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[[682,182,66]] d ≤
n
682
k
182
d
66
kd²/n
1162.452
w
32
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 66, d_Z ≤ 66 · w_X = 32, w_Z = 32 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 66 · witness weight 66 (claimed upper_bound)
witness found by @vprusso · norm-word lift of a Z_31 quotient logical · found at 1 trials · survived 1 trials · 2026-09-21
witness operator (support, 66 qubits)
[28, 29, 59, 60, 90, 91, 121, 122, 152, 153, 183, 184, 214, 215, 245, 246, 276, 277, 307, 308, 338, 339, 345, 348, 354, 356, 376, 379, 385, 387, 407, 410, 416, 418, 438, 441, 447, 449, 469, 472, 478, 480, 500, 503, 509, 511, 531, 534, 540, 542, 562, 565, 571, 573, 593, 596, 602, 604, 624, 627, 633, 635, 655, 658, 664, 666]
d_Z 66 · witness weight 66 (claimed upper_bound)
witness found by @vprusso · norm-word lift of a Z_31 quotient logical · found at 1 trials · survived 1 trials · 2026-09-21
witness operator (support, 66 qubits)
[16, 18, 24, 27, 47, 49, 55, 58, 78, 80, 86, 89, 109, 111, 117, 120, 140, 142, 148, 151, 171, 173, 179, 182, 202, 204, 210, 213, 233, 235, 241, 244, 264, 266, 272, 275, 295, 297, 303, 306, 326, 328, 334, 337, 343, 344, 374, 375, 405, 406, 436, 437, 467, 468, 498, 499, 529, 530, 560, 561, 591, 592, 622, 623, 653, 654]
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 32 · H_Z 32
qubit degrees H_X 16 · H_Z 16
trapping sets H_X (1,16)×682 (2,22)×341 (smallest syndrome weight at each size, connected sets of up to 3 qubits; sizes above 2 skipped under the cost cap)
full (size, syndrome weight): count census for H_X
(1,16): 682 (2,22): 341 (2,24): 1705 (2,26): 7161 (2,28): 27962 (2,30): 83204
trapping sets H_Z (1,16)×682 (2,22)×341 (smallest syndrome weight at each size, connected sets of up to 3 qubits; sizes above 2 skipped under the cost cap)
full (size, syndrome weight): count census for H_Z
(1,16): 682 (2,22): 341 (2,24): 1705 (2,26): 7161 (2,28): 27962 (2,30): 83204

Construction & provenance

authors @natestemen
provenance submitted through the challenge
novelty novelty not audited
construction Generalized bicycle on Z_341 = Z_11 x Z_31 (n = 2*341): H_X = [A|B], H_Z = [B^T|A^T] with circulant A, B built from exponent supports a = [37, 55, 71, 102, 159, 169, 172, 182, 190, 244, 246, 265, 268, 272, 290, 301] (weight 16) and b = [0, 11, 70, 81, 114, 153, 217, 227, 228, 235, 268, 280, 311, 320, 323, 339] (weight 16); row i of a circulant has a 1 in column (i + e) mod 341 for each exponent e. Both supports are codewords of a designed divisor ideal of x341 - 1, mined by masked randomized-information-set search with subgroup-quotient cleanliness filters; k = 2 deg gcd(a(x), b(x), x341 - 1) = 182.
model Claude Claude Fable 5 (claimed, not verified)
date 2026-08-28
notes Witness-backed upper bound, not an exact-distance claim. Screening ladder (randomized information-set trials -> lightest logical): 200000 -> d<=81, 2000000 -> d<=75, 20000000 -> d<=75. Both witnesses have weight 75: the family's block-swap plus index-reversal symmetry maps an X-logical to a Z-logical of equal weight, and both were revalidated independently against the verifier's criteria (in the correct kernel, outside the opposite stabilizer rowspace).
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

