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[[684,4,81]] d ≤
n
684
k
4
d
81
kd²/n
38.3684
w
8
X/Z
1.15

Share this result

Distance

X/Z asymmetry 1.15 · d_X ≤ 93, d_Z ≤ 81 · 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 93 · witness weight 93 (claimed upper_bound)
witness found by @MathysRennela · gf2_fast.dem_rand_witness (verify/gf2_fast.cpp) · found at 2×105 trials · survived 2×105 trials · 2026-10-30
witness operator (support, 93 qubits)
[0, 7, 11, 20, 30, 31, 35, 36, 45, 61, 71, 85, 89, 106, 118, 133, 135, 146, 153, 154, 157, 164, 173, 188, 196, 197, 233, 241, 246, 249, 255, 261, 267, 270, 274, 279, 285, 286, 287, 299, 306, 311, 318, 323, 324, 326, 328, 348, 353, 380, 408, 411, 438, 441, 450, 459, 467, 468, 481, 489, 498, 505, 506, 510, 520, 539, 548, 559, 564, 567, 569, 570, 579, 581, 585, 586, 592, 599, 623, 625, 626, 630, 633, 635, 640, 663, 664, 665, 667, 669, 673, 675, 682]
d_Z 81 · witness weight 81 (claimed upper_bound)
witness found by @MathysRennela · gf2_fast · found at 2×106 trials · 2026-10-30
witness operator (support, 81 qubits)
[0, 19, 31, 32, 40, 47, 48, 49, 52, 76, 78, 91, 92, 101, 108, 124, 132, 144, 147, 148, 174, 175, 205, 211, 214, 216, 218, 222, 224, 247, 273, 277, 283, 285, 294, 298, 299, 303, 304, 313, 333, 334, 343, 344, 347, 357, 369, 372, 382, 385, 391, 396, 404, 407, 411, 425, 475, 479, 495, 507, 521, 523, 526, 530, 553, 555, 584, 589, 593, 594, 597, 605, 640, 643, 653, 659, 660, 662, 667, 677, 678]
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 4 (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 4 · H_Z 4
trapping sets H_X (1,4)×684 (2,4)×189 (3,4)×74 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,4): 684 (2,4): 189 (2,6): 9198 (3,4): 74 (3,6): 6352 (3,8): 184132 (3,10): 16902
trapping sets H_Z (1,4)×684 (2,4)×189 (3,4)×74 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,4): 684 (2,4): 189 (2,6): 9198 (3,4): 74 (3,6): 6352 (3,8): 184132 (3,10): 16902

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction Generalized bicycle on the affine group Aff(F_19) = Z_19 x| Z_18 (2 a primitive root mod 19), order 342; HX=[L(a)|R(b)], HZ=[R(b)^T|L(a)^T] with a=[167,268,58,61], b=[284,292,32,6] over F2, check weight 8. Sampled by research/kit/search.py sample_kasai_affine.
model Beam 1.0 (claimed, not verified)
date 2026-10-30
notes Checked against the board by the submission gate on 2026-10-30: no exact fingerprint match and no WL-signature match against any entry, so no equivalence to an existing entry is claimed. Literature novelty unverified: the [[684,4,81]] parameter set has not been compared against published tables.
family generalized bicycle (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

[[684,4,81]] — weight-8 generalized bicycle on the affine group Aff(F_19)

Direction & hypothesis

Issue #4162 asks for codes in the box n <= 1000, w <= 8, and the weight-8 × unrestricted cell was thin at large n. The families that populate the efficiency frontier sit at check weight 12 to 32, so w = 8 near n ~ 700 had little in it. The structural bet: generalized bicycle over a non-abelian group rather than a cyclic one. Aff(F_q) (the structure behind Kasai's affine-coset construction) has order q(q-1), so a 2BGA block lands at n = 2q(q-1) — q = 19 gives n = 684 exactly — and two weight-4 supports give check weight 8 with no tuning.

What was searched

  • First probe, dropped immediately: cyclic generalized bicycle

    • (research/kit/search.py, sample_cyclic_gb), 3 sampled at seed 1. It reached high rate ([[646,182,<=84]], [[650,146,<=94]]) but at check weight 32, outside the w <= 8 box. Right rate, wrong cell.

  • Main sweep: research/kit/search.py, sample_kasai_affine, weight=4,

    • q_range=(7,19), num=20, seed=2. Screened with search.screen at 500 NumPy RIS trials, min_k=4, min_d=4, board="flag" (direct-sum reject, fingerprint dedup, Weisfeiler-Leman flag). 15 of 20 survived.

  • Packaging: top 7 built through submit.make_submission / save_submission

    • with witnesses from verify/gf2_fast.cpp's dem_rand_witness, 200,000 trials per side per seed, seeds 0 and 1, pair_depth=24, 8 threads.

  • Confirmation: independent distance_rand passes on the fast backend at

    • 100k, 1M, 2M, 4M, then 8M trials per side (8M being the depth CI's own gate reaches), run separately from the packaging search.

  • All 7 went through research/kit/coordination.py gate

    • (verify/validate_candidate.py unchanged): 7 of 7 passed: true, one of them board-advancing.

  • Campaign record: research/campaigns/affine-2bga-n684/campaign.json.

Evidence trail

Confirmation ladder for the submitted code — the point of the table is that every low-trial read was high:

| stage | budget per side | Z | d | |---|---|---|---| | coarse screen, NumPy RIS | 500 trials | — | 111 | | packaging draft, NumPy RIS | 1,000 trials | — | 106 | | packaging, gf2_fast.dem_rand_witness | 200k trials, seeds 0–1 | 92 | 92 | | submission accelerator, gf2_fast.distance_rand | 2M trials | 81 | 81 | | confirmation, gf2_fast.distance_rand | 2M trials, independent seed | 81 | 81 | | confirmation, gf2_fast.distance_rand | 4M trials | 81 | 81 | | confirmation, gf2_fast.distance_rand | 8M trials, CI's own depth | 81 | 81 |

Final claim: witness-backed upper bound, d <= 81 (d_X <= 93, d_Z <= 81). Not exact-certified: n = 684 is well past the certifier's measured envelope (every certificate on the board sits at d <= 13 and k <= 12). Both witnesses ship in the entry with their own witness_provenance.

