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[[864,434,6]] d =
n
864
k
434
d
6
kd²/n
18.0833
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X = 6, d_Z = 6 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[0, 1, 3, 10, 27, 86]
d_Z 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[0, 1, 4, 7, 11, 152]
certificate exact, d = 6 · tropidist b03ec2d4077f (arXiv:2611.08247) exhaustive search · level solver: a solver verdict, no artifact a third party can check without re-running the encoding
X: no logical < 6 exists; Z: no logical < 6 exists

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 12 · H_Z 12 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 8 · H_Z 8
qubit degrees H_X 2 · H_Z 2
trapping sets H_X (1,2)×864 (2,2)×6048 (3,2)×42336 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 864 (2,2): 6048 (3,2): 42336 (3,4): 12096
trapping sets H_Z (1,2)×864 (2,2)×6048 (3,2)×42336 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 864 (2,2): 6048 (3,2): 42336 (3,4): 12096

Construction & provenance

authors @TimoKellerMath
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction Surface code of the orientably-regular map C217.22 of type {8,8} (genus 217) in M. Conder's list of chiral maps of genus 2 to 301, in its mirror image (Conder's relators hold for (r-1, s-1); mirror images give the same code). Rotation group G = <r,s | r8, s8, (r*s)2, s-1*r3*s-1*r-2*s-4*r, s-1*r*s-2*r-3*s2*r-1*s-1*r> of order 1728. Darts = elements of G (right multiplication), faces = cosets g<r>, vertices = cosets g<s>, edges = cosets g<rs> = {g, grs}. Qubits on the 864 edges, X-checks on the 216 vertices (weight 8), Z-checks on the 216 faces (weight 8), incidences mod 2: H_X and H_Z are the boundary maps of the cellular chain complex over F_2, k = 2 - chi = 434, d_Z is the shortest homologically nontrivial cycle of the map and d_X that of the dual map. Found in a census of regular maps (normal subgroups of the triangle groups <r,s | r^p, s^q, (rs)2>, Magma's LowIndexNormalSubgroups). The qubit order is that of the dart permutations in the public package in the references (data/maps.json), whose src/rebuild.py rebuilds these matrices from them and from the presentation.
model Claude Claude Opus 5.5 (claimed, not verified)
builds on https://arxiv.org/abs/1506.04029, https://www.math.auckland.ac.nz/~conder/ChiralMaps301.txt, https://github.com/TimoKellerMath/quantum-error-correction/tree/2e97a5361e7b9327128baa242bdedd333f7d7e12/hyperbolic-map-codes
date 2026-11-10
notes Exact distance d_X = d_Z = 6: tropidist (arXiv:2611.08247) at the board's pinned commit b03ec2d4077f closes both sides (certs/864-434-6.json, level solver); independently two exact programs for check matrices with column weight 2 and an enumeration of all circuits of length <= 6 (21744 X-type and 21744 Z-type logical operators of weight 6, none lighter), see the research note. Novelty: no board entry with these n and k at commit 8042f9da; parameters not found in Breuckmann and Terhal (arXiv:1506.04029), Breuckmann et al. (arXiv:1703.00590), Breuckmann's thesis (arXiv:1802.01520), Mahmoud and Rayan (arXiv:2610.10948), Breuckmann and Burton (arXiv:2202.06647), Mahmoud, Ali and Rayan (arXiv:2504.07800), the catalogs of QEC-pages (Quantum_LDPC_Codes) and qecdb.org; Conder's lists contain the map, not the code. Equivalence with existing entries: checked, none has these n and k.
family topological (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

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

[[864,434,6]]: chiral {8,8} surface code, Conder's map C217.22

Direction & hypothesis

Cell: check weight 8, unrestricted locality (no layout submitted). Surface codes of regular maps of type {p,q} on closed hyperbolic surfaces (Breuckmann and Terhal, arXiv:1506.04029) have k = 2 - chi = (1 - 2/p - 2/q) n + 2, so {8,8} maps give k/n close to 1/2 at check weight 8, while the distance is the systole of the map (of the dual map for d_X) and grows only logarithmically in n. At board commit 8042f9da the entries of check weight at most 8 with d = 6 and the largest kd^2/n were the lifted-product codes [[780,318,6]] to [[1000,406,6]], kd^2/n about 14.6. Hypothesis: {8,8} maps whose systoles reach 6 dominate them, at kd^2/n about 18.

