The game of Go is normally played on a 19x19 board, and sometimes on smaller quadratic boards. However, the board mechanics naturally generalize to arbitrary undirected graphs. The attainable positions in a game can be considered as the nodes of a new graph, and the moves as directed edges between the positions. This induced graph is called the game graph.
Thus every undirected graph induces a Go Game Graph. This repository aims to explore this family of graphs for small board graphs. Of particular interest is finding the longest simple path starting from the empty position, which corresponds to the longest game of go that can be played on the specific board graph.
Go Game Graphs are sparse directed graphs with an abundance of cycles. They range from very small up to arbitrarily large sizes and could be useful for testing various graph algorithms applicable to this kind of graph.
This repository provides:
- Code in Julia and C to generate all Go Game Graphs induced from Board Graphs with up to 12 nodes.
- A list of properties of all Go Game Graphs induced from Board Graphs with up to 7 nodes, and a selection of larger ones.
- Sample maximum length paths.
This table contains all unique Go Game Graphs (up to isomorphism) induced from board graphs with up to 7 nodes, and a selection of larger ones. More explanations follow after the table.
| id | board graph | board nodes | board edges | game nodes | game edges | longest path |
|---|---|---|---|---|---|---|
| 1 |  |
2 | 1 | 5 | 12 | 2 |
| 3 |  |
3 | 2 | 15 | 42 | 14 |
| 7 |  |
3 | 3 | 19 | 54 | 18 |
| 11 |  |
4 | 3 | 41 | 138 | 32 |
| 12 |  |
4 | 2 | 25 | 120 | 24 |
| 13 |  |
4 | 3 | 41 | 144 | 40 |
| 15 |  |
4 | 4 | 49 | 166 | 42 |
| 30 |  |
4 | 4 | 57 | 192 | 48 |
| 31 |  |
4 | 5 | 61 | 204 | 50 |
| 63 |  |
4 | 6 | 65 | 216 | 56 |
| 75 |  |
5 | 4 | 111 | 450 | 59 |
| 76 |  |
5 | 3 | 75 | 390 | 74 |
| 77 |  |
5 | 4 | 107 | 442 | 94 |
| 79 |  |
5 | 5 | 127 | 514 | 79 |
| 86 |  |
5 | 4 | 113 | 492 | 112 |
| 87 |  |
5 | 5 | 125 | 508 | 102 |
| 94 |  |
5 | 5 | 143 | 578 | 104 |
| 95 |  |
5 | 6 | 151 | 602 | 99 |
| 116 |  |
5 | 4 | 95 | 498 | 94 |
| 117 |  |
5 | 5 | 131 | 558 | 122 |
| 119 |  |
5 | 6 | 151 | 606 | 108 |
| 127 |  |
5 | 7 | 159 | 630 | 111 |
| 222 |  |
5 | 6 | 183 | 720 | 116 |
| 223 |  |
5 | 7 | 187 | 732 | 118 |
| 235 |  |
5 | 6 | 151 | 626 | 103 |
| 236 |  |
5 | 5 | 161 | 660 | 130 |
| 237 |  |
5 | 6 | 173 | 692 | 122 |
| 239 |  |
5 | 7 | 183 | 722 | 116 |
| 254 |  |
5 | 7 | 191 | 748 | 130 |
| 255 |  |
5 | 8 | 195 | 760 | 130 |
| 507 |  |
5 | 8 | 203 | 786 | 134 |
| 511 |  |
5 | 9 | 207 | 798 | 142 |
| 1023 |  |
5 | 10 | 211 | 810 | 150 |
| 1099 |  |
6 | 5 | 305 | 1466 | 94 |
| 1100 |  |
6 | 4 | 205 | 1182 | 204 |
| 1101 |  |
6 | 5 | 281 | 1356 | 171 |
| 1103 |  |
6 | 6 | 337 | 1610 | 130 |
| 1108 |  |
6 | 4 | 225 | 1260 | 224 |
| 1109 |  |
6 | 5 | 273 | 1308 | 192 |
| 1110 |  |
6 | 5 | 295 | 1476 | 282 |
| 1111 |  |
6 | 6 | 319 | 1514 | 207 |
| 1118 |  |
6 | 6 | 365 | 1732 | 189 |
| 1119 |  |
6 | 7 | 385 | 1810 | 171 |
| 1140 |  |
6 | 5 | 285 | 1608 | 284 |
| 1141 |  |
6 | 6 | 337 | 1660 | 279 |
| 1143 |  |
6 | 7 | 381 | 1796 | 197 |
| 1151 |  |
6 | 8 | 401 | 1874 | 192 |
| 1182 |  |
6 | 6 | 363 | 1732 | 248 |
| 1183 |  |
6 | 7 | 375 | 1752 | 219 |
| 1184 |  |
6 | 3 | 125 | 900 | 124 |
| 1185 |  |
6 | 4 | 205 | 1212 | 204 |
| 1187 |  |
6 | 5 | 283 | 1412 | 256 |
| 1191 |  |
6 | 6 | 311 | 1476 | 246 |
| 1194 |  |
6 | 5 | 245 | 1418 | 244 |
| 1195 |  |
6 | 6 | 329 | 1612 | 235 |
| 1196 |  |
6 | 5 | 313 | 1620 | 312 |
| 1197 |  |
6 | 6 | 357 | 1696 | 234 |
| 1198 |  |
6 | 6 | 339 | 1686 | 318 |
| 1199 |  |
6 | 7 | 373 | 1750 | 229 |
| 1214 |  |
6 | 7 | 379 | 1796 | 262 |
| 1215 |  |
6 | 8 | 391 | 1816 | 239 |
| 1246 |  |
6 | 7 | 449 | 2082 | 217 |
| 1247 |  |
6 | 8 | 457 | 2106 | 212 |
| 1259 |  |
6 | 7 | 385 | 1858 | 184 |
| 1260 |  |
6 | 6 | 403 | 1936 | 286 |
| 1261 |  |
6 | 7 | 427 | 2004 | 237 |
| 1263 |  |
6 | 8 | 449 | 2082 | 210 |
| 1268 |  |
6 | 6 | 363 | 1856 | 356 |
| 1269 |  |
6 | 7 | 387 | 1890 | 289 |
| 1270 |  |
6 | 7 | 429 | 2028 | 265 |
| 1271 |  |
6 | 8 | 447 | 2074 | 231 |
| 1278 |  |
6 | 8 | 465 | 2146 | 241 |
| 1279 |  |
6 | 9 | 473 | 2170 | 236 |
| 1456 |  |
6 | 5 | 285 | 1644 | 284 |
| 1457 |  |
6 | 6 | 383 | 1898 | 333 |
| 1459 |  |
6 | 7 | 445 | 2068 | 240 |
| 1460 |  |
6 | 6 | 305 | 1752 | 304 |
| 1461 |  |
6 | 7 | 401 | 1972 | 323 |
| 1463 |  |
6 | 8 | 453 | 2096 | 244 |
| 1465 |  |
6 | 7 | 431 | 2040 | 289 |
| 1467 |  |
6 | 8 | 463 | 2134 | 257 |
| 1468 |  |
6 | 7 | 407 | 2014 | 355 |
| 1469 |  |
6 | 8 | 451 | 2112 | 268 |
| 1471 |  |
6 | 9 | 471 | 2162 | 257 |
| 1531 |  |
6 | 9 | 489 | 2230 | 244 |
| 1532 |  |
6 | 8 | 469 | 2184 | 275 |
| 1533 |  |
6 | 9 | 489 | 2234 | 255 |
| 1535 |  |
6 | 10 | 497 | 2258 | 260 |
| 1972 |  |
6 | 7 | 325 | 1860 | 324 |
| 1973 |  |
6 | 8 | 425 | 2088 | 359 |
| 1975 |  |
6 | 9 | 477 | 2212 | 282 |
| 1983 |  |
6 | 10 | 497 | 2262 | 270 |
| 2047 |  |
6 | 11 | 505 | 2286 | 275 |
| 3294 |  |
6 | 8 | 561 | 2544 | 256 |
| 3295 |  |
6 | 9 | 565 | 2556 | 258 |
| 3306 |  |
6 | 7 | 437 | 2128 | 276 |
| 3307 |  |
6 | 8 | 457 | 2206 | 249 |
| 3308 |  |
6 | 7 | 507 | 2368 | 290 |
| 3309 |  |
6 | 8 | 519 | 2404 | 282 |
| 3310 |  |
6 | 8 | 535 | 2458 | 254 |
| 3311 |  |
6 | 9 | 545 | 2490 | 251 |
| 3326 |  |
6 | 9 | 577 | 2608 | 278 |
| 3327 |  |
6 | 10 | 581 | 2620 | 280 |
| 3440 |  |
6 | 6 | 449 | 2196 | 370 |
| 3441 |  |
6 | 7 | 481 | 2300 | 338 |
| 3443 |  |
6 | 8 | 509 | 2380 | 280 |
| 3447 |  |
6 | 9 | 533 | 2448 | 246 |
| 3448 |  |
6 | 7 | 489 | 2312 | 292 |
| 3449 |  |
6 | 8 | 513 | 2400 | 282 |
| 3451 |  |
6 | 9 | 537 | 2482 | 252 |
| 3452 |  |
6 | 8 | 545 | 2508 | 298 |
| 3453 |  |
6 | 9 | 559 | 2548 | 284 |
| 3455 |  |
6 | 10 | 569 | 2578 | 276 |
| 3576 |  |
6 | 8 | 553 | 2524 | 274 |
| 3577 |  |
6 | 9 | 561 | 2552 | 280 |
| 3578 |  |
6 | 9 | 583 | 2640 | 292 |
| 3579 |  |
6 | 10 | 593 | 2670 | 286 |
| 3582 |  |
6 | 10 | 601 | 2696 | 304 |
| 3583 |  |
6 | 11 | 605 | 2708 | 304 |
| 3873 |  |
6 | 6 | 361 | 2052 | 360 |
| 3875 |  |
6 | 7 | 417 | 2108 | 363 |
| 3879 |  |
6 | 8 | 461 | 2240 | 292 |
| 3885 |  |
6 | 8 | 513 | 2412 | 290 |
| 3887 |  |
6 | 9 | 537 | 2484 | 262 |
| 3903 |  |
6 | 10 | 569 | 2580 | 282 |
| 3947 |  |
6 | 9 | 481 | 2318 | 275 |
| 3948 |  |
6 | 8 | 531 | 2480 | 320 |
| 3949 |  |