The calibration numbers are the useful artifact. On this one code the coarse screen read 111 and a 1,000-trial pass read 106, against a depth that converged to 81 — the shallow reads were 31–37% high. Even a 1M-trial pass settled at 92 and was beaten at 2M; 2M, 4M and 8M then all agreed on 81, so the floor held once reached. CONTRIBUTING.md's warning to re-verify at 100k+ trials applies, and 1M was still not the floor here.

Near-misses and what they did at depth:

| candidate | screen | deep | outcome | |---|---|---|---| | [[684,4,81]] (this entry) | 111 | 92 @1M → 81 @2M, held @8M | board-advancing | | [[684,4,62]] a=[266,28,4,85] | 100 | 90 @100k → 62 @1M | collapsed 31%; dominated by [[684,6,77]] | | [[684,10,18]] | 18 | 18, stable | dominated by [[168,10,18]] | | [[312,6,16]] | 16 | 16, stable | dominated by [[128,6,16]] | | [[312,6,12]] | 12 | 12, stable | dominated by [[102,6,13]] | | [[220,10,10]] | 10 | 10, stable | dominated by [[108,10,12]] | | [[84,6,6]] | 6 | 6, stable | dominated by [[32,6,6]] |

Both q = 19 codes moved under depth; the other five held. Six of seven packaged candidates passed the gate and were correctly recorded as non-frontier.

Dead ends

  • Cyclic GB reaches the high-rate cells the issue wants but only at check weight

    • 24–32. Nothing in that family fits w <= 8 at the sampled depths.

  • The issue's Option A target (k/n >= 0.15) was not reached. The affine

    • family at w = 8 produces k = 4..10 over n = 220..684, i.e. rate 0.006 to 0.045, so it competes on d, not on rate. The high-k cells the bicycle families cannot reach are still open.

  • [[684,8,6]] was flagged board_wl (WL signature matches

    • codes/684-8-54.json) and dropped as a probable permutation.

  • 6 of 7 packaged candidates were dominated; only the d axis opened.

Tools

  • Model: Beam 1.0 (matches provenance.model), agent harness: OpenCode.
  • Kit: research/kit/search.py (sampler + screening funnel),

    • research/kit/surrogate.py (RIS surrogate), research/kit/group_algebra.py (metacyclic, build_2bga), research/kit/coordination.py → verify/validate_candidate.py.

  • Accelerator: verify/gf2_fast.cpp, built via make fast

    • (dem_rand_witness for per-side witnesses, distance_rand for confirmation).

  • Compute: roughly 4 CPU-hours, nearly all of it the 1M–8M-trial confirmations

    • at ~10–15 minutes per n = 684 code. The 20-candidate screen itself was seconds.

Reproduction

Rebuild from parameters using only committed code:

import sys; sys.path[:0] = ["research/kit", "verify"]
from group_algebra import metacyclic, build_2bga

# Aff(F_19) = Z_19 x| Z_18 with 2 a primitive root mod 19; order 342.
# Elements (i, j) sit at index i*18 + j.
mul, _ = metacyclic(19, 18, 2)
HX, HZ = build_2bga(mul, a=[167, 268, 58, 61], b=[284, 292, 32, 6])
# HX = [L(a) | R(b)], HZ = [R(b)^T | L(a)^T], each 342 x 684.
# check weight = |a| + |b| = 8;  css_fingerprint = 7de25c54625485fc

The entry itself carries H_X, H_Z and both witnesses, so uv run python verify/qldpc_verify.py codes/684-4-81.json re-checks the whole claim without rebuilding anything.

