//! This file generates the Sobol direction vectors used by this crate's //! Sobol sequence. use std::{env, fs::File, io::Write, path::Path}; /// How many components to generate. const NUM_DIMENSIONS: usize = 256; fn main() { let out_dir = env::var("OUT_DIR").unwrap(); let dest_path = Path::new(&out_dir).join("vectors.inc"); let mut f = File::create(&dest_path).unwrap(); // Init direction vectors. let vectors = generate_direction_vectors(NUM_DIMENSIONS); // Write dimensions limit. f.write_all(format!("pub const MAX_DIMENSION: u32 = {};\n", NUM_DIMENSIONS).as_bytes()) .unwrap(); // Write the vectors. f.write_all("pub const VECTORS: &[[u32; 32]] = &[\n".as_bytes()) .unwrap(); for v in vectors.iter() { f.write_all(" [\n".as_bytes()).unwrap(); for n in v.iter() { f.write_all(format!(" 0x{:08x},\n", *n).as_bytes()) .unwrap(); } f.write_all(" ],\n".as_bytes()).unwrap(); } f.write_all("];\n".as_bytes()).unwrap(); } //====================================================================== // The following code and data are adapted from code and data on this webpage: // // http://web.maths.unsw.edu.au/~fkuo/sobol/ // // From these papers: // // S. Joe and F. Y. Kuo, Remark on Algorithm 659: Implementing Sobol's // quasirandom sequence generator, ACM Trans. Math. Softw. 29, 49-57 // (2003) // // S. Joe and F. Y. Kuo, Constructing Sobol sequences with better // two-dimensional projections, SIAM J. Sci. Comput. 30, 2635-2654 (2008) // // The adapted code and data is under the following license: // // Copyright (c) 2008, Frances Y. Kuo and Stephen Joe // All rights reserved. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are // met: // // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // // * Redistributions in binary form must reproduce the above copyright // notice, this list of conditions and the following disclaimer in the // documentation and/or other materials provided with the // distribution. // // * Neither the names of the copyright holders nor the names of the // University of New South Wales and the University of Waikato // and its contributors may be used to endorse or promote products // derived from this software without specific prior written // permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR // PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR // BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, // WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE // OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN // IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. const SOBOL_BITS: usize = 32; pub fn generate_direction_vectors(dimensions: usize) -> Vec<[u32; SOBOL_BITS]> { assert!(dimensions <= (SOBOL_NUMBERS.len() + 1)); let mut vectors = Vec::new(); // Calculate first dimension, which is just the van der Corput sequence. let mut dim_0 = [0u32; SOBOL_BITS]; for i in 0..SOBOL_BITS { dim_0[i] = 1 << (31 - i); } vectors.push(dim_0); // Do the rest of the dimensions. for dim in 1..dimensions { let mut v = [0u32; SOBOL_BITS]; let numbers = &SOBOL_NUMBERS[dim - 1]; let s = numbers.1; let a = numbers.2; let m = numbers.3; if SOBOL_BITS <= s as usize { for i in 0..SOBOL_BITS { v[i] = m[i] << (31 - i); } } else { for i in 0..