6 | 9 | 559 | 2570 | 281 |
| 3950 |  |
6 | 9 | 543 | 2516 | 310 |
| 3951 |  |
6 | 10 | 569 | 2602 | 279 |
| 3958 |  |
6 | 9 | 573 | 2612 | 294 |
| 3959 |  |
6 | 10 | 589 | 2660 | 282 |
| 3966 |  |
6 | 10 | 591 | 2668 | 308 |
| 3967 |  |
6 | 11 | 601 | 2698 | 300 |
| 4094 |  |
6 | 11 | 609 | 2724 | 318 |
| 4095 |  |
6 | 12 | 613 | 2736 | 318 |
| 7672 |  |
6 | 9 | 617 | 2760 | 300 |
| 7673 |  |
6 | 10 | 625 | 2788 | 316 |
| 7675 |  |
6 | 11 | 637 | 2826 | 322 |
| 7679 |  |
6 | 12 | 641 | 2838 | 332 |
| 7902 |  |
6 | 10 | 601 | 2720 | 304 |
| 7903 |  |
6 | 11 | 605 | 2732 | 308 |
| 7915 |  |
6 | 10 | 605 | 2726 | 282 |
| 7916 |  |
6 | 9 | 593 | 2688 | 300 |
| 7917 |  |
6 | 10 | 613 | 2752 | 304 |
| 7919 |  |
6 | 11 | 625 | 2790 | 310 |
| 7934 |  |
6 | 11 | 633 | 2816 | 318 |
| 7935 |  |
6 | 12 | 637 | 2828 | 328 |
| 8185 |  |
6 | 11 | 633 | 2816 | 332 |
| 8187 |  |
6 | 12 | 645 | 2854 | 336 |
| 8191 |  |
6 | 13 | 649 | 2866 | 346 |
| 16350 |  |
6 | 12 | 653 | 2880 | 342 |
| 16351 |  |
6 | 13 | 657 | 2892 | 352 |
| 16383 |  |
6 | 14 | 661 | 2904 | 362 |
| 32767 |  |
6 | 15 | 665 | 2916 | 372 |
| 33867 | 7 | 6 | 855 | 4770 | 137 | |
| 33868 | 7 | 5 | 555 | 3582 | 554 | |
| 33869 | 7 | 6 | 755 | 4206 | 291 | |
| 33871 | 7 | 7 | 919 | 5090 | 206 | |
| 33876 | 7 | 5 | 615 | 3792 | 614 | |
| 33877 | 7 | 6 | 707 | 3902 | 370 | |
| 33878 | 7 | 6 | 773 | 4422 | 645 | |
| 33879 | 7 | 7 | 833 | 4566 | 368 | |
| 33886 | 7 | 7 | 959 | 5270 | 319 | |
| 33887 | 7 | 8 | 1015 | 5538 | 276 | |
| 33908 | 7 | 6 | 779 | 4836 | 778 | |
| 33909 | 7 | 7 | 875 | 4946 | 584 | |
| 33911 | 7 | 8 | 991 | 5414 | 346 | |
| 33919 | 7 | 9 | 1047 | 5682 | 306 | |
| 33942 | 7 | 6 | 769 | 4348 | 706 | |
| 33943 | 7 | 7 | 805 | 4384 | 406 | |
| 33950 | 7 | 7 | 925 | 5068 | 517 | |
| 33951 | 7 | 8 | 949 | 5114 | 426 | |
| 33952 | 7 | 4 | 375 | 2850 | 374 | |
| 33953 | 7 | 5 | 535 | 3494 | 534 | |
| 33955 | 7 | 6 | 721 | 4082 | 484 | |
| 33956 | 7 | 5 | 615 | 3882 | 614 | |
| 33957 | 7 | 6 | 725 | 4108 | 598 | |
| 33959 | 7 | 7 | 781 | 4246 | 476 | |
| 33962 | 7 | 6 | 635 | 4094 | 634 | |
| 33963 | 7 | 7 | 851 | 4766 | 408 | |
| 33964 | 7 | 6 | 819 | 4766 | 806 | |
| 33965 | 7 | 7 | 903 | 4930 | 461 | |
| 33966 | 7 | 7 | 869 | 4922 | 726 | |
| 33967 | 7 | 8 | 943 | 5100 | 430 | |
| 33972 | 7 | 6 | 735 | 4548 | 734 | |
| 33973 | 7 | 7 | 835 | 4670 | 543 | |
| 33974 | 7 | 7 | 877 | 4950 | 760 | |
| 33975 | 7 | 8 | 935 | 5052 | 449 | |
| 33982 | 7 | 8 | 957 | 5212 | 551 | |
| 33983 | 7 | 9 | 981 | 5258 | 464 | |
| 34014 | 7 | 8 | 1139 | 6124 | 367 | |
| 34015 | 7 | 9 | 1159 | 6202 | 348 | |
| 34027 | 7 | 8 | 1015 | 5634 | 305 | |
| 34028 | 7 | 7 | 1025 | 5658 | 552 | |
| 34029 | 7 | 8 | 1085 | 5884 | 415 | |
| 34031 | 7 | 9 | 1143 | 6146 | 341 | |
| 34036 | 7 | 7 | 949 | 5468 | 900 | |
| 34037 | 7 | 8 | 985 | 5500 | 645 | |
| 34038 | 7 | 8 | 1083 | 5904 | 511 | |
| 34039 | 7 | 9 | 1125 | 6044 | 409 | |
| 34046 | 7 | 9 | 1171 | 6268 | 403 | |
| 34047 | 7 | 10 | 1191 | 6346 | 382 | |
| 34224 | 7 | 6 | 855 | 5274 | 854 | |
| 34225 | 7 | 7 | 985 | 5550 | 773 | |
| 34227 | 7 | 8 | 1111 | 5974 | 426 | |
| 34228 | 7 | 7 | 915 | 5622 | 914 | |
| 34229 | 7 | 8 | 1027 | 5758 | 755 | |
| 34231 | 7 | 9 | 1127 | 6038 | 430 | |
| 34233 | 7 | 8 | 1085 | 5910 | 571 | |
| 34235 | 7 | 9 | 1157 | 6180 | 439 | |
| 34236 | 7 | 8 | 1049 | 5902 | 844 | |
| 34237 | 7 | 9 | 1129 | 6102 | 527 | |
| 34239 | 7 | 10 | 1173 | 6244 | 447 | |
| 34299 | 7 | 10 | 1223 | 6482 | 398 | |
| 34300 | 7 | 9 | 1175 | 6326 | 508 | |
| 34301 | 7 | 10 | 1219 | 6468 | 423 | |
| 34303 | 7 | 11 | 1239 | 6546 | 420 | |
| 34740 | 7 | 8 | 975 | 5970 | 974 | |
| 34741 | 7 | 9 | 1091 | 6110 | 843 | |
| 34743 | 7 | 10 | 1191 | 6390 | 526 | |
| 34751 | 7 | 11 | 1235 | 6532 | 445 | |
| 34815 | 7 | 12 | 1255 | 6610 | 442 | |
| 35038 | 7 | 8 | 1109 | 5928 | 485 | |
| 35039 | 7 | 9 | 1121 | 5948 | 456 | |
| 35040 | 7 | 5 | 565 | 3816 | 564 | |
| 35041 | 7 | 6 | 625 | 4040 | 624 | |
| 35042 | 7 | 6 | 783 | 4580 | 756 | |
| 35043 | 7 | 7 | 837 | 4712 | 627 | |
| 35046 | 7 | 7 | 889 | 4858 | 558 | |
| 35047 | 7 | 8 | 913 | 4906 | 510 | |
| 35050 | 7 | 7 | 909 | 5250 | 810 | |
| 35051 | 7 | 8 | 969 | 5386 | 540 | |
| 35052 | 7 | 7 | 1017 | 5616 | 691 | |
| 35053 | 7 | 8 | 1053 | 5680 | 509 | |
| 35054 | 7 | 8 | 1067 | 5796 | 583 | |
| 35055 | 7 | 9 | 1097 | 5854 | 474 | |
| 35070 | 7 | 9 | 1141 | 6072 | 527 | |
| 35071 | 7 | 10 | 1153 | 6092 | 494 | |
| 35128 | 7 | 6 | 759 | 4506 | 690 | |
| 35129 | 7 | 7 | 847 | 4810 | 776 | |
| 35131 | 7 | 8 | 923 | 5000 | 564 | |
| 35135 | 7 | 9 | 951 | 5064 | 542 | |
| 35176 | 7 | 6 | 715 | 4606 | 714 | |
| 35177 | 7 | 7 | 949 | 5338 | 616 | |
| 35178 | 7 | 7 | 755 | 4822 | 754 | |
| 35179 | 7 | 8 | 995 | 5558 | 574 | |
| 35180 | 7 | 7 | 983 | 5582 | 846 | |
| 35181 | 7 | 8 | 1091 | 5840 | 487 | |
| 35182 | 7 | 8 | 1009 | 5660 | 792 | |
| 35183 | 7 | 9 | 1107 | 5896 | 478 | |
| 35184 | 7 | 6 | 867 | 5190 | 866 | |
| 35185 | 7 | 7 | 999 | 5514 | 647 | |
| 35186 | 7 | 7 | 941 | 5466 | 920 | |
| 35187 | 7 | 8 | 1053 | 5710 | 544 | |
| 35190 | 7 | 8 | 1001 | 5628 | 804 | |
| 35191 | 7 | 9 | 1089 | 5816 | 492 | |
| 35192 | 7 | 7 | 965 | 5482 | 803 | |
| 35193 | 7 | 8 | 1053 | 5710 | 577 | |
| 35194 | 7 | 8 | 1013 | 5706 | 828 | |
| 35195 | 7 | 9 | 1101 | 5916 | 516 | |
| 35196 | 7 | 8 | 1079 | 5900 | 697 | |
| 35197 | 7 | 9 | 1129 | 6000 | 523 | |
| 35198 | 7 | 9 | 1111 | 5986 | 607 | |
| 35199 | 7 | 10 | 1145 | 6054 | 516 | |
| 35320 | 7 | 8 | 1093 | 5882 | 556 | |
| 35321 | 7 | 9 | 1121 | 5946 | 542 | |
| 35322 | 7 | 9 | 1149 | 6158 | 619 | |
| 35323 | 7 | 10 | 1183 | 6226 | 522 | |
| 35326 | 7 | 10 | 1189 | 6272 | 557 | |
| 35327 | 7 | 11 | 1201 | 6292 | 536 | |
| 35616 | 7 | 5 | 475 | 3630 | 474 | |
| 35617 | 7 | 6 | 779 | 4950 | 778 | |
| 35618 | 7 | 6 | 655 | 4362 | 654 | |
| 35619 | 7 | 7 | 897 | 5196 | 801 | |
| 35622 | 7 | 7 | 865 | 5042 | 660 | |
| 35623 | 7 | 8 | 957 | 5350 | 708 | |
| 35626 | 7 | 7 | 755 | 4842 | 754 | |
| 35627 | 7 | 8 | 997 | 5594 | 662 | |
| 35628 | 7 | 7 | 923 | 5406 | 896 | |
| 35629 | 7 | 8 | 1055 | 5754 | 588 | |
| 35630 | 7 | 8 | 1001 | 5640 | 794 | |
| 35631 | 7 | 9 | 1093 | 5872 | 548 | |
| 35646 | 7 | 9 | 1109 | 5946 | 564 | |
| 35647 | 7 | 10 | 1137 | 6010 | 548 | |
| 35690 | 7 | 8 | 795 | 5058 | 794 | |
| 35691 | 7 | 9 | 1043 | 5814 | 640 | |
