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[[514,128,52]] d ≤
n
514
k
128
d
52
kd²/n
673.37
w
32
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 52, d_Z ≤ 52 · 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 52 · witness weight 52 (claimed upper_bound)
witness operator (support, 52 qubits)
[38, 44, 49, 65, 69, 71, 73, 93, 125, 134, 140, 150, 153, 162, 168, 176, 193, 198, 203, 209, 213, 216, 239, 241, 268, 269, 275, 283, 291, 293, 295, 300, 301, 319, 343, 344, 348, 355, 357, 364, 390, 401, 406, 428, 432, 440, 446, 461, 468, 474, 498, 513]
d_Z 52 · witness weight 52 (claimed upper_bound)
witness operator (support, 52 qubits)
[11, 15, 17, 18, 20, 38, 44, 57, 60, 76, 77, 119, 128, 145, 177, 194, 196, 205, 227, 232, 242, 253, 306, 309, 313, 316, 328, 330, 334, 337, 339, 341, 365, 368, 388, 413, 437, 438, 444, 450, 451, 457, 458, 460, 462, 467, 480, 486, 493, 498, 501, 502]
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 15–17 (mean 16.0) · H_Z 15–17 (mean 16.0)
trapping sets H_X (1,15)×257 (2,22)×257 (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): 257 (1,17): 257 (2,22): 257 (2,24): 2056 (2,26): 8481 (2,28): 29298 (2,30): 30840 (2,32): 13107
trapping sets H_Z (1,15)×257 (2,22)×257 (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): 257 (1,17): 257 (2,22): 257 (2,24): 2056 (2,26): 8481 (2,28): 29298 (2,30): 30840 (2,32): 13107

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty known parameter set; see provenance notes
construction Cyclic generalized-bicycle code on the ring x257 - 1 with a(x) = x8 + x15 + x29 + x50 + x55 + x66 + x72 + x104 + x120 + x129 + x148 + x183 + x189 + x193 + x212, b(x) = x25 + x59 + x68 + x128 + x133 + x179 + x186 + x187 + x195 + x197 + x199 + x201 + x203 + x210 + x212 + x215 + x256; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T]. a and b are low-weight codewords of the ideal of a divisor of x257 - 1 of degree 64, fixing k = 2 deg gcd(a, b, x^m - 1) = 128.
model Claude Claude Opus 5 (claimed, not verified)
date 2026-10-12
notes Designed-divisor construction: the divisor is a product of cyclotomic-coset minimal polynomials over GF(2^ord_2(m)), so its degree and hence k are chosen rather than inherited, and a and b are drawn from its ideal by information-set decoding. Distance is a witness-backed upper bound from 24 random information-set seeds at 2,000,000 trials each; both witnesses re-verified against these matrices.
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

[[514,128,52]] weight-32 cyclic generalized-bicycle from a designed divisor

Direction & hypothesis

No board entry at n <= 514 reaches k >= 108 and d >= 42 at any row weight, so the opening was dimension and distance together at moderate blocklength. Reaching it needs a construction that selects k rather than inheriting it. Since k = 2 deg gcd(a, b, x^m - 1), choosing a divisor of x^m - 1 and drawing a and b from its ideal does exactly that: here the divisor has degree 64 and k = 128.

Two facts govern the construction, both checked rather than assumed. x^m - 1 is squarefree over GF(2) only for odd m, so m = 257 is usable and the even moduli of a residue sweep are not. And the usable a and b are low-weight codewords of the cyclic code the divisor generates, found by information-set decoding inside that ideal.

What was searched

The divisor is built as a product of cyclotomic-coset minimal polynomials over GF(2^16), so its degree is chosen; sampling sparse polynomials and taking gcds with x^m - 1 lands on a target degree almost never and kept 0 of 12 draws in an earlier attempt. Sweeping the ratio deg g / m from 0.04 to 0.30 across many coset subsets at nine odd moduli produced 299 priced candidates, of which 245 were undominated after folding and 137 were distinct shapes.

Evidence trail

The claim is a witness-backed upper bound with weight-52 witnesses on both sides.

random information set, 24 seeds x 2e6 52 (median 56, maximum 58) research/foldbound.py, uncapped no folded logical found verify/validate_candidate.py passed, not refuted

Unusually for this family, the symmetric fold finds nothing here, so it neither refutes the claim nor supports it, and the binding evidence is the trial-based search alone. The witnesses are the lightest the 24-seed scan found on each side, and both were re-verified against the committed matrices: in the kernel of the opposite checks, outside the row space of their own side, weight recounted. The gate reports no distance-only peers and no shared Weisfeiler-Leman signature.

Dead ends

Row weight is the construction's price and the schema is its ceiling. schema/code.schema.json caps each check's support at 32 entries, so a heavier code cannot be submitted whatever it scores. Two candidates from this same sweep passed full 24-seed gates at row weights 48 and 58, one of them scoring kd^2/n = 1493.1, and neither is submittable. Attempting to rebuild the heavier one under the cap failed outright: the lightest codewords in its degree-101 divisor's ideal are weight 26 to 34, so any pair of generators sums to at least 52. A Gilbert-Varshamov estimate had suggested weight 16 was reachable, which is wrong for a cyclic ideal because that bound describes random codes.

Triage figures from this construction are not trustworthy. Ranking by a 20,000-trial reading overstated one candidate's score by a factor of five, and the deeper the search the lower every distance went: this code was screened at 62 and gated at 52, and a sibling went 86, then 82, then 74.

Tools

Claude Opus 5 under Claude Code. verify/gf2_fast for the random information-set search, research/foldbound.py for the symmetric fold, verify/validate_candidate.py for the gate. The divisor construction and its sweep are described above in enough detail to rewrite; they are not committed here. The 24-seed scan took 6,544s on eight cores.

Reproduction

ring x^257 - 1 H_X = [circ(a) | circ(b)] H_Z = [circ(b)^T | circ(a)^T]

n = 2m = 514 and k = 2 deg gcd(a, b, x^m - 1) = 128. The exponents of a and b are in codes/514-128-52.json under provenance.construction.