Parity checks

X-checks 342 (max weight 8) · Z-checks 342 (max weight 8)
H_X (342 checks, sparse supports)
[20, 32, 211, 227, 354, 400, 472, 680] [21, 33, 212, 228, 355, 455, 599, 663] [22, 34, 213, 229, 356, 510, 564, 628] [23, 35, 214, 230, 357, 439, 557, 673] [18, 24, 215, 231, 358, 396, 530, 656] [19, 25, 198, 232, 359, 369, 451, 621] [20, 26, 199, 233, 342, 388, 550, 560] [21, 27, 200, 216, 343, 407, 425, 435] [22, 28, 201, 217, 344, 462, 498, 526] [23, 29, 202, 218, 345, 365, 571, 643] [24, 30, 203, 219, 346, 384, 446, 590] [25, 31, 204, 220, 347, 421, 483, 537] [26, 32, 205, 221, 348, 376, 494, 610] [27, 33, 206, 222, 349, 395, 521, 639] [28, 34, 207, 223, 350, 414, 586, 666] [29, 35, 208, 224, 351, 479, 487, 649] [18, 30, 209, 225, 352, 606, 614, 632] [19, 31, 210, 226, 353, 517, 543, 579] [92, 140, 155, 265, 356, 372, 418, 490] [93, 141, 156, 266, 373, 473, 617, 681] [94, 142, 157, 267, 374, 528, 582, 646] [95, 143, 158, 268, 349, 375, 457, 575] [96, 126, 159, 269, 376, 414, 548, 674] [97, 127, 160, 252, 377, 387, 469, 639] [98, 128, 161, 253, 360, 406, 568, 578] [99, 129, 144, 254, 361, 425, 443, 453] [100, 130, 145, 255, 362, 480, 516, 544] [101, 131, 146, 256, 363, 383, 589, 661] [102, 132, 147, 257, 364, 402, 464, 608] [103, 133, 148, 258, 365, 439, 501, 555] [104, 134, 149, 259, 366, 394, 512, 628] [105, 135, 150, 260, 367, 413, 539, 657] [106, 136, 151, 261, 342, 368, 432, 604] [107, 137, 152, 262, 369, 497, 505, 667] [90, 138, 153, 263, 370, 624, 632, 650] [91, 139, 154, 264, 371, 535, 561, 597] [83, 164, 248, 319, 374, 390, 436, 508] [84, 165, 249, 320, 357, 391, 491, 635] [85, 166, 250, 321, 392, 546, 600, 664] [86, 167, 251, 322, 367, 393, 475, 593] [87, 168, 234, 323, 350, 394, 432, 566] [88, 169, 235, 306, 395, 405, 487, 657] [89, 170, 236, 307, 378, 424, 586, 596] [72, 171, 237, 308, 379, 443, 461, 471] [73, 172, 238, 309, 380, 498, 534, 562] [74, 173, 239, 310, 381, 401, 607, 679] [75, 174, 240, 311, 382, 420, 482, 626] [76, 175, 241, 312, 383, 457, 519, 573] [77, 176, 242, 313, 384, 412, 530, 646] [78, 177, 243, 314, 385, 431, 557, 675] [79, 178, 244, 315, 360, 386, 450, 622] [80, 179, 245, 316, 343, 387, 515, 523] [81, 162, 246, 317, 388, 642, 650, 668] [82, 163, 247, 318, 389, 553, 579, 615] [11, 14, 31, 236, 392, 408, 454, 526] [12, 15, 32, 237, 375, 409, 509, 653] [13, 16, 33, 238, 410, 564, 618, 682] [14, 17, 34, 239, 385, 411, 493, 611] [0, 15, 35, 240, 368, 412, 450, 584] [1, 16, 18, 241, 413, 423, 505, 675] [2, 17, 19, 242, 396, 442, 604, 614] [0, 3, 20, 243, 397, 461, 479, 489] [1, 4, 21, 244, 398, 516, 552, 580] [2, 5, 22, 245, 355, 399, 419, 625] [3, 6, 23, 246, 400, 438, 500, 644] [4, 7, 24, 247, 401, 475, 537, 591] [5, 8, 25, 248, 402, 430, 548, 664] [6, 9, 26, 249, 351, 403, 449, 575] [7, 10, 27, 250, 378, 404, 468, 640] [8, 11, 28, 251, 361, 405, 533, 541] [9, 12, 29, 234, 344, 406, 660, 668] [10, 13, 30, 235, 407, 571, 597, 633] [85, 122, 281, 308, 410, 426, 472, 544] [86, 123, 282, 309, 393, 427, 527, 671] [87, 124, 283, 310, 358, 428, 582, 636] [88, 125, 284, 311, 403, 429, 511, 629] [89, 108, 285, 312, 386, 430, 468, 602] [72, 109, 286, 313, 351, 431, 441, 523] [73, 110, 287, 314, 414, 460, 622, 632] [74, 111, 270, 315, 415, 479, 497, 507] [75, 112, 271, 316, 416, 534, 570, 598] [76, 113, 272, 317, 373, 417, 437, 643] [77, 114, 273, 318, 418, 456, 518, 662] [78, 115, 274, 319, 419, 493, 555, 609] [79, 116, 275, 320, 420, 448, 566, 682] [80, 117, 276, 321, 369, 421, 467, 593] [81, 118, 277, 322, 396, 422, 486, 658] [82, 119, 278, 323, 379, 423, 551, 559] [83, 120, 279, 306, 344, 362, 424, 678] [84, 121, 280, 307, 425, 589, 615, 651] [38, 139, 209, 230, 428, 444, 490, 562] [39, 140, 210, 231, 347, 411, 445, 545] [40, 141, 211, 232, 376, 446, 600, 654] [41, 142, 212, 233, 421, 447, 529, 647] [42, 143, 213, 216, 404, 448, 486, 620] [43, 126, 214, 217, 369, 449, 459, 541] [44, 127, 215, 218, 432, 478, 640, 650] [45, 128, 198, 219, 433, 497, 515, 525] [46, 129, 199, 220, 434, 552, 588, 616] [47, 130, 200, 221, 391, 435, 455, 661] [48, 131, 201, 222, 436, 474, 536, 680] [49, 132, 202, 223, 437, 511, 573, 627] [50, 133, 203, 224, 358, 438, 466, 584] [51, 134, 204, 225, 387, 439, 485, 611] [52, 135, 205, 226, 414, 440, 504, 676] [53, 136, 206, 227, 397, 441, 569, 577] [36, 137, 207, 228, 354, 362, 380, 442] [37, 138, 208, 229, 443, 607, 633, 669] [110, 137, 193, 338, 446, 462, 508, 580] [111, 138, 194, 339, 365, 429, 463, 563] [112, 139, 195, 340, 394, 