| 35692 | 7 | 8 | 1031 | 5838 | 899 | |
| 35693 | 7 | 9 | 1139 | 6096 | 552 | |
| 35694 | 7 | 9 | 1057 | 5916 | 858 | |
| 35695 | 7 | 10 | 1155 | 6152 | 546 | |
| 35702 | 7 | 9 | 1125 | 6108 | 690 | |
| 35703 | 7 | 10 | 1181 | 6224 | 530 | |
| 35710 | 7 | 10 | 1165 | 6222 | 636 | |
| 35711 | 7 | 11 | 1199 | 6290 | 546 | |
| 35838 | 7 | 11 | 1205 | 6336 | 581 | |
| 35839 | 7 | 12 | 1217 | 6356 | 560 | |
| 36062 | 7 | 9 | 1367 | 7186 | 446 | |
| 36063 | 7 | 10 | 1375 | 7210 | 441 | |
| 36074 | 7 | 8 | 1103 | 6134 | 485 | |
| 36075 | 7 | 9 | 1159 | 6402 | 422 | |
| 36076 | 7 | 8 | 1249 | 6726 | 566 | |
| 36077 | 7 | 9 | 1273 | 6800 | 518 | |
| 36078 | 7 | 9 | 1313 | 6976 | 451 | |
| 36079 | 7 | 10 | 1335 | 7058 | 428 | |
| 36084 | 7 | 8 | 1121 | 6284 | 763 | |
| 36085 | 7 | 9 | 1145 | 6330 | 668 | |
| 36086 | 7 | 9 | 1307 | 6950 | 504 | |
| 36087 | 7 | 10 | 1325 | 6998 | 474 | |
| 36094 | 7 | 10 | 1399 | 7330 | 488 | |
| 36095 | 7 | 11 | 1407 | 7354 | 483 | |
| 36208 | 7 | 7 | 1125 | 6298 | 868 | |
| 36209 | 7 | 8 | 1189 | 6518 | 686 | |
| 36211 | 7 | 9 | 1253 | 6742 | 513 | |
| 36212 | 7 | 8 | 1205 | 6634 | 787 | |
| 36213 | 7 | 9 | 1253 | 6756 | 582 | |
| 36215 | 7 | 10 | 1301 | 6902 | 461 | |
| 36216 | 7 | 8 | 1203 | 6536 | 560 | |
| 36217 | 7 | 9 | 1259 | 6776 | 511 | |
| 36219 | 7 | 10 | 1319 | 7034 | 426 | |
| 36220 | 7 | 9 | 1331 | 7084 | 547 | |
| 36221 | 7 | 10 | 1361 | 7180 | 493 | |
| 36223 | 7 | 11 | 1383 | 7258 | 466 | |
| 36272 | 7 | 7 | 1063 | 6166 | 1016 | |
| 36273 | 7 | 8 | 1125 | 6316 | 802 | |
| 36274 | 7 | 8 | 1249 | 6756 | 653 | |
| 36275 | 7 | 9 | 1297 | 6886 | 503 | |
| 36276 | 7 | 8 | 1113 | 6424 | 1035 | |
| 36277 | 7 | 9 | 1173 | 6548 | 758 | |
| 36278 | 7 | 9 | 1275 | 6858 | 626 | |
| 36279 | 7 | 10 | 1317 | 6960 | 494 | |
| 36280 | 7 | 8 | 1221 | 6678 | 706 | |
| 36281 | 7 | 9 | 1261 | 6796 | 627 | |
| 36282 | 7 | 9 | 1327 | 7056 | 588 | |
| 36283 | 7 | 10 | 1353 | 7128 | 528 | |
| 36284 | 7 | 9 | 1277 | 6930 | 691 | |
| 36285 | 7 | 10 | 1313 | 7012 | 565 | |
| 36286 | 7 | 10 | 1355 | 7152 | 550 | |
| 36287 | 7 | 11 | 1373 | 7198 | 516 | |
| 36344 | 7 | 9 | 1339 | 7074 | 519 | |
| 36345 | 7 | 10 | 1355 | 7128 | 516 | |
| 36346 | 7 | 10 | 1409 | 7388 | 519 | |
| 36347 | 7 | 11 | 1431 | 7466 | 492 | |
| 36348 | 7 | 10 | 1411 | 7412 | 548 | |
| 36349 | 7 | 11 | 1429 | 7458 | 514 | |
| 36350 | 7 | 11 | 1447 | 7530 | 530 | |
| 36351 | 7 | 12 | 1455 | 7554 | 525 | |
| 36641 | 7 | 7 | 931 | 5800 | 930 | |
| 36643 | 7 | 8 | 1035 | 5922 | 776 | |
| 36644 | 7 | 7 | 1007 | 5962 | 1000 | |
| 36645 | 7 | 8 | 1085 | 6250 | 999 | |
| 36646 | 7 | 8 | 1095 | 6134 | 703 | |
| 36647 | 7 | 9 | 1143 | 6348 | 717 | |
| 36651 | 7 | 9 | 1151 | 6382 | 529 | |
| 36652 | 7 | 8 | 1195 | 6582 | 764 | |
| 36653 | 7 | 9 | 1259 | 6816 | 602 | |
| 36654 | 7 | 9 | 1251 | 6734 | 558 | |
| 36655 | 7 | 10 | 1307 | 6968 | 491 | |
| 36660 | 7 | 8 | 1131 | 6546 | 1083 | |
| 36661 | 7 | 9 | 1193 | 6692 | 870 | |
| 36662 | 7 | 9 | 1271 | 6896 | 675 | |
| 36663 | 7 | 10 | 1311 | 7006 | 573 | |
| 36670 | 7 | 10 | 1355 | 7138 | 531 | |
| 36671 | 7 | 11 | 1371 | 7192 | 524 | |
| 36715 | 7 | 10 | 1207 | 6650 | 468 | |
| 36716 | 7 | 9 | 1297 | 6974 | 623 | |
| 36717 | 7 | 10 | 1361 | 7224 | 501 | |
| 36718 | 7 | 10 | 1321 | 7048 | 571 | |
| 36719 | 7 | 11 | 1383 | 7306 | 478 | |
| 36724 | 7 | 9 | 1317 | 7132 | 738 | |
| 36725 | 7 | 10 | 1365 | 7262 | 585 | |
| 36726 | 7 | 10 | 1389 | 7334 | 559 | |
| 36727 | 7 | 11 | 1421 | 7434 | 505 | |
| 36734 | 7 | 11 | 1425 | 7452 | 541 | |
| 36735 | 7 | 12 | 1447 | 7530 | 514 | |
| 36788 | 7 | 9 | 1181 | 6804 | 1117 | |
| 36789 | 7 | 10 | 1241 | 6924 | 852 | |
| 36790 | 7 | 10 | 1343 | 7234 | 719 | |
| 36791 | 7 | 11 | 1385 | 7336 | 587 | |
| 36798 | 7 | 11 | 1427 | 7476 | 572 | |
| 36799 | 7 | 12 | 1445 | 7522 | 538 | |
| 36862 | 7 | 12 | 1463 | 7594 | 553 | |
| 36863 | 7 | 13 | 1471 | 7618 | 548 | |
| 39344 | 7 | 7 | 915 | 5796 | 914 | |
| 39345 | 7 | 8 | 1193 | 6660 | 802 | |
| 39347 | 7 | 9 | 1343 | 7070 | 502 | |
| 39348 | 7 | 8 | 935 | 5904 | 934 | |
| 39349 | 7 | 9 | 1211 | 6734 | 792 | |
| 39351 | 7 | 10 | 1351 | 7098 | 506 | |
| 39352 | 7 | 8 | 1201 | 6730 | 894 | |
| 39353 | 7 | 9 | 1317 | 7052 | 634 | |
| 39355 | 7 | 10 | 1381 | 7228 | 546 | |
| 39356 | 7 | 9 | 1225 | 6846 | 912 | |
| 39357 | 7 | 10 | 1337 | 7130 | 614 | |
| 39359 | 7 | 11 | 1389 | 7256 | 546 | |
| 39416 | 7 | 9 | 1357 | 7226 | 633 | |
| 39417 | 7 | 10 | 1405 | 7372 | 595 | |
| 39419 | 7 | 11 | 1437 | 7466 | 568 | |
| 39420 | 7 | 10 | 1381 | 7342 | 659 | |
| 39421 | 7 | 11 | 1425 | 7444 | 573 | |
| 39423 | 7 | 12 | 1445 | 7494 | 568 | |
| 39572 | 7 | 7 | 755 | 4942 | 754 | |
| 39573 | 7 | 8 | 995 | 5702 | 573 | |
| 39574 | 7 | 8 | 1057 | 6110 | 957 | |
| 39575 | 7 | 9 | 1135 | 6300 | 661 | |
| 39582 | 7 | 9 | 1255 | 6806 | 636 | |
| 39583 | 7 | 10 | 1299 | 6920 | 516 | |
| 39584 | 7 | 6 | 805 | 5232 | 804 | |
| 39585 | 7 | 7 | 1083 | 6198 | 909 | |
| 39587 | 7 | 8 | 1241 | 6710 | 648 | |
| 39588 | 7 | 7 | 865 | 5536 | 864 | |
| 39589 | 7 | 8 | 1137 | 6406 | 818 | |
| 39591 | 7 | 9 | 1265 | 6790 | 620 | |
| 39594 | 7 | 8 | 1205 | 6650 | 846 | |
| 39595 | 7 | 9 | 1315 | 6980 | 588 | |
| 39596 | 7 | 8 | 1157 | 6546 | 917 | |
| 39597 | 7 | 9 | 1299 | 6934 | 558 | |
| 39598 | 7 | 9 | 1265 | 6866 | 712 | |
| 39599 | 7 | 10 | 1343 | 7074 | 560 | |
| 39604 | 7 | 8 | 915 | 5806 | 914 | |
| 39605 | 7 | 9 | 1187 | 6630 | 766 | |
| 39606 | 7 | 9 | 1197 | 6696 | 856 | |
| 39607 | 7 | 10 | 1319 | 7006 | 546 | |
| 39614 | 7 | 10 | 1311 | 7018 | 616 | |
| 39615 | 7 | 11 | 1363 | 7144 | 548 | |
| 39644 | 7 | 9 | 1169 | 6532 | 817 | |
| 39645 | 7 | 10 | 1193 | 6578 | 725 | |
| 39646 | 7 | 10 | 1355 | 7198 | 558 | |
| 39647 | 7 | 11 | 1373 | 7246 | 530 | |
| 39657 | 7 | 9 | 1295 | 6964 | 694 | |
| 39659 | 7 | 10 | 1381 | 7270 | 553 | |
| 39660 | 7 | 9 | 1285 | 7010 | 768 | |
| 39661 | 7 | 10 | 1355 | 7200 | 609 | |
| 39663 | 7 | 11 | 1413 | 7382 | 532 | |
| 39664 | 7 | 8 | 1171 | 6630 | 983 | |
| 39665 | 7 | 9 | 1275 | 6922 | 720 | |
| 39666 | 7 | 9 | 1339 | 7172 | 673 | |
| 39667 | 7 | 10 | 1399 | 7334 | 558 | |
| 39668 | 7 | 9 | 1225 | 6890 | 973 | |
| 39669 | 7 | 10 | 1327 | 7142 | 658 | |
| 39670 | 7 | 10 | 1369 | 7282 | 638 | |
| 39671 | 7 | 11 | 1419 | 7404 | 546 | |
| 39673 | 7 | 10 | 1323 | 7068 | 684 | |
| 39674 | 7 | 10 | 1385 | 7306 | 601 | |
