[[674,168,74]] · QEC Challenge

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[[674,168,74]] d ≤

674

168

kd²/n

1364.938

X/Z

1.03

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Distance

X/Z asymmetry 1.03 · d_X ≤ 76, d_Z ≤ 74 · w_X = 30, w_Z = 30 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 76 · witness weight 76 (claimed upper_bound)

witness found by @vprusso · ris_gpu recover, pair depth 8 · found at 3×10⁸ trials · survived 3×10⁸ trials · 2026-09-23

witness operator (support, 76 qubits)

[9, 23, 36, 54, 63, 92, 99, 103, 109, 122, 128, 144, 148, 165, 197, 202, 203, 207, 209, 219, 227, 246, 248, 254, 274, 276, 283, 287, 289, 292, 302, 312, 316, 318, 324, 329, 333, 334, 340, 354, 356, 360, 378, 415, 416, 433, 436, 448, 459, 476, 497, 498, 507, 508, 527, 538, 539, 547, 569, 581, 584, 587, 595, 602, 615, 621, 623, 624, 626, 628, 635, 638, 640, 641, 666, 668]

d_Z 74 · witness weight 74 (claimed upper_bound)

witness found by @vprusso · verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified) · found at 3×10⁸ trials · survived 3×10⁸ trials · 2026-09-24

witness operator (support, 74 qubits)

[5, 12, 13, 16, 21, 27, 31, 32, 38, 39, 49, 56, 58, 65, 69, 72, 73, 74, 75, 76, 77, 78, 79, 85, 99, 102, 103, 105, 106, 107, 114, 119, 125, 129, 133, 136, 146, 148, 150, 151, 152, 176, 185, 186, 188, 189, 196, 199, 203, 214, 215, 225, 228, 230, 233, 236, 250, 263, 277, 286, 294, 300, 312, 323, 355, 361, 367, 385, 416, 528, 593, 641, 663, 673]

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 30 · H_Z 30

qubit degrees H_X 15 · H_Z 15

trapping sets H_X (1,15)×674 (2,24)×3033 (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

(1,15): 674 (2,24): 3033 (2,26): 24264 (2,28): 88968

trapping sets H_Z (1,15)×674 (2,24)×3033 (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

(1,15): 674 (2,24): 3033 (2,26): 24264 (2,28): 88968

Construction & provenance

authors @vprusso

provenance submitted through the challenge

novelty novelty not audited

construction Four-factor m337 ideal: g=33893924722822194880126641; A=[14, 23, 27, 44, 45, 50, 113, 177, 185, 212, 222, 247, 251, 271, 305]; B=[34, 56, 66, 73, 92, 108, 115, 174, 176, 180, 200, 209, 214, 314, 330]

date 2026-09-23

notes Witness-backed upper bound d <= 76, not an exact-distance claim. Both submitted weight-76 logicals were found by GPU RIS recovery with pair depth 8, 300000000 trials per side, seed 1, and independently CPU-validated. Earlier native searches supported a bound of 80, which was refuted first to 78 by CI and then to 76 by the GPU audit. Literature novelty is unverified. Exact construction and correction details are in the accompanying note.

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

[[674,168,74]]: distance revision of the board's [[674,168,76]] entry

Revision history

[[674,168,74]] supersedes the board's [[674,168,76]] entry. The code, its checks, its layout, and its original provenance are unchanged; only the distance block is corrected. A GPU random-information-set search (verify/ris_gpu.py, recover mode, 300,000,000 trials per side, pair depth 0, seed 4102) exhibits a weight-74 Z logical, so the previous witness-backed bound was overstated and the honest parameter set is [[674,168,74]]. The headline falls from kd^2/n = 1439.72 to 1364.94. Each lighter witness is carried in the entry with the budget it was found at; the other side keeps its original witness where it was not refuted. Distance remains an upper bound, not an exact claim.