464, 618, 672] [113, 140, 196, 341, 439, 465, 547, 665] [114, 141, 197, 324, 422, 466, 504, 638] [115, 142, 180, 325, 387, 467, 477, 559] [116, 143, 181, 326, 450, 496, 658, 668] [117, 126, 182, 327, 451, 515, 533, 543] [118, 127, 183, 328, 452, 570, 606, 634] [119, 128, 184, 329, 409, 453, 473, 679] [120, 129, 185, 330, 356, 454, 492, 554] [121, 130, 186, 331, 455, 529, 591, 645] [122, 131, 187, 332, 376, 456, 484, 602] [123, 132, 188, 333, 405, 457, 503, 629] [124, 133, 189, 334, 352, 432, 458, 522] [125, 134, 190, 335, 415, 459, 587, 595] [108, 135, 191, 336, 372, 380, 398, 460] [109, 136, 192, 337, 345, 461, 625, 651] [65, 104, 182, 247, 464, 480, 526, 598] [66, 105, 183, 248, 383, 447, 481, 581] [67, 106, 184, 249, 348, 412, 482, 636] [68, 107, 185, 250, 457, 483, 565, 683] [69, 90, 186, 251, 440, 484, 522, 656] [70, 91, 187, 234, 405, 485, 495, 577] [71, 92, 188, 235, 344, 468, 514, 676] [54, 93, 189, 236, 469, 533, 551, 561] [55, 94, 190, 237, 470, 588, 624, 652] [56, 95, 191, 238, 355, 427, 471, 491] [57, 96, 192, 239, 374, 472, 510, 572] [58, 97, 193, 240, 473, 547, 609, 663] [59, 98, 194, 241, 394, 474, 502, 620] [60, 99, 195, 242, 423, 475, 521, 647] [61, 100, 196, 243, 370, 450, 476, 540] [62, 101, 197, 244, 433, 477, 605, 613] [63, 102, 180, 245, 390, 398, 416, 478] [64, 103, 181, 246, 363, 479, 643, 669] [212, 254, 301, 335, 482, 498, 544, 616] [213, 255, 302, 336, 401, 465, 499, 599] [214, 256, 303, 337, 366, 430, 500, 654] [215, 257, 304, 338, 359, 475, 501, 583] [198, 258, 305, 339, 458, 502, 540, 674] [199, 259, 288, 340, 423, 503, 513, 595] [200, 260, 289, 341, 352, 362, 486, 532] [201, 261, 290, 324, 487, 551, 569, 579] [202, 262, 291, 325, 488, 606, 642, 670] [203, 263, 292, 326, 373, 445, 489, 509] [204, 264, 293, 327, 392, 490, 528, 590] [205, 265, 294, 328, 491, 565, 627, 681] [206, 266, 295, 329, 412, 492, 520, 638] [207, 267, 296, 330, 441, 493, 539, 665] [208, 268, 297, 331, 388, 468, 494, 558] [209, 269, 298, 332, 451, 495, 623, 631] [210, 252, 299, 333, 408, 416, 434, 496] [211, 253, 300, 334, 345, 381, 497, 661] [13, 263, 320, 326, 500, 516, 562, 634] [14, 264, 321, 327, 419, 483, 517, 617] [15, 265, 322, 328, 384, 448, 518, 672] [16, 266, 323, 329, 377, 493, 519, 601] [17, 267, 306, 330, 350, 476, 520, 558] [0, 268, 307, 331, 441, 521, 531, 613] [1, 269, 308, 332, 370, 380, 504, 550] [2, 252, 309, 333, 505, 569, 587, 597] [3, 253, 310, 334, 346, 506, 624, 660] [4, 254, 311, 335, 391, 463, 507, 527] [5, 255, 312, 336, 410, 508, 546, 608] [6, 256, 313, 337, 357, 509, 583, 645] [7, 257, 314, 338, 430, 510, 538, 656] [8, 258, 315, 339, 459, 511, 557, 683] [9, 259, 316, 340, 406, 486, 512, 576] [10, 260, 317, 341, 469, 513, 641, 649] [11, 261, 318, 324, 426, 434, 452, 514] [12, 262, 319, 325, 363, 399, 515, 679] [56, 67, 86, 191, 518, 534, 580, 652] [57, 68, 87, 192, 437, 501, 535, 635] [58, 69, 88, 193, 348, 402, 466, 536] [59, 70, 89, 194, 395, 511, 537, 619] [60, 71, 72, 195, 368, 494, 538, 576] [54, 61, 73, 196, 459, 539, 549, 631] [55, 62, 74, 197, 388, 398, 522, 568] [56, 63, 75, 180, 523, 587, 605, 615] [57, 64, 76, 181, 364, 524, 642, 678] [58, 65, 77, 182, 409, 481, 525, 545] [59, 66, 78, 183, 428, 526, 564, 626] [60, 67, 79, 184, 375, 527, 601, 663] [61, 68, 80, 185, 448, 528, 556, 674] [62, 69, 81, 186, 359, 477, 529, 575] [63, 70, 82, 187, 424, 504, 530, 594] [64, 71, 83, 188, 487, 531, 659, 667] [54, 65, 84, 189, 444, 452, 470, 532] [55, 66, 85, 190, 355, 381, 417, 533] [119, 121, 128, 194, 536, 552, 598, 670] [120, 122, 129, 195, 455, 519, 553, 653] [121, 123, 130, 196, 366, 420, 484, 554] [122, 124, 131, 197, 413, 529, 555, 637] [123, 125, 132, 180, 386, 512, 556, 594] [108, 124, 133, 181, 477, 557, 567, 649] [109, 125, 134, 182, 406, 416, 540, 586] [108, 110, 135, 183, 541, 605, 623, 633] [109, 111, 136, 184, 354, 382, 542, 660] [110, 112, 137, 185, 427, 499, 543, 563] [111, 113, 138, 186, 446, 544, 582, 644] [112, 114, 139, 187, 393, 545, 619, 681] [113, 115, 140, 188, 350, 466, 546, 574] [114, 116, 141, 189, 377, 495, 547, 593] [115, 117, 142, 190, 442, 522, 548, 612] [116, 118, 143, 191, 343, 505, 549, 677] [117, 119, 126, 192, 462, 470, 488, 550] [118, 120, 127, 193, 373, 399, 435, 551] [47, 175, 200, 302, 346, 554, 570, 616] [48, 176, 201, 303, 473, 537, 571, 671] [49, 177, 202, 304, 384, 438, 502, 572] [50, 178, 203, 305, 431, 547, 573, 655] [51, 179, 204, 288, 404, 530, 574, 612] [52, 162, 205, 289, 495, 575, 585, 667] [53, 163, 206, 290, 