| 39675 | 7 | 11 | 1417 | 7400 | 574 | |
| 39676 | 7 | 10 | 1333 | 7182 | 690 | |
| 39677 | 7 | 11 | 1377 | 7284 | 611 | |
| 39678 | 7 | 11 | 1417 | 7420 | 567 | |
| 39679 | 7 | 12 | 1437 | 7470 | 562 | |
| 39856 | 7 | 8 | 955 | 6032 | 954 | |
| 39857 | 7 | 9 | 1241 | 6916 | 874 | |
| 39859 | 7 | 10 | 1391 | 7326 | 572 | |
| 39860 | 7 | 9 | 975 | 6140 | 974 | |
| 39861 | 7 | 10 | 1259 | 6990 | 862 | |
| 39863 | 7 | 11 | 1399 | 7354 | 574 | |
| 39864 | 7 | 9 | 1245 | 6940 | 928 | |
| 39865 | 7 | 10 | 1371 | 7294 | 666 | |
| 39867 | 7 | 11 | 1435 | 7464 | 576 | |
| 39868 | 7 | 10 | 1269 | 7056 | 948 | |
| 39869 | 7 | 11 | 1391 | 7366 | 644 | |
| 39871 | 7 | 12 | 1443 | 7492 | 576 | |
| 39928 | 7 | 10 | 1373 | 7290 | 656 | |
| 39929 | 7 | 11 | 1421 | 7436 | 619 | |
| 39931 | 7 | 12 | 1453 | 7530 | 592 | |
| 39932 | 7 | 11 | 1397 | 7406 | 678 | |
| 39933 | 7 | 12 | 1441 | 7508 | 597 | |
| 39935 | 7 | 13 | 1461 | 7558 | 592 | |
| 40440 | 7 | 10 | 1475 | 7660 | 550 | |
| 40441 | 7 | 11 | 1493 | 7726 | 569 | |
| 40443 | 7 | 12 | 1519 | 7822 | 559 | |
| 40444 | 7 | 11 | 1499 | 7776 | 586 | |
| 40445 | 7 | 12 | 1519 | 7826 | 568 | |
| 40447 | 7 | 13 | 1527 | 7850 | 575 | |
| 40670 | 7 | 11 | 1447 | 7578 | 540 | |
| 40671 | 7 | 12 | 1455 | 7602 | 537 | |
| 40683 | 7 | 11 | 1455 | 7590 | 488 | |
| 40684 | 7 | 10 | 1431 | 7520 | 582 | |
| 40685 | 7 | 11 | 1469 | 7642 | 549 | |
| 40687 | 7 | 12 | 1495 | 7738 | 538 | |
| 40692 | 7 | 10 | 1407 | 7490 | 671 | |
| 40693 | 7 | 11 | 1455 | 7608 | 561 | |
| 40694 | 7 | 11 | 1473 | 7680 | 578 | |
| 40695 | 7 | 12 | 1493 | 7730 | 560 | |
| 40702 | 7 | 12 | 1511 | 7802 | 562 | |
| 40703 | 7 | 13 | 1519 | 7826 | 569 | |
| 40880 | 7 | 9 | 1269 | 7110 | 987 | |
| 40881 | 7 | 10 | 1385 | 7428 | 721 | |
| 40883 | 7 | 11 | 1449 | 7604 | 631 | |
| 40884 | 7 | 10 | 1293 | 7226 | 1011 | |
| 40885 | 7 | 11 | 1405 | 7506 | 707 | |
| 40887 | 7 | 12 | 1457 | 7632 | 639 | |
| 40888 | 7 | 10 | 1423 | 7530 | 652 | |
| 40889 | 7 | 11 | 1471 | 7668 | 595 | |
| 40891 | 7 | 12 | 1509 | 7790 | 574 | |
| 40892 | 7 | 11 | 1447 | 7646 | 687 | |
| 40893 | 7 | 12 | 1497 | 7768 | 595 | |
| 40895 | 7 | 13 | 1517 | 7818 | 590 | |
| 40952 | 7 | 11 | 1491 | 7724 | 575 | |
| 40953 | 7 | 12 | 1509 | 7790 | 594 | |
| 40955 | 7 | 13 | 1535 | 7886 | 583 | |
| 40956 | 7 | 12 | 1515 | 7840 | 610 | |
| 40957 | 7 | 13 | 1535 | 7890 | 592 | |
| 40959 | 7 | 14 | 1543 | 7914 | 599 | |
| 48020 | 7 | 9 | 1015 | 6366 | 1014 | |
| 48021 | 7 | 10 | 1307 | 7234 | 912 | |
| 48022 | 7 | 10 | 1313 | 7276 | 944 | |
| 48023 | 7 | 11 | 1445 | 7614 | 652 | |
| 48030 | 7 | 11 | 1463 | 7686 | 661 | |
| 48031 | 7 | 12 | 1515 | 7812 | 587 | |
| 48052 | 7 | 10 | 1035 | 6474 | 1034 | |
| 48053 | 7 | 11 | 1331 | 7350 | 954 | |
| 48055 | 7 | 12 | 1471 | 7714 | 671 | |
| 48063 | 7 | 13 | 1523 | 7840 | 603 | |
| 48086 | 7 | 11 | 1443 | 7630 | 673 | |
| 48087 | 7 | 12 | 1495 | 7756 | 605 | |
| 48094 | 7 | 12 | 1513 | 7828 | 609 | |
| 48095 | 7 | 13 | 1533 | 7878 | 604 | |
| 48116 | 7 | 11 | 1337 | 7392 | 985 | |
| 48117 | 7 | 12 | 1469 | 7730 | 693 | |
| 48119 | 7 | 13 | 1521 | 7856 | 625 | |
| 48127 | 7 | 14 | 1541 | 7906 | 620 | |
| 49118 | 7 | 13 | 1551 | 7950 | 606 | |
| 49119 | 7 | 14 | 1559 | 7974 | 613 | |
| 49140 | 7 | 12 | 1487 | 7802 | 701 | |
| 49141 | 7 | 13 | 1539 | 7928 | 627 | |
| 49143 | 7 | 14 | 1559 | 7978 | 622 | |
| 49151 | 7 | 15 | 1567 | 8002 | 629 | |
| 64436 | 7 | 11 | 1055 | 6582 | 1054 | |
| 64437 | 7 | 12 | 1355 | 7466 | 995 | |
| 64439 | 7 | 13 | 1495 | 7830 | 711 | |
| 64447 | 7 | 14 | 1547 | 7956 | 643 | |
| 64511 | 7 | 15 | 1567 | 8006 | 638 | |
| 65535 | 7 | 16 | 1575 | 8030 | 645 | |
| 101598 | 7 | 10 | 1695 | 8744 | 549 | |
| 101599 | 7 | 11 | 1699 | 8756 | 551 | |
| 101610 | 7 | 9 | 1355 | 7464 | 612 | |
| 101611 | 7 | 10 | 1375 | 7542 | 584 | |
| 101612 | 7 | 9 | 1541 | 8148 | 628 | |
| 101613 | 7 | 10 | 1553 | 8184 | 618 | |
| 101614 | 7 | 10 | 1613 | 8418 | 527 | |
| 101615 | 7 | 11 | 1623 | 8450 | 524 | |
| 101630 | 7 | 11 | 1727 | 8888 | 587 | |
| 101631 | 7 | 12 | 1731 | 8900 | 589 | |
| 101736 | 7 | 8 | 1265 | 7096 | [726, 727] | |
| 101737 | 7 | 9 | 1319 | 7358 | [670, 674] | |
| 101739 | 7 | 10 | 1375 | 7626 | [593, 604] | |
| 101740 | 7 | 9 | 1545 | 8156 | 561 | |
| 101741 | 7 | 10 | 1573 | 8258 | 535 | |
| 101743 | 7 | 11 | 1599 | 8354 | 511 | |
| 101744 | 7 | 8 | 1399 | 7662 | 860 | |
| 101745 | 7 | 9 | 1431 | 7782 | 812 | |
| 101746 | 7 | 9 | 1475 | 7926 | 671 | |
| 101747 | 7 | 10 | 1503 | 8020 | 621 | |
| 101750 | 7 | 10 | 1539 | 8124 | 520 | |
| 101751 | 7 | 11 | 1563 | 8200 | 496 | |
| 101752 | 7 | 9 | 1495 | 8012 | 634 | |
| 101753 | 7 | 10 | 1519 | 8106 | 623 | |
| 101754 | 7 | 10 | 1559 | 8276 | 567 | |
| 101755 | 7 | 11 | 1583 | 8366 | 541 | |
| 101756 | 7 | 10 | 1631 | 8520 | 609 | |
| 101757 | 7 | 11 | 1645 | 8564 | 595 | |
| 101758 | 7 | 11 | 1661 | 8618 | 572 | |
| 101759 | 7 | 12 | 1671 | 8650 | 566 | |
| 101880 | 7 | 10 | 1643 | 8542 | 578 | |
| 101881 | 7 | 11 | 1651 | 8570 | 582 | |
| 101882 | 7 | 11 | 1733 | 8938 | 600 | |
| 101883 | 7 | 12 | 1743 | 8970 | 594 | |
| 101886 | 7 | 12 | 1775 | 9088 | 634 | |
| 101887 | 7 | 13 | 1779 | 9100 | 634 | |
| 102176 | 7 | 7 | 1083 | 6726 | 1082 | |
| 102177 | 7 | 8 | 1159 | 7170 | 1158 | |
| 102178 | 7 | 8 | 1221 | 7026 | 1042 | |
| 102179 | 7 | 9 | 1275 | 7306 | 1029 | |
| 102182 | 7 | 9 | 1351 | 7470 | 707 | |
| 102183 | 7 | 10 | 1375 | 7582 | 721 | |
| 102186 | 7 | 9 | 1337 | 7492 | 801 | |
| 102187 | 7 | 10 | 1391 | 7754 | [751, 752] | |
| 102188 | 7 | 9 | 1487 | 8026 | 714 | |
| 102189 | 7 | 10 | 1519 | 8154 | 680 | |
| 102190 | 7 | 10 | 1555 | 8258 | 584 | |
| 102191 | 7 | 11 | 1579 | 8350 | 568 | |
| 102206 | 7 | 11 | 1659 | 8606 | 590 | |
| 102207 | 7 | 12 | 1667 | 8634 | 592 | |
| 102250 | 7 | 10 | 1391 | 7754 | [750, 754] | |
| 102251 | 7 | 11 | 1447 | 8022 | [670, 684] | |
| 102252 | 7 | 10 | 1617 | 8552 | 638 | |
| 102253 | 7 | 11 | 1645 | 8654 | 610 | |
| 102254 | 7 | 11 | 1645 | 8654 | 617 | |
| 102255 | 7 | 12 | 1671 | 8750 | 593 | |
| 102262 | 7 | 11 | 1707 | 8852 | 588 | |
| 102263 | 7 | 12 | 1723 | 8904 | 576 | |
| 102270 | 7 | 12 | 1749 | 9002 | 624 | |
| 102271 | 7 | 13 | 1759 | 9034 | 618 | |
| 102398 | 7 | 13 | 1791 | 9152 | 657 | |
| 102399 | 7 | 14 | 1795 | 9164 | 657 | |
| 103864 | 7 | 9 | 1539 | 8208 | 680 | |
| 103865 | 7 | 10 | 1579 | 8336 | 636 | |
