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[[931,169,3]] d ≤
n
931
k
169
d
3
kd²/n
1.634
w
4
X/Z
1
g
1.63
r
1.4142
layers
1
swaps
5

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Distance

X/Z asymmetry 1 · d_X ≤ 3, d_Z ≤ 3 · w_X = 4, w_Z = 4 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 3 · witness weight 3 (claimed upper_bound)
witness found by @vprusso · gf2_fast.distance_rand_witness pd8 threads8 · found at 106 trials · 2026-09-24
witness operator (support, 3 qubits)
[222, 251, 252]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness found by @vprusso · submit.make_submission / NumPy lightest_logical · found at 1 trials · 2026-09-24
witness operator (support, 3 qubits)
[789, 819, 850]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 4 · H_Z 8 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 2–4 (mean 3.817) · H_Z 2–4 (mean 3.877)
qubit degrees H_X 1–3 (mean 1.591) · H_Z 1–2 (mean 1.557)
trapping sets H_X (1,1)×389 (2,0)×18 (3,0)×549 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 389 (1,2): 534 (1,3): 8 (2,0): 18 (2,1): 1084 (2,2): 1013 (2,3): 29 (3,0): 549 (3,1): 2043 (3,2): 1986 (3,3): 1072 (3,4): 342 (3,5): 8
trapping sets H_Z (1,1)×412 (2,0)×48 (3,0)×577 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 412 (1,2): 519 (2,0): 48 (2,1): 1096 (2,2): 980 (3,0): 577 (3,1): 2062 (3,2): 1942 (3,3): 998 (3,4): 316
witness diameter X 2.2361 · Z 2.2361 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 1.414
X checkZ checkqubit site (931)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release
routing cost 5 nearest-neighbor SWAPs per round in total, at most 1 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction Derived from the pinned 31x31 checkerboard code by @mathysrennela. Original qubit indices are retained as labels throughout. First perform these degree-one grafts, removing the indicated type's unique incident check, the qubit column from both matrices, and its coordinate: [{"side":"X","original_qubit":30,"removed_support_original":[29,30]},{"side":"X","original_qubit":930,"removed_support_original":[899,930]},{"side":"Z","original_qubit":960,"removed_support_original":[929,960]},{"side":"Z","original_qubit":31,"removed_support_original":[0,31]},{"side":"Z","original_qubit":0,"removed_support_original":[0,1]},{"side":"X","original_qubit":61,"removed_support_original":[29,61]},{"side":"X","original_qubit":899,"removed_support_original":[899,931]},{"side":"Z","original_qubit":929,"removed_support_original":[929,959]},{"side":"X","original_qubit":6,"removed_support_original":[6,7,37,38]},{"side":"X","original_qubit":16,"removed_support_original":[16,17,47,48]},{"side":"X","original_qubit":26,"removed_support_original":[26,27,57,58]},{"side":"X","original_qubit":279,"removed_support_original":[248,249,279,280]},{"side":"X","original_qubit":371,"removed_support_original":[370,371,401,402]},{"side":"X","original_qubit":589,"removed_support_original":[558,559,589,590]},{"side":"X","original_qubit":681,"removed_support_original":[680,681,711,712]}]. Then perform these pivot contractions in order, XORing the pivot into every other same-type row incident on its qubit, deleting that pivot row and qubit column, and applying research/local2d/boundary_engine.py _cleanup after each contraction: [{"side":"Z","original_qubit":4,"pivot_support_original":[4,5],"degree":1,"cleanup_removed_original":[]},{"side":"Z","original_qubit":14,"pivot_support_original":[14,15],"degree":1,"cleanup_removed_original":[]},{"side":"Z","original_qubit":24,"pivot_support_original":[24,25],"degree":1,"cleanup_removed_original":[]},{"side":"Z","original_qubit":309,"pivot_support_original":[309,340],"degree":1,"cleanup_removed_original":[]},{"side":"Z","original_qubit":341,"pivot_support_original":[310,341],"degree":1,"cleanup_removed_original":[]},{"side":"Z","original_qubit":619,"pivot_support_original":[619,650],"degree":1,"cleanup_removed_original":[]},{"side":"Z","original_qubit":651,"pivot_support_original":[620,651],"degree":1,"cleanup_removed_original":[]},{"side":"X","original_qubit":931,"pivot_support_original":[900,901,931,932],"degree":1,"cleanup_removed_original":[900]},{"side":"X","original_qubit":940,"pivot_support_original":[908,909,939,940],"degree":1,"cleanup_removed_original":[]},{"side":"X","original_qubit":944,"pivot_support_original":[912,913,943,944],"degree":1,"cleanup_removed_original":[]},{"side":"X","original_qubit":950,"pivot_support_original":[918,919,949,950],"degree":1,"cleanup_removed_original":[]},{"side":"X","original_qubit":954,"pivot_support_original":[922,923,953,954],"degree":1,"cleanup_removed_original":[]},{"side":"X","original_qubit":909,"pivot_support_original":[909,941],"degree":1,"cleanup_removed_original":[]},{"side":"X","original_qubit":919,"pivot_support_original":[919,951],"degree":1,"cleanup_removed_original":[]}]. All selected pivots have degree one; cleanup additionally removes original qubit900 after the X931 move. The29 selected moves remove30 qubits total. Keep surviving columns and rows in the order produced by these operations.
builds on https://github.com/unitaryfoundation/qldpc-challenge/blob/110d467f046370612cd7fd2d6bbff5e439837ffd/codes/961-169-3.json
date 2026-09-24
notes Known checkerboard family. Distance is a witnessed upper bound, not an exact claim. Literature novelty is unverified. Final-matrix audit budgets are separate from ancestor searches and rejected proposals.
family topological (a tag, not a ranking)
locality 2D-local single (computed from the layout)
weight class weight ≤ 4 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[931,169,3]] — boundary reductions of the mod-5 checkerboard code

