * len(e)\n# ANCHOR_END: elem_precomp\n# identify whether a node is Dirichlet\nis_DBC = [False] * len(x)\nfor i in DBC:\n    is_DBC[i] = True\n# ANCHOR: contact_area\ncontact_area = [side_len / n_seg] * len(x)     # perimeter split to each node\n# ANCHOR_END: contact_area\n# compute reduced basis using 0: no reduction; 1: polynomial functions; 2: modal reduction\nmethod = 1\norder = 1\nreduced_basis = utils.compute_reduced_basis(x, e, vol, IB, mu_lame, lam, method, order)\nabd_anchor_basis = utils.compute_abd_anchor_basis(x)\n\n# simulation with visualization\nresolution = np.array([900, 900])\noffset = resolution / 2\nscale = 200\ndef screen_projection(x):\n    return [offset[0] + scale * x[0], resolution[1] - (offset[1] + scale * x[1])]\n\ntime_step = 0\nsquare_mesh.write_to_file(time_step, x, e)\nscreen = pygame.display.set_mode(resolution)\nrunning = True\nwhile running:\n    # run until the user asks to quit\n    for event in pygame.event.get():\n        if event.type == pygame.QUIT:\n            running = False\n    \n    print('### Time step', time_step, '###')\n\n    # fill the background and draw the square\n    screen.fill((255, 255, 255))\n    pygame.draw.aaline(screen, (0, 0, 255), screen_projection([-2, y_ground]), screen_projection([2, y_ground]))   # ground\n    # draw abd \n    if draw_abd and method == 1 and order == 1: \n        for i in range(3):\n            reduced_vars = np.linalg.solve(np.transpose(reduced_basis) @ reduced_basis, np.transpose(reduced_basis) @ x.reshape(-1))\n            abd_anchors = abd_anchor_basis @ reduced_vars\n            pygame.draw.circle(screen, (255, 0, 0), screen_projection(abd_anchors[2 * i: 2 * i + 2]), 0.1 * side_len / n_seg * scale)\n        pygame.draw.aaline(screen, (255, 0, 0), screen_projection(abd_anchors[0:2]), screen_projection(abd_anchors[2:4]))\n        pygame.draw.aaline(screen, (255, 0, 0), screen_projection(abd_anchors[2:4]), screen_projection(abd_anchors[4:6]))\n        pygame.draw.aaline(screen, (255, 0, 0), screen_projection(abd_anchors[4:6]), screen_projection(abd_anchors[0:2]))\n    for eI in e:\n        # ANCHOR: draw_tri\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[0]]), screen_projection(x[eI[1]]))\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[1]]), screen_projection(x[eI[2]]))\n        pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[2]]), screen_projection(x[eI[0]]))\n        # ANCHOR_END: draw_tri\n    for xI in x:\n        pygame.draw.circle(screen, (0, 0, 255), screen_projection(xI), 0.1 * side_len / n_seg * scale)\n\n    pygame.display.flip()   # flip the display\n\n    # step forward simulation and wait for screen refresh\n    [x, v] = time_integrator.step_forward(x, e, v, m, vol, IB, mu_lame, lam, y_ground, contact_area, is_DBC, reduced_basis, h, 1e-2)\n    time_step += 1\n    pygame.time.wait(int(h * 1000))\n    square_mesh.write_to_file(time_step, x, e)\n\npygame.quit()"
  },
  {
    "path": "9_reduced_DOF/square_mesh.py",
    "content": "import numpy as np\nimport os\n\ndef generate(side_length, n_seg):\n    # sample nodes uniformly on a square\n    x = np.array([[0.0, 0.0]] * ((n_seg + 1) ** 2))\n    step = side_length / n_seg\n    for i in range(0, n_seg + 1):\n        for j in range(0, n_seg + 1):\n            x[i * (n_seg + 1) + j] = [-side_length / 2 + i * step, -side_length / 2 + j * step]\n    \n    # ANCHOR: tri_vert_ind\n    # connect the nodes with triangle elements\n    e = []\n    for i in range(0, n_seg):\n        for j in range(0, n_seg):\n            # triangulate each cell following a symmetric