Parity checks

X-checks 257 (max weight 32) · Z-checks 257 (max weight 32)
H_X (257 checks, sparse supports)
[8, 15, 29, 50, 55, 66, 72, 104, 120, 129, 148, 183, 189, 193, 212, 282, 316, 325, 385, 390, 436, 443, 444, 452, 454, 456, 458, 460, 467, 469, 472, 513] [9, 16, 30, 51, 56, 67, 73, 105, 121, 130, 149, 184, 190, 194, 213, 257, 283, 317, 326, 386, 391, 437, 444, 445, 453, 455, 457, 459, 461, 468, 470, 473] [10, 17, 31, 52, 57, 68, 74, 106, 122, 131, 150, 185, 191, 195, 214, 258, 284, 318, 327, 387, 392, 438, 445, 446, 454, 456, 458, 460, 462, 469, 471, 474] [11, 18, 32, 53, 58, 69, 75, 107, 123, 132, 151, 186, 192, 196, 215, 259, 285, 319, 328, 388, 393, 439, 446, 447, 455, 457, 459, 461, 463, 470, 472, 475] [12, 19, 33, 54, 59, 70, 76, 108, 124, 133, 152, 187, 193, 197, 216, 260, 286, 320, 329, 389, 394, 440, 447, 448, 456, 458, 460, 462, 464, 471, 473, 476] [13, 20, 34, 55, 60, 71, 77, 109, 125, 134, 153, 188, 194, 198, 217, 261, 287, 321, 330, 390, 395, 441, 448, 449, 457, 459, 461, 463, 465, 472, 474, 477] [14, 21, 35, 56, 61, 72, 78, 110, 126, 135, 154, 189, 195, 199, 218, 262, 288, 322, 331, 391, 396, 442, 449, 450, 458, 460, 462, 464, 466, 473, 475, 478] [15, 22, 36, 57, 62, 73, 79, 111, 127, 136, 155, 190, 196, 200, 219, 263, 289, 323, 332, 392, 397, 443, 450, 451, 459, 461, 463, 465, 467, 474, 476, 479] [16, 23, 37, 58, 63, 74, 80, 112, 128, 137, 156, 191, 197, 201, 220, 264, 290, 324, 333, 393, 398, 444, 451, 452, 460, 462, 464, 466, 468, 475, 477, 480] [17, 24, 38, 59, 64, 75, 81, 113, 129, 138, 157, 192, 198, 202, 221, 265, 291, 325, 334, 394, 399, 445, 452, 453, 461, 463, 465, 467, 469, 476, 478, 481] [18, 25, 39, 60, 65, 76, 82, 114, 130, 139, 158, 193, 199, 203, 222, 266, 292, 326, 335, 395, 400, 446, 453, 454, 462, 464, 466, 468, 470, 477, 479, 482] [19, 26, 40, 61, 66, 77, 83, 115, 131, 140, 159, 194, 200, 204, 223, 267, 293, 327, 336, 396, 401, 447, 454, 455, 463, 465, 467, 469, 471, 478, 480, 483] [20, 27, 41, 62, 67, 78, 84, 116, 132, 141, 160, 195, 201, 205, 224, 268, 294, 328, 337, 397, 402, 448, 455, 456, 464, 466, 468, 470, 472, 479, 481, 484] [21, 28, 42, 63, 68, 79, 85, 117, 133, 142, 161, 196, 202, 206, 225, 269, 295, 329, 338, 398, 403, 449, 456, 457, 465, 467, 469, 471, 473, 480, 482, 485] [22, 29, 43, 64, 69, 80, 86, 118, 134, 143, 162, 197, 203, 207, 226, 270, 296, 330, 339, 399, 404, 450, 457, 458, 466, 468, 470, 472, 474, 481, 483, 486] [23, 30, 44, 65, 70, 81, 87, 119, 135, 144, 163, 198, 204, 208, 227, 271, 297, 331, 340, 400, 405, 451, 458, 459, 467, 469, 471, 473, 475, 482, 484, 487] [24, 31, 45, 66, 71, 82, 88, 120, 136, 145, 164, 199, 205, 209, 228, 272, 298, 332, 341, 401, 406, 452, 459, 460, 468, 470, 472, 474, 476, 483, 485, 488] [25, 32, 46, 67, 72, 83, 89, 121, 137, 146, 165, 200, 206, 210, 229, 273, 299, 333, 342, 402, 407, 453, 460, 461, 469, 471, 473, 475, 477, 484, 486, 489] [26, 33, 47, 68, 73, 84, 90, 122, 138, 147, 166, 201, 207, 211, 230, 274, 300, 334, 343, 403, 408, 454, 461, 462, 470, 472, 474, 476, 478, 485, 487, 490] [27, 34, 48, 69, 74, 85, 91, 123, 139, 148, 167, 202, 208, 212, 231, 275, 301, 335, 344, 404, 409, 455, 462, 463, 471, 473, 475, 477, 479, 486, 488, 491] [28, 35, 49, 70, 75, 86, 92, 124, 140, 149, 168, 203, 209, 213, 232, 276, 302, 336, 345, 405, 410, 456, 463, 464, 472, 474, 476, 478, 480, 487, 489, 492] [29, 36, 50, 71, 76, 87, 93, 125, 141, 150, 169, 204, 210, 214, 233, 277, 303, 337, 346, 406, 411, 457, 464, 465, 473, 475, 477, 479, 481, 488, 490, 493] [30, 37, 51, 72, 77, 88, 94, 126, 142, 151, 170, 205, 211, 215, 234, 278, 304, 338, 347, 407, 412, 458, 465, 466, 474, 476, 478, 480, 482, 489, 491, 494] [31, 38, 52, 73, 78, 89, 95, 127, 143, 152, 171, 206, 212, 216, 235, 279, 305, 339, 348, 408, 413, 459, 466, 467, 475, 477, 479, 481, 483, 490, 492, 495] [32, 39, 53, 74, 79, 90, 96, 128, 144, 153, 172, 207, 213, 217, 236, 280, 306, 340, 349, 409, 414, 460, 467, 468, 476, 478, 480, 482, 484, 491, 493, 496] [33, 40, 54, 75, 80, 91, 97, 129, 145, 154, 173, 208, 214, 218, 237, 281, 307, 341, 350, 410, 415, 461, 468, 469, 477, 479, 481, 483, 485, 492, 494, 497] [34, 41, 55, 76, 81, 92, 98, 130, 146, 155, 174, 209, 215, 219, 238, 282, 308, 342, 351, 411, 416, 462, 469, 470, 478, 480, 482, 484, 486, 493, 495, 498] [35, 42, 56, 77, 82, 93, 99, 131, 147, 156, 175, 210, 216, 220, 239, 283, 309, 343, 352, 412, 417, 463, 470, 471, 479, 481, 483, 485, 487, 494, 496, 499] [36, 43, 57, 78, 83, 94, 100, 132, 148, 157, 176, 211, 217, 221, 240, 284, 310, 344, 353, 413, 418, 464, 471, 472, 480, 482, 484, 486, 488, 495, 497, 500] [37, 44, 58, 79, 84, 95, 101, 133, 149, 158, 177, 212, 218, 222, 241, 285, 311, 345, 354, 414, 419, 465, 472, 473, 481, 483, 485, 487, 489, 496, 498, 501] [38, 45, 59, 80, 85, 96, 102, 134, 150, 159, 178, 213, 219, 223, 242, 286, 312, 346, 355, 415, 420, 466, 473, 474, 482, 484, 486, 488, 490, 497, 499, 502] [39, 46, 60, 81, 86, 97, 103, 135, 151, 160, 179, 214, 220, 224, 243, 287, 313, 347, 356, 416, 421, 467, 474, 475, 483, 485, 487, 