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

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Distance

X/Z asymmetry 1 · d_X ≤ 66, d_Z ≤ 66 · w_X = 32, w_Z = 32 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 66 · witness weight 66 (claimed upper_bound)
witness found by @vprusso · norm-word lift of a Z_31 quotient logical · found at 1 trials · survived 1 trials · 2026-09-21
witness operator (support, 66 qubits)
[10, 14, 28, 41, 45, 59, 72, 76, 90, 103, 107, 121, 134, 138, 152, 165, 169, 183, 196, 200, 214, 227, 231, 245, 258, 262, 276, 289, 293, 307, 320, 324, 338, 343, 356, 358, 374, 387, 389, 405, 418, 420, 436, 449, 451, 467, 480, 482, 498, 511, 513, 529, 542, 544, 560, 573, 575, 591, 604, 606, 622, 635, 637, 653, 666, 668]
d_Z 66 · witness weight 66 (claimed upper_bound)
witness found by @vprusso · norm-word lift of a Z_31 quotient logical · found at 1 trials · survived 1 trials · 2026-09-21
witness operator (support, 66 qubits)
[14, 16, 29, 45, 47, 60, 76, 78, 91, 107, 109, 122, 138, 140, 153, 169, 171, 184, 200, 202, 215, 231, 233, 246, 262, 264, 277, 293, 295, 308, 324, 326, 339, 344, 358, 362, 375, 389, 393, 406, 420, 424, 437, 451, 455, 468, 482, 486, 499, 513, 517, 530, 544, 548, 561, 575, 579, 592, 606, 610, 623, 637, 641, 654, 668, 672]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 32 · H_Z 32
qubit degrees H_X 16 · H_Z 16
trapping sets H_X (1,16)×682 (2,22)×341 (smallest syndrome weight at each size, connected sets of up to 3 qubits; sizes above 2 skipped under the cost cap)
full (size, syndrome weight): count census for H_X
(1,16): 682 (2,22): 341 (2,24): 1705 (2,26): 7161 (2,28): 27962 (2,30): 83204
trapping sets H_Z (1,16)×682 (2,22)×341 (smallest syndrome weight at each size, connected sets of up to 3 qubits; sizes above 2 skipped under the cost cap)
full (size, syndrome weight): count census for H_Z
(1,16): 682 (2,22): 341 (2,24): 1705 (2,26): 7161 (2,28): 27962 (2,30): 83204

Construction & provenance

authors @JiahaoYao
provenance submitted through the challenge
novelty novelty not audited
construction Generalized bicycle on Z_341 = Z_11 x Z_31 with HX=[A|B], HZ=[B^T|A^T]; weight-16 supports a=[0, 1, 36, 58, 115, 135, 141, 161, 177, 212, 248, 280, 285, 289, 327, 333] and b=[0, 1, 12, 14, 23, 67, 76, 84, 128, 133, 181, 199, 270, 305, 310, 314]. Both words lie in the published leader's degree-91 cyclic ideal.
model OpenAI GPT-5 (Codex) (claimed, not verified)
builds on https://unitaryfoundation.github.io/qldpc-challenge/codes/682-182-75.html, https://arxiv.org/abs/2203.17216
date 2026-08-29
notes Distance is a witness-backed upper bound, not exact. Fresh-seed ladder: 4,000 (both sides) -> d<=85; 100,000 (both sides) -> d<=82; 200,000 (X side via GB symmetry) -> d<=82; 2,000,000 -> d<=79; 20,000,000 -> d<=76. The trusted gate reported no exact duplicate and no WL-equivalent board entry as of 2026-08-29. Literature novelty is unverified.
family generalized bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight > 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[682,182,66]]: distance revision of the board's [[682,182,76]] entry

Revision history

[[682,182,66]] supersedes the board's [[682,182,76]] entry. The code, its checks, its layout, and its original provenance are unchanged; only the distance claim is corrected. Reducing both generator polynomials modulo x^31 - 1 gives a [[62,22]] generalized-bicycle quotient code with a weight-6 logical; multiplying that logical by the norm word N_11(x) = 1 + x^31 + ... + x^310 lifts it to a weight-66 logical of the full code on each side. This is exact algebra, not a sampled search, and each lifted operator was re-validated against the committed check matrices. The lift exhibits a weight-66 X-logical and a weight-66 Z-logical, so the previous witness-backed bound d <= 76 was overstated and the honest parameter set is [[682,182,66]]. The headline falls from kd^2/n = 1541.4 to 1162.45. Each lighter witness is carried in the entry with the budget it was found at and survived; the other side keeps its original witness where it was not refuted. Distance remains an upper bound, not an exact claim.

Evidence

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

| side | claimed | lightest logical found | trials | seed | CPU-verified | |---|---|---|---|---|---| | X | 76 | 66 | 1 | 0 | yes | | Z | 76 | 66 | 1 | 0 | yes |

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

Original note, with the file paths updated

[[682,182,76]] — a second Z_341 ideal pocket generalized bicycle

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

Direction & hypothesis

The target was the weight-9plus / unrestricted cell. Its leader was the [[682,182,d<=75]], weight-32 generalized bicycle on Z_341, with operational efficiency 182*75^2/682 = 1501.10. The submitted code has the same n, k, and maximum check weight, so a weight-76 logical witness is the one-point bar: 182*76^2/682 = 1541.40.