| 103867 | 7 | 11 | 1611 | 8428 | 580 | |
| 103871 | 7 | 12 | 1635 | 8496 | 548 | |
| 103928 | 7 | 10 | 1663 | 8680 | 616 | |
| 103929 | 7 | 11 | 1687 | 8768 | 609 | |
| 103931 | 7 | 12 | 1711 | 8850 | 582 | |
| 103932 | 7 | 11 | 1719 | 8876 | 639 | |
| 103933 | 7 | 12 | 1733 | 8916 | 625 | |
| 103935 | 7 | 13 | 1743 | 8946 | 618 | |
| 104011 | 7 | 9 | 1159 | 6546 | 443 | |
| 104012 | 7 | 8 | 1233 | 6962 | 787 | |
| 104013 | 7 | 9 | 1293 | 7184 | 651 | |
| 104015 | 7 | 10 | 1351 | 7442 | 558 | |
| 104020 | 7 | 8 | 1409 | 7664 | 750 | |
| 104021 | 7 | 9 | 1445 | 7772 | 660 | |
| 104022 | 7 | 9 | 1479 | 7934 | 663 | |
| 104023 | 7 | 10 | 1509 | 8030 | 613 | |
| 104030 | 7 | 10 | 1549 | 8196 | 543 | |
| 104031 | 7 | 11 | 1575 | 8290 | 519 | |
| 104052 | 7 | 9 | 1533 | 8184 | 735 | |
| 104053 | 7 | 10 | 1577 | 8316 | 635 | |
| 104055 | 7 | 11 | 1613 | 8428 | 581 | |
| 104063 | 7 | 12 | 1639 | 8514 | 552 | |
| 104082 | 7 | 8 | 1169 | 6852 | 1127 | |
| 104083 | 7 | 9 | 1205 | 6880 | 903 | |
| 104086 | 7 | 9 | 1311 | 7324 | 766 | |
| 104087 | 7 | 10 | 1353 | 7464 | 673 | |
| 104094 | 7 | 10 | 1549 | 8204 | 562 | |
| 104095 | 7 | 11 | 1573 | 8280 | 540 | |
| 104096 | 7 | 7 | 1247 | 7098 | 1120 | |
| 104097 | 7 | 8 | 1335 | 7458 | 1034 | |
| 104099 | 7 | 9 | 1409 | 7720 | 826 | |
| 104100 | 7 | 8 | 1363 | 7526 | 844 | |
| 104101 | 7 | 9 | 1433 | 7784 | 694 | |
| 104103 | 7 | 10 | 1489 | 7976 | 616 | |
| 104106 | 7 | 9 | 1425 | 7808 | 839 | |
| 104107 | 7 | 10 | 1493 | 8038 | 647 | |
| 104108 | 7 | 9 | 1553 | 8232 | 662 | |
| 104109 | 7 | 10 | 1597 | 8364 | 578 | |
| 104110 | 7 | 10 | 1583 | 8336 | 640 | |
| 104111 | 7 | 11 | 1617 | 8434 | 582 | |
| 104114 | 7 | 9 | 1425 | 7832 | 878 | |
| 104115 | 7 | 10 | 1485 | 8004 | 654 | |
| 104118 | 7 | 10 | 1495 | 8056 | 672 | |
| 104119 | 7 | 11 | 1549 | 8220 | 548 | |
| 104126 | 7 | 11 | 1613 | 8436 | 604 | |
| 104127 | 7 | 12 | 1637 | 8504 | 572 | |
| 104154 | 7 | 10 | 1403 | 7712 | 658 | |
| 104155 | 7 | 11 | 1423 | 7790 | 632 | |
| 104156 | 7 | 10 | 1589 | 8396 | 690 | |
| 104157 | 7 | 11 | 1601 | 8432 | 676 | |
| 104158 | 7 | 11 | 1661 | 8666 | 584 | |
| 104159 | 7 | 12 | 1671 | 8698 | 580 | |
| 104168 | 7 | 9 | 1445 | 7848 | 723 | |
| 104169 | 7 | 10 | 1505 | 8104 | 652 | |
| 104171 | 7 | 11 | 1567 | 8362 | 561 | |
| 104172 | 7 | 10 | 1657 | 8656 | 647 | |
| 104173 | 7 | 11 | 1685 | 8746 | 611 | |
| 104175 | 7 | 12 | 1711 | 8834 | 582 | |
| 104176 | 7 | 9 | 1511 | 8142 | 786 | |
| 104177 | 7 | 10 | 1549 | 8274 | 731 | |
| 104178 | 7 | 10 | 1585 | 8424 | 659 | |
| 104179 | 7 | 11 | 1619 | 8534 | 607 | |
| 104180 | 7 | 10 | 1627 | 8572 | 680 | |
| 104181 | 7 | 11 | 1659 | 8668 | 622 | |
| 104182 | 7 | 11 | 1675 | 8722 | 600 | |
| 104183 | 7 | 12 | 1699 | 8792 | 570 | |
| 104184 | 7 | 10 | 1557 | 8290 | 692 | |
| 104185 | 7 | 11 | 1581 | 8378 | 681 | |
| 104186 | 7 | 11 | 1623 | 8556 | 615 | |
| 104187 | 7 | 12 | 1647 | 8638 | 588 | |
| 104188 | 7 | 11 | 1695 | 8796 | 655 | |
| 104189 | 7 | 12 | 1709 | 8836 | 641 | |
| 104190 | 7 | 12 | 1725 | 8892 | 619 | |
| 104191 | 7 | 13 | 1735 | 8922 | 612 | |
| 104368 | 7 | 9 | 1471 | 8058 | 941 | |
| 104369 | 7 | 10 | 1547 | 8322 | 743 | |
| 104371 | 7 | 11 | 1611 | 8520 | 592 | |
| 104372 | 7 | 10 | 1503 | 8178 | 905 | |
| 104373 | 7 | 11 | 1575 | 8416 | 701 | |
| 104375 | 7 | 12 | 1635 | 8596 | 576 | |
| 104376 | 7 | 10 | 1609 | 8518 | 660 | |
| 104377 | 7 | 11 | 1653 | 8664 | 614 | |
| 104379 | 7 | 12 | 1691 | 8784 | 564 | |
| 104380 | 7 | 11 | 1665 | 8714 | 690 | |
| 104381 | 7 | 12 | 1699 | 8812 | 632 | |
| 104383 | 7 | 13 | 1723 | 8880 | 600 | |
| 104440 | 7 | 11 | 1679 | 8744 | 640 | |
| 104441 | 7 | 12 | 1703 | 8832 | 633 | |
| 104443 | 7 | 13 | 1727 | 8914 | 606 | |
| 104444 | 7 | 12 | 1735 | 8940 | 663 | |
| 104445 | 7 | 13 | 1749 | 8980 | 649 | |
| 104447 | 7 | 14 | 1759 | 9010 | 642 | |
| 105976 | 7 | 11 | 1799 | 9212 | 644 | |
| 105977 | 7 | 12 | 1807 | 9240 | 650 | |
| 105978 | 7 | 12 | 1829 | 9328 | 667 | |
| 105979 | 7 | 13 | 1839 | 9358 | 661 | |
| 105982 | 7 | 13 | 1847 | 9384 | 683 | |
| 105983 | 7 | 14 | 1851 | 9396 | 683 | |
| 106206 | 7 | 12 | 1775 | 9136 | 643 | |
| 106207 | 7 | 13 | 1779 | 9148 | 645 | |
| 106208 | 7 | 9 | 1533 | 8190 | 706 | |
| 106209 | 7 | 10 | 1557 | 8302 | 724 | |
| 106210 | 7 | 10 | 1641 | 8602 | 638 | |
| 106211 | 7 | 11 | 1665 | 8690 | 626 | |
| 106214 | 7 | 11 | 1705 | 8814 | 634 | |
| 106215 | 7 | 12 | 1713 | 8842 | 642 | |
| 106218 | 7 | 11 | 1725 | 8964 | 611 | |
| 106219 | 7 | 12 | 1751 | 9054 | 584 | |
| 106220 | 7 | 11 | 1757 | 9072 | 640 | |
| 106221 | 7 | 12 | 1773 | 9120 | 628 | |
| 106222 | 7 | 12 | 1797 | 9212 | 647 | |
| 106223 | 7 | 13 | 1807 | 9242 | 640 | |
| 106238 | 7 | 13 | 1839 | 9360 | 679 | |
| 106239 | 7 | 14 | 1843 | 9372 | 679 | |
| 106273 | 7 | 9 | 1301 | 7474 | 1124 | |
| 106274 | 7 | 9 | 1325 | 7406 | 849 | |
| 106275 | 7 | 10 | 1381 | 7670 | 816 | |
| 106278 | 7 | 10 | 1401 | 7700 | 723 | |
| 106279 | 7 | 11 | 1425 | 7812 | 743 | |
| 106280 | 7 | 9 | 1451 | 7918 | 774 | |
| 106281 | 7 | 10 | 1515 | 8206 | 734 | |
| 106282 | 7 | 10 | 1509 | 8132 | 704 | |
| 106283 | 7 | 11 | 1569 | 8382 | 622 | |
| 106284 | 7 | 10 | 1585 | 8426 | 674 | |
| 106285 | 7 | 11 | 1621 | 8554 | 630 | |
| 106286 | 7 | 11 | 1621 | 8544 | 628 | |
| 106287 | 7 | 12 | 1645 | 8628 | 608 | |
| 106296 | 7 | 10 | 1603 | 8462 | 616 | |
| 106297 | 7 | 11 | 1627 | 8574 | 634 | |
| 106298 | 7 | 11 | 1677 | 8730 | 616 | |
| 106299 | 7 | 12 | 1701 | 8816 | 596 | |
| 106302 | 7 | 12 | 1725 | 8884 | 632 | |
| 106303 | 7 | 13 | 1733 | 8912 | 632 | |
| 106344 | 7 | 10 | 1567 | 8408 | 713 | |
| 106345 | 7 | 11 | 1631 | 8672 | 641 | |
| 106346 | 7 | 11 | 1591 | 8502 | 714 | |
| 106347 | 7 | 12 | 1655 | 8762 | 622 | |
| 106348 | 7 | 11 | 1703 | 8916 | 681 | |
| 106349 | 7 | 12 | 1733 | 9014 | 644 | |
| 106350 | 7 | 12 | 1717 | 8960 | 675 | |
| 106351 | 7 | 13 | 1743 | 9046 | 646 | |
| 106352 | 7 | 10 | 1679 | 8812 | 654 | |
| 106353 | 7 | 11 | 1715 | 8940 | 620 | |
| 106354 | 7 | 11 | 1735 | 9012 | 654 | |
| 106355 | 7 | 12 | 1765 | 9110 | 618 | |
| 106358 | 7 | 12 | 1779 | 9152 | 640 | |
| 106359 | 7 | 13 | 1795 | 9200 | 628 | |
| 106360 | 7 | 11 | 1743 | 9030 | 636 | |
| 106361 | 7 | 12 | 1767 | 9116 | 624 | |
| 106362 | 7 | 12 | 1773 | 9146 | 663 | |
| 106363 | 7 | 13 | 1799 | 9234 | 634 | |