[[682,182,66]]: distance revision of the board's [[682,182,75]] entry

Revision history

[[682,182,66]] supersedes the board's [[682,182,75]] entry. The code, its checks, its layout, and its original provenance are unchanged; only the distance claim is corrected. Reducing both generator polynomials modulo x^31 - 1 gives a [[62,22]] generalized-bicycle quotient code with a weight-6 logical; multiplying that logical by the norm word N_11(x) = 1 + x^31 + ... + x^310 lifts it to a weight-66 logical of the full code on each side. This is exact algebra, not a sampled search, and each lifted operator was re-validated against the committed check matrices. The lift exhibits a weight-66 X-logical and a weight-66 Z-logical, so the previous witness-backed bound d <= 75 was overstated and the honest parameter set is [[682,182,66]]. The headline falls from kd^2/n = 1501.1 to 1162.45. Each lighter witness is carried in the entry with the budget it was found at and survived; the other side keeps its original witness where it was not refuted. Distance remains an upper bound, not an exact claim.

Evidence

The witnesses are not sampled: they are the norm-word lifts of a weight-6 logical of the Z_31 quotient code, computed exactly and re-validated here (in the kernel of the opposite side's checks, outside the row space of its own side). The sampling-budget fields in witness_provenance therefore carry the placeholder 1 and the tool field names the construction. The same mechanism bounds every generalized-bicycle code on a composite Z_m whose gcd with x^m - 1 keeps a factor of the quotient: the quotient code's distance times the norm-word weight.

| side | claimed | lightest logical found | trials | seed | CPU-verified | |---|---|---|---|---|---| | X | 75 | 66 | 1 | 0 | yes | | Z | 75 | 66 | 1 | 0 | yes |

The two [[682,182]] entries are the same code up to a permutation (issue #1651), so the same bound applies to both, and both are refiled at 66. Score kd^2/n falls from 1541.4 and 1501.1 to 1162.4. A randomized-information-set search does not find this operator at 300 million trials; it sits in a low-dimensional subspace the search rarely samples.

Original note, with the file paths updated

[[682,182,75]] — generalized bicycle on the pseudoprime block Z_341

Distance is a witness-backed upper bound (d <= 75), not an exact claim.

Direction & hypothesis

The unrestricted any-weight cell, where the board's headline is the prime-lift GB [[674,170,76]] (kd²/n = 1456.85, m = 337) above the m = 333 family (1300.90). The idea: 341 = 11·31 is the smallest base-2 Fermat pseudoprime, so ord_341(2) = 10 and x^341−1 splits as (x−1) · six degree-5 factors · 31 degree-10 factors — a much finer divisor-degree grid than m = 337 (steps of 21) at a slightly longer block (n = 682) under the n ≤ 700 cap. Finer degree control opens k between the m=337 family's 170 and 210, where the score bar drops from d ≥ 77 (k = 170) to d ≥ 74 (k = 182): 182·74²/682 = 1461 > 1456.85.

What was searched

Clean degree-85 divisors of x^341−1, where "clean" encodes subgroup-quotient poison rules specific to composite m: never the Φ₁₁ degree-10 factor (the coset of multiples of 31), at most two of the six degree-5 factors, and per-word quotient-projection caps (mod-31 projection gcd degree ≤ 11; mod-11 projection neither 0 nor all-ones). Violating any of these hands the code a norm-word logical of weight 11·w or 31·w for small w — the first naive sweep screened d ≤ 11 on every candidate.

Mining used gf2_fast.dem_rand_witness as a masked classical-codeword miner (min |e| with He = 0, Le ≠ 0; ~85k trials/s): mask rows built from CRT combinatorial rectangles ({i1,i2}×{j1,j2} ⊂ Z_11×Z_31, XOR of two per row) are exactly orthogonal to the whole norm-lift subspace, which otherwise dominates every ideal's light stratum (the weight-11 norm word divides every clean divisor's ideal). After each find, the found word's whole generated ideal joins an exclusion space and later masks are drawn from its dual kernel — without this, minimum-weight search returns only junk strata (five weight-16 orbits of one degree-95 divisor all shared a degree-141 subideal; every pair screened at k = 282, d ≤ 12).