489, 491, 498, 500, 503] [40, 47, 61, 82, 87, 98, 104, 136, 152, 161, 180, 215, 221, 225, 244, 288, 314, 348, 357, 417, 422, 468, 475, 476, 484, 486, 488, 490, 492, 499, 501, 504] [41, 48, 62, 83, 88, 99, 105, 137, 153, 162, 181, 216, 222, 226, 245, 289, 315, 349, 358, 418, 423, 469, 476, 477, 485, 487, 489, 491, 493, 500, 502, 505] [42, 49, 63, 84, 89, 100, 106, 138, 154, 163, 182, 217, 223, 227, 246, 290, 316, 350, 359, 419, 424, 470, 477, 478, 486, 488, 490, 492, 494, 501, 503, 506] [43, 50, 64, 85, 90, 101, 107, 139, 155, 164, 183, 218, 224, 228, 247, 291, 317, 351, 360, 420, 425, 471, 478, 479, 487, 489, 491, 493, 495, 502, 504, 507] [44, 51, 65, 86, 91, 102, 108, 140, 156, 165, 184, 219, 225, 229, 248, 292, 318, 352, 361, 421, 426, 472, 479, 480, 488, 490, 492, 494, 496, 503, 505, 508] [45, 52, 66, 87, 92, 103, 109, 141, 157, 166, 185, 220, 226, 230, 249, 293, 319, 353, 362, 422, 427, 473, 480, 481, 489, 491, 493, 495, 497, 504, 506, 509] [46, 53, 67, 88, 93, 104, 110, 142, 158, 167, 186, 221, 227, 231, 250, 294, 320, 354, 363, 423, 428, 474, 481, 482, 490, 492, 494, 496, 498, 505, 507, 510] [47, 54, 68, 89, 94, 105, 111, 143, 159, 168, 187, 222, 228, 232, 251, 295, 321, 355, 364, 424, 429, 475, 482, 483, 491, 493, 495, 497, 499, 506, 508, 511] [48, 55, 69, 90, 95, 106, 112, 144, 160, 169, 188, 223, 229, 233, 252, 296, 322, 356, 365, 425, 430, 476, 483, 484, 492, 494, 496, 498, 500, 507, 509, 512] [49, 56, 70, 91, 96, 107, 113, 145, 161, 170, 189, 224, 230, 234, 253, 297, 323, 357, 366, 426, 431, 477, 484, 485, 493, 495, 497, 499, 501, 508, 510, 513] [50, 57, 71, 92, 97, 108, 114, 146, 162, 171, 190, 225, 231, 235, 254, 257, 298, 324, 358, 367, 427, 432, 478, 485, 486, 494, 496, 498, 500, 502, 509, 511] [51, 58, 72, 93, 98, 109, 115, 147, 163, 172, 191, 226, 232, 236, 255, 258, 299, 325, 359, 368, 428, 433, 479, 486, 487, 495, 497, 499, 501, 503, 510, 512] [52, 59, 73, 94, 99, 110, 116, 148, 164, 173, 192, 227, 233, 237, 256, 259, 300, 326, 360, 369, 429, 434, 480, 487, 488, 496, 498, 500, 502, 504, 511, 513] [0, 53, 60, 74, 95, 100, 111, 117, 149, 165, 174, 193, 228, 234, 238, 257, 260, 301, 327, 361, 370, 430, 435, 481, 488, 489, 497, 499, 501, 503, 505, 512] [1, 54, 61, 75, 96, 101, 112, 118, 150, 166, 175, 194, 229, 235, 239, 258, 261, 302, 328, 362, 371, 431, 436, 482, 489, 490, 498, 500, 502, 504, 506, 513] [2, 55, 62, 76, 97, 102, 113, 119, 151, 167, 176, 195, 230, 236, 240, 257, 259, 262, 303, 329, 363, 372, 432, 437, 483, 490, 491, 499, 501, 503, 505, 507] [3, 56, 63, 77, 98, 103, 114, 120, 152, 168, 177, 196, 231, 237, 241, 258, 260, 263, 304, 330, 364, 373, 433, 438, 484, 491, 492, 500, 502, 504, 506, 508] [4, 57, 64, 78, 99, 104, 115, 121, 153, 169, 178, 197, 232, 238, 242, 259, 261, 264, 305, 331, 365, 374, 434, 439, 485, 492, 493, 501, 503, 505, 507, 509] [5, 58, 65, 79, 100, 105, 116, 122, 154, 170, 179, 198, 233, 239, 243, 260, 262, 265, 306, 332, 366, 375, 435, 440, 486, 493, 494, 502, 504, 506, 508, 510] [6, 59, 66, 80, 101, 106, 117, 123, 155, 171, 180, 199, 234, 240, 244, 261, 263, 266, 307, 333, 367, 376, 436, 441, 487, 494, 495, 503, 505, 507, 509, 511] [7, 60, 67, 81, 102, 107, 118, 124, 156, 172, 181, 200, 235, 241, 245, 262, 264, 267, 308, 334, 368, 377, 437, 442, 488, 495, 496, 504, 506, 508, 510, 512] [8, 61, 68, 82, 103, 108, 119, 125, 157, 173, 182, 201, 236, 242, 246, 263, 265, 268, 309, 335, 369, 378, 438, 443, 489, 496, 497, 505, 507, 509, 511, 513] [9, 62, 69, 83, 104, 109, 120, 126, 158, 174, 183, 202, 237, 243, 247, 257, 264, 266, 269, 310, 336, 370, 379, 439, 444, 490, 497, 498, 506, 508, 510, 512] [10, 63, 70, 84, 105, 110, 121, 127, 159, 175, 184, 203, 238, 244, 248, 258, 265, 267, 270, 311, 337, 371, 380, 440, 445, 491, 498, 499, 507, 509, 511, 513] [11, 64, 71, 85, 106, 111, 122, 128, 160, 176, 185, 204, 239, 245, 249, 257, 259, 266, 268, 271, 312, 338, 372, 381, 441, 446, 492, 499, 500, 508, 510, 512] [12, 65, 72, 86, 107, 112, 123, 129, 161, 177, 186, 205, 240, 246, 250, 258, 260, 267, 269, 272, 313, 339, 373, 382, 442, 447, 493, 500, 501, 509, 511, 513] [13, 66, 73, 87, 108, 113, 124, 130, 162, 178, 187, 206, 241, 247, 251, 257, 259, 261, 268, 270, 273, 314, 340, 374, 383, 443, 448, 494, 501, 502, 510, 512] [14, 67, 74, 88, 109, 114, 125, 131, 163, 179, 188, 207, 242, 248, 252, 258, 260, 262, 269, 271, 274, 315, 341, 375, 384, 444, 449, 495, 502, 503, 511, 513] [15, 68, 75, 89, 110, 115, 126, 132, 164, 180, 189, 208, 243, 249, 253, 257, 259, 261, 263, 270, 272, 275, 316, 342, 376, 385, 445, 450, 496, 503, 504, 512] [16, 69, 76, 90, 111, 116, 127, 133, 165, 181, 190, 209, 244, 250, 254, 258, 260, 262, 264, 271, 273, 276, 317, 343, 377, 386, 446, 451, 497, 504, 505, 513] [17, 70, 77, 91, 112, 117, 128, 134, 166, 182, 191, 210, 245, 251, 255, 257, 259, 261, 263, 265, 272, 274, 277, 318, 344, 378, 387, 447, 452, 498, 505, 506] [18, 71, 78, 92, 113, 118, 129, 135, 167, 183, 192, 211, 246, 252, 256, 258, 260, 262, 264, 266, 273, 275, 278, 319, 345, 379, 388, 448, 453, 499, 506, 