Repository: benedekrozemberczki/EdMot Branch: master Commit: 48bf1771ca6d Files: 11 Total size: 468.2 KB Directory structure: gitextract_vvd36bvh/ ├── .github/ │ └── FUNDING.yml ├── LICENSE ├── README.md ├── input/ │ ├── cora_edges.csv │ ├── cora_features.json │ └── cora_target.csv ├── output/ │ └── cora_membership.json └── src/ ├── edmot.py ├── main.py ├── param_parser.py └── utils.py ================================================ FILE CONTENTS ================================================ ================================================ FILE: .github/FUNDING.yml ================================================ github: [benedekrozemberczki] ================================================ FILE: LICENSE ================================================ GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 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But first, please read . ================================================ FILE: README.md ================================================ EdMot ================================ [![Arxiv](https://img.shields.io/badge/ArXiv-1906.04560-orange.svg)](https://arxiv.org/abs/1906.04560) [![codebeat badge](https://codebeat.co/badges/70ecf9b1-226c-487a-bbc7-9e6eedbf7e22)](https://codebeat.co/projects/github-com-benedekrozemberczki-edmot-master) [![repo size](https://img.shields.io/github/repo-size/benedekrozemberczki/EdMot.svg)](https://github.com/benedekrozemberczki/EdMot/archive/master.zip) [![benedekrozemberczki](https://img.shields.io/twitter/follow/benrozemberczki?style=social&logo=twitter)](https://twitter.com/intent/follow?screen_name=benrozemberczki) A **NetworkX** implementation of *"EdMot: An Edge Enhancement Approach for Motif-aware Community Detection"* (KDD 2019).

--------------------------------- ### Abstract

Network community detection is a hot research topic in network analysis. Although many methods have been proposed for community detection, most of them only take into consideration the lower-order structure of the network at the level of individual nodes and edges. Thus, they fail to capture the higher-order characteristics at the level of small dense subgraph patterns, e.g., motifs. Recently, some higher-order methods have been developed but they typically focus on the motif-based hypergraph which is assumed to be a connected graph. However, such assumption cannot be ensured in some real-world networks. In particular, the hypergraph may become fragmented. That is, it may consist of a large number of connected components and isolated nodes, despite the fact that the original network is a connected graph. Therefore, the existing higher-order methods would suffer seriously from the above fragmentation issue, since in these approaches, nodes without connection in hypergraph can't be grouped together even if they belong to the same community. To address the above fragmentation issue, we propose an Edge enhancement approach for Motif-aware community detection (EdMot ). The main idea is as follows. Firstly, a motif-based hypergraph is constructed and the top K largest connected components in the hypergraph are partitioned into modules. Afterwards, the connectivity structure within each module is strengthened by constructing an edge set to derive a clique from each module. Based on the new edge set, the original connectivity structure of the input network is enhanced to generate a rewired network, whereby the motif-based higher-order structure is leveraged and the hypergraph fragmentation issue is well addressed. Finally, the rewired network is partitioned to obtain the higher-order community structure. Extensive experiments have been conducted on eight real-world datasets and the results show the effectiveness of the proposed method in improving the community detection performance of state-of-the-art methods.

The model is now also available in the package [Karate Club](https://github.com/benedekrozemberczki/karateclub). This repository provides a NetworkX implementation of EdMot as described in the papers: > EdMot: An Edge Enhancement Approach for Motif-aware Community Detection > Pei-Zhen Li, Ling Huang, Chang-Dong Wang, and Jian-Huang Lai . > KDD, 2019. > [[Paper]](https://arxiv.org/abs/1906.04560) A Matlab implementation of EdMot is available [[here]](https://github.com/lipzh5/EdMot_pro). ### Requirements The codebase is implemented in Python 3.5.2. package versions used for development are just below. ``` networkx 2.4 tqdm 4.28.1 pandas 0.23.4 texttable 1.5.0 argparse 1.1.0 python-louvain 0.11 ``` ### Datasets

The code takes the **edge list** of the graph in a csv file. Every row indicates an edge between two nodes separated by a comma. The first row is a header. Nodes should be indexed starting with 0. A sample graph for `Cora` is included in the `input/` directory.

### Options Training a model is handled by the `src/main.py` script which provides the following command line arguments. #### Input and output options ``` --edge-path STR Edge list csv. Default is `input/cora_edges.csv`. --membership-path STR Features json. Default is `output/cora_membership.json`. ``` #### Model options ``` --cutoff INT Random seed. Default is 2. --components INT Number of motif components. Default is 1. ``` ### Examples The following commands learn an EdMot Clustering. ```sh $ python src/main.py ```

Increasing the motif graph component number. ```sh $ python src/main.py --components 2 ``` -------------------------------------------------------------------------------- **License** - [GNU License](https://github.com/benedekrozemberczki/EdMot/blob/master/LICENSE) -------------------------------------------------------------------------------- ================================================ FILE: input/cora_edges.csv ================================================ id_1,id_2 0,633 0,1862 0,2582 1,2 1,652 1,654 2,1 2,332 2,1454 2,1666 2,1986 3,2544 4,1016 4,1256 4,1761 4,2175 4,2176 5,1629 5,1659 5,2546 6,373 6,1042 6,1416 6,1602 7,208 8,269 8,281 8,1996 9,723 9,2614 10,476 10,2545 11,1655 11,1839 12,1001 12,1318 12,2661 12,2662 13,1701 13,1810 14,158 14,2034 14,2075 14,2077 14,2668 15,1090 15,1093 15,1271 15,2367 16,970 16,1632 16,2444 16,2642 17,24 17,927 17,1315 17,1316 17,2140 18,139 18,1560 18,1786 18,2082 18,2145 19,1939 20,1072 20,2269 20,2270 20,2374 20,2375 21,1043 21,2310 22,39 22,1234 22,1702 22,1703 22,2238 23,2159 24,17 24,201 24,598 24,1636 24,1701 24,2139 24,2141 25,1301 25,1344 25,2011 25,2317 26,99 26,122 26,123 26,2454 26,2455 27,606 27,1810 27,2360 27,2578 28,1687 29,963 29,2645 30,697 30,738 30,1358 30,1416 30,2162 30,2343 31,1594 32,279 32,518 32,1850 32,1973 33,286 33,588 33,698 33,911 33,1051 33,2040 33,2119 33,2120 33,2121 34,1358 35,895 35,1296 35,1913 36,1146 36,1505 36,1552 36,1640 36,1781 36,2094 36,2106 36,2107 37,60 37,1190 37,2427 38,429 38,862 38,863 38,1160 39,22 39,1349 39,1522 39,1532 39,1634 39,1965 39,2357 40,507 40,866 40,1364 41,175 41,596 41,644 41,1914 42,87 42,1372 43,152 43,963 43,1530 43,1653 43,2399 43,2400 44,1582 44,2624 44,2701 45,733 45,1219 45,1986 45,2303 45,2667 45,2668 46,1604 46,2366 47,163 47,1579 48,598 48,714 48,1031 48,1662 48,1666 48,2041 48,2205 48,2206 48,2471 49,1666 49,2034 50,1441 51,457 51,710 51,1392 51,2213 51,2214 51,2215 52,1139 52,1467 52,2053 52,2172 52,2182 53,1103 53,1358 53,1739 54,401 54,767 55,60 55,210 55,323 55,651 55,771 55,787 55,815 55,1079 55,1156 55,1983 55,2020 55,2021 56,412 56,447 56,1616 56,1849 57,2418 58,1715 59,105 59,580 59,609 59,615 59,1067 59,1287 59,1358 59,1627 59,1725 59,2651 60,37 60,55 60,1527 61,1080 61,1309 61,1416 61,2162 61,2312 62,485 63,1322 64,1209 64,1737 64,2616 65,239 65,543 65,619 65,771 65,1156 65,1293 65,1628 65,2021 65,2418 65,2419 66,2631 67,282 67,540 67,2628 68,391 68,1358 68,1986 69,604 69,1013 69,1351 69,1914 69,1920 69,1926 69,2189 70,441 70,2184 71,206 71,1986 71,2691 72,1103 72,1358 73,449 73,558 73,797 73,876 73,1035 73,1136 73,1189 73,1214 73,1358 73,1723 73,1745 73,1751 74,544 74,586 74,1042 74,1118 74,1416 74,1517 74,2052 74,2155 74,2419 75,84 75,583 75,2222 75,2223 75,2224 75,2225 76,88 76,2018 76,2178 77,659 77,1803 78,1219 78,1329 78,1418 79,603 79,2097 80,257 80,1117 80,2049 81,347 81,423 81,527 81,2180 82,1138 82,1634 83,1520 83,2581 84,75 84,284 84,2223 84,2224 84,2226 85,1065 85,2487 85,2488 86,429 86,1336 86,2034 86,2295 87,42 87,842 87,2164 88,76 88,130 88,162 88,300 88,415 88,498 88,696 88,737 88,743 88,815 88,841 88,851 88,1174 88,1288 88,1309 88,1394 88,1494 88,1527 88,1658 88,1677 88,1713 88,1732 88,1741 88,1847 88,1882 88,1908 88,2010 88,2011 88,2012 88,2013 88,2014 88,2015 88,2016 88,2017 88,2178 88,2394 89,258 89,884 89,1087 89,1094 89,1157 89,1401 89,1530 89,1585 89,1653 89,2463 90,155 90,156 90,817 90,1358 91,330 91,1046 91,2001 91,2122 91,2123 91,2380 92,898 92,1836 93,550 93,950 93,1495 93,2151 94,195 94,586 94,675 94,733 94,934 94,1649 94,1966 94,2263 94,2355 94,2357 94,2490 95,334 95,456 95,693 95,734 95,736 95,861 95,1303 95,1535 95,1580 95,1602 95,1628 95,1838 95,2054 95,2074 95,2181 95,2182 95,2183 95,2197 95,2199 95,2200 95,2201 96,2217 97,661 97,1353 98,1521 99,26 99,122 99,123 99,2454 99,2455 99,2604 100,1602 100,2056 101,281 101,1358 101,1589 102,109 