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[[482,98,51]] d ≤
n
482
k
98
d
51
kd²/n
528.834
w
24
X/Z
1.06

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Distance

X/Z asymmetry 1.06 · d_X ≤ 51, d_Z ≤ 54 · w_X = 24, w_Z = 24 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 51 · witness weight 51 (claimed upper_bound)
witness operator (support, 51 qubits)
[2, 34, 41, 43, 58, 63, 67, 90, 91, 110, 118, 124, 129, 139, 143, 160, 166, 185, 191, 192, 200, 214, 227, 239, 255, 267, 272, 288, 290, 307, 311, 324, 328, 345, 347, 365, 366, 372, 379, 384, 385, 392, 403, 407, 416, 421, 422, 437, 450, 463, 472]
d_Z 54 · witness weight 54 (claimed upper_bound)
witness operator (support, 54 qubits)
[1, 29, 50, 51, 53, 60, 71, 86, 87, 90, 94, 107, 108, 110, 112, 128, 135, 137, 139, 149, 169, 170, 178, 181, 198, 206, 210, 219, 220, 230, 240, 241, 253, 255, 257, 268, 274, 279, 281, 286, 302, 324, 353, 373, 379, 380, 393, 412, 413, 415, 417, 426, 438, 477]
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 24 · H_Z 24
qubit degrees H_X 12 · H_Z 12
trapping sets H_X (1,12)×482 (2,16)×241 (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
(1,12): 482 (2,16): 241 (2,18): 1205 (2,20): 14219 (2,22): 33499
trapping sets H_Z (1,12)×482 (2,16)×241 (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
(1,12): 482 (2,16): 241 (2,18): 1205 (2,20): 14219 (2,22): 33499

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction Cyclic generalized bicycle at m=241, a prime with ord_2(m)=24, so the nontrivial cyclotomic cosets of 2 all have size 24. The divisor g is one such coset's minimal polynomial, of degree 49, which fixes k = 2 deg g = 98 by construction. The pair (a,b) was then drawn from the ideal (g) by information-set decoding over sparse supports, keeping weights 12 and 12; both are odd, so x+1 does not divide the gcd and no weight-m block logical is forced. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 482 qubits at uniform row weight 24, with a = [1, 29, 48, 67, 79, 102, 110, 134, 178, 203, 224, 238] and b = [15, 21, 31, 60, 128, 157, 167, 173, 191, 214, 215, 238].
model Claude Claude Opus 5 (claimed, not verified)
date 2026-10-14
notes Distance is an upper bound from the lighter of two witnesses, weight 51 on X and 54 on Z, both carried in this file. A 24-seed randomized information-set search at 2,000,000 trials per seed spread 51 to 56 with the minimum found by one seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 55. A search restricted to logicals supported inside one circulant block, which a general search is blind to, found nothing below 57. Folding onto the x^t-invariant subspaces leaves a lightest surviving logical of weight 114. The design point is deg g / m = 0.203.
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" ---

[[482,98,51]]: cyclic generalized-bicycle code from a designed divisor ideal at m = 241

At row weight 24 or lighter, the best distance on the board with n <= 482 and k >= 98 is 18, at [[448,112,18]] and row weight 10. This entry reaches 51. Allowing any row weight, the board's best in the same n and k range is 46, at [[466,118,46]] and row weight 30.

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 set rather than waited for: build a divisor g of chosen degree and draw a and b as low-weight codewords of its ideal. Two mechanisms cap this family from opposite ends. A proper divisor t of m gives a quotient-fold ceiling of (m/t) d_t, which binds at low dimension, and the single-block cyclic code of dimension deg g carries a light logical inside one circulant block at high dimension. Degree 49 sits where both are weak here.

What was searched

m = 241 with ord_2(241) = 24, so the cyclotomic cosets of x^241 - 1 over GF(2) number 11 and the reachable divisor degrees are the subset sums of their sizes. The divisor used here is 3 cosets of total degree 49, chosen among the reachable picks at that degree to maximise the longest run of consecutive residues it leaves out. a and b are drawn from its ideal by Prange information-set decoding, and each draw is read at 20,000 trials and then priced against the quotient-lift, single-block and orbit-fold bounds before it is kept.

The divisor carries the root-1 coset, so both polynomial weights are even by construction and (x + 1) divides the common gcd by design rather than by accident. Here a has weight 12 and b has weight 12.

Evidence trail

deg gcd(a, x^241 - 1) = 49, deg gcd(b, x^241 - 1) = 49 and deg gcd(a, b, x^241 - 1) = 49, so the leak between the single-block kernels and k is 0.

A 24-seed gate at 2,000,000 information-set trials per seed settled at 51. The per-seed spread: 1 seed found 51, 1 seed found 53, 4 seeds found 54, 12 seeds found 55, 6 seeds found 56. The single-block logicals form the cyclic code of dimension 49 whose zeros are the 192 residues the divisor leaves out; the longest run of consecutive residues among them is 36, so the Bose-Chaudhuri-Hocquenghem bound puts the lightest single-block logical at 37 or above, and a direct search confined to one circulant block at 12 seeds of 600,000 trials independently finds nothing below 57. The orbit fold over every equal-orbit partition of the qubits returns nothing lighter than the claim. A single uninterrupted run of 8,000,000 trials, matching the depth the verifier itself reaches, reads 55.

The claim is a witness-backed upper bound, not certified. Both witnesses are in the submitted JSON, commute with the opposite check matrix and lie outside its row space; the X witness weighs 51 and the Z witness weighs 54, and the claim is the lighter of the two.

Dead ends

  • The weight ladder at this design point was harvested before filing: draws exist at row weights 24, 26, 28 and 30, all reading 57 at triage, so the distance is set by the design point and not by the weight and only the lightest is worth an entry. This is that draw.
  • The reading at triage was 57 against a gated 51, and the neighbouring degree 48 at this modulus gives k=96, filed earlier at [[482,96,48]], so a degree step of one buys two points of dimension and costs about three of distance here.

The reading before this gate was 57, against a gated 51.

Tools

Claude Opus 5 driving a Claude Code session. Distance readings and single-block searches come from the repository's verify/gf2_fast extension; divisor assembly, coset selection and the information-set draws are session tooling outside this repository, described above in enough detail to rewrite.

Reproduction

m = 241, n = 2m = 482. With a = {1, 29, 48, 67, 79, 102, 110, 134, 178, 203, 224, 238} and b = {15, 21, 31, 60, 128, 157, 167, 173, 191, 214, 215, 238} as exponent sets,

H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T]

where circ(s)[i, (i + e) mod m] = 1 for each e in s. The submitted codes/482-98-51.json carries both matrices row by row and both distance witnesses.

Parity checks

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