~20 trawled divisors at 600k trials each yielded 5 genuine weight ≤ 16 orbits. Star-mining the subset divisors (degree ≥ 85) of one hit's own gcd found further weight-16 orbits sharing a degree-91 ideal — the pocket both finalists came from. All pooled words with pairwise shared factor degree ≥ 85 and row weight |a|+|b| ≤ 32 were screened at 4k RIS trials; ladder rungs at 200k / 2M / 20M with sound kill bars (any rung reading below the score-bar distance kills, since every reading is an upper bound).

Evidence trail

Submitted claim: d <= 75, a witness-backed upper bound.

Submitted code (supports below), two independent ladder passes:

  • pass 1: 4k → d ≤ 88; 200k → 81; 2M → 79; 20M → 75
  • pass 2 (fresh seeds): 200k → 81; 2M → 75; 20M → 75, weight-75 Z witness

The weight-75 floor was sighted by three independent seeds across ~42M total trials. A sibling pair (same a, different b from the same pocket) read 86/80/78/77 on pass 1 but its second pass found 75 as well — the 77 did not hold, so it is parameter-identical to this code and was not submitted separately. A third within-pocket pair screened at d ≤ 17 and died at the 200k rung both passes: within-pocket pairs can still collapse.

Score: 182·75²/682 = 1501.10 vs the board's 1456.85 ([[674,170,76]]). The claim survives a 1-point refutation (74 → 1461.4, still above the incumbent); a 2-point refutation (73 → 1416) would drop it below.

Both witnesses have weight 75: the family's block-swap plus index-reversal symmetry maps an X-logical (u|v) to a Z-logical (rev v|rev u) of equal weight, so d_X = d_Z here. Both were revalidated with verify/gf2.py criteria (in the correct kernel, outside the opposite stabilizer rowspace) independently of the compiled search that proposed them.

Dead ends

  • Naive divisor sampling on Z_341 is poisoned (see above): every candidate

    • screened at d ≤ 11–12 until the poison rules were derived.

  • Minimum-weight mining without ideal exclusion finds only junk strata

    • (the k = 282, d ≤ 12 cluster above).

  • The high-k thesis (k = 190–210 via degree 95–105 divisors) fails under

    • the weight-32 row cap: after cleanliness filters, 0/12 degree-100 divisors were fertile; genuine light-word counts track the Gilbert-Varshamov estimate E[#weight-16] ≈ 2^(92.6−D) and vanish above degree ~87.

  • Weight-14-based pairs (k = 172/192) all collapsed at the 4k screen

    • (d ≤ 16–17): genuine 14s should not exist by GV, so any found 14 is structured in ways the per-word filters do not fully catch.

Tools

Claude Fable 5 (matches provenance.model), one 18-core Apple Silicon machine, one session (~5 h wall). gf2_fast (verify/gf2_fast.cpp) for all RIS screening, witness search, and light-word mining; verify/gf2.py criteria for independent witness revalidation. The search driver was a single-session Python script on top of the kit's numpy core and gf2_fast (phases: factorize x^341−1 over GF(1024) → clean-divisor fertility probe → trawl with masked exclusion mining and star search → screen → kill-bar ladder → package); it is not committed — the "What was searched" section above specifies the method completely enough to rewrite it.

Reproduction

m = 341, n = 2m = 682. Build the two circulants from these exponent supports (row i of a circulant has a 1 in column (i + e) mod 341 for each exponent e), then H_X = [A | B], H_Z = [B^T | A^T]:

a = [37, 55, 71, 102, 159, 169, 172, 182, 190, 244, 246, 265, 268, 272, 290, 301]
b = [0, 11, 70, 81, 114, 153, 217, 227, 228, 235, 268, 280, 311, 320, 323, 339]

gcd(a(x), b(x), x^341−1) has degree 91, giving k = 182. The committed codes/682-182-66-b.json carries both weight-75 witnesses.

Parity checks

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