102,1251 102,1448 102,1561 102,1623 102,1871 102,1878 102,2256 103,139 103,306 103,484 103,608 103,1775 103,1790 104,401 104,864 104,1065 104,2210 105,59 105,1721 105,2476 105,2651 106,2461 107,541 107,971 107,1113 107,1650 108,1647 108,2157 108,2209 109,102 109,124 109,133 109,153 109,176 109,236 109,289 109,306 109,318 109,426 109,459 109,519 109,563 109,610 109,1045 109,1337 109,1346 109,1624 109,1661 109,1769 109,1772 109,1779 109,1785 109,1787 109,1789 109,1805 109,1998 109,2045 109,2092 109,2093 109,2094 109,2095 110,567 110,1161 110,1262 110,1599 110,2279 111,758 111,1169 111,1358 111,1762 111,2492 111,2643 112,306 112,487 112,1623 112,2080 113,540 113,747 113,1884 114,610 114,2288 114,2506 115,973 116,1076 116,1501 117,259 117,2537 118,255 118,388 118,446 118,454 118,554 118,581 118,842 118,1029 118,1343 118,1507 118,1538 118,1616 118,1690 118,1851 118,2010 118,2030 118,2112 118,2165 118,2166 119,379 119,646 119,1537 119,1549 119,1901 119,1959 120,483 120,514 120,816 120,1842 120,2405 121,589 121,802 121,980 121,1158 121,1910 121,2251 121,2252 122,26 122,99 122,2454 122,2455 123,26 123,99 123,2455 123,2604 124,109 124,306 124,1367 124,1622 124,2478 125,458 125,2363 126,236 126,306 126,1551 126,1623 126,2045 126,2079 127,2604 128,233 128,370 128,392 128,2270 129,441 129,701 130,88 130,1982 130,2017 131,834 131,2169 132,379 132,479 132,904 132,1022 132,1959 133,109 133,399 133,452 133,1623 133,1670 133,1777 133,1784 133,2045 133,2082 134,406 135,137 135,2095 135,2144 136,831 137,135 137,2144 137,2329 137,2504 138,236 138,306 138,1776 139,18 139,103 139,306 139,660 139,910 139,1623 139,1780 139,2045 140,582 140,623 141,740 141,1002 141,2034 142,456 142,525 142,1628 142,2049 142,2181 143,316 143,598 143,1701 144,145 144,213 144,1593 144,2192 145,144 145,213 145,537 145,1165 145,1593 145,2622 146,897 146,1468 146,1907 146,1927 146,2059 147,1519 147,1976 148,378 148,381 148,602 148,714 148,2518 149,1080 149,1416 149,1655 149,2025 150,310 150,914 150,1942 151,1986 151,2236 151,2238 151,2335 152,43 152,884 152,2238 152,2240 153,109 153,236 153,306 153,459 153,1623 153,2045 154,326 154,364 154,819 154,1238 154,1339 154,1358 154,1444 154,1568 154,1752 154,1753 154,1754 154,2525 155,90 155,156 155,817 155,1358 155,1689 155,1736 155,1763 156,90 156,155 156,817 156,1358 156,1689 156,1763 157,598 157,1701 157,1870 157,2493 158,14 158,180 158,1701 158,2034 159,180 159,2308 160,277 160,553 160,743 160,745 160,1986 160,2000 160,2009 161,842 161,2010 162,88 162,323 162,1174 162,1268 162,1667 163,47 164,210 164,211 165,598 165,1473 165,2706 165,2707 166,271 166,2617 167,168 167,1056 167,2437 167,2482 168,167 168,2437 168,2438 169,1994 169,2706 170,1067 170,1358 171,775 171,790 171,1548 172,240 172,512 172,756 172,1692 172,2187 173,687 173,1033 173,1358 173,1586 174,629 174,1358 174,1742 174,2334 175,41 175,596 175,955 175,1914 175,2135 175,2217 175,2388 176,109 176,231 176,973 177,726 177,1639 177,2679 177,2682 178,833 179,197 179,231 179,1986 180,158 180,159 180,775 180,790 180,791 180,1020 180,1807 180,2004 180,2037 180,2076 181,1013 181,1359 181,1464 181,1683 182,183 182,997 183,182 183,997 183,1837 184,520 185,297 185,2003 186,1228 186,1319 186,1536 186,1672 186,2580 186,2702 187,1208 188,1169 188,1727 189,564 189,1072 189,1262 189,1509 190,491 190,2135 191,382 191,608 191,1677 191,1791 191,1998 191,2385 192,2472 193,441 193,458 194,473 194,1050 194,1451 194,2564 194,2646 195,94 195,2424 196,429 196,442 196,2122 197,179 197,231 197,2412 198,1255 199,420 199,1869 200,1439 200,2676 201,24 201,297 201,570 201,598 201,1701 201,1986 201,2430 202,353 202,1173 202,1250 202,1345 203,854 203,857 203,963 203,1115 203,1869 204,415 205,1701 205,1869 206,71 206,2691 207,833 208,7 209,2681 210,55 210,164 210,1079 210,1614 210,1626 210,1671 210,1905 210,1906 210,1907 210,2309 211,164 211,356 211,1394 211,1908 211,1909 212,1290 213,144 213,145 213,1593 213,2192 214,2194 215,1701 215,1986 215,2045 216,1542 216,1701 217,243 217,2473 217,2474 218,482 218,733 218,781 218,792 218,1020 218,1348 218,1382 218,2076 218,2091 218,2119 218,2594 219,507 219,1413 219,1542 220,376 220,817 220,913 221,817 222,821 223,744 223,1154 223,1761 224,1810 224,2034 225,2255 226,1701 227,534 227,883 228,322 228,848 228,1358 228,1721 228,1871 229,1053 229,1405 229,1894 229,2118 230,549 230,577 230,1095 230,1217 230,1810 231,176 231,179 231,197 231,232 231,387 231,551 231,1701 231,1868 231,2217 232,231 232,869 232,1701 232,1864 232,1986 233,128 234,610 234,2591 235,1701 236,109 236,126 236,138 236,153 236,306 236,1072 236,1572 236,2045 236,2046 236,2078 236,2079 237,2539 238,1828 239,65 239,619 239,887 239,910 239,1069 239,1220 239,1274 239,1376 239,1759 239,1909 239,2021 239,2182 239,2418 240,172 240,512 240,756 240,1472 240,1692 241,1441 242,279 242,838 242,1131 242,2280 243,217 243,473 243,2474 243,2647 243,2648 244,565 244,1072 244,1358 244,1610 245,782 245,1162 246,936 246,1358 246,1687 246,2515 247,2583 248,1264 248,1531 248,1964 249,621 249,1884 249,1978 250,2429 251,253 251,507 251,812 251,1300 251,1413 251,1542 251,1933 252,711 252,973 252,1973 252,2485 253,251 253,507 253,1413 254,507 254,1211 255,118 255,1266 255,1343 255,2112 256,756 257,80 257,964 257,1388 257,2180 258,89 258,963 258,1094 258,1153 258,1240 258,1401 258,2645 259,117 259,2537 260,365 261,873 261,1479 261,1701 261,1894 262,1351 262,1464 263,364 263,732 263,1103 264,472 264,844 264,1826 264,1902 265,1441 266,578 266,809 266,2227 266,2229 267,670 267,2000 267,2373 268,1740 268,2451 269,8 269,321 269,418 269,2543 269,2551 270,279 270,838 270,1195 270,1215 270,2280 271,166 271,638 271,1970 271,2387 271,2498 272,2012 273,374 273,846 274,748 274,749 275,805 275,1967 276,1463 276,1695 276,2133 277,160 277,553 277,696 277,973 277,1869 278,1185 279,32 279,242 279,270 279,304 279,502 279,666 279,838 279,1195 279,2165 279,2280 279,2344 279,2423 280,1535 280,2155 281,8 281,101 281,746 281,1000 281,1347 281,1382 281,2244 281,2247 282,67 282,747 283,1559 283,2250 284,84 284,583 284,2222 284,2223 284,2224 284,2225 284,2226 285,502 285,1999 286,33 286,442 286,698 287,2705 288,618 289,109 289,1358 289,1722 290,328 290,567 290,687 290,1765 290,2359 291,1692 292,2562 293,2038 294,306 294,2047 295,1176 295,1177 296,732 296,2685 297,185 297,201 297,598 297,899 297,1542 298,607 298,1095 298,1325 299,1484 299,2383 299,2386 299,2387 299,2498 300,88 300,415 300,634 301,1169 301,2492 302,306 302,350 302,719 302,1158 302,1253 303,719 303,1670 303,2143 304,279 304,1172 304,1857 304,2423 305,1416 305,1927 306,103 306,109 306,112 306,124 306,126 306,138 306,139 306,153 306,236 306,294 306,302 306,308 306,329 306,350 306,417 306,426 306,452 306,476 306,487 306,519 306,542 306,554 306,573 306,581 306,608 306,655 306,656 306,719 306,887 306,910 306,958 306,973 306,1009 306,1045 306,1072 306,1158 306,1193 306,1245 306,1251 306,1346 306,1367 306,1483 306,1490 306,1551 306,1572 306,1584 306,1640 306,1651 306,1656 306,1705 306,1770 306,1771 306,1772 306,1775 306,1779 306,1781 306,1782 306,1787 306,1797 306,1798 306,1799 306,1802 306,1804 306,1805 306,1856 306,2045 306,2046 306,2048 306,2078 306,2080 306,2084 306,2085 306,2086 306,2087 306,2088 306,2089 306,2090 306,2091 307,991 308,306 308,350 308,1253 308,1670 308,2045 309,383 309,2268 309,2305 310,150 310,352 310,875 310,892 310,990 310,1241 310,1272 310,1331 310,1581 310,1815 310,1944 310,1945 310,1946 310,1947 310,1948 310,1949 310,1950 311,343 311,690 311,1132 311,1865 312,1610 312,1722 312,1740 313,2296 314,1623 314,2000 315,408 315,423 315,1602 315,1921 315,2232 316,143 316,598 316,766 316,845 316,920 316,1073 316,1297 316,1821 316,1868 316,2004 317,1624 317,1785 318,109 318,563 318,1701 318,2045 319,1205 320,348 320,1597 321,269 321,1083 321,1450 322,228 323,55 323,162 323,498 323,2020 323,2022 324,827 324,2156 324,2194 325,787 325,1848 326,154 326,1358 326,1754 327,928 327,1325 327,1996 327,2063 327,2064 328,290 328,951 328,1250 329,306 329,1798 329,2598 330,91 330,1505 330,2123 331,1527 331,2480 332,2 332,665 332,2003 332,2122 332,2615 333,1358 333,1694 334,95 334,693 334,1013 335,1701 335,1986 336,1944 336,1950 337,1214 337,1358 337,1499 337,1776 338,1413 338,1542 338,1934 339,813 340,584 340,2463 341,613 341,1358 341,1389 341,1546 341,2045 342,1072 342,1512 343,311 343,1701 344,389 344,441 344,661 344,854 344,2323 345,833 346,999 346,1358 347,81 347,408 347,423 347,525 348,320 348,1643 348,2248 348,2250 349,419 349,465 349,2427 350,302 350,306 350,308 350,406 350,656 350,1623 350,1640 350,1775 350,1778 350,1782 350,2084 350,2085 350,2089 350,2090 351,1810 352,310 352,1294 352,1944 353,202 353,1173 353,1345 353,2507 354,659 354,1803 354,2453 355,1668 356,211 356,498 356,1259 356,2018 356,2116 357,657 357,1154 357,1358 357,2652 358,2642 359,389 359,1483 359,1620 360,1409 360,1824 361,2681 362,1966 363,1003 364,154 364,263 364,732 364,819 364,970 364,1306 364,1358 364,1606 364,1632 364,1756 364,2642 365,260 365,2469 366,553 366,745 366,1583 366,1986 367,2083 367,2451 368,428 368,996 368,1194 368,1366 368,1545 368,2249 368,2393 369,385 369,2484 370,128 370,1408 370,1414 370,1415 370,2269 371,720 371,1354 371,1414 371,1415 371,1441 371,1553 371,2375 372,626 372,1710 372,1834 372,2377 373,6 373,1025 373,1042 