507] [0, 19, 72, 79, 93, 114, 119, 130, 136, 168, 184, 193, 212, 247, 253, 259, 261, 263, 265, 267, 274, 276, 279, 320, 346, 380, 389, 449, 454, 500, 507, 508] [1, 20, 73, 80, 94, 115, 120, 131, 137, 169, 185, 194, 213, 248, 254, 260, 262, 264, 266, 268, 275, 277, 280, 321, 347, 381, 390, 450, 455, 501, 508, 509] [2, 21, 74, 81, 95, 116, 121, 132, 138, 170, 186, 195, 214, 249, 255, 261, 263, 265, 267, 269, 276, 278, 281, 322, 348, 382, 391, 451, 456, 502, 509, 510] [3, 22, 75, 82, 96, 117, 122, 133, 139, 171, 187, 196, 215, 250, 256, 262, 264, 266, 268, 270, 277, 279, 282, 323, 349, 383, 392, 452, 457, 503, 510, 511] [0, 4, 23, 76, 83, 97, 118, 123, 134, 140, 172, 188, 197, 216, 251, 263, 265, 267, 269, 271, 278, 280, 283, 324, 350, 384, 393, 453, 458, 504, 511, 512] [1, 5, 24, 77, 84, 98, 119, 124, 135, 141, 173, 189, 198, 217, 252, 264, 266, 268, 270, 272, 279, 281, 284, 325, 351, 385, 394, 454, 459, 505, 512, 513] [2, 6, 25, 78, 85, 99, 120, 125, 136, 142, 174, 190, 199, 218, 253, 257, 265, 267, 269, 271, 273, 280, 282, 285, 326, 352, 386, 395, 455, 460, 506, 513] [3, 7, 26, 79, 86, 100, 121, 126, 137, 143, 175, 191, 200, 219, 254, 257, 258, 266, 268, 270, 272, 274, 281, 283, 286, 327, 353, 387, 396, 456, 461, 507] [4, 8, 27, 80, 87, 101, 122, 127, 138, 144, 176, 192, 201, 220, 255, 258, 259, 267, 269, 271, 273, 275, 282, 284, 287, 328, 354, 388, 397, 457, 462, 508] [5, 9, 28, 81, 88, 102, 123, 128, 139, 145, 177, 193, 202, 221, 256, 259, 260, 268, 270, 272, 274, 276, 283, 285, 288, 329, 355, 389, 398, 458, 463, 509] [0, 6, 10, 29, 82, 89, 103, 124, 129, 140, 146, 178, 194, 203, 222, 260, 261, 269, 271, 273, 275, 277, 284, 286, 289, 330, 356, 390, 399, 459, 464, 510] [1, 7, 11, 30, 83, 90, 104, 125, 130, 141, 147, 179, 195, 204, 223, 261, 262, 270, 272, 274, 276, 278, 285, 287, 290, 331, 357, 391, 400, 460, 465, 511] [2, 8, 12, 31, 84, 91, 105, 126, 131, 142, 148, 180, 196, 205, 224, 262, 263, 271, 273, 275, 277, 279, 286, 288, 291, 332, 358, 392, 401, 461, 466, 512] [3, 9, 13, 32, 85, 92, 106, 127, 132, 143, 149, 181, 197, 206, 225, 263, 264, 272, 274, 276, 278, 280, 287, 289, 292, 333, 359, 393, 402, 462, 467, 513] [4, 10, 14, 33, 86, 93, 107, 128, 133, 144, 150, 182, 198, 207, 226, 257, 264, 265, 273, 275, 277, 279, 281, 288, 290, 293, 334, 360, 394, 403, 463, 468] [5, 11, 15, 34, 87, 94, 108, 129, 134, 145, 151, 183, 199, 208, 227, 258, 265, 266, 274, 276, 278, 280, 282, 289, 291, 294, 335, 361, 395, 404, 464, 469] [6, 12, 16, 35, 88, 95, 109, 130, 135, 146, 152, 184, 200, 209, 228, 259, 266, 267, 275, 277, 279, 281, 283, 290, 292, 295, 336, 362, 396, 405, 465, 470] [7, 13, 17, 36, 89, 96, 110, 131, 136, 147, 153, 185, 201, 210, 229, 260, 267, 268, 276, 278, 280, 282, 284, 291, 293, 296, 337, 363, 397, 406, 466, 471] [8, 14, 18, 37, 90, 97, 111, 132, 137, 148, 154, 186, 202, 211, 230, 261, 268, 269, 277, 279, 281, 283, 285, 292, 294, 297, 338, 364, 398, 407, 467, 472] [9, 15, 19, 38, 91, 98, 112, 133, 138, 149, 155, 187, 203, 212, 231, 262, 269, 270, 278, 280, 282, 284, 286, 293, 295, 298, 339, 365, 399, 408, 468, 473] [10, 16, 20, 39, 92, 99, 113, 134, 139, 150, 156, 188, 204, 213, 232, 263, 270, 271, 279, 281, 283, 285, 287, 294, 296, 299, 340, 366, 400, 409, 469, 474] [11, 17, 21, 40, 93, 100, 114, 135, 140, 151, 157, 189, 205, 214, 233, 264, 271, 272, 280, 282, 284, 286, 288, 295, 297, 300, 341, 367, 401, 410, 470, 475] [12, 18, 22, 41, 94, 101, 115, 136, 141, 152, 158, 190, 206, 215, 234, 265, 272, 273, 281, 283, 285, 287, 289, 296, 298, 301, 342, 368, 402, 411, 471, 476] [13, 19, 23, 42, 95, 102, 116, 137, 142, 153, 159, 191, 207, 216, 235, 266, 273, 274, 282, 284, 286, 288, 290, 297, 299, 302, 343, 369, 403, 412, 472, 477] [14, 20, 24, 43, 96, 103, 117, 138, 143, 154, 160, 192, 208, 217, 236, 267, 274, 275, 283, 285, 287, 289, 291, 298, 300, 303, 344, 370, 404, 413, 473, 478] [15, 21, 25, 44, 97, 104, 118, 139, 144, 155, 161, 193, 209, 218, 237, 268, 275, 276, 284, 286, 288, 290, 292, 299, 301, 304, 345, 371, 405, 414, 474, 479] [16, 22, 26, 45, 98, 105, 119, 140, 145, 156, 162, 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401, 442, 468, 502, 511] [2, 34, 50, 59, 78, 113, 119, 123, 142, 195, 202, 216, 237, 242, 253, 315, 320, 366, 373, 374, 382, 384, 386, 388, 390, 397, 399, 402, 443, 469, 503, 512] [3, 35, 51, 60, 79, 114, 120, 124, 143, 196, 203, 217, 238, 243, 254, 316, 321, 367, 374, 375, 383, 385, 387, 389, 391, 398, 400, 403, 444, 470, 504, 513] [4, 36, 52, 61, 80, 115, 121, 125, 144, 197, 204, 218, 239, 244, 255, 257, 317, 322, 368, 375, 376, 384, 386, 388, 390, 392, 399, 401, 404, 445, 471, 505] [5, 37, 53, 62, 81, 116, 122, 126, 145, 198, 205, 219, 240, 245, 256, 258, 318, 323, 369, 376, 377, 385, 387, 389, 391, 393, 400, 402, 405, 446, 472, 506] [0, 6, 38, 54, 63, 82, 117, 123, 127, 146, 199, 206, 220, 241, 246, 259, 319, 324, 370, 377, 378, 386, 388, 390, 392, 394, 401, 403, 406, 447, 473, 507] [1, 7, 39, 55, 64, 83, 118, 124, 128, 147, 200, 207, 221, 242, 247, 260, 320, 325, 371, 378, 