Author: @vprusso.

Direction & hypothesis

This code reduces the data-qubit count of @mathysrennela's [[961,169,3]] checkerboard plaquette code while retaining a witnessed distance upper bound of 3, maximum check weight 4, one layer and interaction radius √2. Every surviving qubit keeps its source coordinate. Its geometric score upper bound is

g = 4kd²/(nρ²r⁴) = 1521/931 = 1.6337271751,

3.2223% above the source's 1521/961 = 1.5827263267, using 30 fewer data qubits. The source and its attribution are preserved in [codes/961-169-3.json](../codes/961-169-3.json). This is a finite reduction of an existing checkerboard construction, not a new code-family claim. Literature novelty remains unverified.

What was searched

Three earlier corner grafts gave 958 qubits. The subsequent deterministic degree-one search considered 120 proposals from that code and 120 from @npdeep's [656-qubit code](../codes/656-114-3.json). Across those 240 proposals, 129 were rejected structurally for exposing displayed weight-one stabilizers; 111 were packaged and 12 were accepted as screening survivors. All 12 accepted moves belonged to the 958-qubit branch, producing 946 qubits.

A further 240 proposals allowed either a degree-one pivot or a local weight-two contraction, followed by the existing stabilizer cleanup routine. Fifty proposals exceeded the permitted check weight or radius; 190 were packaged and 14 were accepted, leaving 931 qubits. All 14 accepted pivots had degree one. One move also exposed a weight-one stabilizer whose cleanup removed a second qubit. Thus the complete lineage contains 29 explicit moves and removes 30 sites.

Each packaged proposal received one NumPy kit trial per side, followed when eligible by 200 native trials per side and then 2,000 fresh native trials per side, pair depth 8 and four threads. Graft initialization seeds were 925200000+i, with native seeds 925300000+i and 925400000+i, where i is the global proposal index. Contraction seeds used bases 925500000, 925600000 and 925700000 plus the contraction index. The kit's Z-side seed is one greater than its X-side seed.

Evidence trail

The final matrix is contraction proposal c207. Its own initial kit seeds were 925500207 and 925500208; native screening seeds 925600207 and 925700207 retained weight 3. Independent confirmation then ran 100,000 trials per side at seed 925120931 and 1,000,000 per side at seed 925121931, pair depth 8 and eight threads. Both returned a weight-3 X logical. The final X witness comes from the latter return; the Z witness comes from the final matrix's initial kit search.

