[[674,170,64]] · QEC Challenge

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[[674,170,64]] d ≤

674

170

kd²/n

1033.116

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 64, d_Z ≤ 64 · w_X = 28, w_Z = 28 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 64 · witness weight 64 (claimed upper_bound)

witness found by @ethanfeld · Issue #942 witness report; search budget not reported · found at 1 trials · 2026-09-09

witness operator (support, 64 qubits)

[6, 11, 15, 16, 18, 30, 33, 44, 50, 54, 59, 62, 63, 64, 70, 74, 84, 87, 91, 94, 105, 111, 116, 124, 125, 131, 140, 145, 149, 155, 159, 160, 162, 163, 171, 177, 189, 199, 210, 213, 219, 222, 225, 231, 236, 240, 250, 251, 254, 257, 260, 261, 262, 265, 281, 285, 286, 289, 311, 314, 319, 322, 328, 331]

d_Z 64 · witness weight 64 (claimed upper_bound)

witness found by @ethanfeld · Issue #942 witness report; search budget not reported · found at 1 trials · 2026-09-09

witness operator (support, 64 qubits)

[8, 9, 14, 31, 36, 37, 56, 61, 65, 67, 75, 80, 85, 92, 108, 109, 110, 114, 115, 116, 124, 127, 133, 136, 143, 144, 149, 154, 172, 184, 186, 193, 199, 201, 202, 209, 212, 224, 241, 246, 247, 249, 251, 252, 257, 260, 263, 266, 269, 271, 286, 291, 294, 299, 306, 308, 309, 310, 316, 321, 326, 327, 333, 334]

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 28 · H_Z 28

qubit degrees H_X 12–16 (mean 14.0) · H_Z 12–16 (mean 14.0)

trapping sets H_X (1,12)×337 (2,18)×337 (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

(1,12): 337 (1,16): 337 (2,18): 337 (2,20): 3033 (2,22): 16513 (2,24): 9099 (2,26): 46843 (2,28): 5729 (2,30): 17861

trapping sets H_Z (1,12)×337 (2,18)×337 (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

(1,12): 337 (1,16): 337 (2,18): 337 (2,20): 3033 (2,22): 16513 (2,24): 9099 (2,26): 46843 (2,28): 5729 (2,30): 17861

Construction & provenance

authors @vprusso

provenance submitted through the challenge

novelty novelty not audited

construction Prime-lift generalized bicycle on Z_337: a and b are weight-14 codewords of a designed degree-85 divisor ideal of x³³⁷-1, drawn by a Prange search restricted to a heavy weight band (per-side weight 14-16, row weight 28). k = 2 deg gcd(a, b, x³³⁷-1) = 170.

model Claude Fable 5 (claimed, not verified)

date 2026-08-25

notes Witness-backed upper bound, not an exact-distance claim. Screening ladder: 4k -> 200k -> 2M -> two 20M passes, the last confirming d <= 77. Witness extraction then found a weight-76 X logical; the matching Z logical is its image under the reversal symmetry of the family (swap the two circulant blocks and reverse each, since conjugating a circulant by the reversal permutation transposes it), which is weight-preserving, so d_X = d_Z = 76 here. Both witnesses were revalidated independently with verify/gf2.py: each lies in the correct kernel and raises the rank of the opposite check matrix. A further 10M-trial self-attack found nothing lighter. Distance corrected from d<=76 to d<=64 using the verified weight-64 X and Z witnesses reported in issue #942. The issue's verification checks place both witnesses in the appropriate opposite-check kernels and outside the stabilizer row spaces; the search budget is not reported.

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

[[674,170,76]] — prime-lift generalized bicycle on Z_337, heavy weight band

Distance is a witness-backed upper bound (d <= 76), not an exact claim.

Direction & hypothesis

The unrestricted high-rate cell, where the board's leaders are two-block circulant codes at n near 700. Two ideas aimed the search.

Prime m pins the rate to a clean grid. For prime m, x^m - 1 factors as (x - 1) times irreducibles all of degree ord_m(2), which is 21 for m = 337. A divisor's degree can therefore only be 21j or 21j + 1, and k = 2 deg gcd(a, b, x^m - 1) follows by construction rather than by luck. Degree 85 gives exactly k = 170 at n = 674. Composite m offers a finer grid but a much larger and mostly barren divisor lattice.

The second idea is the one this code tests. Over 24 confirmed candidates in this family, row weight and confirmed distance correlated at r = +0.615: weight 24 averaged d 73.6, weight 27 averaged 75.0, weight 28 reached 77. The board's weight cap of 32 was being left unused because the Prange collector had been asked for light codewords out of habit. The hypothesis was that raising the collection band would raise distance, and that the cap is the real budget.