What was searched

A census of all regular maps of type {p,q}, 3 <= p,q <= 8, 1/p + 1/q < 1/2, with at most 2000 edges (chiral {8,8} maps up to 1000 edges): the normal subgroups of index 2E of the triangle groups <r,s | r^p, s^q, (rs)^2> in which r, s, rs keep their orders (Magma's LowIndexNormalSubgroups), the non-orientable maps from the extended triangle groups, and 2000 cyclic covers of the orientable maps with n <= 1000 (random voltage classes, seeds recorded). In total 2174 orientable and 340 non-orientable maps (up to duality and mirror image) and 2000 covers, 7063 codes with their X/Z duals, each with exact d_X and d_Z by the programs below. At board commit 8042f9da, 254 parameter points of the census were undominated; we submit nine of them, one per pull request, and left out the points we found in the literature: [[896,386,6]] ({7,7}) and [[960,194,8]] ({5,5}) are data points of Fig. 3.7 of Breuckmann's thesis (arXiv:1802.01520), [[588,254,6]] and [[273,119,5]] are in its Table 3.1. This code is the chiral {8,8} map C217.22 of M. Conder's list (census orientation: its mirror image, same code). It is the only {8,8} map of the census with 864 edges and d = 6. Sources checked without finding it: Breuckmann and Terhal (arXiv:1506.04029), Breuckmann et al. (arXiv:1703.00590), Breuckmann's thesis (arXiv:1802.01520), Mahmoud and Rayan (arXiv:2610.10948), Breuckmann and Burton (arXiv:2202.06647), Mahmoud, Ali and Rayan (arXiv:2504.07800), the catalogs of QEC-pages (Quantum_LDPC_Codes) and qecdb.org; Conder's lists contain the maps, not the codes.

Evidence trail

  • k = 434 = 864 - 215 - 215 (ranks over GF(2)) = 2 - chi; H_X H_Z^T = 0; every qubit lies in two X-checks and two Z-checks, so both sides are graph-like (computed).
  • Upper bound: an X-type and a Z-type logical operator of weight 6, in the entry.
  • Lower bound, exact, by four computations: (1) graphlike_A, shortest cycles with logical annotations in F_2^k; (2) graphlike_B, shortest paths in the double covers of the check graph given by the logical operators, written independently; their exactness is proved in github.com/TimoKellerMath/quantum-error-correction @ 2e97a5361e7b9327128baa242bdedd333f7d7e12, hyperbolic-map-codes/src/graphlike_A/NOTES.md and hyperbolic-map-codes/src/graphlike_B/NOTES.md, and they agree on all 7063 census codes; (3) an enumeration of all circuits of length at most 6 with a row-space test: the graph of the map and its dual have no circuit shorter than 6, and all 21744 circuits of length 6 are nontrivial, on both sides; (4) tropidist (Cheng, Guo and Pan, arXiv:2611.08247) at the board's pinned commit b03ec2d4077f, one thread, 600 s limit, on the board's css-sides problems: exact 6 and 6 in 2.3 s and 2.2 s, recorded in certs/864-434-6.json.
  • Final claim: d_X = d_Z = 6, exact (computer-assisted; the four computations agree). 21744 X-type and 21744 Z-type logical operators have weight 6.

Dead ends

  • Within the census no {8,8}, {6,6} or {7,7} map reaches d = 7; d >= 7 occurs only for {3,7}, {4,5}, {4,6} and {5,5} (n <= 2000).
  • Among the 1005 {8,8} maps of the census (up to mirror image), 19 have d = 6 (from n = 640 on) and none more; 937 have d = 2 or 4.

Tools

Claude Opus 5.5 (Claude Code). Magma V2.30 for the census (LowIndexNormalSubgroups, coset actions, the presentations and Conder's names); Python for the map codes; the C programs graphlike_A and graphlike_B and the Python circuit enumeration, all in the public package below; tropidist b03ec2d4077f. The largest Magma run of the census (orientable {6,6} maps, index at most 4000) took 33 CPU minutes; exact distances of all 7063 codes took 46 s with graphlike_A and 76 s with graphlike_B.

Reproduction

G = <r,s | r^8, s^8, (r*s)^2, s^-1*r^3*s^-1*r^-2*s^-4*r, s^-1*r*s^-2*r^-3*s^2*r^-1*s^-1*r> (order 1728); qubits = edges {g, grs}, X-checks = vertices g<s>, Z-checks = faces g<r>, incidences mod 2. In hyperbolic-map-codes/ of github.com/TimoKellerMath/quantum-error-correction @ 2e97a5361e7b: make check runs hyperbolic-map-codes/src/rebuild.py (standard library), which rebuilds these matrices from the stored darts and from the presentation, checks Conder's relators, k and the witnesses; make distances runs graphlike_A, graphlike_B and the circuit enumeration; make tropidist-inputs writes the tropidist problems.

Parity checks

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