(s as usize) { v[i] = m[i] << (31 - i); } for i in (s as usize)..SOBOL_BITS { v[i] = v[i - s as usize] ^ (v[i - s as usize] >> s); for k in 1..s { v[i] ^= ((a >> (s - 1 - k)) & 1) * v[i - k as usize]; } } } vectors.push(v); } vectors } /// (d, s, a, m) #[rustfmt::skip] static SOBOL_NUMBERS: [(u32, u32, u32, &[u32]); 1023] = [ (2, 1, 0, &[1]), (3, 2, 1, &[1, 3]), (4, 3, 1, &[1, 3, 1]), (5, 3, 2, &[1, 1, 1]), (6, 4, 1, &[1, 1, 3, 3]), (7, 4, 4, &[1, 3, 5, 13]), (8, 5, 2, &[1, 1, 5, 5, 17]), (9, 5, 4, &[1, 1, 5, 5, 5]), (10, 5, 7, &[1, 1, 7, 11, 19]), (11, 5, 11, &[1, 1, 5, 1, 1]), (12, 5, 13, &[1, 1, 1, 3, 11]), (13, 5, 14, &[1, 3, 5, 5, 31]), (14, 6, 1, &[1, 3, 3, 9, 7, 49]), (15, 6, 13, &[1, 1, 1, 15, 21, 21]), (16, 6, 16, &[1, 3, 1, 13, 27, 49]), (17, 6, 19, &[1, 1, 1, 15, 7, 5]), (18, 6, 22, &[1, 3, 1, 15, 13, 25]), (19, 6, 25, &[1, 1, 5, 5, 19, 61]), (20, 7, 1, &[1, 3, 7, 11, 23, 15, 103]), (21, 7, 4, &[1, 3, 7, 13, 13, 15, 69]), (22, 7, 7, &[1, 1, 3, 13, 7, 35, 63]), (23, 7, 8, &[1, 3, 5, 9, 1, 25, 53]), (24, 7, 14, &[1, 3, 1, 13, 9, 35, 107]), (25, 7, 19, &[1, 3, 1, 5, 27, 61, 31]), (26, 7, 21, &[1, 1, 5, 11, 19, 41, 61]), (27, 7, 28, &[1, 3, 5, 3, 3, 13, 69]), (28, 7, 31, &[1, 1, 7, 13, 1, 19, 1]), (29, 7, 32, &[1, 3, 7, 5, 13, 19, 59]), (30, 7, 37, &[1, 1, 3, 9, 25, 29, 41]), (31, 7, 41, &[1, 3, 5, 13, 23, 1, 55]), (32, 7, 42, &[1, 3, 7, 3, 13, 59, 17]), (33, 7, 50, &[1, 3, 1, 3, 5, 53, 69]), (34, 7, 55, &[1, 1, 5, 5, 23, 33, 13]), (35, 7, 56, &[1, 1, 7, 7, 1, 61, 123]), (36, 7, 59, &[1, 1, 7, 9, 13, 61, 49]), (37, 7, 62, &[1, 3, 3, 5, 3, 55, 33]), (38, 8, 14, &[1, 3, 1, 15, 31, 13, 49, 245]), (39, 8, 21, &[1, 3, 5, 15, 31, 59, 63, 97]), (40, 8, 22, &[1, 3, 1, 11, 11, 11, 77, 249]), (41, 8, 38, &[1, 3, 1, 11, 27, 43, 71, 9]), (42, 8, 47, &[1, 1, 7, 15, 21, 11, 81, 45]), (43, 8, 49, &[1, 3, 7, 3, 25, 31, 65, 79]), (44, 8, 50, &[1, 3, 1, 1, 19, 11, 3, 205]), (45, 8, 52, &[1, 1, 5, 9, 19, 21, 29, 157]), (46, 8, 56, &[1, 3, 7, 11, 1, 33, 89, 185]), (47, 8, 67, &[1, 3, 3, 3, 15, 9, 79, 71]), (48, 8, 70, &[1, 3, 7, 11, 15, 39, 119, 27]), (49, 8, 84, &[1, 1, 3, 1, 11, 31, 97, 225]), (50, 8, 97, &[1, 1, 1, 3, 23, 43, 57, 177]), (51, 8, 103, &[1, 3, 7, 7, 17, 17, 37, 71]), (52, 8, 115, &[1, 3, 1, 5, 27, 63, 123, 213]), (53, 8, 122, &[1, 1, 3, 5, 11, 43, 53, 133]), (54, 9, 8, &[1, 3, 5, 5, 29, 17, 47, 173, 479]), (55, 9, 13, &[1, 3, 3, 11, 3, 1, 109, 9, 69]), (56, 9, 16, &[1, 1, 1, 5, 17, 39, 23, 5, 343]), (57, 9, 22, &[1, 3, 1, 5, 25, 15, 31, 103, 499]), (58, 9, 25, &[1, 1, 1, 11, 11, 17, 63, 105, 183]), (59, 9, 44, &[1, 1, 5, 11, 9, 29, 97, 231, 363]), (60, 9, 47, &[1, 1, 5, 15, 19, 45, 41, 7, 383]), (61, 9, 52, &[1, 3, 7, 7, 31, 19, 83, 137, 221]), (62, 