379, 387, 389, 391, 393, 395, 402, 404, 407, 448, 474, 508] [2, 8, 40, 56, 65, 84, 119, 125, 129, 148, 201, 208, 222, 243, 248, 261, 321, 326, 372, 379, 380, 388, 390, 392, 394, 396, 403, 405, 408, 449, 475, 509] [3, 9, 41, 57, 66, 85, 120, 126, 130, 149, 202, 209, 223, 244, 249, 262, 322, 327, 373, 380, 381, 389, 391, 393, 395, 397, 404, 406, 409, 450, 476, 510] [4, 10, 42, 58, 67, 86, 121, 127, 131, 150, 203, 210, 224, 245, 250, 263, 323, 328, 374, 381, 382, 390, 392, 394, 396, 398, 405, 407, 410, 451, 477, 511] [5, 11, 43, 59, 68, 87, 122, 128, 132, 151, 204, 211, 225, 246, 251, 264, 324, 329, 375, 382, 383, 391, 393, 395, 397, 399, 406, 408, 411, 452, 478, 512] [6, 12, 44, 60, 69, 88, 123, 129, 133, 152, 205, 212, 226, 247, 252, 265, 325, 330, 376, 383, 384, 392, 394, 396, 398, 400, 407, 409, 412, 453, 479, 513] [7, 13, 45, 61, 70, 89, 124, 130, 134, 153, 206, 213, 227, 248, 253, 257, 266, 326, 331, 377, 384, 385, 393, 395, 397, 399, 401, 408, 410, 413, 454, 480] [8, 14, 46, 62, 71, 90, 125, 131, 135, 154, 207, 214, 228, 249, 254, 258, 267, 327, 332, 378, 385, 386, 394, 396, 398, 400, 402, 409, 411, 414, 455, 481] [9, 15, 47, 63, 72, 91, 126, 132, 136, 155, 208, 215, 229, 250, 255, 259, 268, 328, 333, 379, 386, 387, 395, 397, 399, 401, 403, 410, 412, 415, 456, 482] [10, 16, 48, 64, 73, 92, 127, 133, 137, 156, 209, 216, 230, 251, 256, 260, 269, 329, 334, 380, 387, 388, 396, 398, 400, 402, 404, 411, 413, 416, 457, 483] [0, 11, 17, 49, 65, 74, 93, 128, 134, 138, 157, 210, 217, 231, 252, 261, 270, 330, 335, 381, 388, 389, 397, 399, 401, 403, 405, 412, 414, 417, 458, 484] [1, 12, 18, 50, 66, 75, 94, 129, 135, 139, 158, 211, 218, 232, 253, 262, 271, 331, 336, 382, 389, 390, 398, 400, 402, 404, 406, 413, 415, 418, 459, 485] [2, 13, 19, 51, 67, 76, 95, 130, 136, 140, 159, 212, 219, 233, 254, 263, 272, 332, 337, 383, 390, 391, 399, 401, 403, 405, 407, 414, 416, 419, 460, 486] [3, 14, 20, 52, 68, 77, 96, 131, 137, 141, 160, 213, 220, 234, 255, 264, 273, 333, 338, 384, 391, 392, 400, 402, 404, 406, 408, 415, 417, 420, 461, 487] [4, 15, 21, 53, 69, 78, 97, 132, 138, 142, 161, 214, 221, 235, 256, 265, 274, 334, 339, 385, 392, 393, 401, 403, 405, 407, 409, 416, 418, 421, 462, 488] [0, 5, 16, 22, 54, 70, 79, 98, 133, 139, 143, 162, 215, 222, 236, 266, 275, 335, 340, 386, 393, 394, 402, 404, 406, 408, 410, 417, 419, 422, 463, 489] [1, 6, 17, 23, 55, 71, 80, 99, 134, 140, 144, 163, 216, 223, 237, 267, 276, 336, 341, 387, 394, 395, 403, 405, 407, 409, 411, 418, 420, 423, 464, 490] [2, 7, 18, 24, 56, 72, 81, 100, 135, 141, 145, 164, 217, 224, 238, 268, 277, 337, 342, 388, 395, 396, 404, 406, 408, 410, 412, 419, 421, 424, 465, 491] [3, 8, 19, 25, 57, 73, 82, 101, 136, 142, 146, 165, 218, 225, 239, 269, 278, 338, 343, 389, 396, 397, 405, 407, 409, 411, 413, 420, 422, 425, 466, 492] [4, 9, 20, 26, 58, 74, 83, 102, 137, 143, 147, 166, 219, 226, 240, 270, 279, 339, 344, 390, 397, 398, 406, 408, 410, 412, 414, 421, 423, 426, 467, 493] [5, 10, 21, 27, 59, 75, 84, 103, 138, 144, 148, 167, 220, 227, 241, 271, 280, 340, 345, 391, 398, 399, 407, 409, 411, 413, 415, 422, 424, 427, 468, 494] [6, 11, 22, 28, 60, 76, 85, 104, 139, 145, 149, 168, 221, 228, 242, 272, 281, 341, 346, 392, 399, 400, 408, 410, 412, 414, 416, 423, 425, 428, 469, 495] [7, 12, 23, 29, 61, 77, 86, 105, 140, 146, 150, 169, 222, 229, 243, 273, 282, 342, 347, 393, 400, 401, 409, 411, 413, 415, 417, 424, 426, 429, 470, 496] [8, 13, 24, 30, 62, 78, 87, 106, 141, 147, 151, 170, 223, 230, 244, 274, 283, 343, 348, 394, 401, 402, 410, 412, 414, 416, 418, 425, 427, 430, 471, 497] [9, 14, 25, 31, 63, 79, 88, 107, 142, 148, 152, 171, 224, 231, 245, 275, 284, 344, 349, 395, 402, 403, 411, 413, 415, 417, 419, 426, 428, 431, 472, 498] [10, 15, 26, 32, 64, 80, 89, 108, 143, 149, 153, 172, 225, 232, 246, 276, 285, 345, 350, 396, 403, 404, 412, 414, 416, 418, 420, 427, 429, 432, 473, 499] [11, 16, 27, 33, 65, 81, 90, 109, 144, 150, 154, 173, 226, 233, 247, 277, 286, 346, 351, 397, 404, 405, 413, 415, 417, 419, 421, 428, 430, 433, 474, 500] [12, 17, 28, 34, 66, 82, 91, 110, 145, 151, 155, 174, 227, 234, 248, 278, 287, 347, 352, 398, 405, 406, 414, 416, 418, 420, 422, 429, 431, 434, 475, 501] [13, 18, 29, 35, 67, 83, 92, 111, 146, 152, 156, 175, 228, 235, 249, 279, 288, 348, 353, 399, 406, 407, 415, 417, 419, 421, 423, 430, 432, 435, 476, 502] [14, 19, 30, 36, 68, 84, 93, 112, 147, 153, 157, 176, 229, 236, 250, 280, 289, 349, 354, 400, 407, 408, 416, 418, 420, 422, 424, 431, 433, 436, 477, 503] [15, 20, 31, 37, 69, 85, 94, 113, 148, 154, 158, 177, 230, 237, 251, 281, 290, 350, 355, 401, 408, 409, 417, 419, 421, 423, 425, 432, 434, 437, 478, 504] [16, 21, 32, 38, 70, 86, 95, 114, 149, 155, 159, 178, 231, 238, 252, 282, 291, 351, 356, 402, 409, 410, 418, 420, 422, 424, 426, 433, 435, 438, 479, 505] [17, 22, 33, 39, 71, 87, 96, 115, 150, 156, 160, 179, 232, 239, 253, 283, 292, 352, 357, 403, 410, 411, 419, 421, 423, 425, 427, 434, 436, 439, 480, 506] [18, 23, 34, 40, 72, 88, 97, 116, 151, 157, 