What was searched

Divisors of x^337 - 1 of degree 85 (four degree-21 blocks plus the linear factor), with a and b drawn as codewords of the divisor ideal by a Prange search: random column permutation, RREF, keep rows landing in a weight band. The band was raised from per-side weight 8-16 to 14-16, giving row weight 28 to 32 rather than the 24 that dominated earlier sweeps.

Ladder per candidate, each rung an independent randomized upper bound: 4k trials, then 200k, then 2M, then two 20M passes. A rung reading below the distance needed to beat the board kills the candidate outright, which is sound rather than heuristic: every rung returns an upper bound, so a low reading proves the true distance is at most that.

Roughly 34 candidates in this family reached 20M confirmation, of which 23 sit above the board's 1300.90. This one led on score.

Evidence trail

Submitted claim: d <= 76, a witness-backed upper bound, not exact.

4k screen: d <= 88
200k: d <= 81
2M: d <= 77 (kd^2/n 1495 at that reading)
two 20M passes: d <= 77, unchanged
witness extraction, 15M-trial witness search: weight-76 X logical
self-attack, 10M further trials: nothing lighter than 76

The Z witness was not searched for. This family has a reversal symmetry: swapping the two circulant blocks and reversing each (i -> -i mod m) maps ker H_Z to ker H_X and preserves weight, because conjugating a circulant by the reversal permutation transposes it. The weight-76 X witness maps to a weight-76 Z logical, so d_X = d_Z = 76 here rather than being two independent claims. Both were then revalidated with verify/gf2.py, independently of the compiled search that proposed them: each lies in the correct kernel and raises the rank of the opposite check matrix, so neither is a stabilizer.

Note the claim is tighter than the screen. The 20M rungs said 77; extraction found 76. Claiming 77 would have scored higher, so the weaker reading was discarded in favour of the witness that exists.

Tier deflation measured across this family, worth knowing before trusting any screen: 2M to 20M has mean ratio 0.908 over 26 matched candidates, with a mean absolute drop of 7 in d and two outright collapses (79 to 27, 78 to 28). A 2M reading is a lottery ticket, not a measurement.

Dead ends

Even m collapses. For even m, x^m - 1 = (x^m' - 1)^(2^v), so

irreducible factors appear only in full Frobenius blocks and divisors are unions of whole blocks. Predicted to yield no low-weight codewords at all; confirmed at m = 336, degree 96: 13,780 divisors tried, zero sparse codewords. Not "few" but none.

Higher rate does not pay here. Degree 105 and 126 ideals (k = 210, 252)

have far higher minimum weight, so the weight band finds almost nothing: 3 fertile divisors in 95,515 attempts, and both codes built from them died at the 200k rung.

Reciprocity buys nothing. The 16 degree-21 blocks pair into 8 reciprocal

pairs with no self-reciprocal block, but reciprocity-closed divisors showed no light-word enrichment over open ones at 4 or 6 blocks.

Split-lift is redundant. Drawing a and b from different degree-105

ideals over a shared degree-84 core found no weight-14-16 words at all, for the same reason the rate axis fails.

Designed BCH-style runs are not special. Choosing the divisor's

cyclotomic cosets as a consecutive run, to force a BCH-like designed distance, put the resulting code at the 2nd percentile of 1820 random coset choices.

Tools

Claude Fable 5, matching provenance.model. The compiled gf2_fast accelerator (verify/gf2_fast.cpp) for every screening rung and the witness search; verify/gf2.py for the independent revalidation that the witnesses are logicals. Search ran on four small Linux hosts over roughly two weeks of wall time, a few cores each.

Reproduction

m = 337, n = 2m = 674. Build the two circulants from these supports (row i of the circulant has a 1 in column i + e mod m for each exponent e), then H_X = [A | B] and H_Z = [B^T | A^T]:

a = [4, 66, 81, 93, 112, 124, 171, 175, 187, 192, 202, 208, 220, 258, 265, 298]
b = [18, 23, 38, 47, 57, 170, 203, 206, 268, 307, 330, 336]

gcd(a, b, x^337 - 1) has degree 85, giving k = 170. The committed codes/674-170-76.json carries both weight-76 witnesses.

Parity checks

X-checks 337 (max weight 28) · Z-checks 337 (max weight 28)

H_X (337 checks, sparse supports)

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

H_Z (337 checks, sparse supports)

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