374,273 374,413 374,846 374,1101 374,2146 374,2147 374,2149 375,963 375,2401 375,2434 375,2435 376,220 376,672 376,1583 377,678 377,733 377,1265 377,2291 378,148 378,602 379,119 379,132 379,904 379,1022 379,1898 379,1959 380,477 380,930 380,2569 381,148 381,2518 381,2538 382,191 382,1203 382,2034 383,309 383,733 383,1704 383,2268 384,1623 384,1624 385,369 385,2483 385,2484 386,2114 386,2115 386,2117 387,231 387,519 387,2191 388,118 388,1899 388,2497 389,344 389,359 389,704 389,905 389,1077 389,1483 389,1743 389,2450 390,1108 391,68 391,493 391,1986 391,2365 392,128 392,720 392,1415 392,1619 392,1825 392,2269 393,739 394,577 394,849 394,1063 394,1064 394,2351 395,640 395,1147 395,2367 396,1217 396,1988 397,665 397,879 397,1096 397,2329 398,730 398,2177 399,133 399,544 399,1089 399,1769 399,2107 400,1354 401,54 401,104 401,733 401,1065 401,1096 401,1160 402,507 402,776 402,1413 402,1542 402,1932 402,1936 402,1940 403,464 403,806 403,1037 403,1383 403,1742 403,2503 403,2654 404,1170 404,1476 405,738 405,1275 405,1927 405,2059 406,134 406,350 406,505 406,2505 407,409 407,695 407,1681 407,1682 408,315 408,347 408,525 408,734 408,1841 408,2056 409,407 409,1624 409,1681 409,2084 410,676 410,1179 411,1096 411,1488 411,1577 411,2609 412,56 412,1616 412,1849 413,374 414,711 415,88 415,204 415,300 415,525 415,593 415,737 415,818 415,851 415,966 415,1174 415,1309 415,1527 415,1644 415,1677 415,1843 415,1847 415,1850 415,1908 415,2014 415,2178 415,2182 416,519 416,1701 417,306 417,1072 417,1871 417,2034 417,2494 418,269 419,349 420,199 420,1869 421,2213 421,2216 422,545 423,81 423,315 423,347 423,525 423,527 424,436 424,1203 425,2466 426,109 426,306 426,487 426,1772 426,1777 426,1782 426,1789 426,1805 427,565 427,1528 428,368 428,996 428,1257 428,2248 428,2671 429,38 429,86 429,196 429,523 429,705 429,794 429,863 429,1493 429,1618 429,1669 429,1807 429,1889 429,2001 429,2041 429,2043 429,2044 430,2130 431,2694 431,2695 432,1442 432,1597 433,436 433,756 434,1117 434,1524 434,1693 434,2133 434,2408 435,486 435,733 435,1912 436,424 436,433 436,483 436,498 436,668 436,816 436,878 436,885 436,1039 436,1131 436,1332 436,1494 436,1977 436,1978 436,1979 436,1980 436,1981 436,1982 437,498 437,718 437,950 437,1495 437,1985 438,718 438,787 438,1667 438,1983 438,1984 438,1985 439,1169 439,1642 440,441 440,725 440,895 440,1296 440,1913 440,2179 441,70 441,129 441,193 441,344 441,440 441,454 441,671 441,1455 441,1537 441,2094 441,2184 442,196 442,286 442,588 442,627 442,698 442,1051 442,2120 442,2362 443,1010 443,1264 443,1531 443,1966 444,488 444,515 444,582 444,623 444,828 444,2289 444,2290 444,2464 445,909 445,1434 446,118 446,903 446,1507 447,56 447,1616 447,1849 447,2638 448,472 448,1824 448,1826 448,1902 449,73 449,1280 449,1834 449,2581 450,1569 450,2538 451,671 451,935 451,2285 452,133 452,306 452,1258 452,1623 453,1806 453,2305 453,2306 454,118 454,441 454,581 454,973 454,1441 454,1661 454,1917 454,2022 454,2188 454,2189 454,2190 455,1664 455,2147 455,2486 456,95 456,142 456,525 456,544 456,667 456,1580 456,2054 456,2199 456,2347 456,2472 457,51 457,1201 457,2215 457,2216 458,125 458,193 458,1122 458,1276 458,1555 458,1953 459,109 459,153 459,1623 459,1681 460,1986 460,1989 460,2532 461,1203 461,2309 462,1048 463,1702 463,1703 463,1964 463,1966 464,403 464,1758 464,2444 464,2445 465,349 465,896 465,1403 465,1869 465,2304 466,970 466,1305 466,1358 466,1738 466,2546 467,1172 467,1701 467,1708 468,647 468,1311 468,1313 469,620 469,2304 469,2412 470,652 470,854 470,857 470,1097 470,1115 471,1013 471,2013 471,2394 472,264 472,448 472,559 472,844 472,1182 472,1183 472,1825 472,2029 473,194 473,243 473,1575 473,2647 474,1181 475,2219 476,10 476,306 476,1140 476,1800 476,1986 477,380 477,930 477,2569 478,514 478,1978 478,2024 479,132 479,1880 480,598 480,687 480,1426 480,1710 480,2359 480,2372 481,823 481,1287 481,1810 481,2291 482,218 482,790 482,1807 482,1810 482,1812 482,1814 482,2230 482,2307 482,2308 483,120 483,436 483,816 483,2405 484,103 484,542 484,1367 484,1699 484,1775 484,2046 484,2081 485,62 485,839 485,1042 485,2219 486,435 486,2077 486,2667 486,2668 487,112 487,306 487,426 487,655 487,859 487,1705 487,1772 487,1773 487,1782 487,1798 487,2026 487,2080 488,444 488,2547 489,1358 489,2390 489,2391 490,826 490,1131 490,1309 490,1463 490,1879 490,1973 490,1981 490,2099 490,2105 491,190 492,688 492,956 492,1257 492,1533 492,2538 492,2673 492,2678 493,391 493,1244 493,1759 494,2614 495,1327 495,1328 495,2192 496,596 496,711 496,992 497,2419 498,88 498,323 498,356 498,436 498,437 498,1652 499,2457 499,2458 500,2241 501,1358 501,1765 502,279 502,285 502,1976 503,576 503,1692 503,2001 504,1973 504,2394 504,2396 505,406 505,573 505,843 505,1180 505,1251 505,1258 505,1304 505,1448 505,1560 505,1779 505,2083 506,1013 506,1352 506,1914 506,1918 507,40 507,219 507,251 507,253 507,254 507,402 507,812 507,1176 507,1211 507,1300 507,1363 507,1413 507,1931 507,1933 507,1936 507,1940 507,1941 507,2508 508,2325 509,1101 509,2146 509,2148 510,1013 510,1131 510,1171 511,549 511,1810 512,172 512,240 512,756 512,1472 512,1692 513,565 513,657 513,1528 514,120 514,478 514,1314 514,1882 514,1978 515,444 515,623 515,1102 515,2464 515,2465 515,2547 516,1882 516,2104 517,952 517,2105 518,32 518,666 518,1373 518,2423 519,109 519,306 519,387 519,416 519,598 519,836 519,1346 519,1574 519,1670 519,1986 519,1998 519,2045 520,184 521,598 522,2097 523,429 523,949 523,2406 524,552 524,979 524,1169 524,1358 524,2476 525,142 525,347 525,408 525,415 525,423 525,456 525,1540 525,1628 525,2054 525,2057 525,2172 525,2180 525,2181 525,2182 525,2183 526,565 526,1007 526,1216 526,1742 527,81 527,423 528,803 529,1417 529,1419 529,2260 530,1013 530,1505 530,2094 531,606 531,2308 532,1701 532,1863 533,1742 533,2466 534,227 534,609 534,629 534,933 535,2392 535,2641 536,567 536,1894 537,145 537,1165 537,1593 537,1698 537,2192 538,1286 539,711 539,1616 539,2155 540,67 540,113 540,747 540,1441 540,2527 541,107 541,647 541,904 541,1022 541,1360 541,1896 542,306 542,484 542,1245 542,1623 543,65 543,984 544,74 544,399 544,456 544,1580 544,1769 544,2052 544,2199 544,2347 545,422 546,1608 546,2127 547,598 547,1701 548,809 548,843 548,1523 548,1937 548,2138 549,230 549,511 549,1497 549,1810 550,93 551,231 551,2388 552,524 552,1169 552,1358 552,2201 553,160 553,277 553,366 553,745 553,1127 553,1583 553,1995 553,2009 554,118 554,306 554,685 555,1463 556,1623 556,1805 557,1725 558,73 558,876 558,1189 558,1706 558,2585 559,472 559,1182 559,1579 560,774 560,2526 561,1016 562,704 562,1483 562,1735 562,2450 563,109 563,318 563,1337 563,1701 563,2045 564,189 564,1262 564,2476 565,244 565,427 565,513 565,526 565,687 565,1038 565,1361 565,1398 565,1528 565,1610 565,1723 565,2279 566,1907 566,1986 567,110 567,290 567,536 567,631 567,760 567,1262 567,1513 568,1116 568,1223 568,1810 569,1759 569,2512 570,201 570,2430 571,696 571,1570 572,1416 572,2025 572,2418 573,306 573,505 573,643 573,1313 573,2407 574,576 574,1692 574,2001 575,2283 576,503 576,574 576,665 576,1810 576,2348 577,230 577,394 577,849 577,870 577,906 577,1063 577,1129 577,1518 577,2351 577,2352 577,2353 577,2354 578,266 578,1105 578,1879 578,1974 579,994 579,1134 579,1808 580,59 580,744 580,1358 580,1742 580,1758 580,1765 580,2444 580,2445 581,118 581,306 581,454 581,1616 581,1623 581,1792 582,140 582,444 582,2548 582,2549 583,75 583,284 583,2224 583,2225 584,340 584,623 584,2289 584,2463 584,2464 585,2526 586,74 586,94 586,1218 586,1224 586,2155 587,1032 588,33 588,442 588,698 588,2383 589,121 589,980 589,1158 589,1624 590,1441 590,1954 591,642 591,1017 591,1078 591,1423 591,2472 592,2669 593,415 593,1115 593,1474 594,663 594,2195 595,1016 595,1256 595,2176 596,41 596,175 596,496 596,644 596,992 596,1914 597,1104 597,1628 598,24 598,48 598,143 598,157 598,165 598,201 598,297 598,316 598,480 598,519 598,521 598,547 598,637 598,766 598,845 598,869 598,968 598,1003 598,1100 598,1107 598,1297 598,1299 598,1301 598,1473 598,1573 598,1636 598,1821 598,1823 598,1864 598,1870 598,1875 598,2138 598,2707 599,1093 599,1271 600,2394 601,2229 602,148 602,378 603,79 603,716 603,795 603,1248 603,1821 603,1873 603,2045 604,69 604,1351 604,1652 604,1914 604,2109 605,1107 605,2534 606,27 606,531 606,1666 606,2230 606,2360 606,2361 607,298 607,1213 607,1664 608,103 608,191 608,306 608,1623 608,2080 609,59 609,534 609,883 609,1041 609,1358 609,2446 609,2447 609,2448 610,109 610,114 610,234 610,826 610,2287 610,2288 610,2481 611,2690 612,2235 613,341 613,1358 614,888 614,1475 614,2470 615,59 615,2443 616,1358 616,1739 616,2365 616,2503 617,705 617,2034 618,288 618,938 619,65 619,239 620,469 620,923 620,2534 621,249 621,1332 621,1978 621,2018 622,886 622,1002 622,1951 622,1952 623,140 623,444 623,515 623,584 623,2289 623,2464 624,1042 624,1232 625,1024 626,372 626,1358 626,2556 626,2558 627,442 627,2122 627,2238 627,2335 628,1169 628,1725 628,1764 628,2546 629,174 629,534 629,883 630,973 631,567 631,2358 632,1430 633,0 633,1701 633,1866 634,300 634,2227 635,2058 636,2233 637,598 637,1641 638,271 638,783 638,808 638,893 638,924 638,1773 638,2387 639,900 640,395 640,765 640,894 640,1090 640,1598 640,2420 641,2704 642,591 642,2472 643,573 643,1167 643,1538 643,2407 644,41 644,596 644,711 644,728 