161, 180, 233, 240, 254, 284, 293, 353, 358, 404, 411, 412, 420, 422, 424, 426, 428, 435, 437, 440, 481, 507] [19, 24, 35, 41, 73, 89, 98, 117, 152, 158, 162, 181, 234, 241, 255, 285, 294, 354, 359, 405, 412, 413, 421, 423, 425, 427, 429, 436, 438, 441, 482, 508] [20, 25, 36, 42, 74, 90, 99, 118, 153, 159, 163, 182, 235, 242, 256, 286, 295, 355, 360, 406, 413, 414, 422, 424, 426, 428, 430, 437, 439, 442, 483, 509] [0, 21, 26, 37, 43, 75, 91, 100, 119, 154, 160, 164, 183, 236, 243, 287, 296, 356, 361, 407, 414, 415, 423, 425, 427, 429, 431, 438, 440, 443, 484, 510] [1, 22, 27, 38, 44, 76, 92, 101, 120, 155, 161, 165, 184, 237, 244, 288, 297, 357, 362, 408, 415, 416, 424, 426, 428, 430, 432, 439, 441, 444, 485, 511] [2, 23, 28, 39, 45, 77, 93, 102, 121, 156, 162, 166, 185, 238, 245, 289, 298, 358, 363, 409, 416, 417, 425, 427, 429, 431, 433, 440, 442, 445, 486, 512] [3, 24, 29, 40, 46, 78, 94, 103, 122, 157, 163, 167, 186, 239, 246, 290, 299, 359, 364, 410, 417, 418, 426, 428, 430, 432, 434, 441, 443, 446, 487, 513] [4, 25, 30, 41, 47, 79, 95, 104, 123, 158, 164, 168, 187, 240, 247, 257, 291, 300, 360, 365, 411, 418, 419, 427, 429, 431, 433, 435, 442, 444, 447, 488] [5, 26, 31, 42, 48, 80, 96, 105, 124, 159, 165, 169, 188, 241, 248, 258, 292, 301, 361, 366, 412, 419, 420, 428, 430, 432, 434, 436, 443, 445, 448, 489] [6, 27, 32, 43, 49, 81, 97, 106, 125, 160, 166, 170, 189, 242, 249, 259, 293, 302, 362, 367, 413, 420, 421, 429, 431, 433, 435, 437, 444, 446, 449, 490] [7, 28, 33, 44, 50, 82, 98, 107, 126, 161, 167, 171, 190, 243, 250, 260, 294, 303, 363, 368, 414, 421, 422, 430, 432, 434, 436, 438, 445, 447, 450, 491] [8, 29, 34, 45, 51, 83, 99, 108, 127, 162, 168, 172, 191, 244, 251, 261, 295, 304, 364, 369, 415, 422, 423, 431, 433, 435, 437, 439, 446, 448, 451, 492] [9, 30, 35, 46, 52, 84, 100, 109, 128, 163, 169, 173, 192, 245, 252, 262, 296, 305, 365, 370, 416, 423, 424, 432, 434, 436, 438, 440, 447, 449, 452, 493] [10, 31, 36, 47, 53, 85, 101, 110, 129, 164, 170, 174, 193, 246, 253, 263, 297, 306, 366, 371, 417, 424, 425, 433, 435, 437, 439, 441, 448, 450, 453, 494] [11, 32, 37, 48, 54, 86, 102, 111, 130, 165, 171, 175, 194, 247, 254, 264, 298, 307, 367, 372, 418, 425, 426, 434, 436, 438, 440, 442, 449, 451, 454, 495] [12, 33, 38, 49, 55, 87, 103, 112, 131, 166, 172, 176, 195, 248, 255, 265, 299, 308, 368, 373, 419, 426, 427, 435, 437, 439, 441, 443, 450, 452, 455, 496] [13, 34, 39, 50, 56, 88, 104, 113, 132, 167, 173, 177, 196, 249, 256, 266, 300, 309, 369, 374, 420, 427, 428, 436, 438, 440, 442, 444, 451, 453, 456, 497] [0, 14, 35, 40, 51, 57, 89, 105, 114, 133, 168, 174, 178, 197, 250, 267, 301, 310, 370, 375, 421, 428, 429, 437, 439, 441, 443, 445, 452, 454, 457, 498] [1, 15, 36, 41, 52, 58, 90, 106, 115, 134, 169, 175, 179, 198, 251, 268, 302, 311, 371, 376, 422, 429, 430, 438, 440, 442, 444, 446, 453, 455, 458, 499] [2, 16, 37, 42, 53, 59, 91, 107, 116, 135, 170, 176, 180, 199, 252, 269, 303, 312, 372, 377, 423, 430, 431, 439, 441, 443, 445, 447, 454, 456, 459, 500] [3, 17, 38, 43, 54, 60, 92, 108, 117, 136, 171, 177, 181, 200, 253, 270, 304, 313, 373, 378, 424, 431, 432, 440, 442, 444, 446, 448, 455, 457, 460, 501] [4, 18, 39, 44, 55, 61, 93, 109, 118, 137, 172, 178, 182, 201, 254, 271, 305, 314, 374, 379, 425, 432, 433, 441, 443, 445, 447, 449, 456, 458, 461, 502] [5, 19, 40, 45, 56, 62, 94, 110, 119, 138, 173, 179, 183, 202, 255, 272, 306, 315, 375, 380, 426, 433, 434, 442, 444, 446, 448, 450, 457, 459, 462, 503] [6, 20, 41, 46, 57, 63, 95, 111, 120, 139, 174, 180, 184, 203, 256, 273, 307, 316, 376, 381, 427, 434, 435, 443, 445, 447, 449, 451, 458, 460, 463, 504] [0, 7, 21, 42, 47, 58, 64, 96, 112, 121, 140, 175, 181, 185, 204, 274, 308, 317, 377, 382, 428, 435, 436, 444, 446, 448, 450, 452, 459, 461, 464, 505] [1, 8, 22, 43, 48, 59, 65, 97, 113, 122, 141, 176, 182, 186, 205, 275, 309, 318, 378, 383, 429, 436, 437, 445, 447, 449, 451, 453, 460, 462, 465, 506] [2, 9, 23, 44, 49, 60, 66, 98, 114, 123, 142, 177, 183, 187, 206, 276, 310, 319, 379, 384, 430, 437, 438, 446, 448, 450, 452, 454, 461, 463, 466, 507] [3, 10, 24, 45, 50, 61, 67, 99, 115, 124, 143, 178, 184, 188, 207, 277, 311, 320, 380, 385, 431, 438, 439, 447, 449, 451, 453, 455, 462, 464, 467, 508] [4, 11, 25, 46, 51, 62, 68, 100, 116, 125, 144, 179, 185, 189, 208, 278, 312, 321, 381, 386, 432, 439, 440, 448, 450, 452, 454, 456, 463, 465, 468, 509] [5, 12, 26, 47, 52, 63, 69, 101, 117, 126, 145, 180, 186, 190, 209, 279, 313, 322, 382, 387, 433, 440, 441, 449, 451, 453, 455, 457, 464, 466, 469, 510] [6, 13, 27, 48, 53, 64, 70, 102, 118, 127, 146, 181, 187, 191, 210, 280, 314, 323, 383, 388, 434, 441, 442, 450, 452, 454, 456, 458, 465, 467, 470, 511] [7, 14, 28, 49, 54, 65, 71, 103, 119, 128, 147, 182, 188, 192, 211, 281, 315, 324, 384, 389, 435, 442, 443, 451, 453, 455, 457, 459, 466, 468, 471, 512]
H_Z (257 checks, sparse supports)