Evidence

Every GPU proposal was re-validated on the CPU against the committed check matrices (in the kernel of the opposite side's checks, outside the row space of its own side) before it was recorded. The pass is the weekly fresh-seed re-measurement of the board's cell leaders (issue 2025, run of 2026-09-24); every recorded reading is the lightest CPU-verified logical at that budget.

| side | seed | claimed | GPU best weight | CPU-verified witness | trials | |---|---|---|---|---|---| | X | 4101 | 76 | 76 | 76 | 300,000,000 | | Z | 4101 | 76 | 78 | 78 | 300,000,000 | | X | 4102 | 76 | 76 | 76 | 300,000,000 | | Z | 4102 | 76 | 74 | 74 | 300,000,000 |

Original note, with the file paths updated

[[674,168,76]] — cyclic generalized bicycle from a degree-84 ideal

Author: @vprusso. The submitted distance is a witness-backed d <= 76, with maximum check weight 30 and score 168 * 76^2 / 674 = 1439.715134. The code remains undominated in the weight-9plus × unrestricted cell. Its earlier claim of 80 was refuted and replaced with the two weight-76 GPU witnesses now in codes/674-168-74.json. No exact distance or literature novelty is claimed.

Direction & hypothesis

In a cyclic generalized-bicycle code, the common polynomial gcd controls the number of logical qubits, while the sparse generators also affect mixed logical operators. Order 337 offers sixteen degree-21 irreducible factors. Selecting four gives a degree-84 ideal and potentially k=168, changing the constituent code rather than reusing a known low-weight constituent in another presentation of the same ideal. The target was a new tradeoff on the unrestricted weight-9plus frontier.

What was searched

Products of four degree-21 factors were grouped under unit multipliers modulo 337, giving 116 ideal orbits. One already represented on the board was excluded. A fixed 120-second constructor budget visited 30 remaining ideals and recovered four distinct sparse words, one per ideal. The shared NumPy RNG seed was 928300001. The constructor formed the binary rowspace of cyclic shifts of each generator, permuted columns, computed RREF with the native GF(2) core, and retained rows of weight 4 to 18. Words with an extra gcd factor other than x+1 were rejected; translations and Frobenius images were deduplicated.

The submitted word came from catalog index 21 at local RREF iteration 5002, within 6690 iterations and approximately four seconds allocated to that ideal. This timed catalog shared one RNG stream, so the seed and iteration describe discovery rather than a timing-independent replay. The exact supports below make reconstruction independent of discovery timing.

Each recovered word A was paired with B=A^4 modulo x^337+1. Four codes were packaged with one initial witness-search trial per side, then checked using constrained fixed spaces and native searches. The admission check excluded the weight-34 and weight-36 alternatives.

Evidence trail

Every returned proposal was preserved and checked on the original matrices. The initial confirmation ladder ended at 80; subsequent independent searches lowered it to 78 and then 76. The table distinguishes those historical bounds from the submitted value.

| Pass | Trials | Seed | Returned weight | Retained bound | |---|---:|---:|---:|---:| | Frobenius fixed space j=1, X | 20,000 | 928400022 | 84 | 84 | | Frobenius fixed space j=3, X | 20,000 | 928400024 | 84 | 84 | | Frobenius fixed space j=7, X | 20,000 | 928400028 | 84 | 84 | | Native circulant-GB, depth 8 | 20,000 per side | 928400021 | 88 | 84 | | Native general RIS, depth 8 | 10,000 per side | 928400021 | 88 | 84 | | Native general RIS, depth 64, slice 1 | 100,000 per side | 92720301 | 80 | 80 | | Same, slice 2 | 100,000 per side | 92720302 | 82 | 80 | | Same, slice 3 | 100,000 per side | 92720303 | 80 | 80 | | Same, slice 4 | 100,000 per side | 92720304 | 82 | 80 | | Same, slice 5 | 100,000 per side | 92720305 | 82 | 80 | | Independent circulant-GB, depth 16 | 400,000 per side | 928500021 | 84 | 80 | | Original CI native RIS-fast, depth 8 | 8,000,000 | 697454300 | X: 78 | 78 | | GPU RIS recovery, depth 8 | 300,000,000 per side | 1 on each side | X: 76; Z: 76 | 76 | | Corrected CI native RIS-fast, depth 8 | 8,000,000 | 948236592 | 78 | 76 |

For the fixed-space audits, append constraints v[b*337+i] = v[b*337+(2^j*i mod 337)] for b=0,1 to H_Z. Use the complete original Z-logical basis with the native DEM witness search, pair depth 32 and one thread. Constrained kernel dimensions were 9,25,57 and logical ranks were 8,24,56. This restricts physical vectors without assuming that the coefficient permutation preserves the code. Each returned vector was checked against the unrestricted matrices.