644,1258 644,2177 645,891 645,950 645,1267 645,1358 645,1495 645,1824 645,1826 645,1895 645,1898 645,1899 645,1900 645,1901 646,119 647,468 647,541 647,904 647,1267 647,1360 648,1441 649,1171 649,1457 650,819 650,1250 650,1486 650,1557 650,1685 650,1756 650,2083 651,55 651,885 651,1667 651,1984 651,2023 651,2024 651,2156 652,1 652,470 653,1231 654,1 655,306 655,487 655,2080 656,306 656,350 656,2090 657,357 657,513 657,867 657,871 657,1229 657,1254 657,1729 657,1740 657,2440 657,2442 657,2522 657,2523 658,2147 659,77 659,354 659,1803 660,139 660,1623 661,97 661,344 661,807 661,830 661,935 661,1028 661,1045 661,1353 661,1878 661,1879 661,1880 661,1881 661,1882 661,1883 661,1884 661,1885 662,932 663,594 663,2195 664,1701 665,332 665,397 665,576 665,2120 665,2122 666,279 666,518 666,1850 666,1973 667,456 667,2364 667,2472 668,436 669,729 669,1086 669,1124 670,267 670,2606 671,441 671,451 671,973 671,2025 672,376 672,2456 673,1907 673,1986 674,1907 675,94 675,2356 676,410 676,1955 676,2235 677,954 678,377 678,733 679,1395 680,2199 681,1171 681,1445 681,1446 681,1986 682,973 682,1224 683,834 683,2169 684,1282 684,1358 685,554 686,1358 686,2366 687,173 687,290 687,480 687,565 687,1033 687,1171 687,1358 687,1546 687,1586 687,1610 687,1710 687,1721 687,1725 687,2359 687,2372 688,492 688,1257 689,1169 689,1292 689,1317 689,1358 689,1721 690,311 691,2034 691,2130 692,2629 693,95 693,334 693,763 693,1851 693,2108 694,1478 694,2516 695,407 695,948 695,1012 695,1336 695,1681 695,1682 695,1790 695,1998 695,2319 696,88 696,277 696,571 696,1570 697,30 697,1080 698,33 698,286 698,442 698,588 698,1015 699,1701 699,2045 699,2327 700,1691 701,129 701,735 701,739 701,2062 702,777 702,779 702,822 702,993 702,1368 702,1637 702,2069 702,2070 702,2101 703,801 703,1961 703,2497 704,389 704,562 704,969 704,1412 704,1483 704,1743 704,2113 704,2450 705,429 705,617 706,805 706,963 706,1240 706,2238 706,2645 707,763 708,836 708,1358 708,2212 708,2216 709,1896 709,1903 710,51 710,1392 710,2212 710,2213 711,252 711,414 711,496 711,539 711,644 711,1285 711,2111 711,2112 711,2113 712,850 712,1464 712,2480 713,1044 714,48 714,148 714,1385 715,2291 716,603 716,1810 716,1821 716,2409 717,1907 718,437 718,438 718,1416 718,2059 718,2261 719,302 719,303 719,306 719,1623 719,1810 720,371 720,392 720,1441 721,1034 722,1273 722,1567 722,1874 722,2500 722,2501 723,9 723,2614 724,1344 724,2394 724,2395 725,440 725,1104 725,1137 725,1652 725,2071 726,177 726,1533 726,2671 727,1386 727,2570 728,644 728,1070 728,1296 728,2388 728,2553 729,669 729,1159 729,1221 729,1701 729,2534 730,398 731,901 731,1279 731,2199 731,2203 732,263 732,296 732,364 732,1756 732,2685 733,45 733,94 733,218 733,377 733,383 733,401 733,435 733,678 733,759 733,794 733,862 733,1062 733,1160 733,1192 733,1265 733,1294 733,1329 733,1682 733,1817 733,1818 733,2008 733,2011 733,2035 733,2268 733,2291 733,2301 733,2302 733,2303 733,2304 734,95 734,408 734,736 734,751 734,964 734,1006 734,1388 734,1841 734,2056 734,2197 734,2202 734,2277 735,701 735,739 735,1237 735,1543 735,1881 735,1958 735,2060 735,2061 735,2062 736,95 736,734 736,751 736,964 736,1006 736,1388 736,1631 736,1841 736,2197 736,2202 737,88 737,415 737,1269 737,1630 737,1974 737,2136 737,2178 738,30 738,405 738,1080 738,1927 738,2162 739,393 739,701 739,735 739,1237 739,1543 739,1881 739,1958 740,141 740,1002 740,2033 741,831 741,1011 741,1088 741,1282 741,2093 742,1483 742,1620 742,1743 743,88 743,160 743,745 743,1239 743,1570 743,1986 744,223 744,580 744,1154 744,1358 745,160 745,366 745,553 745,743 745,1127 745,1986 745,1995 745,2009 746,281 746,1303 746,2006 747,113 747,282 747,540 747,1538 748,274 748,1103 748,1145 748,1169 748,1358 748,1374 748,1550 748,1568 748,1617 748,1732 748,2553 749,274 749,1333 749,2155 750,1441 751,734 751,736 751,1204 751,2198 751,2202 752,957 752,2083 752,2451 753,1269 753,1880 754,1358 754,1483 754,2450 755,1277 755,1898 755,2071 756,172 756,240 756,256 756,433 756,512 756,885 756,1469 756,1472 756,1692 756,2186 756,2187 757,1284 757,1358 757,2421 758,111 758,1358 758,1762 758,2492 759,733 759,1703 760,567 760,985 760,1426 760,1513 760,2459 760,2460 761,1401 761,1443 762,859 762,2448 763,693 763,707 763,1635 764,796 764,1358 764,1606 764,1612 765,640 765,1147 765,2367 766,316 766,598 766,845 766,1297 766,1868 767,54 767,873 767,1701 767,2314 768,1566 768,1723 768,1724 769,1927 770,1894 770,2117 771,55 771,65 771,1080 771,1156 772,908 773,1072 773,1505 774,560 775,171 775,180 775,2075 776,402 776,1413 776,1542 777,702 778,779 778,1224 778,1370 778,1914 778,1919 779,702 779,778 779,1224 779,1370 779,1592 779,1914 779,1919 779,1973 780,2341 781,218 781,2402 782,245 783,638 783,893 783,1061 783,1143 783,2376 784,960 784,1701 785,1664 786,947 787,55 787,325 787,438 788,1031 788,1952 788,2033 788,2041 788,2205 789,1240 789,1703 790,171 790,180 790,482 790,1548 790,1810 791,180 791,2034 791,2130 792,218 792,1488 792,1558 792,1986 792,2555 793,1896 793,1902 793,1903 793,2592 794,429 794,733 794,863 794,1160 794,1590 795,603 795,1645 795,1810 796,764 796,1103 796,1317 796,1358 797,73 797,800 797,1358 797,1833 797,2359 798,1381 798,1793 798,1794 798,1795 799,961 800,797 800,820 800,889 800,1834 801,703 801,1470 801,1961 801,2516 802,121 802,1307 803,528 803,2100 804,1307 805,275 805,706 805,963 805,2236 806,403 806,1383 807,661 807,1226 807,1955 807,1956 808,638 808,924 808,1785 808,2383 809,266 809,548 809,1115 809,2228 809,2229 810,1068 811,855 811,900 812,251 812,507 812,1300 812,1413 812,1542 813,339 813,2376 814,893 814,1158 814,2382 814,2383 815,55 815,88 815,1174 815,1344 815,2017 815,2018 816,120 816,436 816,483 816,1842 816,1980 816,2282 816,2405 817,90 817,155 817,156 817,220 817,221 817,1736 817,1763 817,2456 818,415 818,1999 819,154 819,364 819,650 819,1358 819,1606 820,800 820,889 821,222 822,702 822,1973 823,481 823,1169 823,1358 823,1765 823,2221 824,1831 825,1765 826,490 826,610 826,2287 826,2528 827,324 827,1039 827,1921 827,1999 828,444 828,1795 828,2464 829,1816 830,661 830,1914 830,2100 831,136 831,741 831,1011 831,1358 831,1638 831,1733 831,2093 832,2600 833,178 833,207 833,345 833,1130 833,1641 833,1678 833,2036 833,2495 833,2595 834,131 834,683 834,876 834,2168 835,1121 835,1134 835,1654 835,1810 836,519 836,708 836,1013 836,1131 836,1343 836,1572 836,2078 836,2403 837,1422 837,2248 837,2670 838,242 838,270 838,279 838,868 838,1131 838,2280 839,485 839,965 839,2277 840,1903 840,2481 841,88 841,2034 842,87 842,118 842,161 842,2016 843,505 843,548 843,2339 843,2542 844,264 844,472 844,1902 845,316 845,598 845,766 846,273 846,374 846,2146 847,2189 847,2422 848,228 848,985 848,1373 849,394 849,577 849,1993 849,2351 850,712 850,1464 850,2278 851,88 851,415 851,1309 851,2018 852,1800 853,1169 853,1358 853,1762 854,203 854,344 854,470 854,857 854,935 854,1097 854,1884 855,811 855,2493 856,1390 856,2248 857,203 857,470 857,854 857,1097 857,1246 858,2182 858,2502 859,487 859,762 859,1030 859,1199 859,2096 860,1427 860,1527 860,1758 861,95 861,1397 861,2068 861,2330 862,38 862,733 863,38 863,429 863,794 863,1160 863,1590 864,104 864,1065 864,2210 865,2653 866,40 866,1049 867,657 867,871 867,1229 867,1252 867,2439 867,2440 867,2442 867,2522 867,2523 868,838 868,988 868,1195 868,1341 868,1526 868,1844 868,2099 868,2276 869,232 869,598 869,1440 869,1701 869,1864 870,577 870,1119 870,2126 871,657 871,867 871,1229 871,2530 871,2652 872,1340 872,1413 872,1542 873,261 873,767 873,1358 873,1479 873,1708 873,2313 874,1701 875,310 875,914 875,1942 875,1945 875,1950 876,73 876,558 876,834 876,1358 876,2168 876,2584 877,1176 877,1177 877,1300 877,1413 877,1542 877,1935 878,436 878,885 878,2326 879,397 879,1558 880,973 880,1013 881,1155 881,1199 882,1358 883,227 883,609 883,629 883,933 884,89 884,152 885,436 885,651 885,756 885,878 885,1039 885,2024 885,2386 886,622 886,1400 887,239 887,306 887,910 887,1623 887,1624 888,614 888,1475 888,1556 889,800 889,820 889,1830 889,1831 889,1832 890,1269 890,1314 891,645 891,1674 891,2608 892,310 892,1950 893,638 893,783 893,814 893,911 893,1051 893,2383 894,640 894,1845 894,2367 895,35 895,440 895,1187 895,1296 895,1913 896,465 897,146 897,1152 897,1156 897,1410 897,1494 897,1907 897,1983 897,2295 898,92 898,1835 898,1836 898,2160 899,297 899,1055 899,1858 899,1986 900,639 900,811 901,731 901,1042 901,1279 901,2073 901,2186 901,2199 902,1284 902,1358 902,1604 903,446 903,2030 903,2031 904,132 904,379 904,541 904,647 904,1312 904,1360 904,1959 905,389 905,1282 905,1483 905,1620 906,577 906,2351 906,2353 907,1351 907,1916 908,772 908,1013 909,445 910,139 910,239 910,306 910,887 910,1623 910,2085 911,33 911,893 911,1051 911,1534 911,2376 912,2130 913,220 914,150 914,875 915,1035 915,1740 915,2415 915,2597 916,1026 917,2639 918,1098 918,1542 918,2065 919,1358 920,316 920,1893 921,1914 921,2134 921,2293 922,1307 922,1406 923,620 924,638 924,808 924,2383 925,1222 926,1862 927,17 927,1316 927,2140 928,327 928,1326 928,2063 929,1358 929,2627 930,380 930,477 930,2569 931,1433 932,662 933,534 933,883 933,1038 934,94 934,2356 935,451 935,661 935,854 935,973 935,1873 936,246 936,1067 936,2515 936,2530 936,2641 937,1180 937,1304 937,2096 938,618 938,2027 938,2230 939,2173 940,1829 941,2517 942,1924 942,1952 943,1196 