[1, 42, 45, 47, 54, 56, 58, 60, 62, 70, 71, 78, 124, 129, 189, 198, 232, 302, 321, 325, 331, 366, 385, 394, 410, 442, 448, 459, 464, 485, 499, 506] [2, 43, 46, 48, 55, 57, 59, 61, 63, 71, 72, 79, 125, 130, 190, 199, 233, 303, 322, 326, 332, 367, 386, 395, 411, 443, 449, 460, 465, 486, 500, 507] [3, 44, 47, 49, 56, 58, 60, 62, 64, 72, 73, 80, 126, 131, 191, 200, 234, 304, 323, 327, 333, 368, 387, 396, 412, 444, 450, 461, 466, 487, 501, 508] [4, 45, 48, 50, 57, 59, 61, 63, 65, 73, 74, 81, 127, 132, 192, 201, 235, 305, 324, 328, 334, 369, 388, 397, 413, 445, 451, 462, 467, 488, 502, 509] [5, 46, 49, 51, 58, 60, 62, 64, 66, 74, 75, 82, 128, 133, 193, 202, 236, 306, 325, 329, 335, 370, 389, 398, 414, 446, 452, 463, 468, 489, 503, 510] [6, 47, 50, 52, 59, 61, 63, 65, 67, 75, 76, 83, 129, 134, 194, 203, 237, 307, 326, 330, 336, 371, 390, 399, 415, 447, 453, 464, 469, 490, 504, 511] [7, 48, 51, 53, 60, 62, 64, 66, 68, 76, 77, 84, 130, 135, 195, 204, 238, 308, 327, 331, 337, 372, 391, 400, 416, 448, 454, 465, 470, 491, 505, 512] [8, 49, 52, 54, 61, 63, 65, 67, 69, 77, 78, 85, 131, 136, 196, 205, 239, 309, 328, 332, 338, 373, 392, 401, 417, 449, 455, 466, 471, 492, 506, 513] [9, 50, 53, 55, 62, 64, 66, 68, 70, 78, 79, 86, 132, 137, 197, 206, 240, 257, 310, 329, 333, 339, 374, 393, 402, 418, 450, 456, 467, 472, 493, 507] [10, 51, 54, 56, 63, 65, 67, 69, 71, 79, 80, 87, 133, 138, 198, 207, 241, 258, 311, 330, 334, 340, 375, 394, 403, 419, 451, 457, 468, 473, 494, 508] [11, 52, 55, 57, 64, 66, 68, 70, 72, 80, 81, 88, 134, 139, 199, 208, 242, 259, 312, 331, 335, 341, 376, 395, 404, 420, 452, 458, 469, 474, 495, 509] [12, 53, 56, 58, 65, 67, 69, 71, 73, 81, 82, 89, 135, 140, 200, 209, 243, 260, 313, 332, 336, 342, 377, 396, 405, 421, 453, 459, 470, 475, 496, 510] [13, 54, 57, 59, 66, 68, 70, 72, 74, 82, 83, 90, 136, 141, 201, 210, 244, 261, 314, 333, 337, 343, 378, 397, 406, 422, 454, 460, 471, 476, 497, 511] [14, 55, 58, 60, 67, 69, 71, 73, 75, 83, 84, 91, 137, 142, 202, 211, 245, 262, 315, 334, 338, 344, 379, 398, 407, 423, 455, 461, 472, 477, 498, 512] [15, 56, 59, 61, 68, 70, 72, 74, 76, 84, 85, 92, 138, 143, 203, 212, 246, 263, 316, 335, 339, 345, 380, 399, 408, 424, 456, 462, 473, 478, 499, 513] [16, 57, 60, 62, 69, 71, 73, 75, 77, 85, 86, 93, 139, 144, 204, 213, 247, 257, 264, 317, 336, 340, 346, 381, 400, 409, 425, 457, 463, 474, 479, 500] [17, 58, 61, 63, 70, 72, 74, 76, 78, 86, 87, 94, 140, 145, 205, 214, 248, 258, 265, 318, 337, 341, 347, 382, 401, 410, 426, 458, 464, 475, 480, 501] [18, 59, 62, 64, 71, 73, 75, 77, 79, 87, 88, 95, 141, 146, 206, 215, 249, 259, 266, 319, 338, 342, 348, 383, 402, 411, 427, 459, 465, 476, 481, 502] [19, 60, 63, 65, 72, 74, 76, 78, 80, 88, 89, 96, 142, 147, 207, 216, 250, 260, 267, 320, 339, 343, 349, 384, 403, 412, 428, 460, 466, 477, 482, 503] [20, 61, 64, 66, 73, 75, 77, 79, 81, 89, 90, 97, 143, 148, 208, 217, 251, 261, 268, 321, 340, 344, 350, 385, 404, 413, 429, 461, 467, 478, 483, 504] [21, 62, 65, 67, 74, 76, 78, 80, 82, 90, 91, 98, 144, 149, 209, 218, 252, 262, 269, 322, 341, 345, 351, 386, 405, 414, 430, 462, 468, 479, 484, 505] [22, 63, 66, 68, 75, 77, 79, 81, 83, 91, 92, 99, 145, 150, 210, 219, 253, 263, 270, 323, 342, 346, 352, 387, 406, 415, 431, 463, 469, 480, 485, 506] [23, 64, 67, 69, 76, 78, 80, 82, 84, 92, 93, 100, 146, 151, 211, 220, 254, 264, 271, 324, 343, 347, 353, 388, 407, 416, 432, 464, 470, 481, 486, 507] [24, 65, 68, 70, 77, 79, 81, 83, 85, 93, 94, 101, 147, 152, 212, 221, 255, 265, 272, 325, 344, 348, 354, 389, 408, 417, 433, 465, 471, 482, 487, 508] [25, 66, 69, 71, 78, 80, 82, 84, 86, 94, 95, 102, 148, 153, 213, 222, 256, 266, 273, 326, 345, 349, 355, 390, 409, 418, 434, 466, 472, 483, 488, 509] [0, 26, 67, 70, 72, 79, 81, 83, 85, 87, 95, 96, 103, 149, 154, 214, 223, 267, 274, 327, 346, 350, 356, 391, 410, 419, 435, 467, 473, 484, 489, 510] [1, 27, 68, 71, 73, 80, 82, 84, 86, 88, 96, 97, 104, 150, 155, 215, 224, 268, 275, 328, 347, 351, 357, 392, 411, 420, 436, 468, 474, 485, 490, 511] [2, 28, 69, 72, 74, 81, 83, 85, 87, 89, 97, 98, 105, 151, 156, 216, 225, 269, 276, 329, 348, 352, 358, 393, 412, 421, 437, 469, 475, 486, 491, 512] [3, 29, 70, 73, 75, 82, 84, 86, 88, 90, 98, 99, 106, 152, 157, 217, 226, 270, 277, 330, 349, 353, 359, 394, 413, 422, 438, 470, 476, 487, 492, 513] [4, 30, 71, 74, 76, 83, 85, 87, 89, 91, 99, 100, 107, 153, 158, 218, 227, 257, 271, 278, 331, 350, 354, 360, 395, 414, 423, 439, 471, 477, 488, 493] [5, 31, 72, 75, 77, 84, 86, 88, 90, 92, 100, 101, 108, 154, 159, 219, 228, 258, 272, 279, 332, 351, 355, 361, 396, 415, 424, 440, 472, 478, 489, 494] [6, 32, 73, 76, 78, 85, 87, 89, 91, 93, 101, 102, 109, 155, 160, 220, 229, 259, 273, 280, 333, 352, 356, 362, 397, 416, 425, 441, 473, 479, 490, 495] [7, 33, 74, 77, 79, 86, 88, 90, 92, 94, 102, 103, 110, 156, 161, 221, 230, 260, 274, 281, 334, 353, 357, 363, 398, 417, 426, 442, 474, 480, 491, 496] [8, 34, 75, 78, 80, 87, 89, 91, 93, 95, 103, 104, 111, 157, 162, 222, 231, 261, 275, 282, 335, 354, 358, 364, 399, 418, 427, 443, 475, 481, 492, 497] [9, 35, 76, 79, 81, 88, 90, 92, 94, 96, 104, 105, 112, 158, 163, 223, 232, 