| 106364 | 7 | 12 | 1803 | 9244 | 658 | |
| 106365 | 7 | 13 | 1819 | 9292 | 646 | |
| 106366 | 7 | 13 | 1821 | 9300 | 677 | |
| 106367 | 7 | 14 | 1831 | 9330 | 670 | |
| 106488 | 7 | 12 | 1815 | 9276 | 670 | |
| 106489 | 7 | 13 | 1823 | 9304 | 678 | |
| 106490 | 7 | 13 | 1845 | 9392 | 694 | |
| 106491 | 7 | 14 | 1855 | 9422 | 687 | |
| 106494 | 7 | 14 | 1863 | 9448 | 709 | |
| 106495 | 7 | 15 | 1867 | 9460 | 709 | |
| 111558 | 7 | 10 | 1561 | 8294 | 714 | |
| 111559 | 7 | 11 | 1585 | 8406 | 728 | |
| 111563 | 7 | 11 | 1625 | 8546 | 626 | |
| 111564 | 7 | 10 | 1609 | 8520 | 686 | |
| 111565 | 7 | 11 | 1653 | 8668 | 628 | |
| 111566 | 7 | 11 | 1677 | 8736 | 662 | |
| 111567 | 7 | 12 | 1701 | 8820 | 644 | |
| 111582 | 7 | 12 | 1741 | 8944 | 658 | |
| 111583 | 7 | 13 | 1749 | 8972 | 660 | |
| 111585 | 7 | 10 | 1417 | 7936 | 885 | |
| 111587 | 7 | 11 | 1573 | 8412 | 652 | |
| 111591 | 7 | 12 | 1649 | 8658 | 638 | |
| 111597 | 7 | 12 | 1693 | 8808 | 588 | |
| 111599 | 7 | 13 | 1725 | 8904 | 624 | |
| 111615 | 7 | 14 | 1757 | 9000 | 660 | |
| 112459 | 7 | 11 | 1471 | 8026 | 670 | |
| 112460 | 7 | 10 | 1611 | 8560 | 759 | |
| 112461 | 7 | 11 | 1683 | 8822 | 631 | |
| 112462 | 7 | 11 | 1643 | 8664 | 707 | |
| 112463 | 7 | 12 | 1711 | 8926 | 610 | |
| 112468 | 7 | 10 | 1721 | 8940 | 666 | |
| 112469 | 7 | 11 | 1765 | 9088 | 606 | |
| 112470 | 7 | 11 | 1759 | 9082 | 676 | |
| 112471 | 7 | 12 | 1789 | 9178 | 640 | |
| 112478 | 7 | 12 | 1797 | 9216 | 680 | |
| 112479 | 7 | 13 | 1823 | 9302 | 651 | |
| 112481 | 7 | 10 | 1431 | 7918 | 795 | |
| 112483 | 7 | 11 | 1475 | 8060 | 717 | |
| 112485 | 7 | 11 | 1687 | 8854 | 644 | |
| 112487 | 7 | 12 | 1711 | 8928 | 620 | |
| 112491 | 7 | 12 | 1495 | 8138 | 706 | |
| 112492 | 7 | 11 | 1661 | 8744 | 755 | |
| 112493 | 7 | 12 | 1733 | 9014 | 648 | |
| 112494 | 7 | 12 | 1673 | 8780 | 743 | |
| 112495 | 7 | 13 | 1743 | 9046 | 646 | |
| 112500 | 7 | 11 | 1745 | 9052 | 694 | |
| 112501 | 7 | 12 | 1789 | 9200 | 634 | |
| 112502 | 7 | 12 | 1787 | 9188 | 680 | |
| 112503 | 7 | 13 | 1819 | 9292 | 646 | |
| 112510 | 7 | 13 | 1805 | 9244 | 698 | |
| 112511 | 7 | 14 | 1831 | 9330 | 669 | |
| 112524 | 7 | 10 | 1653 | 8740 | 708 | |
| 112525 | 7 | 11 | 1705 | 8904 | 608 | |
| 112526 | 7 | 11 | 1719 | 8962 | 668 | |
| 112527 | 7 | 12 | 1757 | 9080 | 614 | |
| 112542 | 7 | 12 | 1787 | 9192 | 672 | |
| 112543 | 7 | 13 | 1811 | 9260 | 640 | |
| 112545 | 7 | 10 | 1567 | 8470 | 798 | |
| 112546 | 7 | 10 | 1585 | 8488 | 782 | |
| 112547 | 7 | 11 | 1661 | 8774 | 648 | |
| 112550 | 7 | 11 | 1687 | 8856 | 634 | |
| 112551 | 7 | 12 | 1735 | 9016 | 580 | |
| 112554 | 7 | 11 | 1635 | 8672 | 785 | |
| 112555 | 7 | 12 | 1707 | 8934 | 657 | |
| 112556 | 7 | 11 | 1705 | 8932 | 680 | |
| 112557 | 7 | 12 | 1757 | 9100 | 604 | |
| 112558 | 7 | 12 | 1747 | 9068 | 672 | |
| 112559 | 7 | 13 | 1787 | 9192 | 620 | |
| 112574 | 7 | 13 | 1795 | 9220 | 688 | |
| 112575 | 7 | 14 | 1819 | 9288 | 656 | |
| 112590 | 7 | 12 | 1765 | 9116 | 655 | |
| 112591 | 7 | 13 | 1791 | 9202 | 626 | |
| 112598 | 7 | 12 | 1797 | 9220 | 682 | |
| 112599 | 7 | 13 | 1813 | 9268 | 670 | |
| 112606 | 7 | 13 | 1837 | 9360 | 688 | |
| 112607 | 7 | 14 | 1847 | 9390 | 681 | |
| 112609 | 7 | 11 | 1635 | 8702 | 670 | |
| 112610 | 7 | 11 | 1637 | 8660 | 698 | |
| 112611 | 7 | 12 | 1703 | 8920 | 612 | |
| 112612 | 7 | 11 | 1723 | 8982 | 666 | |
| 112613 | 7 | 12 | 1761 | 9114 | 626 | |
| 112614 | 7 | 12 | 1767 | 9120 | 654 | |
| 112615 | 7 | 13 | 1791 | 9204 | 636 | |
| 112618 | 7 | 12 | 1667 | 8776 | 735 | |
| 112619 | 7 | 13 | 1735 | 9038 | 638 | |
| 112620 | 7 | 12 | 1779 | 9180 | 672 | |
| 112621 | 7 | 13 | 1811 | 9284 | 638 | |
| 112622 | 7 | 13 | 1797 | 9236 | 691 | |
| 112623 | 7 | 14 | 1823 | 9322 | 662 | |
| 112628 | 7 | 12 | 1783 | 9194 | 702 | |
| 112629 | 7 | 13 | 1813 | 9290 | 666 | |
| 112630 | 7 | 13 | 1827 | 9332 | 686 | |
| 112631 | 7 | 14 | 1843 | 9380 | 674 | |
| 112638 | 7 | 14 | 1845 | 9388 | 705 | |
| 112639 | 7 | 15 | 1855 | 9418 | 698 | |
| 114654 | 7 | 14 | 1879 | 9508 | 719 | |
| 114655 | 7 | 15 | 1883 | 9520 | 719 | |
| 114656 | 7 | 11 | 1715 | 8938 | 660 | |
| 114657 | 7 | 12 | 1739 | 9050 | 678 | |
| 114658 | 7 | 12 | 1791 | 9212 | 674 | |
| 114659 | 7 | 13 | 1815 | 9296 | 656 | |
| 114662 | 7 | 13 | 1839 | 9364 | 688 | |
| 114663 | 7 | 14 | 1847 | 9392 | 690 | |
| 114666 | 7 | 13 | 1821 | 9328 | 711 | |
| 114667 | 7 | 14 | 1847 | 9414 | 682 | |
| 114668 | 7 | 13 | 1851 | 9424 | 704 | |
| 114669 | 7 | 14 | 1867 | 9472 | 692 | |
| 114670 | 7 | 14 | 1869 | 9480 | 722 | |
| 114671 | 7 | 15 | 1879 | 9510 | 715 | |
| 114686 | 7 | 15 | 1887 | 9536 | 737 | |
| 114687 | 7 | 16 | 1891 | 9548 | 737 | |
| 127777 | 7 | 9 | 1235 | 7614 | 1234 | |
| 127779 | 7 | 10 | 1355 | 7754 | 1123 | |
| 127783 | 7 | 11 | 1471 | 8198 | 841 | |
| 127787 | 7 | 11 | 1455 | 8030 | 821 | |
| 127789 | 7 | 11 | 1599 | 8598 | 774 | |
| 127791 | 7 | 12 | 1659 | 8794 | 662 | |
| 127806 | 7 | 12 | 1723 | 8966 | 672 | |
| 127807 | 7 | 13 | 1747 | 9078 | 686 | |
| 127851 | 7 | 12 | 1499 | 8172 | 747 | |
| 127853 | 7 | 12 | 1711 | 8966 | 670 | |
| 127855 | 7 | 13 | 1735 | 9040 | 648 | |
| 127862 | 7 | 12 | 1751 | 9088 | 674 | |
| 127863 | 7 | 13 | 1791 | 9228 | 636 | |
| 127870 | 7 | 13 | 1799 | 9240 | 690 | |
| 127871 | 7 | 14 | 1823 | 9324 | 672 | |
| 127998 | 7 | 14 | 1847 | 9392 | 704 | |
| 127999 | 7 | 15 | 1855 | 9420 | 706 | |
| 128875 | 7 | 13 | 1519 | 8250 | [738, 741] | |
| 128876 | 7 | 12 | 1685 | 8856 | 783 | |
| 128877 | 7 | 13 | 1757 | 9126 | 676 | |
| 128878 | 7 | 13 | 1697 | 8892 | 771 | |
| 128879 | 7 | 14 | 1767 | 9158 | 674 | |
| 128884 | 7 | 12 | 1769 | 9164 | 720 | |
| 128885 | 7 | 13 | 1813 | 9312 | 660 | |
| 128886 | 7 | 13 | 1811 | 9300 | 708 | |
| 128887 | 7 | 14 | 1843 | 9404 | 674 | |
| 128894 | 7 | 14 | 1829 | 9356 | 727 | |
| 128895 | 7 | 15 | 1855 | 9442 | 698 | |
| 128958 | 7 | 14 | 1859 | 9452 | 720 | |
| 128959 | 7 | 15 | 1875 | 9500 | 708 | |
| 129022 | 7 | 15 | 1877 | 9508 | 739 | |
| 129023 | 7 | 16 | 1887 | 9538 | 732 | |
| 131070 | 7 | 16 | 1895 | 9564 | 754 | |
| 131071 | 7 | 17 | 1899 | 9576 | 754 | |
| 237048 | 7 | 12 | 1935 | 9768 | 708 | |
| 237049 | 7 | 13 | 1943 | 9796 | 726 | |
| 237051 | 7 | 14 | 1955 | 9834 | 734 | |
| 237055 | 7 | 15 | 1959 | 9846 | 746 | |
| 237274 | 7 | 12 | 1805 | 9334 | 674 | |
| 237275 | 7 | 13 | 1815 | 9366 | 674 | |