That is 1,102,200 native trials per side on this exact matrix, with its one kit trial per side recorded separately. Trials on ancestors and rejected codes are not credited to it. The claim remains witness-backed d≤3, not an exact-distance certificate or a proof that lighter logicals do not exist.

The unchanged candidate gate passed at seed 925129931: structural verification passed, the bounded refuter found no lighter logical, no exact or WL duplicate was identified, and the code advances the weight-4 × local-2d-single board. The [gate receipt](../research/geometric_grafts/931-169-3/official-gate.json) records the verdict. Its reported 8,000 RIS trials are the configured time-capped target, not a separately instrumented completion count.

The compact [search archive](../research/geometric_grafts/931-169-3/search-evidence.json) preserves both initial supports for all 301 packaged proposals and all 99 native returns, including nonimprovements and rejected candidates. It also records the independent ancestor and final audits against their respective matrices. Every proposal matrix is reconstructed by the accompanying recipe, so witnesses can be checked without storing hundreds of full matrix copies.

Dead ends

Of the packaged graft proposals, 99 reached d≤2; of the packaged contraction proposals, 176 reached d≤2. The separate 656-qubit source produced no accepted graft in its 120-proposal budget. These are bounded search results, not exhaustive impossibility claims. Removing boundary qubits can expose a light logical even when rank, commutation and locality remain valid; surviving a shallow search was only a condition for further testing.

Tools

The repository kit packaged every searched code and preserved its witnesses. Native searches used the unchanged gf2_fast.distance_rand_witness; returned supports were checked with the repository's GF(2) witness validator. Cleanup used research/local2d/boundary_engine.py. The two construction searches took about 84 and 192 seconds on four CPU threads; final confirmation used eight threads. No GPU, SAT certificate or new distance checker was used for this submission. The trusted verifier was not modified.

Reproduction

The [recipe](../research/geometric_grafts/931-169-3/recipe.json) identifies the two committed board sources by hashes and gives every move in original qubit indices. To rebuild the final arrays, reproduce all 480 search proposals, and validate all archived supports using the existing checker:

uv run --frozen python research/geometric_grafts/931-169-3/reproduce.py \
  --all-cases --check-witnesses --compare codes/931-169-3.json

The [reproduction script](../research/geometric_grafts/931-169-3/reproduce.py) performs no distance search. It checks exact ordered arrays and coordinates, including the cleanup of original qubit 900. Final stabilizer ranks are 388 and 374, giving 931−388−374=169 logical qubits. The unchanged unit-spaced coordinates give check diameter √2 and one qubit per site.