424, 434, 558, 604] [36, 164, 207, 291, 559, 623, 641, 651] [37, 165, 208, 292, 372, 400, 560, 678] [38, 166, 209, 293, 445, 517, 561, 581] [39, 167, 210, 294, 464, 562, 600, 662] [40, 168, 211, 295, 357, 411, 563, 637] [41, 169, 212, 296, 368, 484, 564, 592] [42, 170, 213, 297, 395, 513, 565, 611] [43, 171, 214, 298, 460, 540, 566, 630] [44, 172, 215, 299, 353, 361, 523, 567] [45, 173, 198, 300, 480, 488, 506, 568] [46, 174, 199, 301, 391, 417, 453, 569] [68, 229, 272, 317, 364, 572, 588, 634] [69, 230, 273, 318, 347, 491, 555, 589] [70, 231, 274, 319, 402, 456, 520, 590] [71, 232, 275, 320, 449, 565, 591, 673] [54, 233, 276, 321, 422, 548, 592, 630] [55, 216, 277, 322, 343, 513, 593, 603] [56, 217, 278, 323, 442, 452, 576, 622] [57, 218, 279, 306, 577, 641, 659, 669] [58, 219, 280, 307, 354, 390, 418, 578] [59, 220, 281, 308, 463, 535, 579, 599] [60, 221, 282, 309, 482, 580, 618, 680] [61, 222, 283, 310, 375, 429, 581, 655] [62, 223, 284, 311, 386, 502, 582, 610] [63, 224, 285, 312, 413, 531, 583, 629] [64, 225, 286, 313, 478, 558, 584, 648] [65, 226, 287, 314, 371, 379, 541, 585] [66, 227, 270, 315, 498, 506, 524, 586] [67, 228, 271, 316, 409, 435, 471, 587] [2, 176, 245, 283, 382, 590, 606, 652] [3, 177, 246, 284, 365, 509, 573, 607] [4, 178, 247, 285, 420, 474, 538, 608] [5, 179, 248, 286, 349, 467, 583, 609] [6, 162, 249, 287, 440, 566, 610, 648] [7, 163, 250, 270, 361, 531, 611, 621] [8, 164, 251, 271, 460, 470, 594, 640] [9, 165, 234, 272, 345, 595, 659, 677] [10, 166, 235, 273, 372, 408, 436, 596] [11, 167, 236, 274, 481, 553, 597, 617] [12, 168, 237, 275, 356, 500, 598, 636] [13, 169, 238, 276, 393, 447, 599, 673] [14, 170, 239, 277, 404, 520, 600, 628] [15, 171, 240, 278, 431, 549, 601, 647] [16, 172, 241, 279, 496, 576, 602, 666] [17, 173, 242, 280, 389, 397, 559, 603] [0, 174, 243, 281, 516, 524, 542, 604] [1, 175, 244, 282, 427, 453, 489, 605] [74, 173, 284, 337, 400, 608, 624, 670] [75, 174, 285, 338, 383, 527, 591, 625] [76, 175, 286, 339, 438, 492, 556, 626] [77, 176, 287, 340, 367, 485, 601, 627] [78, 177, 270, 341, 458, 584, 628, 666] [79, 178, 271, 324, 379, 549, 629, 639] [80, 179, 272, 325, 478, 488, 612, 658] [81, 162, 273, 326, 353, 363, 613, 677] [82, 163, 274, 327, 390, 426, 454, 614] [83, 164, 275, 328, 499, 571, 615, 635] [84, 165, 276, 329, 374, 518, 616, 654] [85, 166, 277, 330, 349, 411, 465, 617] [86, 167, 278, 331, 422, 538, 618, 646] [87, 168, 279, 332, 449, 567, 619, 665] [88, 169, 280, 333, 342, 514, 594, 620] [89, 170, 281, 334, 407, 415, 577, 621] [72, 171, 282, 335, 534, 542, 560, 622] [73, 172, 283, 336, 445, 471, 507, 623] [49, 50, 101, 146, 346, 418, 626, 642] [50, 51, 102, 147, 401, 545, 609, 643] [51, 52, 103, 148, 456, 510, 574, 644] [52, 53, 104, 149, 385, 503, 619, 645] [36, 53, 105, 150, 342, 476, 602, 646] [36, 37, 106, 151, 397, 567, 647, 657] [37, 38, 107, 152, 496, 506, 630, 676] [38, 39, 90, 153, 353, 371, 381, 631] [39, 40, 91, 154, 408, 444, 472, 632] [40, 41, 92, 155, 517, 589, 633, 653] [41, 42, 93, 156, 392, 536, 634, 672] [42, 43, 94, 157, 367, 429, 483, 635] [43, 44, 95, 158, 440, 556, 636, 664] [44, 45, 96, 159, 467, 585, 637, 683] [45, 46, 97, 160, 360, 532, 612, 638] [46, 47, 98, 161, 425, 433, 595, 639] [47, 48, 99, 144, 552, 560, 578, 640] [48, 49, 100, 145, 463, 489, 525, 641] [29, 103, 158, 218, 364, 436, 644, 660] [30, 104, 159, 219, 419, 563, 627, 661] [31, 105, 160, 220, 474, 528, 592, 662] [32, 106, 161, 221, 403, 521, 637, 663] [33, 107, 144, 222, 360, 494, 620, 664] [34, 90, 145, 223, 415, 585, 665, 675] [35, 91, 146, 224, 352, 514, 524, 648] [18, 92, 147, 225, 371, 389, 399, 649] [19, 93, 148, 226, 426, 462, 490, 650] [20, 94, 149, 227, 535, 607, 651, 671] [21, 95, 150, 228, 348, 410, 554, 652] [22, 96, 151, 229, 385, 447, 501, 653] [23, 97, 152, 230, 458, 574, 654, 682] [24, 98, 153, 231, 359, 485, 603, 655] [25, 99, 154, 232, 378, 550, 630, 656] [26, 100, 155, 233, 443, 451, 613, 657] [27, 101, 156, 216, 570, 578, 596, 658] [28, 102, 157, 217, 481, 507, 543, 659] [157, 266, 290, 299, 382, 454, 662, 678] [158, 267, 291, 300, 437, 581, 645, 679] [159, 268, 292, 301, 492, 546, 610, 680] [160, 269, 293, 302, 421, 539, 655, 681] [161, 252, 294, 303, 378, 512, 638, 682] [144, 253, 295, 304, 351, 433, 603, 683] [145, 254, 296, 305, 370, 532, 542, 666] [146, 255, 288, 297, 389, 407, 417, 667] [147, 256, 289, 298, 444, 480, 508, 668] [148, 257, 290, 299, 347, 553, 625, 669] [149, 258, 291, 300, 366, 428, 572, 670] [150, 259, 292, 301, 403, 465, 519, 671] [151, 260, 293, 302, 358, 476, 592, 672] [152, 261, 294, 303, 377, 503, 621, 673] [153, 262, 295, 304, 396, 568, 648, 674] [154, 263, 296, 305, 461, 469, 631, 675] [155, 264, 288, 297, 588, 596, 614, 676] [156, 265, 289, 298, 499, 525, 561, 677]
