[[674,128,81]] · QEC Challenge

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[[674,128,81]] d ≤

674

128

kd²/n

1246.006

X/Z

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Distance

X/Z asymmetry 1 · d_X ≤ 81, d_Z ≤ 81 · 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 81 · witness weight 81 (claimed upper_bound)

witness found by @vprusso · ris_gpu 300M trials/side, Perlmutter A100, CPU-verified · found at 3×10⁸ trials · 2026-10-07

witness operator (support, 81 qubits)

[4, 17, 28, 32, 57, 79, 93, 105, 106, 110, 123, 134, 136, 140, 143, 149, 156, 174, 179, 181, 188, 226, 232, 240, 245, 260, 262, 271, 274, 291, 295, 299, 301, 307, 310, 311, 316, 321, 324, 326, 332, 336, 342, 360, 362, 366, 406, 420, 422, 433, 443, 463, 467, 475, 491, 493, 502, 510, 513, 514, 516, 522, 528, 529, 530, 579, 580, 592, 607, 610, 611, 620, 625, 626, 627, 630, 637, 647, 653, 655, 661]

d_Z 81 · witness weight 81 (claimed upper_bound)

witness found by @vprusso · image of the X witness under the GB transpose automorphism · found at 3×10⁸ trials · 2026-10-07

witness operator (support, 81 qubits)

[13, 19, 21, 27, 37, 44, 47, 48, 49, 54, 63, 64, 67, 82, 94, 95, 144, 145, 146, 152, 158, 160, 161, 164, 172, 181, 183, 199, 207, 211, 231, 241, 252, 254, 268, 308, 312, 314, 332, 338, 342, 348, 350, 353, 358, 363, 364, 367, 373, 375, 379, 383, 400, 403, 412, 414, 429, 434, 442, 448, 486, 493, 495, 500, 518, 525, 531, 534, 538, 540, 551, 564, 568, 569, 581, 595, 617, 642, 646, 657, 670]

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)×674 (2,24)×1011 (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): 674 (2,24): 1011 (2,26): 7414 (2,28): 32352 (2,30): 76162

trapping sets H_Z (1,16)×674 (2,24)×1011 (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): 674 (2,24): 1011 (2,26): 7414 (2,28): 32352 (2,30): 76162

Construction & provenance

authors @vprusso

provenance submitted through the challenge

novelty new parameter set claimed by submitter

construction Cyclic generalized-bicycle code over Z_337: H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T], a = x^[39, 69, 99, 146, 157, 173, 189, 216, 238, 251, 260, 263, 273, 284, 308, 311], b = x^[2, 22, 47, 52, 62, 65, 78, 92, 96, 121, 135, 149, 181, 241, 251, 280], both sparse multiples of a designed divisor g of x³³⁷ - 1 (hex 0x1b2e20f5df4de415d) of degree 64, so k = 2 deg g = 128 by construction. Found by the designed-divisor sampler (PR #2790 lineage) in the 2026-10-07 campaign.

model Claude Fable 5.1 (Claude Code) (claimed, not verified)

date 2026-10-07

notes Readings: 200,000 trials 91; 2,000,000 trials 86 (seed 23); 10,000,000 trials 86 (Perlmutter CPU, seed 777) and 83 (laptop, seed 2026); 300,000,000 GPU trials per side (Perlmutter A100, seed 1): X 81, Z 82, both CPU-verified. Seed 2 at the same depth: X 82, Z 83. Annihilator attack 200,000 trials: nothing below 86. The board's [[674,128,80]] is a designed-divisor GB at the same lift with a different degree-64 divisor (a with 16 terms, b with 14, check weight 30), refuted from 87 to 80 at 1,000,000,000 trials per side; this entry's reading fell from 86 to 81 between 10M and 300M trials and has not been attacked at 1B. The Z witness is the image of the X witness under the GB transpose automorphism (block swap composed with i -> -i mod 337); the GPU read 82 on the Z side directly. Witnessed upper bound.

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

[[674,128,81]] cyclic generalized-bicycle code over Z_337 with k designed from a degree-64 divisor of x^337 - 1

Direction & hypothesis

Cell: weight-9plus x unrestricted. The board's most efficient entries are cyclic generalized-bicycle (GB) codes H_X = [circ(a) | circ(b)] over Z_m with m near 340 and check weight 24 to 32, each built on a designed divisor ideal of x^m - 1 so that k = 2 deg gcd(a, b, x^m - 1) is set before the distance is measured. The designed-divisor sampler of PR #2790 reached that family from Z_305 on its first six draws ([[610,122,73]], PR #2810); this campaign ran it at scale over odd m from 281 to 345 to find Pareto-advancing codes in the cell, whose headline is [[682,172,78]] at kd^2/n = 1534. This entry is the best survivor: at n = 674 the board's [[674,128,80]] (a designed-divisor GB at the same lift on a different degree-64 divisor, check weight 30, refuted from 87 to 80 at 1,000,000,000 trials per side) is the only entry with k >= 128 and d >= 80, and this entry reads 81 at 300,000,000 trials per side, kd^2/n = 1246. The gain over it is one in distance at check weight 32 against 30, so it does not dominate that entry and both stand.