944,2138 945,1072 945,1512 945,1911 945,2388 946,1966 946,2623 947,786 948,695 948,1395 948,1681 948,1682 949,523 950,93 950,437 950,645 951,328 951,1358 952,517 952,2546 953,2565 953,2566 953,2567 954,677 954,1112 955,175 955,1482 955,1914 956,492 956,2677 957,752 957,1154 957,1358 957,1557 957,1685 957,1757 957,2083 957,2167 958,306 958,1072 958,1798 959,2529 960,784 960,1776 960,2650 961,799 961,1728 961,2555 961,2599 962,1062 962,1665 962,1806 962,1807 962,1808 962,1809 962,1810 963,29 963,43 963,203 963,258 963,375 963,706 963,805 963,1094 963,1141 963,1157 963,1417 963,1443 963,1703 963,1785 963,2240 963,2399 963,2400 963,2401 963,2434 964,257 964,734 964,736 964,965 964,1388 964,2198 965,839 965,964 965,1693 965,2197 966,415 967,2659 968,598 968,1603 968,1986 969,704 969,1483 969,1735 969,1743 969,2450 970,16 970,364 970,466 970,1358 970,2365 971,107 971,1650 972,1000 972,2247 972,2579 972,2580 973,115 973,176 973,252 973,277 973,306 973,454 973,630 973,671 973,682 973,880 973,935 973,1072 973,1142 973,1583 973,2016 973,2019 973,2153 974,1496 975,2097 976,998 976,1431 977,1281 978,998 978,1358 979,524 979,1303 979,1503 979,1839 979,1957 979,2207 980,121 980,589 980,1367 980,1623 981,1159 981,1221 982,1091 982,1256 982,1458 982,2175 982,2176 983,2130 984,543 984,1068 984,2265 985,760 985,848 985,1073 985,1149 985,1358 986,2697 987,1175 988,868 989,1507 989,1645 989,2285 989,2436 990,310 990,1054 990,1542 991,307 992,496 992,596 993,702 993,2155 994,579 994,1219 994,1329 994,2309 995,1309 995,1912 995,2385 996,368 996,428 996,1135 996,1257 996,2248 996,2518 997,182 997,183 997,1837 998,976 998,978 998,1103 998,1284 998,1431 998,2365 999,346 999,1358 1000,281 1000,972 1000,1325 1000,2543 1001,12 1001,2662 1002,141 1002,622 1002,740 1002,1952 1002,2033 1002,2034 1003,363 1003,598 1003,1373 1003,1687 1003,2607 1004,1489 1004,1810 1005,1541 1006,734 1006,736 1006,1302 1007,526 1007,1154 1007,1742 1007,2466 1008,1416 1008,1922 1008,2059 1008,2575 1009,306 1009,2096 1010,443 1010,1966 1011,741 1011,831 1012,695 1012,1336 1012,1681 1012,1682 1012,1797 1013,69 1013,181 1013,334 1013,471 1013,506 1013,510 1013,530 1013,836 1013,880 1013,908 1013,1120 1013,1293 1013,1403 1013,1464 1013,1521 1013,1583 1013,1625 1013,1644 1013,1661 1013,1675 1013,1729 1013,1840 1013,1841 1013,1842 1013,1843 1013,1844 1013,1845 1013,1846 1013,1847 1013,1848 1013,1849 1013,1850 1013,1851 1013,2045 1014,1558 1015,698 1015,1068 1015,1143 1015,1385 1015,1425 1015,1452 1015,1481 1015,1519 1015,1618 1015,1788 1015,1789 1015,2262 1015,2263 1016,4 1016,561 1016,595 1016,1256 1016,2176 1017,591 1017,1475 1017,2472 1018,2378 1019,1457 1020,180 1020,218 1020,2075 1020,2077 1020,2667 1021,2309 1022,132 1022,379 1022,541 1022,1168 1022,1276 1022,1961 1022,1962 1022,1963 1023,1701 1023,1986 1023,2568 1024,625 1025,373 1025,1042 1026,916 1026,1303 1026,2034 1026,2531 1027,2394 1028,661 1029,118 1029,2166 1030,859 1031,48 1031,788 1031,1952 1032,587 1033,173 1033,687 1033,2168 1034,721 1035,73 1035,915 1035,1433 1035,1486 1035,1740 1035,1801 1035,1833 1036,2562 1037,403 1037,2447 1037,2654 1038,565 1038,933 1038,1358 1038,2503 1039,436 1039,827 1039,885 1040,1169 1040,1317 1040,1358 1040,1765 1041,609 1041,1243 1041,1358 1041,1466 1041,2390 1041,2448 1042,6 1042,74 1042,373 1042,485 1042,624 1042,901 1042,1025 1042,1047 1042,1118 1042,1125 1042,1198 1042,1481 1042,1517 1042,1628 1042,1925 1042,1926 1042,2051 1042,2052 1042,2054 1042,2055 1042,2073 1042,2198 1042,2333 1043,21 1043,2309 1044,713 1045,109 1045,306 1045,661 1045,1571 1045,1773 1046,91 1046,1510 1046,2336 1046,2387 1046,2587 1047,1042 1047,1588 1047,2333 1048,462 1049,866 1049,1432 1049,1894 1049,2610 1050,194 1050,1081 1050,1230 1050,1320 1050,1342 1050,1380 1050,1569 1050,1634 1050,2563 1050,2564 1051,33 1051,442 1051,893 1051,911 1051,2122 1051,2383 1052,1701 1053,229 1053,1405 1054,990 1054,1099 1054,1432 1054,1577 1054,1605 1054,1950 1055,899 1055,1577 1056,167 1056,2482 1057,2409 1058,1195 1059,1600 1060,1441 1061,783 1061,1196 1061,2376 1062,733 1062,962 1062,1192 1062,1810 1063,394 1063,577 1063,1518 1064,394 1064,2351 1064,2352 1065,85 1065,104 1065,401 1065,864 1065,1096 1065,1699 1065,2211 1066,1574 1067,59 1067,170 1067,936 1067,1216 1067,1830 1067,2307 1067,2448 1068,810 1068,984 1068,1015 1069,239 1070,728 1070,1072 1070,1167 1070,1358 1070,1470 1070,1725 1070,1829 1071,1135 1071,1257 1071,2248 1071,2671 1072,20 1072,189 1072,236 1072,244 1072,306 1072,342 1072,417 1072,773 1072,945 1072,958 1072,973 1072,1070 1072,1262 1072,1358 1072,1478 1072,1483 1072,1505 1072,1725 1072,1733 1072,1740 1072,1784 1072,1797 1072,1798 1072,1799 1072,1800 1072,1801 1072,1802 1072,1803 1072,1804 1072,1805 1073,316 1073,985 1073,2163 1074,1501 1074,1675 1074,1676 1075,1124 1075,1701 1076,116 1077,389 1077,1483 1077,2113 1077,2450 1078,591 1079,55 1079,210 1079,1218 1079,1914 1080,61 1080,149 1080,697 1080,738 1080,771 1080,2162 1080,2344 1081,1050 1081,2563 1082,1534 1082,2386 1083,321 1083,1232 1083,1450 1083,2114 1084,1213 1085,1421 1085,2109 1085,2110 1085,2394 1086,669 1086,1124 1086,2247 1086,2579 1087,89 1087,2434 1088,741 1088,1089 1089,399 1089,1088 1089,1552 1089,2086 1090,15 1090,640 1090,1093 1090,1147 1090,1271 1090,1598 1090,2367 1091,982 1091,1256 1091,2176 1092,1106 1092,1171 1092,2501 1093,15 1093,599 1093,1090 1093,1271 1093,1598 1093,2367 1094,89 1094,258 1094,963 1094,1369 1094,1443 1094,1653 1095,230 1095,298 1095,1325 1095,1810 1095,1986 1095,2613 1096,397 1096,401 1096,411 1096,1065 1096,1633 1097,470 1097,854 1097,857 1097,1115 1097,1869 1098,918 1098,1477 1098,2066 1098,2067 1099,1054 1099,1577 1099,1607 1100,598 1100,1701 1101,374 1101,509 1101,1242 1101,2146 1101,2148 1102,515 1102,1207 1102,2290 1102,2464 1102,2465 1103,53 1103,72 1103,263 1103,748 1103,796 1103,998 1103,1123 1103,1284 1103,1358 1103,1480 1103,1520 1103,1718 1103,1748 1103,1760 1103,1886 1103,1887 1103,1888 1104,597 1104,725 1104,2264 1105,578 1106,1092 1106,1874 1106,2501 1107,598 1107,605 1107,1810 1107,2243 1107,2379 1108,390 1109,1533 1109,2671 1109,2674 1109,2675 1110,1120 1110,1224 1110,2025 1110,2295 1111,1119 1111,1273 1111,2125 1111,2126 1111,2129 1112,954 1113,107 1113,1650 1114,1717 1114,2560 1115,203 1115,470 1115,593 1115,809 1115,1097 1115,1529 1115,2276 1116,568 1116,1223 1117,80 1117,434 1117,1628 1117,2499 1118,74 1118,1042 1118,1416 1118,2155 1119,870 1119,1111 1119,1235 1119,1273 1119,1462 1119,1663 1119,1697 1119,2124 1119,2125 1119,2126 1119,2127 1119,2128 1119,2129 1120,1013 1120,1110 1120,1583 1120,2025 1120,2194 1121,835 1121,1131 1121,1410 1121,1655 1121,1810 1121,2136 1122,458 1123,1103 1123,1358 1124,669 1124,1075 1124,1086 1125,1042 1125,2332 1126,1823 1127,553 1127,745 1127,1583 1127,1986 1128,1441 1128,1954 1128,2275 1129,577 1129,1518 1129,2351 1129,2352 1129,2353 1130,833 1130,2495 1131,242 1131,436 1131,490 1131,510 1131,836 1131,838 1131,1121 1131,1133 1131,1215 1131,1224 1131,1500 1131,1538 1131,1655 1131,1909 1131,1930 1131,2155 1131,2185 1131,2280 1131,2281 1131,2282 1131,2283 1132,311 1133,1131 1133,1500 1133,1538 1133,2185 1134,579 1134,835 1134,2296 1135,996 1135,1071 1135,1257 1135,2248 1135,2518 1135,2671 1135,2678 1136,73 1136,1189 1136,2359 1136,2554 1137,725 1138,82 1138,2248 1138,2250 1139,52 1139,1628 1139,2054 1139,2182 1140,476 1141,963 1141,2294 1142,973 1142,2326 1143,783 1143,1015 1143,1618 1143,2155 1143,2262 1143,2376 1144,1245 1144,1623 1145,748 1145,1169 1145,1358 1146,36 1146,1505 1146,1506 1146,2254 1147,395 1147,765 1147,1090 1147,1598 1147,1865 1147,2367 1147,2371 1148,1317 1148,1747 1148,2220 1148,2221 1149,985 1149,1358 1149,1894 1149,1986 1150,1243 1151,2570 1151,2700 1152,897 1152,1927 1152,2155 1152,2416 1153,258 1153,1401 1154,223 1154,357 1154,744 1154,957 1154,1007 1154,1358 1154,1714 1154,1715 1154,1742 1154,2514 1154,2515 1155,881 1155,1229 1156,55 1156,65 1156,771 1156,897 1157,89 1157,963 1157,2240 1157,2463 1158,121 1158,302 1158,306 1158,589 1158,814 1158,1635 1158,2251 1158,2252 1158,2382 1159,729 1159,981 1159,2534 1160,38 1160,401 1160,733 1160,794 1160,863 1160,2268 1161,110 1162,245 1162,1510 1163,1402 1163,2132 1164,1287 1165,145 1165,537 1165,1593 1166,1986 1166,2582 1167,643 1167,1070 1168,1022 1168,1955 1169,111 1169,188 1169,301 1169,439 1169,524 1169,552 1169,628 1169,689 1169,748 1169,823 1169,853 1169,1040 1169,1145 1169,1358 1169,1714 1169,1719 1169,1720 1169,1731 1169,1734 1169,1737 1169,2220 1169,2476 1169,2492 1170,404 1170,1476 1171,510 1171,649 1171,681 1171,687 1171,1092 1171,1295 1171,1355 1171,1855 1171,1909 1171,2359 1172,304 1172,467 1173,202 1173,353 1173,1250 1174,88 1174,162 1174,415 1174,815 1174,1912 1174,2394 1175,987 1175,2359 1176,295 1176,507 1176,877 1176,1542 1176,1935 1177,295 1177,877 1177,1542 1177,1935 1178,1529 1178,1908 1178,1984 1178,2350 1179,410 1179,1955 1180,505 1180,937 1180,1304 1181,474 1182,472 1182,559 1182,1183 1182,1579 1183,472 1183,1182 1183,1354 1183,1579 1183,1824 1183,1825 1184,1190 1184,2100 1185,278 1185,1460 1185,1992 1185,2349 1185,2358 1185,2589 1185,2590 1186,2535 1186,2574 1187,895 1187,1188 1188,1187 1189,73 1189,558 1189,1136 1189,1358 1189,2359 1190,37 1190,1184 1190,1387 1191,1558 1191,2241 1191,2339 