H_Z (342 checks, sparse supports)
[6, 32, 284, 292, 400, 403, 509, 610] [7, 51, 213, 239, 401, 404, 510, 611] [8, 70, 88, 132, 402, 405, 511, 594] [9, 125, 161, 259, 403, 406, 512, 595] [10, 170, 216, 288, 404, 407, 513, 596] [11, 91, 235, 333, 405, 408, 514, 597] [12, 128, 182, 316, 406, 409, 515, 598] [13, 21, 255, 281, 407, 410, 516, 599] [14, 40, 166, 210, 408, 411, 517, 600] [15, 67, 77, 329, 409, 412, 518, 601] [16, 122, 150, 312, 410, 413, 519, 602] [17, 231, 277, 295, 396, 411, 520, 603] [0, 106, 206, 242, 397, 412, 521, 604] [1, 63, 135, 197, 398, 413, 504, 605] [2, 18, 118, 262, 396, 399, 505, 606] [3, 37, 173, 227, 397, 400, 506, 607] [4, 74, 102, 336, 398, 401, 507, 608] [5, 147, 193, 319, 399, 402, 508, 609] [24, 50, 302, 310, 346, 358, 401, 655] [25, 69, 231, 257, 347, 359, 402, 656] [26, 88, 106, 150, 342, 348, 403, 657] [27, 143, 179, 277, 343, 349, 404, 658] [28, 188, 234, 306, 344, 350, 405, 659] [9, 29, 109, 253, 345, 351, 406, 660] [30, 146, 200, 334, 346, 352, 407, 661] [31, 39, 273, 299, 347, 353, 408, 662] [32, 58, 184, 228, 348, 354, 409, 663] [5, 33, 85, 95, 349, 355, 410, 664] [34, 140, 168, 330, 350, 356, 411, 665] [35, 249, 295, 313, 351, 357, 412, 648] [18, 124, 224, 260, 352, 358, 413, 649] [19, 81, 153, 215, 353, 359, 396, 650] [20, 36, 136, 280, 342, 354, 397, 651] [21, 55, 191, 245, 343, 355, 398, 652] [12, 22, 92, 120, 344, 356, 399, 653] [23, 165, 211, 337, 345, 357, 400, 654] [42, 68, 320, 328, 448, 565, 634, 635] [43, 87, 249, 275, 449, 566, 635, 636] [44, 106, 124, 168, 432, 567, 636, 637] [45, 161, 197, 295, 433, 568, 637, 638] [46, 206, 252, 324, 434, 569, 638, 639] [27, 47, 127, 271, 435, 570, 639, 640] [10, 48, 164, 218, 436, 571, 640, 641] [49, 57, 291, 317, 437, 572, 641, 642] [50, 76, 202, 246, 438, 573, 642, 643] [23, 51, 103, 113, 439, 574, 643, 644] [6, 52, 158, 186, 440, 575, 644, 645] [53, 267, 313, 331, 441, 558, 645, 646] [36, 142, 242, 278, 442, 559, 646, 647] [37, 99, 171, 233, 443, 560, 630, 647] [38, 54, 154, 298, 444, 561, 630, 631] [39, 73, 209, 263, 445, 562, 631, 632] [30, 40, 110, 138, 446, 563, 632, 633] [13, 41, 183, 229, 447, 564, 633, 634] [4, 60, 86, 338, 475, 527, 538, 580] [61, 105, 267, 293, 476, 528, 539, 581] [62, 124, 142, 186, 477, 522, 529, 582] [63, 179, 215, 313, 478, 523, 530, 583] [0, 64, 224, 270, 479, 524, 531, 584] [45, 65, 145, 289, 480, 525, 532, 585] [28, 66, 182, 236, 481, 526, 533, 586] [67, 75, 309, 335, 482, 527, 534, 587] [68, 94, 220, 264, 483, 528, 535, 588] [41, 69, 121, 131, 484, 529, 536, 589] [24, 70, 176, 204, 485, 530, 537, 590] [7, 71, 285, 331, 468, 531, 538, 591] [54, 160, 260, 296, 469, 532, 539, 592] [55, 117, 189, 251, 470, 522, 533, 593] [56, 72, 172, 316, 471, 523, 534, 576] [57, 91, 227, 281, 472, 524, 535, 577] [48, 58, 128, 156, 473, 525, 536, 578] [31, 59, 201, 247, 474, 526, 537, 579] [14, 22, 78, 104, 385, 419, 526, 628] [79, 123, 285, 311, 386, 420, 527, 629] [80, 142, 160, 204, 387, 421, 528, 612] [81, 197, 233, 331, 388, 422, 529, 613] [18, 82, 242, 288, 389, 423, 530, 614] [63, 83, 163, 307, 390, 424, 531, 615] [46, 84, 200, 254, 391, 425, 532, 616] [11, 85, 93, 327, 392, 426, 533, 617] [86, 112, 238, 282, 393, 427, 534, 618] [59, 87, 139, 149, 394, 428, 535, 619] [42, 88, 194, 222, 395, 429, 536, 620] [7, 25, 89, 303, 378, 430, 537, 621] [72, 178, 278, 314, 379, 431, 538, 622] [73, 135, 207, 269, 380, 414, 539, 623] [74, 90, 190, 334, 381, 415, 522, 624] [75, 109, 245, 299, 382, 416, 523, 625] [66, 76, 146, 174, 383, 417, 524, 626] [49, 77, 219, 265, 384, 418, 525, 627] [32, 40, 96, 122, 376, 472, 637, 653] [97, 141, 303, 329, 377, 473, 638, 654] [98, 160, 178, 222, 360, 474, 639, 655] [7, 99, 215, 251, 361, 475, 640, 656] [36, 100, 260, 306, 362, 476, 641, 657] [81, 101, 181, 325, 363, 477, 642, 658] [64, 102, 218, 272, 364, 478, 643, 659] [3, 29, 103, 111, 365, 479, 644, 660] [104, 130, 256, 300, 366, 480, 645, 661] [77, 105, 157, 167, 367, 481, 646, 662] [60, 106, 212, 240, 368, 482, 647, 663] [25, 43, 107, 321, 369, 483, 630, 664] [90, 196, 296, 332, 370, 484, 631, 665] [91, 153, 225, 287, 371, 485, 632, 648] [10, 92, 108, 208, 372, 468, 633, 649] [93, 127, 263, 317, 373, 469, 634, 650] [84, 