pattern:\n            if (i % 2)^(j % 2):\n                e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j, i * (n_seg + 1) + j + 1])\n                e.append([(i + 1) * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1, i * (n_seg + 1) + j + 1])\n            else:\n                e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1])\n                e.append([i * (n_seg + 1) + j, (i + 1) * (n_seg + 1) + j + 1, i * (n_seg + 1) + j + 1])\n    # ANCHOR_END: tri_vert_ind\n\n    return [x, e]\n\ndef write_to_file(frameNum, x, e):\n    # Check if 'output' directory exists; if not, create it\n    if not os.path.exists('output'):\n        os.makedirs('output')\n\n    # create obj file\n    filename = f\"output/{frameNum}.obj\"\n    with open(filename, 'w') as f:\n        # write vertex coordinates\n        for row in x:\n            f.write(f\"v {float(row[0]):.6f} {float(row[1]):.6f} 0.0\\n\") \n        # write vertex indices for each triangle\n        for row in e:\n            #NOTE: vertex indices start from 1 in obj file format\n            f.write(f\"f {row[0] + 1} {row[1] + 1} {row[2] + 1}\\n\")"
  },
  {
    "path": "9_reduced_DOF/time_integrator.py",
    "content": "import copy\nfrom cmath import inf\n\nimport numpy as np\nimport numpy.linalg as LA\nimport scipy.sparse as sparse\nfrom scipy.sparse.linalg import spsolve\n\nimport InertiaEnergy\nimport NeoHookeanEnergy\nimport GravityEnergy\nimport BarrierEnergy\n\ndef step_forward(x, e, v, m, vol, IB, mu_lame, lam, y_ground, contact_area, is_DBC, reduced_basis, h, tol):\n    x_tilde = x + v * h     # implicit Euler predictive position\n    x_n = copy.deepcopy(x)\n\n    # Newton loop\n    iter = 0\n    E_last = IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, h)\n    p = search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, is_DBC, reduced_basis, h)\n    while LA.norm(p, inf) / h > tol:\n        print('Iteration', iter, ':')\n        print('residual =', LA.norm(p, inf) / h)\n\n        # ANCHOR: filter_ls\n        # filter line search\n        alpha = BarrierEnergy.init_step_size(x, y_ground, p)  # avoid interpenetration and tunneling\n        while IP_val(x + alpha * p, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, h) > E_last:\n            alpha /= 2\n        # ANCHOR_END: filter_ls\n        print('step size =', alpha)\n\n        x += alpha * p\n        E_last = IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, h)\n        p = search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, is_DBC, reduced_basis, h)\n        iter += 1\n\n    v = (x - x_n) / h   # implicit Euler velocity update\n    return [x, v]\n\ndef IP_val(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, h):\n    return InertiaEnergy.val(x, x_tilde, m) + h * h * (NeoHookeanEnergy.val(x, e, vol, IB, mu_lame, lam) + GravityEnergy.val(x, m) + BarrierEnergy.val(x, y_ground, contact_area))     # implicit Euler\n\ndef IP_grad(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, h):\n    return InertiaEnergy.grad(x, x_tilde, m) + h * h * (NeoHookeanEnergy.grad(x, e, vol, IB, mu_lame, lam) + GravityEnergy.grad(x, m) + BarrierEnergy.grad(x, y_ground, contact_area))   # implicit Euler\n\ndef IP_hess(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, h):\n    IJV_In = InertiaEnergy.hess(x, x_tilde, m)\n    IJV_MS = NeoHookeanEnergy.hess(x, e, vol, IB, mu_lame, lam)\n    IJV_B = BarrierEnergy.hess(x, y_ground, contact_area)\n    IJV_MS[2] *= h * h    # implicit Euler\n    IJV_B[2] *= h * h     # implicit Euler\n    IJV_In_MS = np.append(IJV_In, IJV_MS, axis=1)\n    