1192,733 1192,1062 1192,1621 1193,306 1193,1705 1194,368 1194,1366 1194,2670 1195,270 1195,279 1195,868 1195,1058 1196,943 1196,1061 1196,1367 1196,1624 1196,2300 1197,1791 1197,1998 1198,1042 1199,859 1199,881 1199,1214 1199,1566 1199,1599 1199,1716 1200,1502 1200,2207 1200,2414 1201,457 1201,2214 1201,2533 1202,1428 1202,1510 1202,2336 1202,2376 1202,2524 1203,382 1203,424 1203,461 1203,1215 1203,1410 1203,1842 1203,2155 1204,751 1204,1330 1204,1602 1204,1838 1204,1839 1205,319 1205,1358 1205,1761 1206,1257 1206,2671 1207,1102 1207,2290 1207,2464 1208,187 1209,64 1209,1358 1209,1737 1210,1648 1211,254 1211,507 1212,1701 1213,607 1213,1084 1213,1290 1214,73 1214,337 1214,1199 1214,1499 1214,1716 1214,1745 1215,270 1215,1131 1215,1203 1215,1894 1216,526 1216,1067 1216,2446 1216,2503 1217,230 1217,396 1218,586 1218,1079 1218,1927 1218,2116 1219,45 1219,78 1219,994 1220,239 1221,729 1221,981 1221,1577 1221,1607 1221,1949 1222,925 1222,1224 1223,568 1223,1116 1224,586 1224,682 1224,778 1224,779 1224,1110 1224,1131 1224,1222 1224,1291 1224,1341 1224,1370 1224,1525 1224,1526 1224,1583 1224,1587 1224,1660 1224,1732 1224,1848 1224,1851 1224,1919 1224,1975 1224,2151 1224,2152 1224,2153 1224,2154 1224,2155 1224,2156 1225,1450 1225,2579 1226,807 1226,1955 1226,1956 1226,2528 1227,1269 1228,186 1228,1536 1228,2580 1229,657 1229,867 1229,871 1229,1155 1229,1254 1229,1308 1229,1358 1229,1384 1229,1506 1229,1627 1229,1749 1229,2439 1229,2440 1229,2441 1229,2442 1230,1050 1230,1342 1231,653 1232,624 1232,1083 1233,2433 1234,22 1234,1702 1234,1703 1234,1966 1235,1119 1235,1462 1235,2126 1235,2577 1236,2479 1237,735 1237,739 1237,1958 1238,154 1238,1358 1239,743 1239,2027 1239,2611 1240,258 1240,706 1240,789 1240,1443 1240,1702 1240,2237 1241,310 1241,1701 1241,1950 1242,1101 1242,2146 1242,2148 1243,1041 1243,1150 1243,1358 1244,493 1245,306 1245,542 1245,1144 1245,1770 1245,2080 1246,857 1247,1679 1248,603 1248,1651 1248,2045 1249,1483 1249,2556 1249,2558 1250,202 1250,328 1250,650 1250,1173 1250,2507 1251,102 1251,306 1251,505 1251,1448 1251,1623 1252,867 1252,2656 1253,302 1253,308 1254,657 1254,1229 1254,1308 1255,198 1255,2248 1256,4 1256,595 1256,982 1256,1016 1256,1091 1256,1761 1256,2175 1256,2176 1257,428 1257,492 1257,688 1257,996 1257,1071 1257,1135 1257,1206 1257,2248 1257,2249 1257,2518 1257,2538 1257,2671 1257,2673 1257,2677 1257,2678 1257,2679 1258,452 1258,505 1258,644 1259,356 1259,2342 1260,1559 1260,2250 1261,2130 1262,110 1262,189 1262,564 1262,567 1262,1072 1262,1509 1263,1407 1264,248 1264,443 1264,1531 1265,377 1265,733 1265,2291 1266,255 1266,1529 1266,1984 1267,645 1267,647 1267,1824 1268,162 1268,1929 1268,2309 1269,737 1269,753 1269,890 1269,1227 1269,1314 1269,1630 1269,1880 1269,2227 1270,1622 1270,2034 1271,15 1271,599 1271,1090 1271,1093 1271,2367 1272,310 1272,1945 1272,1947 1272,1950 1273,722 1273,1111 1273,1119 1273,2034 1273,2124 1273,2125 1273,2126 1273,2129 1274,239 1275,405 1275,1468 1276,458 1276,1022 1276,1962 1277,755 1278,2268 1278,2305 1278,2306 1279,731 1279,901 1279,2186 1279,2203 1280,449 1280,2612 1281,977 1281,1358 1281,1746 1281,1748 1282,684 1282,741 1282,905 1282,1283 1282,1483 1282,1735 1282,1776 1282,2324 1283,1282 1283,1776 1283,2324 1284,757 1284,902 1284,998 1284,1103 1284,1358 1284,1604 1284,2450 1285,711 1285,2182 1286,538 1287,59 1287,481 1287,1164 1287,1358 1288,88 1288,1309 1289,1622 1289,1705 1290,212 1290,1213 1290,2258 1291,1224 1291,1660 1291,2154 1292,689 1292,1317 1292,1358 1293,65 1293,1013 1293,2418 1294,352 1294,733 1295,1171 1295,1987 1296,35 1296,440 1296,728 1296,895 1296,1910 1296,1911 1296,1912 1296,1913 1297,316 1297,598 1297,766 1298,2703 1299,598 1299,1701 1299,1810 1300,251 1300,507 1300,812 1300,877 1300,1542 1300,1933 1300,1940 1300,1941 1300,2508 1301,25 1301,598 1301,1315 1301,1316 1301,1542 1301,2140 1302,1006 1303,95 1303,746 1303,979 1303,1026 1303,2163 1304,505 1304,937 1304,1180 1305,466 1305,1358 1306,364 1306,1317 1307,802 1307,804 1307,922 1307,1444 1307,2536 1308,1229 1308,1254 1308,1627 1309,61 1309,88 1309,415 1309,490 1309,851 1309,995 1309,1288 1309,1338 1309,1625 1309,1677 1309,1741 1309,1882 1309,2015 1309,2102 1309,2103 1309,2178 1310,2692 1311,468 1311,1312 1311,1313 1311,2080 1312,904 1312,1311 1312,1313 1313,468 1313,573 1313,1311 1313,1312 1313,2407 1314,514 1314,890 1314,1269 1315,17 1315,1301 1316,17 1316,927 1316,1301 1316,1679 1317,689 1317,796 1317,1040 1317,1148 1317,1292 1317,1306 1317,1719 1317,1720 1317,1739 1317,2220 1317,2221 1318,12 1318,2661 1318,2662 1319,186 1319,2034 1320,1050 1320,1349 1320,1491 1320,2684 1321,2501 1322,63 1322,2265 1323,1701 1324,2035 1324,2265 1325,298 1325,327 1325,1000 1325,1095 1325,2063 1325,2247 1326,928 1326,2063 1327,495 1327,1328 1327,2161 1328,495 1328,1327 1328,2160 1329,78 1329,733 1329,994 1330,1204 1330,1837 1330,2068 1331,310 1331,1576 1331,1810 1332,436 1332,621 1332,2024 1333,749 1333,1973 1333,2195 1333,2312 1334,1542 1334,1577 1334,1701 1334,1941 1334,1950 1335,1856 1335,2087 1335,2090 1336,86 1336,695 1336,1012 1336,1452 1336,1797 1336,2032 1336,2033 1336,2034 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1604,1358 1605,1054 1605,1950 1605,2663 1606,364 1606,764 1606,819 1607,1099 1607,1221 1607,1542 1608,546 1608,2124 1608,2126 1608,2489 1609,1790 1609,1791 1609,1912 1610,244 1610,312 1610,565 1610,687 1610,2556 1610,2557 1610,2558 1611,1462 1611,2124 1612,764 1613,1356 1614,210 1614,1671 1614,2034 1615,1665 1616,56 1616,118 1616,412 1616,447 1616,539 1616,581 1616,1402 1616,1849 1616,2050 1617,748 1618,429 1618,1015 1618,1143 1618,1425 1618,1789 1619,392 1619,1441 1619,2269 1620,359 1620,742 1620,905 1620,1358 1620,1483 1620,2450 1621,1192 1621,1424 1622,124 1622,1270 1622,1289 1622,2425 1623,102 1623,112 1623,126 1623,133 1623,139 1623,153 1623,314 1623,350 1623,384 1623,452 1623,459 1623,542 1623,556 1623,581 1623,608 1623,660 1623,719 1623,887 1623,910 1623,980 1623,1144 1623,1251 1623,1560 1623,1561 1623,1767 1623,1768 1623,1769 1623,1770 1623,1771 1623,1772 1623,1773 1623,1774 1623,1775 1623,1776 1623,1777 1623,1778 1623,1779 1623,1780 1623,1781 1623,1782 1623,1783 1623,1784 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1975,1421 1975,1676 1975,1973 1975,2109 1975,2110 1976,147 1976,502 1976,1973 1977,436 1977,1526 1978,249 1978,436 1978,478 1978,514 1978,621 1979,436 1979,1842 1979,1980 1979,2178 1979,2405 1980,436 1980,816 1980,1842 1980,1979 1980,2405 1981,436 1981,490 1981,1526 1982,130 1982,436 1983,55 1983,438 1983,897 1983,2034 1984,438 1984,651 1984,1178 1984,1266 1984,1529 1985,437 1985,438 1986,2 1986,45 1986,68 1986,71 1986,151 1986,160 1986,179 1986,201 1986,215 1986,232 1986,335 1986,366 1986,391 1986,460 1986,476 1986,519 1986,566 1986,673 1986,681 1986,743 1986,745 1986,792 1986,899 1986,968 1986,1023 1986,1095 1986,1127 1986,1149 1986,1166 1986,1434 1986,1453 1986,1558 1986,1574 1986,1697 1986,1704 1986,1709 1986,1812 1986,1859 1986,1870 1986,1873 1986,1875 1986,1876 1986,1987 1986,1988 1986,1989 1986,1990 1986,1991 1986,1992 1986,1993 1986,1994 1986,1995 1986,1996 1986,1997 1986,1998 1986,1999 1986,2000 1986,2001 1986,2002 1986,2003 1986,2004 1986,2005 1986,2006 1986,2007 1986,2008 1986,2009 1987,1295 1987,1986 1987,2004 1987,2509 1988,396 1988,1986 1989,460 1989,1986 1990,1986 1991,1986 1991,2325 1992,1185 1992,1986 1993,849 1993,1986 1994,169 1994,1986 1995,553 1995,745 1995,1583 1995,1986 1996,8 1996,327 1996,1986 1996,2063 1996,2064 1997,1347 1997,1986 1997,2412 1998,109 1998,191 1998,519 1998,695 1998,1197 1998,1781 1998,1986 1998,2326 1999,285 1999,818 1999,827 1999,1986 2000,160 2000,267 2000,314 2000,1986 2001,91 2001,429 2001,503 2001,574 2001,1986 2001,2002 2001,2003 2001,2044 2001,2121 2001,2123 2001,2335 2001,2348 2001,2378 2001,2379 2001,2380 2001,2381 2002,1986 2002,2001 2002,2379 2003,185 2003,332 2003,1986 2003,2001 2003,2123 2004,180 2004,316 2004,1986 2004,1987 2005,1986 2006,746 2006,1986 2006,2477 2007,1986 2008,733 2008,1986 2008,2301 2009,160 2009,553 2009,745 2009,1986 2009,2025 2010,88 2010,118 2010,161 2010,2016 2011,25 2011,88 2011,733 2012,88 2012,272 2013,88 2013,471 2014,88 2014,415 2015,88 2015,1309 2015,2071 2016,88 2016,842 2016,973 2016,2010 2016,2071 2017,88 2017,130 2017,815 2017,1487 2017,2467 2018,76 2018,356 2018,621 2018,815 2018,851 2018,1658 2018,2019 2019,973 2019,2018 2020,55 2020,323 2021,55 2021,65 2021,239 2021,1628 2021,2418 2022,323 2022,454 2022,2190 2023,651 2023,1512 2023,2217 2024,478 2024,651 2024,885 2024,1332 2024,2156 2024,2178 2025,149 2025,572 2025,671 2025,1110 2025,1120 2025,1357 2025,1498 2025,1583 2025,2009 2025,2026 2025,2027 2025,2028 2026,487 2026,2025 2026,2045 2026,2096 2027,938 2027,1239 2027,2025 2027,2360 2028,2025 2029,472 2029,1543 2029,1579 2030,118 2030,903 2030,2112 2031,903 2031,2436 2032,1336 2033,740 2033,788 2033,1002 2033,1336 2034,14 2034,49 2034,86 2034,141 2034,158 2034,224 2034,382 2034,417 2034,617 2034,691 2034,791 2034,841 2034,1002 2034,1026 2034,1270 2034,1273 2034,1319 2034,1336 2034,1448 2034,1497 2034,1614 2034,1654 2034,1665 2034,1807 2034,1812 2034,1889 2034,1891 2034,1894 2034,1929 2034,1968 2034,1983 2034,2035 2034,2036 2034,2037 2034,2038 2034,2039 2034,2040 2034,2041 2034,2042 