94, 164, 192, 374, 470, 635, 651] [67, 95, 237, 283, 375, 471, 636, 652] [50, 58, 114, 140, 418, 466, 545, 547] [5, 115, 159, 321, 419, 467, 546, 548] [116, 178, 196, 240, 420, 450, 547, 549] [25, 117, 233, 269, 421, 451, 548, 550] [54, 118, 278, 324, 422, 452, 549, 551] [1, 99, 119, 199, 423, 453, 550, 552] [82, 120, 236, 290, 424, 454, 551, 553] [21, 47, 121, 129, 425, 455, 552, 554] [122, 148, 274, 318, 426, 456, 553, 555] [95, 123, 175, 185, 427, 457, 554, 556] [78, 124, 230, 258, 428, 458, 555, 557] [43, 61, 125, 339, 429, 459, 540, 556] [8, 108, 214, 314, 430, 460, 541, 557] [109, 171, 243, 305, 431, 461, 540, 542] [28, 110, 126, 226, 414, 462, 541, 543] [111, 145, 281, 335, 415, 463, 542, 544] [102, 112, 182, 210, 416, 464, 543, 545] [85, 113, 255, 301, 417, 465, 544, 546] [68, 76, 132, 158, 364, 437, 457, 556] [23, 133, 177, 339, 365, 438, 458, 557] [134, 196, 214, 258, 366, 439, 459, 540] [43, 135, 251, 287, 367, 440, 460, 541] [0, 72, 136, 296, 368, 441, 461, 542] [19, 117, 137, 217, 369, 442, 462, 543] [100, 138, 254, 308, 370, 443, 463, 544] [39, 65, 139, 147, 371, 444, 464, 545] [140, 166, 292, 336, 372, 445, 465, 546] [113, 141, 193, 203, 373, 446, 466, 547] [96, 142, 248, 276, 374, 447, 467, 548] [15, 61, 79, 143, 375, 448, 450, 549] [26, 126, 232, 332, 376, 449, 451, 550] [127, 189, 261, 323, 377, 432, 452, 551] [46, 128, 144, 244, 360, 433, 453, 552] [11, 129, 163, 299, 361, 434, 454, 553] [120, 130, 200, 228, 362, 435, 455, 554] [103, 131, 273, 319, 363, 436, 456, 555] [86, 94, 150, 176, 367, 646, 652, 671] [15, 41, 151, 195, 368, 647, 653, 672] [152, 214, 232, 276, 369, 630, 654, 673] [61, 153, 269, 305, 370, 631, 655, 674] [18, 90, 154, 314, 371, 632, 656, 675] [37, 135, 155, 235, 372, 633, 657, 676] [118, 156, 272, 326, 373, 634, 658, 677] [57, 83, 157, 165, 374, 635, 659, 678] [12, 158, 184, 310, 375, 636, 660, 679] [131, 159, 211, 221, 376, 637, 661, 680] [114, 160, 266, 294, 377, 638, 662, 681] [33, 79, 97, 161, 360, 639, 663, 682] [8, 44, 144, 250, 361, 640, 664, 683] [145, 207, 279, 341, 362, 641, 665, 666] [64, 146, 162, 262, 363, 642, 648, 667] [29, 147, 181, 317, 364, 643, 649, 668] [138, 148, 218, 246, 365, 644, 650, 669] [121, 149, 291, 337, 366, 645, 651, 670] [104, 112, 168, 194, 394, 563, 598, 619] [33, 59, 169, 213, 395, 564, 599, 620] [170, 232, 250, 294, 378, 565, 600, 621] [79, 171, 287, 323, 379, 566, 601, 622] [36, 108, 172, 332, 380, 567, 602, 623] [55, 153, 173, 253, 381, 568, 603, 624] [2, 136, 174, 290, 382, 569, 604, 625] [75, 101, 175, 183, 383, 570, 605, 626] [30, 176, 202, 328, 384, 571, 606, 627] [149, 177, 229, 239, 385, 572, 607, 628] [132, 178, 284, 312, 386, 573, 608, 629] [51, 97, 115, 179, 387, 574, 609, 612] [26, 62, 162, 268, 388, 575, 610, 613] [17, 163, 225, 297, 389, 558, 611, 614] [82, 164, 180, 280, 390, 559, 594, 615] [47, 165, 199, 335, 391, 560, 595, 616] [156, 166, 236, 264, 392, 561, 596, 617] [13, 139, 167, 309, 393, 562, 597, 618] [122, 130, 186, 212, 455, 484, 529, 544] [51, 77, 187, 231, 456, 485, 530, 545] [188, 250, 268, 312, 457, 468, 531, 546] [97, 189, 305, 341, 458, 469, 532, 547] [8, 54, 126, 190, 459, 470, 533, 548] [73, 171, 191, 271, 460, 471, 534, 549] [20, 154, 192, 308, 461, 472, 535, 550] [93, 119, 193, 201, 462, 473, 536, 551] [4, 48, 194, 220, 463, 474, 537, 552] [167, 195, 247, 257, 464, 475, 538, 553] [150, 196, 302, 330, 465, 476, 539, 554] [69, 115, 133, 197, 466, 477, 522, 555] [44, 80, 180, 286, 467, 478, 523, 556] [35, 181, 243, 315, 450, 479, 524, 557] [100, 182, 198, 298, 451, 480, 525, 540] [11, 65, 183, 217, 452, 481, 526, 541] [174, 184, 254, 282, 453, 482, 527, 542] [31, 157, 185, 327, 454, 483, 528, 543] [140, 148, 204, 230, 347, 439, 490, 574] [69, 95, 205, 249, 348, 440, 491, 575] [206, 268, 286, 330, 349, 441, 492, 558] [17, 115, 207, 323, 350, 442, 493, 559] [26, 72, 144, 208, 351, 443, 494, 560] [91, 189, 209, 289, 352, 444, 495, 561] [38, 172, 210, 326, 353, 445, 496, 562] [111, 137, 211, 219, 354, 446, 497, 563] [22, 66, 212, 238, 355, 447, 498, 564] [185, 213, 265, 275, 356, 448, 499, 565] [6, 168, 214, 320, 357, 449, 500, 566] [87, 133, 151, 215, 358, 432, 501, 567] [62, 98, 198, 304, 359, 433, 502, 568] [53, 199, 261, 333, 342, 434, 503, 569] [118, 200, 216, 316, 343, 435, 486, 570] [29, 83, 201, 235, 344, 436, 487, 571] [192, 202, 272, 300, 345, 437, 488, 572] [3, 49, 175, 203, 346, 438, 489, 573] [158, 166, 222, 248, 349, 436, 581, 664] [87, 113, 223, 267, 350, 437, 582, 