Parity checks

X-checks 388 (max weight 4) · Z-checks 374 (max weight 4)
H_X (388 checks, sparse supports)
[0, 23] [52, 53, 83, 84] [114, 115, 145, 146] [176, 177, 207, 208] [298, 299, 329] [358, 359, 389, 390] [420, 421, 451, 452] [482, 483, 513, 514] [604, 605, 635] [664, 665, 695, 696] [726, 727, 757, 758] [788, 789, 819, 820] [23, 24, 53, 54] [84, 85, 115, 116] [208, 209, 239, 240] [269, 270, 299, 300] [329, 330, 359, 360] [390, 391, 421, 422] [514, 515, 545, 546] [575, 576, 605, 606] [635, 636, 665, 666] [696, 697, 727, 728] [820, 821, 851, 852] [1, 2, 24, 25] [116, 117, 147, 148] [178, 179, 209, 210] [240, 241, 270, 271] [300, 301, 330, 331] [422, 423, 453, 454] [484, 485, 515, 516] [546, 547, 576, 577] [606, 607, 636, 637] [728, 729, 759, 760] [790, 791, 821, 822] [852, 853, 881, 882] [25, 26, 55, 56] [86, 87, 117, 118] [148, 149, 179, 180] [210, 211, 241, 242] [331, 332, 361, 362] [392, 393, 423, 424] [454, 455, 485, 486] [516, 517, 547, 548] [637, 638, 667, 668] [698, 699, 729, 730] [760, 761, 791, 792] [822, 823, 853, 854] [882, 883, 908, 909] [3, 26, 27] [56, 57, 87, 88] [118, 119, 149, 150] [242, 243, 272, 273] [302, 303, 332, 333] [362, 363, 393, 394] [424, 425, 455, 456] [548, 549, 578, 579] [608, 609, 638, 639] [668, 669, 699, 700] [730, 731, 761, 762] [854, 855, 883, 884] [27, 28, 57, 58] [150, 151, 181, 182] [212, 213, 243, 244] [273, 274, 303, 304] [333, 334, 363, 364] [456, 457, 487, 488] [518, 519, 549, 550] [579, 580, 609, 610] [639, 640, 669, 670] [762, 763, 793, 794] [824, 825, 855, 856] [884, 885, 910, 911] [58, 59, 89, 90] [120, 121, 151, 152] [182, 183, 213, 214] [244, 245, 274, 275] [364, 365, 395, 396] [426, 427, 457, 458] [488, 489, 519, 520] [550, 551, 580, 581] [670, 671, 701, 702] [732, 733, 763, 764] [794, 795, 825, 826] [856, 857, 885, 886] [29, 30, 59, 60] [90, 91, 121, 122] [152, 153, 183, 184] [275, 276, 305, 306] [335, 336, 365, 366] [396, 397, 427, 428] [458, 459, 489, 490] [581, 582, 611, 612] [641, 642, 671, 672] [702, 703, 733, 734] [764, 765, 795, 796] [886, 887, 912, 913] [5, 6, 30, 31] [60, 61, 91, 92] [184, 185, 215, 216] [246, 247, 276, 277] [306, 307, 336, 337] [366, 367, 397, 398] [490, 491, 521, 522] [552, 553, 582, 583] [612, 613, 642, 643] [672, 673, 703, 704] [796, 797, 827, 828] [858, 859, 887, 888] [92, 93, 123, 124] [154, 155, 185, 186] [216, 217, 247, 248] [277, 278, 307, 308] [398, 399, 429, 430] [460, 461, 491, 492] [522, 523, 553, 554] [583, 584, 613, 614] [704, 705, 735, 736] [766, 767, 797, 798] [828, 829, 859, 860] [7, 8, 32, 33] [62, 63, 93, 94] [124, 125, 155, 156] [186, 187, 217, 218] [308, 309, 338, 339] [368, 369, 399, 400] [430, 431, 461, 462] [492, 493, 523, 524] [614, 615, 644, 645] [674, 675, 705, 706] [736, 737, 767, 768] [798, 799, 829, 830] [33, 34, 63, 64] [94, 95, 125, 126] [218, 219, 249, 250] [279, 280, 309, 310] [339, 340, 369, 370] [400, 401, 431, 432] [524, 525, 555, 556] [585, 586, 615, 616] [645, 646, 675, 676] [706, 707, 737, 738] [830, 831, 861, 862] [889, 890, 915, 916] [9, 10, 34, 35] [126, 127, 157, 158] [188, 