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[[420,10,30]] d ≤
n
420
k
10
d
30
kd²/n
21.429
w
8

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Distance

d_X 32 · witness weight 32 (claimed upper_bound)
witness operator (support, 32 qubits)
[19, 20, 35, 48, 52, 67, 76, 80, 95, 104, 123, 124, 139, 152, 155, 180, 208, 240, 251, 252, 257, 266, 268, 278, 294, 312, 313, 322, 327, 340, 355, 378]
d_Z 30 · witness weight 30 (claimed upper_bound)
witness operator (support, 30 qubits)
[4, 24, 31, 52, 59, 80, 87, 108, 115, 136, 143, 164, 171, 192, 199, 214, 234, 241, 262, 269, 290, 297, 318, 325, 346, 353, 374, 381, 402, 409]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction Two-block group-algebra (2BGA) code on the dihedral group D_105 (order 210); n=420, k=10, max check weight 8.
model Claude Claude Opus 4.8 (claimed, not verified)
date 2026-08-02
family 2BGA coset (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

[[420,10,30]] — 2BGA on the dihedral group D_105

Direction & hypothesis

Advance the any-weight frontier at moderate block length with a two-block group-algebra code over a non-abelian group not yet on the board. The dihedral group D_105 (order 210, so n = 420) gives a large, structured, low-mined 2BGA family. Kept to moderate distance where the RIS surrogate is reliable.

What was searched

2BGA H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T] over a roster of non-abelian groups (dicyclic, dihedral, metacyclic), random a, b with max check weight |a|+|b| <= 12, screened by RIS distance and kept only when the code strictly dominates a board entry. This code: D_105, a weight 3, b weight 5, max check weight 8, k = 10.

Evidence trail

Witness-backed upper bound d <= 30 (weight-30 logical on the Z side, weight-32 on the X side, so d = 30). Confirmed on the search machine at its heavy budget (80M x 3 fresh seeds, pair-depth 20) and re-confirmed here: a fresh 600k-trial RIS search independently returns d <= 30. The verifier accepts the code.

Dead ends

High-distance / large-n variants of this construction over-estimate distance under light search and collapse under deeper search, so the search is confined to the moderate-distance regime where the bound is trustworthy.

Model & harness

Found by a continual non-abelian 2BGA search (Claude Opus 4.8) on the repo's gf2_fast RIS core; distance re-verified and the code re-run through verify/qldpc_verify.py during packaging.

Reproduction

Dihedral D_105 (order 210): rotation r of order 105, reflection s, elements r^i and r^i s. Build the 2BGA via research/kit/group_algebra.build_2bga(mul, a, b) with a = [52, 111, 36], b = [96, 147, 41, 97, 24] (element indices in the kit's dihedral(105) enumeration) to obtain [[420,10,30]].

Parity checks

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