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[[514,96,58]] d ≤
n
514
k
96
d
58
kd²/n
628.296
w
22
X/Z
1.03

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Distance

X/Z asymmetry 1.03 · d_X ≤ 60, d_Z ≤ 58 · w_X = 22, w_Z = 22 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 60 · witness weight 60 (claimed upper_bound)
witness operator (support, 60 qubits)
[4, 12, 17, 18, 52, 59, 60, 70, 71, 83, 98, 103, 105, 118, 133, 142, 153, 161, 168, 172, 175, 179, 190, 212, 216, 217, 219, 220, 221, 228, 249, 260, 269, 271, 272, 275, 288, 293, 342, 346, 355, 362, 363, 384, 398, 410, 419, 428, 431, 434, 437, 453, 454, 455, 460, 462, 469, 471, 472, 487]
d_Z 58 · witness weight 58 (claimed upper_bound)
witness operator (support, 58 qubits)
[1, 17, 18, 30, 36, 40, 43, 49, 50, 54, 58, 72, 79, 108, 117, 120, 141, 148, 158, 159, 160, 161, 184, 193, 221, 224, 228, 248, 258, 264, 272, 301, 302, 306, 307, 311, 317, 321, 322, 327, 330, 335, 338, 354, 356, 359, 386, 387, 405, 453, 464, 479, 480, 487, 488, 497, 509, 512]
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 22 · H_Z 22
qubit degrees H_X 11 · H_Z 11
trapping sets H_X (1,11)×514 (2,14)×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
(1,11): 514 (2,14): 257 (2,16): 257 (2,18): 7967 (2,20): 41634
trapping sets H_Z (1,11)×514 (2,14)×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
(1,11): 514 (2,14): 257 (2,16): 257 (2,18): 7967 (2,20): 41634

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) = x0 + x45 + x74 + x76 + x82 + x109 + x120 + x130 + x176 + x219 + x252, b(x) = x8 + x10 + x48 + x80 + x104 + x126 + x186 + x195 + x200 + x230 + x239; 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 48, fixing k = 2 deg gcd(a, b, x^m - 1) = 96.
model Claude Claude Opus 5 (claimed, not verified)
date 2026-10-13
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. At m=257, a prime, x^m - 1 has one cyclotomic coset of size 1 and sixteen of size 16; the size-1 coset is the root of x + 1, and admitting it drops the BCH bound on the single-block cyclic code from 74 to 44, so both a and b are drawn with at least one odd weight to keep it out. Both single-block gcds equal 48, matching deg gcd(a, b, x^m - 1). Distance is a witness-backed upper bound from 24 random information-set seeds at 2,000,000 trials each over 10,712 s, with the per-seed spread running 58 to 64. A prime modulus admits no quotient fold, and the orbit fold over every equal-orbit partition of the 514 qubits bottoms at a validated lift weight of 146; a single-block circulant search at 12 seeds x 600,000 trials finds nothing under 58. 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

--- author: "@vprusso" ---

[[514,96,58]] — cyclic generalized-bicycle code from a designed divisor ideal

No board entry at n <= 514 reaches k >= 96 and d >= 58 together. The nearest entries with that dimension and distance sit at n = 610 and above, and the best entry at this blocklength is [[514,128,52]] at kd^2/n = 673.4 against 628.3 here, so this adds a distinct corner rather than a better score.

Direction & hypothesis

For a cyclic generalized-bicycle code on x^m - 1, k = 2 deg gcd(a, b, x^m - 1), so the dimension follows from a polynomial gcd and can be chosen. The target was m = 257, which is prime: a proper divisor t of m gives a quotient-fold ceiling of (m/t) d_t, so a prime modulus admits no quotient fold at all and the only structural ceilings left are the two-orbit block swap and the single-block bound.

What was searched

m = 257 with ord_2(257) = 16. The cyclotomic cosets of x^257 - 1 over GF(2) are one of size 1 and sixteen of size 16, so the reachable divisor degrees are multiples of 16 plus an optional 1. A sweep over degrees 32, 48, 80 and 96 drew a and b as low-weight codewords of each divisor's ideal by Prange information-set decoding, screening every draw against the quotient-lift, single-block and orbit-fold bounds before any confirmation time was spent.

Degree 48 gives this code. Triage read 70 at 20,000 trials; the 24-seed confirmation settled it at 58, which is the usual direction and size of that correction in this family.

Evidence trail

Divisor degree 48, so k = 96. Both single-block gcds equal 48, matching deg gcd(a, b, x^m - 1), so neither circulant block carries a kernel wider than k requires.

  • General RIS, 24 random information-set seeds at 2,000,000 trials each

    • (10,712 s): lightest logical weight 58 on Z and 60 on X, per-seed spread 58 to 64 with a median of 62.

  • Orbit fold over every equal-orbit partition of the 514 qubits

    • (research/foldbound.py): lightest validated lift weight 146. A prime modulus leaves only the two-orbit block swap, and it is not binding here.

  • Single-block circulant search, 12 seeds at 600,000 trials: nothing under 58.

The claim is d = 58, a witness-backed upper bound. Both witnesses are in the submission and were re-checked against H_X and H_Z with plain integer arithmetic.

Dead ends

The information-set draw adds the factor x + 1 on its own, and at this modulus that costs real distance. (x+1) divides a polynomial exactly when its weight is even, so it divides gcd(a, b) exactly when both weights are even, and the draw returns even weights roughly half the time. A sweep aiming at degree 48 then lands on k = 98 rather than 96 with nothing to detect it: the common gcd really is degree 49.

Landing two above is the worst case, because the root-1 coset collapses the BCH bound on the single-block cyclic code. At m = 257 that bound reads 90, 86 and 74 at k = 32, 64 and 96, and 64, 52 and 44 at k = 34, 66 and 98. Measured: the k = 98 draws gate at 54 while the first k = 96 draws reach 70 at triage and 58 under confirmation. Rejecting a draw whose two weights are both even costs under half the draws and is what separates those two columns.

Degrees 80, 96 and 112 (k = 160, 192 and 224) produced nothing undominated across 300 draws each on eight processes, despite domination thresholds of only d > 30 at k = 160 and d > 13 at k = 192. The general distance does not reach even those, so a low threshold is not on its own a reason to search a cell.

Tools

Claude Opus 5 under Claude Code. gf2_fast from verify/ for the accelerated RIS and single-block searches, verify/gf2.py for GF(2) rank, nullspace and logical bases, research/foldbound.py for the orbit fold, and verify/validate_candidate.py for the verdict. Divisor assembly and the information-set draw are described above rather than committed. The 24-seed confirmation ran 10,712 s on 6 cores, about 18 core-hours.

Reproduction

m = 257, n = 514, k = 96.

a(x) = 1 + x^45 + x^74 + x^76 + x^82 + x^109 + x^120 + x^130 + x^176 + x^219
     + x^252
b(x) = x^8 + x^10 + x^48 + x^80 + x^104 + x^126 + x^186 + x^195 + x^200
     + x^230 + x^239

H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T], with circ(p)[i, j] = 1 exactly when j - i mod 257 is an exponent of p. The exact supports are in codes/514-96-58.json.

Parity checks

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