189, 219, 220] [250, 251, 280, 281] [310, 311, 340, 341] [432, 433, 463, 464] [494, 495, 525, 526] [556, 557, 586, 587] [616, 617, 646, 647] [738, 739, 769, 770] [800, 801, 831, 832] [862, 863, 890, 891] [35, 36, 65, 66] [96, 97, 127, 128] [158, 159, 189, 190] [220, 221, 251, 252] [341, 342, 371, 372] [402, 403, 433, 434] [464, 465, 495, 496] [526, 527, 557, 558] [647, 648, 677, 678] [708, 709, 739, 740] [770, 771, 801, 802] [832, 833, 863, 864] [11, 36, 37] [66, 67, 97, 98] [128, 129, 159, 160] [252, 253, 282, 283] [312, 313, 342, 343] [372, 373, 403, 404] [434, 435, 465, 466] [558, 559, 588, 589] [618, 619, 648, 649] [678, 679, 709, 710] [740, 741, 771, 772] [864, 865, 892, 893] [37, 38, 67, 68] [160, 161, 191, 192] [222, 223, 253, 254] [283, 284, 313, 314] [343, 344, 373, 374] [466, 467, 497, 498] [528, 529, 559, 560] [589, 590, 619, 620] [649, 650, 679, 680] [772, 773, 803, 804] [834, 835, 865, 866] [893, 894, 918, 919] [68, 69, 99, 100] [130, 131, 161, 162] [192, 193, 223, 224] [254, 255, 284, 285] [374, 375, 405, 406] [436, 437, 467, 468] [498, 499, 529, 530] [560, 561, 590, 591] [680, 681, 711, 712] [742, 743, 773, 774] [804, 805, 835, 836] [866, 867, 894, 895] [39, 40, 69, 70] [100, 101, 131, 132] [162, 163, 193, 194] [285, 286, 315, 316] [345, 346, 375, 376] [406, 407, 437, 438] [468, 469, 499, 500] [591, 592, 621, 622] [651, 652, 681, 682] [712, 713, 743, 744] [774, 775, 805, 806] [895, 896, 920, 921] [13, 14, 40, 41] [70, 71, 101, 102] [194, 195, 225, 226] [256, 257, 286, 287] [316, 317, 346, 347] [376, 377, 407, 408] [500, 501, 531, 532] [562, 563, 592, 593] [622, 623, 652, 653] [682, 683, 713, 714] [806, 807, 837, 838] [868, 869, 896, 897] [102, 103, 133, 134] [164, 165, 195, 196] [226, 227, 257, 258] [287, 288, 317, 318] [408, 409, 439, 440] [470, 471, 501, 502] [532, 533, 563, 564] [593, 594, 623, 624] [714, 715, 745, 746] [776, 777, 807, 808] [838, 839, 869, 870] [15, 16, 42, 43] [72, 73, 103, 104] [134, 135, 165, 166] [196, 197, 227, 228] [318, 319, 348, 349] [378, 379, 409, 410] [440, 441, 471, 472] [502, 503, 533, 534] [624, 625, 654, 655] [684, 685, 715, 716] [746, 747, 777, 778] [808, 809, 839, 840] [43, 44, 73, 74] [104, 105, 135, 136] [228, 229, 259, 260] [289, 290, 319, 320] [349, 350, 379, 380] [410, 411, 441, 442] [534, 535, 565, 566] [595, 596, 625, 626] [655, 656, 685, 686] [716, 717, 747, 748] [840, 841, 871, 872] [898, 899, 923, 924] [17, 18, 44, 45] [136, 137, 167, 168] [198, 199, 229, 230] [260, 261, 290, 291] [320, 321, 350, 351] [442, 443, 473, 474] [504, 505, 535, 536] [566, 567, 596, 597] [626, 627, 656, 657] [748, 749, 779, 780] [810, 811, 841, 842] [872, 873, 899, 900] [45, 46, 75, 76] [106, 107, 137, 138] [168, 169, 199, 200] [230, 231, 261, 262] [351, 352, 381, 382] [412, 413, 443, 444] [474, 475, 505, 506] [536, 537, 567, 568] [657, 658, 687, 688] [718, 719, 749, 750] [780, 781, 811, 812] [842, 843, 873, 874] [19, 46, 47] [76, 77, 107, 108] [138, 139, 169, 170] [262, 263, 292, 293] [322, 323, 352, 353] [382, 383, 413, 414] [444, 445, 475, 476] [568, 569, 598, 