| 237278 | 7 | 13 | 1847 | 9484 | 710 | |
| 237279 | 7 | 14 | 1851 | 9496 | 714 | |
| 237288 | 7 | 11 | 1823 | 9364 | 656 | |
| 237289 | 7 | 12 | 1851 | 9470 | 662 | |
| 237291 | 7 | 13 | 1883 | 9586 | 657 | |
| 237292 | 7 | 12 | 1871 | 9548 | 674 | |
| 237293 | 7 | 13 | 1891 | 9612 | 686 | |
| 237295 | 7 | 14 | 1903 | 9650 | 695 | |
| 237304 | 7 | 12 | 1885 | 9590 | 684 | |
| 237305 | 7 | 13 | 1893 | 9618 | 700 | |
| 237306 | 7 | 13 | 1915 | 9704 | 700 | |
| 237307 | 7 | 14 | 1927 | 9742 | 711 | |
| 237310 | 7 | 14 | 1935 | 9768 | 721 | |
| 237311 | 7 | 15 | 1939 | 9780 | 733 | |
| 237560 | 7 | 13 | 1951 | 9832 | 732 | |
| 237561 | 7 | 14 | 1959 | 9860 | 750 | |
| 237563 | 7 | 15 | 1971 | 9898 | 758 | |
| 237567 | 7 | 16 | 1975 | 9910 | 770 | |
| 241483 | 7 | 12 | 1771 | 9210 | 580 | |
| 241484 | 7 | 11 | 1761 | 9182 | 650 | |
| 241485 | 7 | 12 | 1807 | 9338 | 634 | |
| 241487 | 7 | 13 | 1839 | 9454 | 634 | |
| 241492 | 7 | 11 | 1793 | 9276 | 658 | |
| 241493 | 7 | 12 | 1831 | 9408 | 658 | |
| 241494 | 7 | 12 | 1841 | 9456 | 664 | |
| 241495 | 7 | 13 | 1861 | 9520 | 678 | |
| 241502 | 7 | 13 | 1883 | 9604 | 676 | |
| 241503 | 7 | 14 | 1895 | 9642 | 690 | |
| 241524 | 7 | 12 | 1857 | 9504 | 670 | |
| 241525 | 7 | 13 | 1895 | 9636 | 678 | |
| 241527 | 7 | 14 | 1915 | 9700 | 702 | |
| 241535 | 7 | 15 | 1927 | 9738 | 725 | |
| 241611 | 7 | 13 | 1863 | 9522 | 654 | |
| 241612 | 7 | 12 | 1831 | 9428 | 654 | |
| 241613 | 7 | 13 | 1859 | 9512 | 648 | |
| 241614 | 7 | 13 | 1883 | 9604 | 680 | |
| 241615 | 7 | 14 | 1895 | 9642 | 690 | |
| 241630 | 7 | 14 | 1927 | 9760 | 718 | |
| 241631 | 7 | 15 | 1931 | 9772 | 730 | |
| 241633 | 7 | 12 | 1847 | 9476 | 684 | |
| 241634 | 7 | 12 | 1869 | 9540 | 692 | |
| 241635 | 7 | 13 | 1897 | 9644 | 694 | |
| 241638 | 7 | 13 | 1909 | 9680 | 716 | |
| 241639 | 7 | 14 | 1917 | 9708 | 732 | |
| 241642 | 7 | 13 | 1899 | 9652 | 710 | |
| 241643 | 7 | 14 | 1931 | 9766 | 703 | |
| 241644 | 7 | 13 | 1919 | 9728 | 708 | |
| 241645 | 7 | 14 | 1939 | 9792 | 718 | |
| 241646 | 7 | 14 | 1939 | 9792 | 732 | |
| 241647 | 7 | 15 | 1951 | 9830 | 740 | |
| 241662 | 7 | 15 | 1959 | 9856 | 750 | |
| 241663 | 7 | 16 | 1963 | 9868 | 762 | |
| 245707 | 7 | 14 | 1943 | 9802 | 724 | |
| 245708 | 7 | 13 | 1909 | 9702 | 712 | |
| 245709 | 7 | 14 | 1939 | 9792 | 718 | |
| 245711 | 7 | 15 | 1951 | 9830 | 740 | |
| 245720 | 7 | 13 | 1933 | 9772 | 730 | |
| 245721 | 7 | 14 | 1941 | 9800 | 748 | |
| 245722 | 7 | 14 | 1963 | 9884 | 746 | |
| 245723 | 7 | 15 | 1975 | 9922 | 754 | |
| 245726 | 7 | 15 | 1983 | 9948 | 764 | |
| 245727 | 7 | 16 | 1987 | 9960 | 776 | |
| 245752 | 7 | 14 | 1975 | 9920 | 762 | |
| 245753 | 7 | 15 | 1983 | 9948 | 780 | |
| 245755 | 7 | 16 | 1995 | 9986 | 786 | |
| 245759 | 7 | 17 | 1999 | 9998 | 798 | |
| 255567 | 7 | 12 | 1527 | 8466 | [756, 776] | |
| 255574 | 7 | 11 | 1697 | 8996 | 710 | |
| 255575 | 7 | 12 | 1725 | 9098 | 694 | |
| 255583 | 7 | 13 | 1751 | 9194 | 678 | |
| 255605 | 7 | 12 | 1787 | 9296 | 660 | |
| 255607 | 7 | 13 | 1829 | 9446 | 700 | |
| 255613 | 7 | 13 | 1803 | 9348 | 660 | |
| 255615 | 7 | 14 | 1839 | 9478 | 702 | |
| 255655 | 7 | 12 | 1809 | 9366 | 670 | |
| 255662 | 7 | 12 | 1821 | 9400 | 644 | |
| 255663 | 7 | 13 | 1861 | 9542 | 674 | |
| 255678 | 7 | 13 | 1871 | 9568 | 646 | |
| 255679 | 7 | 14 | 1891 | 9632 | 684 | |
| 255727 | 7 | 14 | 1895 | 9666 | 690 | |
| 255734 | 7 | 13 | 1895 | 9660 | 674 | |
| 255735 | 7 | 14 | 1915 | 9724 | 702 | |
| 255743 | 7 | 15 | 1927 | 9762 | 725 | |
| 255925 | 7 | 13 | 1875 | 9582 | 688 | |
| 255927 | 7 | 14 | 1917 | 9730 | 728 | |
| 255933 | 7 | 14 | 1927 | 9756 | 696 | |
| 255935 | 7 | 15 | 1947 | 9820 | 734 | |
| 255999 | 7 | 16 | 1959 | 9858 | 756 | |
| 257758 | 7 | 14 | 1871 | 9596 | 738 | |
| 257759 | 7 | 15 | 1875 | 9608 | 742 | |
| 257771 | 7 | 14 | 1907 | 9698 | 687 | |
| 257772 | 7 | 13 | 1895 | 9660 | 702 | |
| 257773 | 7 | 14 | 1915 | 9724 | 716 | |
| 257774 | 7 | 14 | 1939 | 9816 | 728 | |
| 257775 | 7 | 15 | 1951 | 9854 | 741 | |
| 257787 | 7 | 15 | 1927 | 9762 | 725 | |
| 257790 | 7 | 15 | 1959 | 9880 | 751 | |
| 257791 | 7 | 16 | 1963 | 9892 | 763 | |
| 257905 | 7 | 13 | 1909 | 9700 | 688 | |
| 257907 | 7 | 14 | 1951 | 9848 | 712 | |
| 257911 | 7 | 15 | 1971 | 9912 | 748 | |
| 257913 | 7 | 14 | 1929 | 9764 | 726 | |
| 257915 | 7 | 15 | 1963 | 9886 | 735 | |
| 257916 | 7 | 14 | 1951 | 9848 | 726 | |
| 257917 | 7 | 15 | 1971 | 9912 | 748 | |
| 257919 | 7 | 16 | 1983 | 9950 | 770 | |
| 258041 | 7 | 15 | 1949 | 9828 | 764 | |
| 258042 | 7 | 15 | 1971 | 9912 | 762 | |
| 258043 | 7 | 16 | 1983 | 9950 | 770 | |
| 258046 | 7 | 16 | 1991 | 9976 | 780 | |
| 258047 | 7 | 17 | 1995 | 9988 | 792 | |
| 262136 | 7 | 15 | 1983 | 9948 | 778 | |
| 262137 | 7 | 16 | 1991 | 9976 | 796 | |
| 262139 | 7 | 17 | 2003 | 10014 | 802 | |
| 262143 | 7 | 18 | 2007 | 10026 | 814 | |
| 507851 | 7 | 15 | 2011 | 10050 | 786 | |
| 507852 | 7 | 14 | 1975 | 9944 | 760 | |
| 507853 | 7 | 15 | 2007 | 10040 | 780 | |
| 507855 | 7 | 16 | 2019 | 10078 | 802 | |
| 507870 | 7 | 16 | 2027 | 10104 | 810 | |
| 507871 | 7 | 17 | 2031 | 10116 | 822 | |
| 507903 | 7 | 18 | 2035 | 10128 | 834 | |
| 515577 | 7 | 15 | 1983 | 9972 | 778 | |
| 515579 | 7 | 16 | 1995 | 10010 | 788 | |
| 515583 | 7 | 17 | 1999 | 10022 | 800 | |
| 515806 | 7 | 15 | 1995 | 10004 | 760 | |
| 515807 | 7 | 16 | 1999 | 10016 | 772 | |
| 515819 | 7 | 15 | 1987 | 9978 | 750 | |
| 515820 | 7 | 14 | 1975 | 9940 | 728 | |
| 515821 | 7 | 15 | 1995 | 10004 | 762 | |
| 515823 | 7 | 16 | 2007 | 10042 | 784 | |
| 515838 | 7 | 16 | 2015 | 10068 | 794 | |
| 515839 | 7 | 17 | 2019 | 10080 | 806 | |
| 516089 | 7 | 16 | 2015 | 10068 | 796 | |
| 516091 | 7 | 17 | 2027 | 10106 | 816 | |
| 516095 | 7 | 18 | 2031 | 10118 | 828 | |
| 524239 | 7 | 17 | 2027 | 10106 | 818 | |
| 524254 | 7 | 17 | 2035 | 10132 | 826 | |
| 524255 | 7 | 18 | 2039 | 10144 | 838 | |
| 524287 | 7 | 19 | 2043 | 10156 | 850 | |
| 1048059 | 7 | 18 | 2047 | 10170 | 846 | |
| 1048063 | 7 | 19 | 2051 | 10182 | 858 | |
| 1048575 | 7 | 20 | 2055 | 10194 | 870 | |
| 2097151 | 7 | 21 | 2059 | 10206 | 882 | |
| 2168480 | 8 | 7 | 2401 | 16320 | 2400 | |
| 6466304 | 8 | 8 | 3457 | 22464 | 3256 | |
| 6533952 | 8 | 10 | 4125 | 25608 | [2118, 2120] | |
| 6709089 | 8 | 13 | 4627 | 28128 | [1860, 1868] | |
| 15054720 | 8 | 12 | 5273 | 30912 | [1457, 1488] | |