2034,2130 2035,733 2035,1324 2035,2034 2036,833 2036,2034 2037,180 2037,2034 2038,293 2038,2034 2039,1889 2039,2034 2039,2042 2040,33 2040,2034 2040,2120 2040,2122 2041,48 2041,429 2041,788 2041,2034 2042,2034 2042,2039 2043,429 2043,2406 2044,429 2044,2001 2045,109 2045,126 2045,133 2045,139 2045,153 2045,215 2045,236 2045,306 2045,308 2045,318 2045,341 2045,519 2045,563 2045,603 2045,699 2045,1013 2045,1248 2045,1337 2045,1448 2045,1651 2045,1772 2045,1776 2045,1784 2045,1787 2045,1791 2045,1830 2045,1852 2045,1856 2045,2026 2045,2046 2045,2047 2045,2048 2046,236 2046,306 2046,484 2046,2045 2046,2048 2047,294 2047,2045 2048,306 2048,2045 2048,2046 2049,80 2049,142 2050,1616 2050,2485 2051,1042 2051,1926 2051,2364 2052,74 2052,544 2052,1042 2052,1926 2053,52 2053,1628 2054,95 2054,456 2054,525 2054,1042 2054,1139 2054,1540 2054,1602 2054,1628 2054,2133 2055,1042 2055,1588 2055,1628 2055,2198 2056,100 2056,408 2056,734 2056,1628 2056,1680 2056,1841 2056,2311 2056,2576 2057,525 2057,1628 2058,635 2058,1378 2058,2150 2059,146 2059,405 2059,718 2059,1008 2059,1435 2059,1906 2060,735 2061,735 2062,701 2062,735 2063,327 2063,928 2063,1325 2063,1326 2063,1996 2064,327 2064,1996 2065,918 2065,2066 2065,2067 2066,1098 2066,1477 2066,2065 2066,2122 2067,1098 2067,1477 2067,2065 2068,861 2068,1330 2068,1377 2069,702 2069,1377 2069,2070 2070,702 2070,1377 2070,2069 2071,725 2071,755 2071,1435 2071,1566 2071,1592 2071,1840 2071,2015 2071,2016 2072,1395 2072,1602 2072,2182 2073,901 2073,1042 2073,1602 2074,95 2074,1602 2074,2181 2074,2277 2075,14 2075,775 2075,1020 2075,2076 2075,2077 2075,2091 2075,2667 2075,2668 2076,180 2076,218 2076,2075 2076,2077 2076,2667 2077,14 2077,486 2077,1020 2077,1704 2077,2075 2077,2076 2078,236 2078,306 2078,836 2078,1776 2079,126 2079,236 2079,1802 2080,112 2080,306 2080,487 2080,608 2080,655 2080,1245 2080,1311 2080,1367 2080,1459 2080,1770 2081,484 2081,1705 2082,18 2082,133 2083,367 2083,505 2083,650 2083,752 2083,957 2083,1483 2083,1550 2083,1557 2083,1685 2083,2168 2084,306 2084,350 2084,409 2085,306 2085,350 2085,910 2085,1490 2085,2089 2086,306 2086,1089 2086,1505 2086,2094 2087,306 2087,1335 2088,306 2088,1797 2089,306 2089,350 2089,2085 2090,306 2090,350 2090,656 2090,1335 2091,218 2091,306 2091,2075 2092,109 2093,109 2093,741 2093,831 2094,36 2094,109 2094,441 2094,530 2094,2086 2094,2106 2095,109 2095,135 2095,2145 2095,2329 2095,2504 2096,859 2096,937 2096,1009 2096,1784 2096,1856 2096,2026 2097,79 2097,522 2097,975 2097,2098 2098,2097 2099,490 2099,868 2099,1526 2099,2425 2100,803 2100,830 2100,1184 2100,2101 2101,702 2101,2100 2102,1309 2102,1912 2102,2385 2103,1309 2103,1912 2103,2385 2104,516 2105,490 2105,517 2106,36 2106,2094 2107,36 2107,399 2107,1505 2107,1781 2108,693 2108,1519 2109,604 2109,1085 2109,1396 2109,1421 2109,1975 2109,2110 2110,1085 2110,1421 2110,1975 2110,2109 2111,711 2112,118 2112,255 2112,711 2112,1690 2112,2030 2112,2436 2113,704 2113,711 2113,1077 2113,1483 2113,1743 2113,2450 2114,386 2114,1083 2114,2509 2114,2519 2114,2588 2115,386 2115,2117 2115,2519 2116,356 2116,1218 2117,386 2117,770 2117,1508 2117,1846 2117,1867 2117,1894 2117,2115 2117,2118 2118,229 2118,1894 2118,2117 2119,33 2119,218 2120,33 2120,442 2120,665 2120,2040 2120,2637 2121,33 2121,2001 2121,2122 2122,91 2122,196 2122,332 2122,627 2122,665 2122,1051 2122,2040 2122,2066 2122,2121 2122,2123 2123,91 2123,330 2123,2001 2123,2003 2123,2122 2123,2380 2124,1119 2124,1273 2124,1608 2124,1611 2124,2125 2124,2126 2124,2127 2125,1111 2125,1119 2125,1273 2125,2124 2125,2126 2126,870 2126,1111 2126,1119 2126,1235 2126,1273 2126,1608 2126,2124 2126,2125 2127,546 2127,1119 2127,2124 2127,2130 2128,1119 2128,2129 2129,1111 2129,1119 2129,1273 2129,2128 2130,430 2130,691 2130,791 2130,912 2130,983 2130,1261 2130,1889 2130,1890 2130,1891 2130,2034 2130,2127 2130,2249 2131,1463 2131,2133 2131,2182 2132,1163 2132,1463 2132,1482 2132,1683 2133,276 2133,434 2133,1463 2133,1695 2133,2054 2133,2131 2133,2182 2134,921 2134,1351 2135,175 2135,190 2135,2282 2136,737 2136,1121 2136,1655 2136,1671 2137,1394 2137,1487 2137,1671 2138,548 2138,598 2138,944 2139,24 2139,1636 2139,2140 2139,2141 2140,17 2140,927 2140,1301 2140,1679 2140,2139 2141,24 2141,1636 2141,2139 2141,2142 2142,2141 2143,303 2143,1367 2143,1777 2143,1787 2144,135 2144,137 2144,2145 2144,2329 2144,2331 2144,2504 2145,18 2145,1512 2145,2095 2145,2144 2146,374 2146,509 2146,846 2146,1101 2146,1242 2146,2147 2146,2148 2147,374 2147,455 2147,658 2147,1664 2147,2146 2147,2486 2148,509 2148,1101 2148,1242 2148,2146 2149,374 2150,1378 2150,2058 2151,93 2151,1224 2151,2423 2152,1224 2152,2385 2153,973 2153,1224 2153,2155 2154,1224 2154,1291 2154,1587 2154,1660 2155,74 2155,280 2155,539 2155,586 2155,749 2155,993 2155,1118 2155,1131 2155,1143 2155,1152 2155,1203 2155,1224 2155,1535 2155,2153 2155,2293 2155,2294 2155,2295 2156,324 2156,651 2156,1224 2156,2024 2157,108 2157,1835 2157,2158 2157,2159 2157,2160 2158,2157 2159,23 2159,2157 2159,2160 2160,898 2160,1328 2160,1647 2160,1698 2160,1835 2160,2157 2160,2159 2160,2161 2161,1327 2161,2160 2162,30 2162,61 2162,738 2162,1080 2162,2163 2163,1073 2163,1303 2163,1348 2163,1502 2163,2162 2164,87 2164,2217 2164,2282 2165,118 2165,279 2165,1343 2166,118 2166,1029 2167,957 2168,834 2168,876 2168,1033 2168,1557 2168,1586 2168,1726 2168,2083 2168,2169 2169,131 2169,683 2169,1546 2169,1547 2169,2168 2170,1357 2170,2171 2171,2170 2172,52 2172,525 2172,1467 2172,1628 2172,2182 2173,939 2173,2174 2174,2173 2175,4 2175,982 2175,1256 2175,1761 2175,2176 2176,4 2176,595 2176,982 2176,1016 2176,1091 2176,1256 2176,1382 2176,2175 2177,398 2177,644 2177,2367 2177,2371 2178,76 2178,88 2178,415 2178,737 2178,1309 2178,1979 2178,2024 2179,440 2180,81 2180,257 2180,525 2180,2182 2180,2183 2181,95 2181,142 2181,525 2181,1388 2181,2074 2181,2196 2181,2197 2181,2202 2182,52 2182,95 2182,239 2182,415 2182,525 2182,858 2182,1139 2182,1285 2182,1515 2182,1838 2182,2072 2182,2131 2182,2133 2182,2172 2182,2180 2182,2198 2182,2231 2182,2232 2182,2233 2183,95 2183,525 2183,2180 2184,70 2184,441 2185,1131 2185,1133 2185,1500 2185,1538 2186,756 2186,901 2186,1279 2186,1692 2186,2199 2187,172 2187,756 2187,1472 2187,1692 2188,454 2189,69 2189,454 2189,847 2189,1395 2189,1682 2189,1926 2190,454 2190,2022 2191,387 2192,144 2192,213 2192,495 2192,537 2193,2194 2194,214 2194,324 2194,1120 2194,2193 2194,2195 2195,594 2195,663 2195,1333 2195,2194 2196,1631 2196,2181 2197,95 2197,734 2197,736 2197,965 2197,1388 2197,2181 2198,751 2198,964 2198,1042 2198,2055 2198,2182 2199,95 2199,456 2199,544 2199,680 2199,731 2199,901 2199,1580 2199,2186 2199,2200 2199,2201 2200,95 2200,1580 2200,2199 2201,95 2201,552 2201,2199 2202,734 2202,736 2202,751 2202,2181 2203,731 2203,1279 2203,1801 2203,2330 2203,2511 2204,1951 2204,1952 2204,2521 2205,48 2205,788 2205,1952 2206,48 2206,1951 2206,1952 2207,979 2207,1200 2207,2241 2208,1483 2209,108 2209,1504 2209,1647 2210,104 2210,864 2211,1065 2211,2356 2212,708 2212,710 2212,1392 2212,2216 2213,51 2213,421 2213,710 2214,51 2214,1201 2214,2216 2215,51 2215,457 2215,1724 2215,2216 2216,421 2216,457 2216,708 2216,1724 2216,2212 2216,2214 2216,2215 2217,96 2217,175 2217,231 2217,2023 2217,2164 2218,1411 2218,1459 2219,475 2219,485 2219,1838 2220,1148 2220,1169 2220,1317 2220,2221 2220,2525 2221,823 2221,1148 2221,1317 2221,1739 2221,2220 2221,2507 2222,75 2222,284 2222,2224 2222,2225 2223,75 2223,84 2223,284 2223,2224 2224,75 2224,84 2224,284 2224,583 2224,2222 2224,2223 2224,2225 2224,2226 2225,75 2225,284 2225,583 2225,2222 2225,2224 2226,84 2226,284 2226,2224 2227,266 2227,634 2227,1269 2227,1399 2227,1630 2227,2228 2228,809 2228,1396 2228,1501 2228,2227 2228,2394 2228,2395 2229,266 2229,601 2229,809 2230,482 2230,606 2230,938 2230,2296 2231,2182 2231,2292 2232,315 2232,1376 2232,2182 2233,636 2233,2182 2233,2291 2234,1515 2235,612 2235,676 2235,1955 2236,151 2236,805 2236,1969 2236,2237 2237,1240 2237,2236 2237,2238 2238,22 2238,151 2238,152 2238,627 2238,706 2238,1702 2238,1703 2238,1969 2238,2237 2238,2239 2238,2240 2239,2238 2240,152 2240,963 2240,1157 2240,1443 2240,1530 2240,2238 2240,2399 2241,500 2241,1191 2241,1503 2241,1957 2241,2207 2241,2242 2242,2241 2242,2539 2243,1107 2243,1503 2243,2244 2243,2245 2243,2246 2244,281 2244,2243 2245,2243 2245,2246 2246,1595 2246,2243 2246,2245 2246,2247 2247,281 2247,972 2247,1086 2247,1325 2247,2246 2247,2509 2247,2543 2248,348 2248,428 2248,837 2248,856 2248,996 2248,1071 2248,1135 2248,1138 2248,1255 2248,1257 2248,1366 2248,1461 2248,1545 2248,2249 2249,368 2249,1257 2249,2130 2249,2248 2249,2518 2249,2671 2250,283 2250,348 2250,1138 2250,1260 2251,121 2251,1158 2251,2252 2252,121 2252,1158 2252,2251 2253,1697 2254,1146 2255,225 2256,102 2256,1878 2257,1728 2258,1290 2259,1419 2259,1436 2259,2335 2259,2337 2260,529 2260,1417 2260,1419 2261,718 2261,1474 2262,1015 2262,1143 2263,94 2263,1015 2263,2490 2264,1104 2265,984 2265,1322 2265,1324 2266,1395 2266,2267 2266,2321 2266,2364 2267,1395 2267,2266 2268,309 2268,383 2268,733 2268,1160 2268,1278 2268,2291 2269,20 2269,370 2269,392 2269,1415 2269,1619 2269,1903 2269,2270 2270,20 2270,128 2270,1354 2270,1414 2270,2269 2270,2375 2271,1441 2272,1441 2273,1441 