665] [6, 224, 286, 304, 351, 438, 583, 648] [35, 133, 225, 341, 352, 439, 584, 649] [44, 90, 162, 226, 353, 440, 585, 650] [109, 207, 227, 307, 354, 441, 586, 651] [2, 56, 190, 228, 355, 442, 587, 652] [129, 155, 229, 237, 356, 443, 588, 653] [40, 84, 230, 256, 357, 444, 589, 654] [203, 231, 283, 293, 358, 445, 590, 655] [24, 186, 232, 338, 359, 446, 591, 656] [105, 151, 169, 233, 342, 447, 592, 657] [80, 116, 216, 322, 343, 448, 593, 658] [9, 71, 217, 279, 344, 449, 576, 659] [136, 218, 234, 334, 345, 432, 577, 660] [47, 101, 219, 253, 346, 433, 578, 661] [210, 220, 290, 318, 347, 434, 579, 662] [21, 67, 193, 221, 348, 435, 580, 663] [176, 184, 240, 266, 382, 412, 473, 601] [105, 131, 241, 285, 383, 413, 474, 602] [24, 242, 304, 322, 384, 396, 475, 603] [17, 53, 151, 243, 385, 397, 476, 604] [62, 108, 180, 244, 386, 398, 477, 605] [127, 225, 245, 325, 387, 399, 478, 606] [20, 74, 208, 246, 388, 400, 479, 607] [147, 173, 247, 255, 389, 401, 480, 608] [58, 102, 248, 274, 390, 402, 481, 609] [221, 249, 301, 311, 391, 403, 482, 610] [14, 42, 204, 250, 392, 404, 483, 611] [123, 169, 187, 251, 393, 405, 484, 594] [98, 134, 234, 340, 394, 406, 485, 595] [27, 89, 235, 297, 395, 407, 468, 596] [10, 154, 236, 252, 378, 408, 469, 597] [65, 119, 237, 271, 379, 409, 470, 598] [228, 238, 308, 336, 380, 410, 471, 599] [39, 85, 211, 239, 381, 411, 472, 600] [194, 202, 258, 284, 365, 502, 511, 670] [123, 149, 259, 303, 366, 503, 512, 671] [42, 260, 322, 340, 367, 486, 513, 672] [35, 71, 169, 261, 368, 487, 514, 673] [80, 126, 198, 262, 369, 488, 515, 674] [1, 145, 243, 263, 370, 489, 516, 675] [38, 92, 226, 264, 371, 490, 517, 676] [165, 191, 265, 273, 372, 491, 518, 677] [76, 120, 266, 292, 373, 492, 519, 678] [239, 267, 319, 329, 374, 493, 520, 679] [32, 60, 222, 268, 375, 494, 521, 680] [141, 187, 205, 269, 376, 495, 504, 681] [16, 116, 152, 252, 377, 496, 505, 682] [45, 107, 253, 315, 360, 497, 506, 683] [28, 172, 254, 270, 361, 498, 507, 666] [83, 137, 255, 289, 362, 499, 508, 667] [12, 246, 256, 326, 363, 500, 509, 668] [57, 103, 229, 257, 364, 501, 510, 669] [212, 220, 276, 302, 421, 592, 599, 616] [141, 167, 277, 321, 422, 593, 600, 617] [16, 60, 278, 340, 423, 576, 601, 618] [53, 89, 187, 279, 424, 577, 602, 619] [98, 144, 216, 280, 425, 578, 603, 620] [19, 163, 261, 281, 426, 579, 604, 621] [56, 110, 244, 282, 427, 580, 605, 622] [183, 209, 283, 291, 428, 581, 606, 623] [94, 138, 284, 310, 429, 582, 607, 624] [5, 257, 285, 337, 430, 583, 608, 625] [50, 78, 240, 286, 431, 584, 609, 626] [159, 205, 223, 287, 414, 585, 610, 627] [34, 134, 170, 270, 415, 586, 611, 628] [63, 125, 271, 333, 416, 587, 594, 629] [46, 190, 272, 288, 417, 588, 595, 612] [101, 155, 273, 307, 418, 589, 596, 613] [2, 30, 264, 274, 419, 590, 597, 614] [75, 121, 247, 275, 420, 591, 598, 615] [230, 238, 294, 320, 491, 562, 673, 682] [159, 185, 295, 339, 492, 563, 674, 683] [16, 34, 78, 296, 493, 564, 666, 675] [71, 107, 205, 297, 494, 565, 667, 676] [116, 162, 234, 298, 495, 566, 668, 677] [37, 181, 279, 299, 496, 567, 669, 678] [74, 128, 262, 300, 497, 568, 670, 679] [201, 227, 301, 309, 498, 569, 671, 680] [112, 156, 302, 328, 499, 570, 672, 681] [13, 23, 275, 303, 500, 571, 673, 682] [68, 96, 258, 304, 501, 572, 674, 683] [177, 223, 241, 305, 502, 573, 666, 675] [52, 152, 188, 288, 503, 574, 667, 676] [9, 81, 143, 289, 486, 575, 668, 677] [64, 208, 290, 306, 487, 558, 669, 678] [119, 173, 291, 325, 488, 559, 670, 679] [20, 48, 282, 292, 489, 560, 671, 680] [93, 139, 265, 293, 490, 561, 672, 681] [248, 256, 312, 338, 383, 430, 508, 583] [15, 177, 203, 313, 384, 431, 509, 584] [34, 52, 96, 314, 385, 414, 510, 585] [89, 125, 223, 315, 386, 415, 511, 586] [134, 180, 252, 316, 387, 416, 512, 587] [55, 199, 297, 317, 388, 417, 513, 588] [92, 146, 280, 318, 389, 418, 514, 589] [219, 245, 319, 327, 390, 419, 515, 590] [4, 130, 174, 320, 391, 420, 516, 591] [31, 41, 293, 321, 392, 421, 517, 592] [86, 114, 276, 322, 393, 422, 518, 593] [195, 241, 259, 323, 394, 423, 519, 576] [70, 170, 206, 306, 395, 424, 520, 577] [27, 99, 161, 307, 378, 425, 521, 578] [82, 226, 308, 324, 379, 426, 504, 579] [1, 137, 191, 309, 380, 427, 505, 580] [38, 66, 300, 310, 381, 428, 506, 581] [111, 157, 283, 311, 382, 429, 507, 582] [14, 266, 274, 330, 454, 493, 520, 617] [33, 195, 221, 331, 455, 494, 521, 618] [52, 70, 114, 332, 456, 495, 504, 619] [107, 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Code ID 684-4-81 · download JSON · raw on GitHub