599] [628, 629, 658, 659] [688, 689, 719, 720] [750, 751, 781, 782] [874, 875, 901, 902] [47, 48, 77, 78] [170, 171, 201, 202] [232, 233, 263, 264] [293, 294, 323, 324] [353, 354, 383, 384] [476, 477, 507, 508] [538, 539, 569, 570] [599, 600, 629, 630] [659, 660, 689, 690] [782, 783, 813, 814] [844, 845, 875, 876] [902, 903, 926, 927] [78, 79, 109, 110] [140, 141, 171, 172] [202, 203, 233, 234] [264, 265, 294, 295] [384, 385, 415, 416] [446, 447, 477, 478] [508, 509, 539, 540] [570, 571, 600, 601] [690, 691, 721, 722] [752, 753, 783, 784] [814, 815, 845, 846] [876, 877, 903, 904] [49, 50, 79, 80] [110, 111, 141, 142] [172, 173, 203, 204] [295, 296, 325, 326] [355, 356, 385, 386] [416, 417, 447, 448] [478, 479, 509, 510] [601, 602, 631, 632] [661, 662, 691, 692] [722, 723, 753, 754] [784, 785, 815, 816] [904, 905, 928, 929] [21, 22, 50, 51] [80, 81, 111, 112] [204, 205, 235, 236] [266, 267, 296, 297] [326, 327, 356, 357] [386, 387, 417, 418] [510, 511, 541, 542] [572, 573, 602, 603] [632, 633, 662, 663] [692, 693, 723, 724] [816, 817, 847, 848] [878, 879, 905, 906] [112, 113, 143, 144] [174, 175, 205, 206] [236, 237, 267, 268] [297, 327, 328] [418, 419, 449, 450] [480, 481, 511, 512] [542, 543, 573, 574] [603, 633, 634] [724, 725, 755, 756] [786, 787, 817, 818] [848, 849, 879, 880] [906, 930] [82, 113] [207, 238] [513, 544] [819, 850] [907, 908] [916, 917] [924, 925] [4, 5] [6, 7] [6, 32] [12, 13] [14, 15] [14, 42] [20, 21] [114, 115] [144, 174] [144, 175] [145, 176] [388, 419] [420, 421] [450, 480] [450, 481] [451, 482] [694, 725] [726, 727] [756, 786] [756, 787] [757, 788] [888, 914] [897, 922]
H_Z (374 checks, sparse supports)
[83, 84, 114, 115] [145, 146, 176, 177] [207, 208, 238, 239] [269, 298, 299] [389, 390, 420, 421] [451, 452, 482, 483] [513, 514, 544, 545] [575, 604, 605] [695, 696, 726, 727] [757, 758, 788, 789] [819, 820, 850, 851] [0, 1, 23, 24] [53, 54, 84, 85] [177, 178, 208, 209] [239, 240, 269, 270] [299, 300, 329, 330] [359, 360, 390, 391] [483, 484, 514, 515] [545, 546, 575, 576] [605, 606, 635, 636] [665, 666, 696, 697] [789, 790, 820, 821] [851, 852, 881] [24, 25, 54, 55] [85, 86, 116, 117] [147, 148, 178, 179] [270, 271, 300, 301] [330, 331, 360, 361] [391, 392, 422, 423] [453, 454, 484, 485] [576, 577, 606, 607] [636, 637, 666, 667] [697, 698, 728, 729] [759, 760, 790, 791] [881, 882, 907, 908] [55, 56, 86, 87] [117, 118, 148, 149] [179, 180, 210, 211] [241, 242, 271, 272] [361, 362, 392, 393] [423, 424, 454, 455] [485, 486, 516, 517] [547, 548, 577, 578] [667, 668, 698, 699] [729, 730, 760, 761] [791, 792, 822, 823] [853, 854, 882, 883] [26, 27, 56, 57] [149, 150, 180, 181] [211, 212, 242, 243] [272, 273, 302, 303] [332, 333, 362, 363] [455, 456, 486, 487] [517, 518, 548, 549] [578, 579, 608, 609] [638, 639, 668, 669] [761, 762, 792, 793] [823, 824, 854, 855] [883, 884, 909, 910] [3, 27, 28] [57, 58, 88, 89] [119, 120, 150, 151] [243, 244, 273, 274] [303, 304, 333, 334] [363, 364, 394, 395] [425, 426, 456, 457] [549, 550, 579, 580] [609, 610, 639, 640] [669, 670, 700, 701] [731, 