262, 276, 283, 336, 355, 359, 365, 400, 419, 428, 444, 476, 482, 493, 498] [10, 36, 77, 80, 82, 89, 91, 93, 95, 97, 105, 106, 113, 159, 164, 224, 233, 263, 277, 284, 337, 356, 360, 366, 401, 420, 429, 445, 477, 483, 494, 499] [11, 37, 78, 81, 83, 90, 92, 94, 96, 98, 106, 107, 114, 160, 165, 225, 234, 264, 278, 285, 338, 357, 361, 367, 402, 421, 430, 446, 478, 484, 495, 500] [12, 38, 79, 82, 84, 91, 93, 95, 97, 99, 107, 108, 115, 161, 166, 226, 235, 265, 279, 286, 339, 358, 362, 368, 403, 422, 431, 447, 479, 485, 496, 501] [13, 39, 80, 83, 85, 92, 94, 96, 98, 100, 108, 109, 116, 162, 167, 227, 236, 266, 280, 287, 340, 359, 363, 369, 404, 423, 432, 448, 480, 486, 497, 502] [14, 40, 81, 84, 86, 93, 95, 97, 99, 101, 109, 110, 117, 163, 168, 228, 237, 267, 281, 288, 341, 360, 364, 370, 405, 424, 433, 449, 481, 487, 498, 503] [15, 41, 82, 85, 87, 94, 96, 98, 100, 102, 110, 111, 118, 164, 169, 229, 238, 268, 282, 289, 342, 361, 365, 371, 406, 425, 434, 450, 482, 488, 499, 504] [16, 42, 83, 86, 88, 95, 97, 99, 101, 103, 111, 112, 119, 165, 170, 230, 239, 269, 283, 290, 343, 362, 366, 372, 407, 426, 435, 451, 483, 489, 500, 505] [17, 43, 84, 87, 89, 96, 98, 100, 102, 104, 112, 113, 120, 166, 171, 231, 240, 270, 284, 291, 344, 363, 367, 373, 408, 427, 436, 452, 484, 490, 501, 506] [18, 44, 85, 88, 90, 97, 99, 101, 103, 105, 113, 114, 121, 167, 172, 232, 241, 271, 285, 292, 345, 364, 368, 374, 409, 428, 437, 453, 485, 491, 502, 507] [19, 45, 86, 89, 91, 98, 100, 102, 104, 106, 114, 115, 122, 168, 173, 233, 242, 272, 286, 293, 346, 365, 369, 375, 410, 429, 438, 454, 486, 492, 503, 508] [20, 46, 87, 90, 92, 99, 101, 103, 105, 107, 115, 116, 123, 169, 174, 234, 243, 273, 287, 294, 347, 366, 370, 376, 411, 430, 439, 455, 487, 493, 504, 509] [21, 47, 88, 91, 93, 100, 102, 104, 106, 108, 116, 117, 124, 170, 175, 235, 244, 274, 288, 295, 348, 367, 371, 377, 412, 431, 440, 456, 488, 494, 505, 510] [22, 48, 89, 92, 94, 101, 103, 105, 107, 109, 117, 118, 125, 171, 176, 236, 245, 275, 289, 296, 349, 368, 372, 378, 413, 432, 441, 457, 489, 495, 506, 511] [23, 49, 90, 93, 95, 102, 104, 106, 108, 110, 118, 119, 126, 172, 177, 237, 246, 276, 290, 297, 350, 369, 373, 379, 414, 433, 442, 458, 490, 496, 507, 512] [24, 50, 91, 94, 96, 103, 105, 107, 109, 111, 119, 120, 127, 173, 178, 238, 247, 277, 291, 298, 351, 370, 374, 380, 415, 434, 443, 459, 491, 497, 508, 513] [25, 51, 92, 95, 97, 104, 106, 108, 110, 112, 120, 121, 128, 174, 179, 239, 248, 257, 278, 292, 299, 352, 371, 375, 381, 416, 435, 444, 460, 492, 498, 509] [26, 52, 93, 96, 98, 105, 107, 109, 111, 113, 121, 122, 129, 175, 180, 240, 249, 258, 279, 293, 300, 353, 372, 376, 382, 417, 436, 445, 461, 493, 499, 510] [27, 53, 94, 97, 99, 106, 108, 110, 112, 114, 122, 123, 130, 176, 181, 241, 250, 259, 280, 294, 301, 354, 373, 377, 383, 418, 437, 446, 462, 494, 500, 511] [28, 54, 95, 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419, 440, 454, 461] [1, 3, 10, 12, 14, 16, 18, 26, 27, 34, 80, 85, 145, 154, 188, 214, 255, 258, 277, 281, 287, 322, 341, 350, 366, 398, 404, 415, 420, 441, 455, 462] [2, 4, 11, 13, 15, 17, 19, 27, 28, 35, 81, 86, 146, 155, 189, 215, 256, 259, 278, 282, 288, 323, 342, 351, 367, 399, 405, 416, 421, 442, 456, 463] [0, 3, 5, 12, 14, 16, 18, 20, 28, 29, 36, 82, 87, 147, 156, 190, 216, 260, 279, 283, 289, 324, 343, 352, 368, 400, 406, 417, 422, 443, 457, 464] [1, 4, 6, 13, 15, 17, 19, 21, 29, 30, 37, 83, 88, 148, 157, 191, 217, 261, 280, 284, 290, 325, 344, 353, 369, 401, 407, 418, 423, 444, 458, 465] [2, 5, 7, 14, 16, 18, 20, 22, 30, 31, 38, 84, 89, 149, 158, 192, 218, 262, 281, 285, 291, 326, 345, 354, 370, 402, 408, 419, 424, 445, 459, 466] [3, 6, 8, 15, 17, 19, 21, 23, 31, 32, 39, 85, 90, 150, 159, 193, 219, 263, 282, 286, 292, 327, 346, 355, 371, 403, 409, 420, 425, 446, 460, 467] [4, 7, 9, 16, 18, 20, 22, 24, 32, 33, 40, 86, 91, 151, 160, 194, 220, 264, 283, 287, 293, 328, 347, 356, 372, 404, 410, 421, 426, 447, 461, 468] [5, 8, 10, 17, 19, 21, 23, 25, 33, 34, 41, 87, 92, 152, 161, 195, 221, 265, 284, 288, 294, 329, 348, 357, 373, 405, 411, 422, 427, 448, 462, 469] [6, 9, 11, 18, 20, 22, 24, 26, 34, 35, 42, 88, 93, 153, 162, 196, 222, 266, 285, 289, 295, 330, 349, 358, 374, 406, 412, 423, 428, 449, 463, 470] [7, 10, 12, 19, 21, 23, 25, 27, 35, 36, 43, 89, 94, 154, 163, 197, 223, 267, 286, 290, 296, 331, 350, 359, 375, 407, 413, 424, 429, 450, 464, 471] [8, 11, 13, 20, 22, 24, 26, 28, 36, 37, 44, 90, 95, 155, 164, 198, 224, 268, 287, 291, 297, 332, 351, 360, 376, 408, 414, 425, 430, 451, 465, 472] [9, 12, 14, 21, 23, 25, 27, 29, 37, 38, 45, 91, 96, 156, 165, 199, 225, 269, 288, 292, 298, 333, 352, 361, 377, 409, 415, 426, 431, 452, 466, 473] [10, 13, 15, 22, 24, 26, 28, 30, 38, 39, 46, 92, 97, 157, 166, 200, 226, 270, 289, 293, 299, 334, 353, 362, 378, 410, 416, 427, 432, 453, 467, 474] [11, 14, 16, 23, 25, 27, 29, 31, 39, 40, 47, 93, 98, 158, 167, 201, 227, 271, 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Code ID 514-128-52 · download JSON · raw on GitHub