IJV = np.append(IJV_In_MS, IJV_B, axis=1)\n    H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()\n    return H\n\n# ANCHOR: search_dir\ndef search_dir(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, is_DBC, reduced_basis, h):\n    projected_hess = IP_hess(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, h)\n    reshaped_grad = IP_grad(x, e, x_tilde, m, vol, IB, mu_lame, lam, y_ground, contact_area, h).reshape(len(x) * 2, 1)\n    # eliminate DOF by modifying gradient and Hessian for DBC:\n    for i, j in zip(*projected_hess.nonzero()):\n        if is_DBC[int(i / 2)] | is_DBC[int(j / 2)]: \n            projected_hess[i, j] = (i == j)\n    for i in range(0, len(x)):\n        if is_DBC[i]:\n            reshaped_grad[i * 2] = reshaped_grad[i * 2 + 1] = 0.0\n    reduced_hess = reduced_basis.T.dot(projected_hess.dot(reduced_basis)) # applying chain rule\n    reduced_grad = reduced_basis.T.dot(reshaped_grad) # applying chain rule\n    return (reduced_basis.dot(spsolve(reduced_hess, -reduced_grad))).reshape(len(x), 2) # transform to full space after the solve\n# ANCHOR_END: search_dir"
  },
  {
    "path": "9_reduced_DOF/utils.py",
    "content": "import math\nimport numpy as np\nimport numpy.linalg as LA\n\nimport scipy.sparse as sparse\nfrom scipy.sparse.linalg import eigsh\n\nimport NeoHookeanEnergy\n\ndef make_PSD(hess):\n    [lam, V] = LA.eigh(hess)    # Eigen decomposition on symmetric matrix\n    # set all negative Eigenvalues to 0\n    for i in range(0, len(lam)):\n        lam[i] = max(0, lam[i])\n    return np.matmul(np.matmul(V, np.diag(lam)), np.transpose(V))\n\n# ANCHOR: find_positive_real_root\ndef smallest_positive_real_root_quad(a, b, c, tol = 1e-6):\n    # return negative value if no positive real root is found\n    t = 0\n    if abs(a) <= tol:\n        if abs(b) <= tol: # f(x) = c > 0 for all x\n            t = -1\n        else:\n            t = -c / b\n    else:\n        desc = b * b - 4 * a * c\n        if desc > 0:\n            t = (-b - math.sqrt(desc)) / (2 * a) # if a > 0, this is either the smaller positive root, or both roots are negative; \n            # if a < 0, there are 1 negative and 1 positive real roots, and we just need the positive one.\n            if t < 0:\n                t = (-b + math.sqrt(desc)) / (2 * a)\n        else: # desv<0 ==> imag, f(x) > 0 for all x > 0\n            t = -1\n    return t\n# ANCHOR_END: find_positive_real_root\n\ndef compute_abd_anchor_basis(x):\n    c = x.mean(axis=0)\n    diag = np.linalg.norm(x.max(axis=0) - x.min(axis=0))\n    scale = diag / math.sqrt(2)\n    c -= 1/3 * scale\n    anchors = np.stack([c, c + np.asarray([scale, 0]), c + np.asarray([0, scale])], axis=0)\n\n    basis = np.zeros((len(anchors) * 2, 6)) # 1, x, y for both x- and y-displacements\n    for i in range(len(anchors)):\n        for d in range(2):\n            basis[i * 2 + d][d * 3] = 1\n            basis[i * 2 + d][d * 3 + 1] = anchors[i][0]\n            basis[i * 2 + d][d * 3 + 2] = anchors[i][1]\n    return basis\n\n# ANCHOR: compute_reduced_basis\ndef compute_reduced_basis(x, e, vol, IB, mu_lame, lam, method, order):\n    if method == 0: # full basis, no reduction\n        basis = np.zeros((len(x) * 2, len(x) * 2))\n        for i in range(len(x) * 2):\n            basis[i][i] = 1\n        return basis\n    elif method == 1: # polynomial basis\n        if order == 1: # linear basis, or affine basis\n            basis = np.zeros((len(x) * 2, 6)) # 1, x, y for both x- and y-displacements\n            for i in range(len(x)):\n                for