732, 762, 763] [855, 856, 884, 885] [28, 29, 58, 59] [89, 90, 120, 121] [151, 152, 182, 183] [213, 214, 244, 245] [334, 335, 364, 365] [395, 396, 426, 427] [457, 458, 488, 489] [519, 520, 550, 551] [640, 641, 670, 671] [701, 702, 732, 733] [763, 764, 794, 795] [825, 826, 856, 857] [4, 5, 29, 30] [121, 122, 152, 153] [183, 184, 214, 215] [245, 246, 275, 276] [305, 306, 335, 336] [427, 428, 458, 459] [489, 490, 520, 521] [551, 552, 581, 582] [611, 612, 641, 642] [733, 734, 764, 765] [795, 796, 826, 827] [857, 858, 886, 887] [30, 31, 60, 61] [91, 92, 122, 123] [215, 216, 246, 247] [276, 277, 306, 307] [336, 337, 366, 367] [397, 398, 428, 429] [521, 522, 552, 553] [582, 583, 612, 613] [642, 643, 672, 673] [703, 704, 734, 735] [827, 828, 858, 859] [887, 888, 913, 914] [6, 7, 31, 32] [61, 62, 92, 93] [123, 124, 154, 155] [185, 186, 216, 217] [307, 308, 337, 338] [367, 368, 398, 399] [429, 430, 460, 461] [491, 492, 522, 523] [613, 614, 643, 644] [673, 674, 704, 705] [735, 736, 766, 767] [797, 798, 828, 829] [93, 94, 124, 125] [155, 156, 186, 187] [217, 218, 248, 249] [278, 279, 308, 309] [399, 400, 430, 431] [461, 462, 492, 493] [523, 524, 554, 555] [584, 585, 614, 615] [705, 706, 736, 737] [767, 768, 798, 799] [829, 830, 860, 861] [889, 915] [8, 9, 33, 34] [63, 64, 94, 95] [187, 188, 218, 219] [249, 250, 279, 280] [309, 310, 339, 340] [369, 370, 400, 401] [493, 494, 524, 525] [555, 556, 585, 586] [615, 616, 645, 646] [675, 676, 706, 707] [799, 800, 830, 831] [861, 862, 889, 890] [34, 35, 64, 65] [95, 96, 126, 127] [157, 158, 188, 189] [280, 281, 310, 311] [340, 341, 370, 371] [401, 402, 432, 433] [463, 464, 494, 495] [586, 587, 616, 617] [646, 647, 676, 677] [707, 708, 738, 739] [769, 770, 800, 801] [890, 891, 916, 917] [65, 66, 96, 97] [127, 128, 158, 159] [189, 190, 220, 221] [251, 252, 281, 282] [371, 372, 402, 403] [433, 434, 464, 465] [495, 496, 526, 527] [557, 558, 587, 588] [677, 678, 708, 709] [739, 740, 770, 771] [801, 802, 832, 833] [863, 864, 891, 892] [36, 37, 66, 67] [159, 160, 190, 191] [221, 222, 252, 253] [282, 283, 312, 313] [342, 343, 372, 373] [465, 466, 496, 497] [527, 528, 558, 559] [588, 589, 618, 619] [648, 649, 678, 679] [771, 772, 802, 803] [833, 834, 864, 865] [892, 893, 918] [11, 37, 38] [67, 68, 98, 99] [129, 130, 160, 161] [253, 254, 283, 284] [313, 314, 343, 344] [373, 374, 404, 405] [435, 436, 466, 467] [559, 560, 589, 590] [619, 620, 649, 650] [679, 680, 710, 711] [741, 742, 772, 773] [865, 866, 893, 894] [38, 39, 68, 69] [99, 100, 130, 131] [161, 162, 192, 193] [223, 224, 254, 255] [344, 345, 374, 375] [405, 406, 436, 437] [467, 468, 498, 499] [529, 530, 560, 561] [650, 651, 680, 681] [711, 712, 742, 743] [773, 774, 804, 805] [835, 836, 866, 867] [12, 13, 39, 40] [131, 132, 162, 163] [193, 194, 224, 225] [255, 256, 285, 286] [315, 316, 345, 346] [437, 438, 468, 469] [499, 500, 530, 531] [561, 562, 591, 592] [621, 622, 651, 652] [743, 744, 774, 775] [805, 806, 836, 837] [867, 868, 895, 896] [40, 41, 70, 71] [101, 102, 132, 133] [225, 226, 256, 257] [286, 287, 316, 317] [346, 