The five depth-64 slices used two threads. The independent structural pass used one thread and found a pure-block weight-84 X logical. The original weight-80 X witness, with block weights 42 and 38, came from seed 92720301; its Z image was independently checked. Those historical supports are not the submitted weight-76 witnesses. Both submitted supports came from the GPU recovery search and were independently CPU-validated. The JSON records 300 million samples as the search budget; its found/survived fields refer to that same pass and must not be added together as separate runs.

The early local candidate gate passed at 80 with seed 92868021 and an 8,000-trial refutation report. The original CI run then refuted that claim with a weight-78 X logical. This is a concrete failure of shallow distance confirmation, not evidence for an exact distance.

On the corrected head b721f48199f990bddc0259f429dee7dee6d036d4, the independent CI run passed on September 24, 2026. Its receipt records seed 948236592, 400,000 structural trials, a Python RIS target of 105,880 under a 240-second cap, the syndrome-decoder cross-check, and all 8,000,000 native RIS-fast trials. The Python target is not a measurement of completed iterations. No logical lighter than 76 was found. Structural verification and authorship passed; there was no exact board duplicate or Weisfeiler–Lehman match, and the frontier check found no dominator. The trusted verifier commit was 110d467f046370612cd7fd2d6bbff5e439837ffd; validator source SHA-256: 51f8d78b055c03be4b951a44f88bbca2b5d9c029c353eacfb183aa0ad32815e1. These finite searches do not prove that 76 is minimal.

Dead ends

The four-factor batch also produced a k=170, weight-36 candidate whose bound fell from 84 to 80 after 500,000 trials per side, and a k=168, weight-34 candidate that fell from 84 to 78 after 200,000 trials per side. Both exceed the maximum check weight of 32. The fourth candidate, also weight 36, fell to 76 in the j=7 fixed-space audit. Complete structural admission checks should precede expensive confirmation.

Earlier three-factor ideals at this order produced shallow bounds 96,92,90,94. Fresh 100,000-trial general searches at depth 64 lowered them to 88,88,87,89. The submitted pair's later 80→78→76 reduction reinforces the same lesson.

Tools

Construction used Python, NumPy, SymPy factorization, the repository's cyclic GB constructor and submission kit, and its native GF(2) routines. Searches used the unchanged native general, circulant-GB and DEM cores, followed by GPU RIS recovery and original-matrix witness validation. The constructor took approximately 122 seconds including setup. The five initial general slices took about nine minutes and the independent structural pass about 89 seconds. No exact-distance certificate is claimed.

Reproduction

Work over F_2[x]/(x^337+1). Let C(S) be the 337 by 337 binary circulant whose row i has ones at (i+s) mod 337 for s in S. Use:

A = [14,23,27,44,45,50,113,177,185,212,222,247,251,271,305]
B = [34,56,66,73,92,108,115,174,176,180,200,209,214,314,330]
H_X = [C(A) | C(B)]
H_Z = [C(B)^T | C(A)^T]

B multiplies every A exponent by 4 modulo 337. Row i of H_X contains (i+a) mod 337 and 337+(i+b) mod 337; row i of H_Z contains (i-b) mod 337 and 337+(i-a) mod 337. This specifies every matrix entry. The circulants commute, implying CSS commutation. Each matrix has 337 rows, 674 columns and rank 253, so k=674-253-253=168. Every check has weight 30.

Encode a binary polynomial f as the integer sum(f_i * 2^i). The four irreducible factor bitmasks are 2332367,2437221,2932169,3612295. Their product over F_2 is g84 = 33893924722822194880126641. Both gcds with x^337+1 equal g84, of degree 84. The degree-85 parity extension (x+1)*g84 has bitmask 43653333958895553830659027 and divides neither selected 15-term word. The full matrices and both current logical supports are committed in codes/674-168-74.json.

Parity checks

X-checks 337 (max weight 30) · Z-checks 337 (max weight 30)

H_X (337 checks, sparse supports)

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

H_Z (337 checks, sparse supports)

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