What was searched

Sampler: for each odd m, divisors g of x^m - 1 with 2 deg g in 100 to 200

(about six per m from the irreducible-factor products), and for each g, sparse multiples a and b of g at weight 12 to 16 by a Prange search in the kernel of the circulant of the reciprocal check polynomial, plus Frobenius images of found words; pairs whose gcd exceeds g discarded. 4,815 draws in all: m = 305 (1,459), 331 (1,321), 337 (1,256), 329 (610), 287 (135), 281 (133), 327 (105), 325 (53), 345 (43), 323 (30), 333 (12).

Ladder (fast RIS, pair depth 32): 2,000 trials on every draw, keeping only

draws whose reading would be Pareto-advancing at their (n, k) (4,179 of 4,815 at that depth, which says how little a 2,000-trial reading means here); 20,000 trials on those (298 survivors); 200,000 trials (44 survivors over m = 305, 323, 325, 327, 329, 337, 345); then 10,000,000 trials per side on the six best by kd^2/n, run on a Perlmutter CPU node, seed 777. The three Z_327 members of that six collapsed from 82 to 28, 32 and 40; the three Z_337 members held at 84 to 86.

This code: g = 0x1b2e20f5df4de415d (degree 64), a with 16 terms

(exponents 39, 69, 99, 146, 157, 173, 189, 216, 238, 251, 260, 263, 273, 284, 308, 311) and b with 16 (2, 22, 47, 52, 62, 65, 78, 92, 96, 121, 135, 149, 181, 241, 251, 280); check weight 32. Five of the 44 stage-3 survivors share this divisor.

Evidence trail

Each reported operator was re-verified in Python (zero syndrome against the opposite checks, outside the row space of its own checks, weight recounted); verify/qldpc_verify.py re-checks both witnesses.

| instrument | trials | seed | lightest logical | |---|---:|---:|---:| | fast RIS, pair depth 32 | 2,000 | campaign | above 90 | | fast RIS, pair depth 32 | 20,000 | campaign | above 90 | | fast RIS, pair depth 32 | 200,000 | campaign | 91 | | fast RIS, pair depth 32 (laptop) | 2,000,000 | 23 | 86 | | fast RIS, pair depth 32 (Perlmutter) | 10,000,000 | 777 | 86 | | fast RIS, pair depth 32 (laptop, second seed) | 10,000,000 | 2026 | 83 | | annihilator attack, four single-block subspaces | 200,000 | 11 | nothing below 86 | | ris_gpu, pair depth 8 (Perlmutter A100), X side | 300,000,000 | 1 | 81 | | ris_gpu, pair depth 8 (Perlmutter A100), Z side | 300,000,000 | 1 | 82 | | ris_gpu, pair depth 8 (Perlmutter A100), X side | 300,000,000 | 2 | 82 | | ris_gpu, pair depth 8 (Perlmutter A100), Z side | 300,000,000 | 2 | 83 | | the gate's own refutation (validate_candidate.py) | 8,000 | gate | nothing below 81 |

The GB code has the automorphism (left, i) -> (right, -i mod 337), (right, j) -> (left, -j mod 337), which maps H_X onto H_Z, so d_X = d_Z and the other side's witness is the image of the one found. The committed Z witness is the image of the weight-81 X witness; the GPU's own Z reading was 82. Final claim: d <= 81 on both sides, a witnessed upper bound at 300,000,000 GPU trials per side, the depth the cell's leaders were attacked at, with two seeds (the second read 82 on X and 83 on Z). The reading fell from 86 at 10,000,000 trials to 81 at 300,000,000, and the board's sibling at this lift fell from 87 to 80 only at 1,000,000,000 trials, so a 1,000,000,000-trial attack is the next thing this entry should face; every GPU-proposed operator was re-verified on the CPU before it counted.

Dead ends

Z_327: three survivors at k = 150 read 82 at 200,000 trials and

kd^2/n = 1542, above the headline; at 10,000,000 trials they read 28, 32 and 40. Those divisors are mixtures across the residue classes mod 3 of Z_327 rather than direct sums (checked), so the collapse is a genuine light logical, not a decomposition.

m = 305, 331 and 329 took three quarters of the draws and produced

nothing that survived 200,000 trials beyond what PR #2810 already filed.

Of the three Z_337 survivors, [[674,126,84]] (weight 31) and

[[674,126,86]] (weight 30) passed the gate against the board at their 10,000,000-trial readings but are dominated in the cell by this entry at 86; their 300,000,000-trial passes are queued behind this one on the same GPU job, and they are not filed.

Tools

Claude Fable 5.1 (Claude Code) driving the repo kit: research/kit/gf2poly.py and research/kit/search.py for the construction, research/kit/surrogate.py (fast backend) for the ladder, research/kit/annihilator.py, and verify/validate_candidate.py for the gate. The sampler and ladder ran on a laptop (about 10 hours, 6 threads); the six 10,000,000-trial passes ran in parallel on one Perlmutter CPU node in 11 minutes (36 threads each, NERSC project gen0030); the second 10,000,000-trial seed ran on the laptop; the 300,000,000-trial passes ran on one Perlmutter A100 (verify/ris_gpu.py, about 61 minutes per seed).

Reproduction

m = 337, H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with the exponent sets above (circ(a)_{i,j} = 1 iff j - i mod 337 is an exponent of a). k = 128 by construction, recomputed by the verifier. The JSON carries both check matrices and both witnesses, so the entry verifies without the search.

Parity checks

X-checks 337 (max weight 32) · Z-checks 337 (max weight 32)

H_X (337 checks, sparse supports)

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

H_Z (337 checks, sparse supports)

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