| 15062688 | 8 | 12 | 5313 | 30992 | [1448, 1488] | |
| 15071136 | 8 | 14 | 5569 | 32168 | [1512, 1528] | |
| 33150580 | 8 | 16 | 5865 | 33504 | 1560 | |
| 268435455 | 8 | 28 | 6305 | 34992 | 2032 | |
| 272804608 | 9 | 8 | 6649 | 50592 | 6648 | |
| 816133056 | 9 | 12 | 12675 | 86200 | [4692, 4810] | |
| 816140800 | 9 | 9 | 9577 | 69984 | [9230, 9264] | |
| 820437760 | 9 | 12 | 12305 | 85384 | [6333, 6562] | |
| 830985889 | 9 | 15 | 14715 | 96876 | [3253, 3638] | |
| 1932875168 | 9 | 15 | 16387 | 105516 | [3215, 3378] | |
| 1932907696 | 9 | 16 | 16891 | 107960 | [0, 3378] | |
| 1932908036 | 9 | 15 | 15579 | 102576 | [3796, 3920] | |
| 4076070560 | 9 | 18 | 17923 | 113076 | [3343, 3402] | |
| 4135458444 | 9 | 18 | 17767 | 112572 | [3140, 3276] | |
| 68719476735 | 9 | 36 | 19171 | 118098 | 4590 | |
| 69267182080 | 10 | 9 | 18413 | 155052 | 18412 | |
| 207522258944 | 10 | 10 | 26525 | 215340 | [25933, 26044] | |
| 208065556480 | 10 | 13 | 35117 | 269608 | [18344, 19398] | |
| 209488594209 | 10 | 17 | 40413 | 303976 | [0, 18952] | |
| 484034048000 | 10 | 15 | 45285 | 329600 | [9356, 11090] | |
| 484034564608 | 10 | 15 | 45245 | 329640 | [9358, 10310] | |
| 484048828416 | 10 | 17 | 48677 | 347336 | [7490, 8876] | |
| 35184372088831 | 10 | 45 | 58025 | 393660 | 10220 | |
| 35323174871040 | 11 | 10 | 50991 | 470778 | 50990 | |
| 105899441274880 | 11 | 11 | 73459 | 655974 | [31100, 72688] | |
| 106037702582272 | 11 | 15 | 104951 | 881642 | [0, 63720] | |
| 36028797018963967 | 11 | 55 | 175099 | 1299078 | 22506 | |
| 36099512088150016 | 12 | 11 | 141209 | 1418352 | 141208 | |
| 108263005566271488 | 12 | 12 | 203433 | 1981728 | [96974, 202032] | |
| 108263350782918656 | 12 | 17 | 321689 | 2873612 | [99104, 131416] | |
| 108333582633402368 | 12 | 16 | 299681 | 2737544 | [153661, 192074] | |
| 108511984910469665 | 12 | 21 | 387763 | 3350876 | [0, 85226] | |
| 108512163153855521 | 12 | 21 | 354189 | 3167808 | [0, 184646] | |
| 252590061719912448 | 12 | 18 | 386229 | 3374784 | [51261, 97928] | |
| 252590061786513408 | 12 | 18 | 386225 | 3374352 | [0, 105292] | |
| 252590612549468160 | 12 | 20 | 415865 | 3565936 | [0, 75426] | |
| 252590612683702272 | 12 | 22 | 437593 | 3725240 | [0, 74100] | |
| 253083261389635584 | 12 | 20 | 419065 | 3575408 | [0, 69448] | |
| 253084088995282944 | 12 | 21 | 433353 | 3673776 | [0, 65132] | |
| 253084155833548800 | 12 | 22 | 448765 | 3774336 | [0, 52014] | |
| 253158749555917124 | 12 | 21 | 407501 | 3538188 | [0, 109136] | |
| 541243891326517248 | 12 | 24 | 480897 | 3987024 | [0, 40892] | |
| 542232239771271200 | 12 | 24 | 474585 | 3956640 | [32878, 46040] | |
| 542232240836624416 | 12 | 24 | 475001 | 3957424 | [0, 45560] | |
| 73786976294838206463 | 12 | 66 | 527345 | 4251528 | 49128 |
| Column | Description |
|---|---|
| id | Written in binary this encodes the edges in the board graph. Multiple id numbers describe isomorphic graphs; only the smallest id for each isomorphy class is listed. |
| board graph | Depiction of the board graph. |
| board nodes | Number of nodes in the board graph. |
| board edges | Number of edges in the board graph. |
| game nodes | Number of nodes in the game graph. Corresponds to the number of legal positions. |
| game edges | Number of edges in the game graph. Corresponds to the number of distinct moves. |
| longest path | Length of the longest simple path starting at node 1 (empty position). This is measured by the number of edges, or equivalently go moves, in the path. Written as an interval if there is a gap between the lower and the upper bound. A lower bound of 0 means that no serious attempt to find a long path has been made. |
Note: The table contains no board graphs with isolated nodes since they induce game graphs isomorphic to the same graph without the isolated nodes.
The game mechanics of go can be described in terms of graph theory. We leave aside the questions about how to compute scores or determine the winner, which are certainly very interesting in themselves but not needed to derive the game graphs.
Go is played on a board which in abstract form is an undirected graph. Normally this forms a 19x19 cartesian grid but here we consider any such graph.
Call the board graph B. Two nodes in B are called neighbors if
there is an edge between them. Each node has one of three labels,
Empty, White, or Black, and we call a configuration of labels
on B a position. The game starts from the position where all labels
are Empty (the empty position). Moves consist of turning one Empty
node into White or Black, which can have side effects for the
labels elsewhere on the board graph. Specifically, making a Black
move at node N consists of the following steps:
- Change the label of
NfromEmptytoBlack. - For each neighbor
N'ofNwithWhitelabel, find the maximum connected componentCofWhitelabelled nodes that includesN'. If no node ofChas a neighbor withEmptylabel, change the label of all nodes inCtoEmpty. - Find the maximum connected component
CofBlacklabelled nodes that includesN. If no node ofChas a neighbor withEmptylabel, change the label of all nodes inCtoEmpty.
Making a White move is done conversely, with opposite roles of the
White and Black labels.
A position can be reached by a sequence of moves if and only if each
maximum connected component of White or Black nodes is neighbor
to at least one Empty node. These positions are called legal
positions.
Now we can form a secondary graph structure called a Game Graph G,
with the set of legal positions on B as nodes and an edge from p1
to p2 if and only if p1 != p2 and there is a move transforming
p1 into p2.
Remarks:
- If a move made at node
Nresults inNbecoming empty, it is called a suicide in go terminology and is forbidden by some go rule variants. - Here suicide moves are allowed unless they lead to the same position being immediately repeated (single stone suicide in go terminology). The latter prevents self-edges in the game graphs.
- Normal go is played with alternating colors. This is not taken into account here, neither are passes. In fact, consecutive moves by the same color can be simulated by the other color passing.
- Isolated nodes in the board graph can never be labeled anything
other than
Emptyand the induced game graph will be isomorphic to the one induced from a board where the isolated node is removed.