347, 376, 377] [407, 408, 438, 439] [531, 532, 562, 563] [592, 593, 622, 623] [652, 653, 682, 683] [713, 714, 744, 745] [837, 838, 868, 869] [896, 897, 921, 922] [14, 15, 41, 42] [71, 72, 102, 103] [133, 134, 164, 165] [195, 196, 226, 227] [317, 318, 347, 348] [377, 378, 408, 409] [439, 440, 470, 471] [501, 502, 532, 533] [623, 624, 653, 654] [683, 684, 714, 715] [745, 746, 776, 777] [807, 808, 838, 839] [103, 104, 134, 135] [165, 166, 196, 197] [227, 228, 258, 259] [288, 289, 318, 319] [409, 410, 440, 441] [471, 472, 502, 503] [533, 534, 564, 565] [594, 595, 624, 625] [715, 716, 746, 747] [777, 778, 808, 809] [839, 840, 870, 871] [898, 923] [16, 17, 43, 44] [73, 74, 104, 105] [197, 198, 228, 229] [259, 260, 289, 290] [319, 320, 349, 350] [379, 380, 410, 411] [503, 504, 534, 535] [565, 566, 595, 596] [625, 626, 655, 656] [685, 686, 716, 717] [809, 810, 840, 841] [871, 872, 898, 899] [44, 45, 74, 75] [105, 106, 136, 137] [167, 168, 198, 199] [290, 291, 320, 321] [350, 351, 380, 381] [411, 412, 442, 443] [473, 474, 504, 505] [596, 597, 626, 627] [656, 657, 686, 687] [717, 718, 748, 749] [779, 780, 810, 811] [899, 900, 924, 925] [75, 76, 106, 107] [137, 138, 168, 169] [199, 200, 230, 231] [261, 262, 291, 292] [381, 382, 412, 413] [443, 444, 474, 475] [505, 506, 536, 537] [567, 568, 597, 598] [687, 688, 718, 719] [749, 750, 780, 781] [811, 812, 842, 843] [873, 874, 900, 901] [46, 47, 76, 77] [169, 170, 200, 201] [231, 232, 262, 263] [292, 293, 322, 323] [352, 353, 382, 383] [475, 476, 506, 507] [537, 538, 568, 569] [598, 599, 628, 629] [658, 659, 688, 689] [781, 782, 812, 813] [843, 844, 874, 875] [901, 902, 926] [19, 47, 48] [77, 78, 108, 109] [139, 140, 170, 171] [263, 264, 293, 294] [323, 324, 353, 354] [383, 384, 414, 415] [445, 446, 476, 477] [569, 570, 599, 600] [629, 630, 659, 660] [689, 690, 720, 721] [751, 752, 782, 783] [875, 876, 902, 903] [48, 49, 78, 79] [109, 110, 140, 141] [171, 172, 202, 203] [233, 234, 264, 265] [354, 355, 384, 385] [415, 416, 446, 447] [477, 478, 508, 509] [539, 540, 570, 571] [660, 661, 690, 691] [721, 722, 752, 753] [783, 784, 814, 815] [845, 846, 876, 877] [20, 21, 49, 50] [141, 142, 172, 173] [203, 204, 234, 235] [265, 266, 295, 296] [325, 326, 355, 356] [447, 448, 478, 479] [509, 510, 540, 541] [571, 572, 601, 602] [631, 632, 661, 662] [753, 754, 784, 785] [815, 816, 846, 847] [877, 878, 904, 905] [50, 51, 80, 81] [111, 112, 142, 143] [235, 236, 266, 267] [296, 297, 326, 327] [356, 357, 386, 387] [417, 418, 448, 449] [541, 542, 572, 573] [602, 603, 632, 633] [662, 663, 692, 693] [723, 724, 754, 755] [847, 848, 878, 879] [905, 906, 929, 930] [22, 51] [81, 82, 112, 113] [143, 144, 174, 175] [205, 206, 236, 237] [327, 328, 357] [387, 388, 418, 419] [449, 450, 480, 481] [511, 512, 542, 543] [633, 634, 663] [693, 694, 724, 725] [755, 756, 786, 787] [817, 818, 848, 849] [1, 2] [9, 10] [17, 18] [52, 83] [237, 268] [358, 389] [543, 574] [664, 695] [849, 880] [910, 911] [912, 913] [918, 919] [920, 921] [926, 927] [928, 929]
Code ID 931-169-3 · download JSON · raw on GitHub