d in range(2):\n                    basis[i * 2 + d][d * 3] = 1\n                    basis[i * 2 + d][d * 3 + 1] = x[i][0]\n                    basis[i * 2 + d][d * 3 + 2] = x[i][1]\n        elif order == 2: # quadratic polynomial basis \n            basis = np.zeros((len(x) * 2, 12)) # 1, x, y, x^2, xy, y^2 for both x- and y-displacements\n            for i in range(len(x)):\n                for d in range(2):\n                    basis[i * 2 + d][d * 6] = 1\n                    basis[i * 2 + d][d * 6 + 1] = x[i][0]\n                    basis[i * 2 + d][d * 6 + 2] = x[i][1]\n                    basis[i * 2 + d][d * 6 + 3] = x[i][0] * x[i][0]\n                    basis[i * 2 + d][d * 6 + 4] = x[i][0] * x[i][1]\n                    basis[i * 2 + d][d * 6 + 5] = x[i][1] * x[i][1]\n        elif order == 3: # cubic polynomial basis\n            basis = np.zeros((len(x) * 2, 20)) # 1, x, y, x^2, xy, y^2, x^3, x^2y, xy^2, y^3 for both x- and y-displacements\n            for i in range(len(x)):\n                for d in range(2):\n                    basis[i * 2 + d][d * 10] = 1\n                    basis[i * 2 + d][d * 10 + 1] = x[i][0]\n                    basis[i * 2 + d][d * 10 + 2] = x[i][1]\n                    basis[i * 2 + d][d * 10 + 3] = x[i][0] * x[i][0]\n                    basis[i * 2 + d][d * 10 + 4] = x[i][0] * x[i][1]\n                    basis[i * 2 + d][d * 10 + 5] = x[i][1] * x[i][1]\n                    basis[i * 2 + d][d * 10 + 6] = x[i][0] * x[i][0] * x[i][0]\n                    basis[i * 2 + d][d * 10 + 7] = x[i][0] * x[i][0] * x[i][1]\n                    basis[i * 2 + d][d * 10 + 8] = x[i][0] * x[i][1] * x[i][1]\n                    basis[i * 2 + d][d * 10 + 9] = x[i][1] * x[i][1] * x[i][1]\n        else:\n            print(\"unsupported order of polynomial basis for reduced DOF\")\n            exit()\n        return basis\n    else: # modal-order reduction\n        if order <= 0 or order >= len(x) * 2:\n            print(\"invalid number of target basis for modal reduction\")\n            exit()\n        IJV = NeoHookeanEnergy.hess(x, e, vol, IB, mu_lame, lam, project_PSD=False)\n        H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()\n        eigenvalues, eigenvectors = eigsh(H, k=order, which='SM') # get 'order' eigenvectors with smallest eigenvalues \n        return eigenvectors\n# ANCHOR_END: compute_reduced_basis"
  },
  {
    "path": "LICENSE",
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  },
  {
    "path": "pyproject.toml",
    "content": "[project]\nname = \"solid-sim-tutorial\"\nversion = \"0.1.0\"\ndescription = \"Add your description here\"\nreadme = \"README.md\"\nrequires-python = \">=3.13\"\ndependencies = [\n    \"matplotlib>=3.10.3\",\n    \"numpy>=2.3.1\",\n    \"scikit-learn>=1.7.0\",\n]\n"
  },
  {
    "path": "readme.md",
    "content": "# Solid Simulation Tutorials\n\nA curated collection of Python examples focused on optimization-based solid simulation with guarantees on algorithmic convergence, penetration-free and inversion-free conditions. The examples are designed for ease of readability and understanding.\n\nIntroductory sections (with * following the titles) for each of the examples in this repository can be found in the free online book [Physics-based Simulation](https://phys-sim-book.github.io/).\n\nA [MUDA](https://github.com/MuGdxy/muda)-based GPU version of the tutorial written by Zhaofeng Luo ([@Roushelfy](https://github.com/Roushelfy)) can be found at [solid-sim-tutorial-gpu](https://github.com/phys-sim-book/solid-sim-tutorial-gpu).\n"
  }
]