The leader note identifies a degree-91 cyclic ideal containing several sparse weight-16 words. The hypothesis was that additional words in that same ideal could form pairings with a lighter-logical spectrum different from the published pair, while preserving k = 182 and row weight 32.

What was searched

Let a_leader be the published leader's first circulant support. The row span of circ(a_leader) has dimension 250, so its right-orthogonal parity check has rank 91. The compiled randomized-information-set routine was used as a classical ideal-word miner: find nonzero v with H v = 0, then validate it again with the repository's Python GF(2) implementation.

Eight mining runs used 100,000 trials each, pair depth 24, 8 threads, seed 341202608 + 104729*i for i=0,...,7. They recovered four weight-16 dihedral orbits: the published leader word plus three additional orbits. Adding the published second leader word gave five source words. Pairing them with both relative orientations, fixing simultaneous reflection symmetry, and deduplicating exact stabilizer row spaces produced 26 candidates with total row weight at most 32.

The 4,000-trial screen eliminated 21 candidates. Fifteen had k=42 and already gave logicals of weight 111--119, below their score bar of 157. Six k=182 candidates collapsed to weight 2 or 17. Five survived, including the published leader as a calibration control. The control read 84, 80, 80, and 76 at the 4,000, 100,000, 200,000, and 2,000,000 rungs; its committed weight-75 witness shows why the control must not be mistaken for convergence.

The submitted pairing is:

a = [0, 1, 36, 58, 115, 135, 141, 161, 177, 212, 248, 280, 285, 289, 327, 333]
b = [0, 1, 12, 14, 23, 67, 76, 84, 128, 133, 181, 199, 270, 305, 310, 314]

Evidence trail

All distance readings below are upper bounds backed by explicit logicals. The first two rungs searched both CSS sides with 8 threads; the later rungs searched the X side with 12 threads and used the generalized-bicycle block-swap plus index-reversal involution to transfer the result to Z. Pair depth was 24 throughout.

| trials | seed | lightest logical | |---:|---:|---:| | 4,000 | 4529517267604857886 | 85 | | 100,000 | 4529517363605145886 | 82 | | 200,000 | 4529517463605445886 | 82 | | 2,000,000 | 4529519263610845886 | 79 | | 20,000,000 | 4529537263664845886 | 76 |

The 20M run took 2,001.9 seconds. Its weight-76 X witness was rechecked outside the compiled proposer: it lies in ker(H_Z) and outside rowspace(H_X). For an X vector u|v, the map u|v -> rev(v)|rev(u) gives the submitted weight-76 Z witness; that vector was separately checked in ker(H_X) and outside rowspace(H_Z).

The trusted candidate gate passed with fresh seed 1490401218: structure, n/k, CSS commutation, weight class, and both witnesses verified; 8,000 fresh RIS trials found nothing lighter; exact-fingerprint and WL-signature checks found no equivalent board entry. This is board-relative only. No literature novelty or lower bound d >= 76 is claimed.

Dead ends

  • Low-depth inflation was substantial: this candidate moved `85 -> 82 -> 79

    • -> 76`. The 20M rung was necessary; submitting the 2M reading would have overstated the board score by 8.1%.

  • Same-orbit and opposite-orientation pairings frequently carried structured

    • weight-2 or weight-17 logicals despite having the desired ideal degree.

  • The k=42 branch could not meet the required distance 157 and was killed at

    • the first rung.

  • Three other new k=182 pairings read 78, 77, and 77 at 2M trials, but were

    • not promoted without the 20M confirmation used here.

  • No independent BP+OSD corroboration or exact MILP lower-bound certificate was

    • completed. At n=682, k=182, exact certification is outside the challenge's demonstrated envelope.

  • Generalized bicycle codes are well mined, and this search deliberately starts

    • from the published leader's ideal. Literature novelty remains unverified.

Tools

OpenAI GPT-5 (Codex) ran the search and packaging workflow. The repository was at commit d7bab47; CPython 3.13 under uv built the shipped C++ bit-packed GF(2) backend. Search ran on an Intel i7-8700K (6 cores / 12 threads) with 48 GB RAM; peak memory was below 60 MB. The five-candidate 2M rung took 17m31s, and the selected 20M confirmation took 33m24s. Compiled proposals were always revalidated with the repository's independent Python GF(2) routines.

Reproduction

Set m=341. For support s, form a binary circulant C(s) with row i containing column (i+e) mod m for each e in s. With the supports above, set

A = C(a), B = C(b)
H_X = [A | B]
H_Z = [B^T | A^T]

Both check matrices have rank 250, so k = 682 - 250 - 250 = 182; every row has weight 32, and the circulant construction gives CSS commutation. The JSON contains the two weight-76 supports. Recompute all structural and witness facts with:

uv run python verify/qldpc_verify.py codes/682-182-66.json

For the search reading, build the X logical-detection basis, run 20,000,000 randomized-information-set trials at pair depth 24 with seed 4529537263664845886, and validate the returned support with independent GF(2) kernel and row-space tests. Treat 76 only as the resulting upper bound.

Parity checks

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