2274,1370 2274,1441 2274,1527 2275,1128 2275,1441 2275,1954 2276,868 2276,1115 2276,1844 2277,734 2277,839 2277,2074 2278,850 2278,1359 2279,110 2279,565 2279,2466 2280,242 2280,270 2280,279 2280,838 2280,1131 2281,1131 2281,1842 2281,2405 2282,816 2282,1131 2282,1351 2282,1655 2282,2135 2282,2164 2283,575 2283,1131 2283,1382 2284,1901 2284,2285 2285,451 2285,989 2285,2284 2285,2286 2286,1549 2286,1901 2286,2285 2287,610 2287,826 2287,2288 2288,114 2288,610 2288,2287 2289,444 2289,584 2289,623 2289,2464 2290,444 2290,1102 2290,1207 2290,2464 2290,2496 2291,377 2291,481 2291,715 2291,733 2291,1265 2291,1682 2291,2233 2291,2268 2291,2292 2292,2231 2292,2291 2293,921 2293,1535 2293,2155 2294,1141 2294,2155 2295,86 2295,897 2295,1110 2295,1655 2295,2155 2296,313 2296,1134 2296,2230 2297,1796 2297,2298 2297,2299 2298,2297 2299,1795 2299,2297 2300,1196 2301,733 2301,2008 2302,733 2302,1692 2303,45 2303,733 2303,2541 2304,465 2304,469 2304,733 2304,2385 2305,309 2305,453 2305,1278 2305,1818 2305,1909 2305,2306 2306,453 2306,1278 2306,1818 2306,2305 2306,2552 2307,482 2307,1067 2307,1742 2308,159 2308,482 2308,531 2308,2559 2309,210 2309,461 2309,994 2309,1021 2309,1043 2309,1268 2309,1399 2309,1869 2310,21 2310,1920 2311,2056 2311,2576 2312,61 2312,1333 2313,873 2313,1708 2314,767 2314,1708 2315,1344 2316,1343 2317,25 2317,1403 2317,1928 2318,1681 2318,1779 2319,695 2319,1681 2319,1682 2320,1681 2320,1682 2321,1682 2321,2266 2322,1705 2323,344 2323,1444 2324,1282 2324,1283 2324,1735 2324,1776 2325,508 2325,1768 2325,1991 2326,878 2326,1142 2326,1782 2326,1998 2327,699 2327,1490 2327,1778 2327,2328 2328,2327 2329,137 2329,397 2329,2095 2329,2144 2329,2330 2329,2331 2330,861 2330,2203 2330,2329 2331,2144 2331,2329 2332,1125 2332,1481 2332,1669 2333,1042 2333,1047 2333,1588 2334,174 2334,1725 2335,151 2335,627 2335,1385 2335,1474 2335,1481 2335,1519 2335,2001 2335,2259 2335,2336 2336,1046 2336,1202 2336,1428 2336,2335 2336,2524 2337,2259 2338,1558 2338,2555 2339,843 2339,1191 2339,1558 2339,2340 2340,1558 2340,2339 2341,780 2342,1259 2343,30 2343,2344 2344,279 2344,1080 2344,2343 2344,2475 2345,1692 2346,1469 2346,1692 2346,2349 2347,456 2347,544 2347,1692 2348,576 2348,1692 2348,2001 2349,1185 2349,1460 2349,1469 2349,1498 2349,1692 2349,2346 2349,2358 2350,1178 2350,1417 2350,1529 2351,394 2351,577 2351,849 2351,906 2351,1064 2351,1129 2352,577 2352,1064 2352,1129 2353,577 2353,906 2353,1129 2354,577 2355,94 2355,2356 2355,2357 2356,675 2356,934 2356,2211 2356,2355 2356,2357 2357,39 2357,94 2357,1846 2357,2355 2357,2356 2358,631 2358,1185 2358,1460 2358,1469 2358,2349 2359,290 2359,480 2359,687 2359,797 2359,1136 2359,1171 2359,1175 2359,1189 2359,1433 2359,1834 2359,2372 2360,27 2360,606 2360,2027 2360,2578 2361,606 2362,442 2363,125 2363,1555 2364,667 2364,2051 2364,2266 2365,391 2365,616 2365,970 2365,998 2365,1565 2365,1709 2365,1738 2366,46 2366,686 2366,1738 2367,15 2367,395 2367,765 2367,894 2367,1090 2367,1093 2367,1147 2367,1271 2367,1598 2367,2177 2367,2368 2367,2369 2367,2370 2367,2371 2368,2367 2368,2370 2369,2367 2369,2370 2370,2367 2370,2368 2370,2369 2371,1147 2371,2177 2371,2367 2372,480 2372,687 2372,2359 2373,267 2374,20 2375,20 2375,371 2375,1404 2375,2270 2376,783 2376,813 2376,911 2376,1061 2376,1143 2376,1202 2376,1428 2377,372 2378,1018 2378,2001 2379,1107 2379,2001 2379,2002 2380,91 2380,2001 2380,2123 2381,1662 2381,1666 2381,2001 2382,814 2382,1158 2382,2383 2383,299 2383,588 2383,808 2383,814 2383,893 2383,924 2383,1051 2383,1484 2383,1635 2383,2382 2384,1655 2385,191 2385,995 2385,1338 2385,2102 2385,2103 2385,2152 2385,2304 2386,299 2386,885 2386,1082 2387,271 2387,299 2387,638 2387,1046 2387,1406 2387,1510 2388,175 2388,551 2388,728 2388,945 2388,1377 2388,1914 2389,1740 2389,2451 2390,489 2390,1041 2390,1740 2390,2391 2390,2451 2391,489 2391,1740 2391,2390 2391,2451 2392,535 2392,1740 2392,2451 2393,368 2393,1634 2394,88 2394,471 2394,504 2394,600 2394,724 2394,1027 2394,1085 2394,1174 2394,1396 2394,1399 2394,1420 2394,1421 2394,2228 2394,2395 2394,2396 2394,2397 2395,724 2395,1396 2395,1501 2395,2228 2395,2394 2396,504 2396,1420 2396,2394 2397,2394 2398,1662 2398,2493 2399,43 2399,963 2399,1443 2399,2240 2399,2434 2400,43 2400,963 2401,375 2401,963 2401,2434 2401,2435 2402,781 2402,2403 2403,836 2403,2402 2404,1912 2405,120 2405,483 2405,816 2405,1842 2405,1979 2405,1980 2405,2281 2406,523 2406,2043 2407,573 2407,643 2407,1313 2408,434 2408,1693 2409,716 2409,1057 2410,2411 2411,2410 2412,197 2412,469 2412,1997 2413,1725 2413,2414 2413,2415 2414,1200 2414,2413 2415,915 2415,2413 2415,2597 2416,1152 2416,2417 2417,2416 2418,57 2418,65 2418,239 2418,572 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networkx as nx from tqdm import tqdm class EdMot(object): """ Edge Motif Clustering Class. """ def __init__(self, graph, component_count, cutoff): """ :param graph: NetworkX object. :param component_count: Number of extract motif hypergraph components. :param cutoff: Motif edge cut-off value. """ self.graph = graph self.component_count = component_count self.cutoff = cutoff def _overlap(self, node_1, node_2): """ Calculating the neighbourhood overlap for a pair of nodes. :param node_1: Source node 1. :param node_2: Source node 2. :return neighbourhood overlap: Overlap score. """ nodes_1 = self.graph.neighbors(node_1) nodes_2 = self.graph.neighbors(node_2) return len(set(nodes_1).intersection(set(nodes_2))) def _calculate_motifs(self): """ Enumerating pairwise motif counts. """ print("\nCalculating overlaps.\n") edges = [e for e in tqdm(self.graph.edges()) if self._overlap(e[0], e[1]) >= self.cutoff] self.motif_graph = nx.from_edgelist(edges) def _extract_components(self): """ Extracting connected components from motif graph. """ print("\nExtracting components.\n") components = [c for c in nx.connected_components(self.motif_graph)] components = [[len(c), c] for c in components] components.sort(key=lambda x: x[0], reverse=True) important_components = [components[comp][1] for comp in range(self.component_count if len(components)>=self.component_count else len(components))] self.blocks = [list(graph) for graph in important_components] def _fill_blocks(self): """ Filling the dense blocks of the adjacency matrix. """ print("Adding edge blocks.\n") new_edges = [(n_1, n_2) for nodes in self.blocks for n_1 in nodes for n_2 in nodes if n_1!= n_2] self.graph.add_edges_from(new_edges) def fit(self): """ Clustering the target graph. """ self._calculate_motifs() self._extract_components() self._fill_blocks() partition = community.best_partition(self.graph) return partition ================================================ FILE: src/main.py ================================================ """ Running the model.""" from edmot import EdMot from param_parser import parameter_parser from utils import tab_printer, graph_reader, membership_saver def main(): """ Parsing command line parameters, reading data, fitting EdMot and scoring the model. """ args = parameter_parser() tab_printer(args) graph = graph_reader(args.edge_path) model = EdMot(graph, args.components, args.cutoff) memberships = model.fit() membership_saver(args.membership_path, memberships) if __name__ == "__main__": main() ================================================ FILE: src/param_parser.py ================================================ """Parameter parsing from the command line.""" import argparse def parameter_parser(): """ A method to parse up command line parameters. By default it trains on the Cora dataset. The default hyperparameters give a good quality representation without grid search. """ parser = argparse.ArgumentParser(description="Run EdMot.") parser.add_argument("--edge-path", nargs="?", default="./input/cora_edges.csv", help="Edge list csv.") parser.add_argument("--membership-path", nargs="?", default="./output/cora_membership.json", help="Cluster memberhip json.") parser.add_argument("--components", type=int, default=2, help="Number of components. Default is 2.") parser.add_argument("--cutoff", type=int, default=50, help="Minimal overlap cutoff. Default is 50.") return parser.parse_args() ================================================ FILE: src/utils.py ================================================ """Utils for reading and writing.""" import json import pandas as pd import networkx as nx from texttable import Texttable def tab_printer(args): """ Function to print the logs in a nice tabular format. :param args: Parameters used for the model. """ args = vars(args) keys = sorted(args.keys()) t = Texttable() t.add_rows([["Parameter", "Value"]]) t.add_rows([[k.replace("_", " ").capitalize(), args[k]] for k in keys]) print(t.draw()) def graph_reader(path): """ Function to read the graph from the path. :param path: Path to the edge list. :return graph: NetworkX object returned. """ graph = nx.from_edgelist(pd.read_csv(path).values.tolist()) graph.remove_edges_from(nx.selfloop_edges(graph)) return graph def membership_saver(membership_path, membership): """ Saving the membership dictionary as a JSON. :param membership_path: Path to save the JSON. :param membership: Membership dictionary with cluster ids. """ with open(membership_path, "w") as f: json.dump(membership, f)