9, 55, &[1, 1, 1, 3, 23, 15, 111, 223, 83]), (63, 9, 59, &[1, 1, 5, 13, 31, 15, 55, 25, 161]), (64, 9, 62, &[1, 1, 3, 13, 25, 47, 39, 87, 257]), (65, 9, 67, &[1, 1, 1, 11, 21, 53, 125, 249, 293]), (66, 9, 74, &[1, 1, 7, 11, 11, 7, 57, 79, 323]), (67, 9, 81, &[1, 1, 5, 5, 17, 13, 81, 3, 131]), (68, 9, 82, &[1, 1, 7, 13, 23, 7, 65, 251, 475]), (69, 9, 87, &[1, 3, 5, 1, 9, 43, 3, 149, 11]), (70, 9, 91, &[1, 1, 3, 13, 31, 13, 13, 255, 487]), (71, 9, 94, &[1, 3, 3, 1, 5, 63, 89, 91, 127]), (72, 9, 103, &[1, 1, 3, 3, 1, 19, 123, 127, 237]), (73, 9, 104, &[1, 1, 5, 7, 23, 31, 37, 243, 289]), (74, 9, 109, &[1, 1, 5, 11, 17, 53, 117, 183, 491]), (75, 9, 122, &[1, 1, 1, 5, 1, 13, 13, 209, 345]), (76, 9, 124, &[1, 1, 3, 15, 1, 57, 115, 7, 33]), (77, 9, 137, &[1, 3, 1, 11, 7, 43, 81, 207, 175]), (78, 9, 138, &[1, 3, 1, 1, 15, 27, 63, 255, 49]), (79, 9, 143, &[1, 3, 5, 3, 27, 61, 105, 171, 305]), (80, 9, 145, &[1, 1, 5, 3, 1, 3, 57, 249, 149]), (81, 9, 152, &[1, 1, 3, 5, 5, 57, 15, 13, 159]), (82, 9, 157, &[1, 1, 1, 11, 7, 11, 105, 141, 225]), (83, 9, 167, &[1, 3, 3, 5, 27, 59, 121, 101, 271]), (84, 9, 173, &[1, 3, 5, 9, 11, 49, 51, 59, 115]), (85, 9, 176, &[1, 1, 7, 1, 23, 45, 125, 71, 419]), (86, 9, 181, &[1, 1, 3, 5, 23, 5, 105, 109, 75]), (87, 9, 182, &[1, 1, 7, 15, 7, 11, 67, 121, 453]), (88, 9, 185, &[1, 3, 7, 3, 9, 13, 31, 27, 449]), (89, 9, 191, &[1, 3, 1, 15, 19, 39, 39, 89, 15]), (90, 9, 194, &[1, 1, 1, 1, 1, 33, 73, 145, 379]), (91, 9, 199, &[1, 3, 1, 15, 15, 43, 29, 13, 483]), (92, 9, 218, &[1, 1, 7, 3, 19, 27, 85, 131, 431]), (93, 9, 220, &[1, 3, 3, 3, 5, 35, 23, 195, 349]), (94, 9, 227, &[1, 3, 3, 7, 9, 27, 39, 59, 297]), (95, 9, 229, &[1, 1, 3, 9, 11, 17, 13, 241, 157]), (96, 9, 230, &[1, 3, 7, 15, 25, 57, 33, 189, 213]), (97, 9, 234, &[1, 1, 7, 1, 9, 55, 73, 83, 217]), (98, 9, 236, &[1, 3, 3, 13, 19, 27, 23, 113, 249]), (99, 9, 241, &[1, 3, 5, 3, 23, 43, 3, 253, 479]), (100, 9, 244, &[1, 1, 5, 5, 11, 5, 45, 117, 217]), (101, 9, 253, &[1, 3, 3, 7, 29, 37, 33, 123, 147]), (102, 10, 4, &[1, 3, 1, 15, 5, 5, 37, 227, 223, 459]), (103, 10, 13, &[1, 1, 7, 5, 5, 39, 63, 255, 135, 487]), (104, 10, 19, &[1, 3, 1, 7, 9, 7, 87, 249, 217, 599]), (105, 10, 22, &[1, 1, 3, 13, 9, 47, 7, 225, 363, 247]), (106, 10, 50, &[1, 3, 7, 13, 19, 13, 9, 67, 9, 737]), (107, 10, 55, &[1, 3, 5, 5, 19, 59, 7, 41, 319, 677]), (108, 10, 64, &[1, 1, 5, 3, 31, 63, 15, 43, 207, 789]), (109, 10, 69, &[1, 1, 7, 9, 13, 39, 3, 47, 497, 169]), (110, 10, 98, &[1, 3, 1, 7, 21, 17, 97, 19, 415, 905]), (111, 10, 107, &[1, 3, 7, 1, 3, 31, 71, 111, 165, 127]), (112, 10, 115, &[1, 1, 5, 11, 1, 61, 83, 119, 203, 847]), (113, 10, 121, &[1, 3, 3, 13, 9, 61, 19, 97, 47, 35]), (114, 10, 127, &[1, 1, 7, 7, 15, 29, 63, 95, 417, 469]), (115, 10, 134, &[1, 3, 1, 9, 25, 9, 71, 57, 213, 385]), (116, 10, 140, &[1, 3, 5, 13, 31, 47, 101, 57, 39, 341]), (117, 10, 145, &[1, 1, 3, 3, 31, 57, 125, 173, 365, 551]), (118, 10, 152, &[1, 3, 7, 1, 13, 57, 67, 157, 451, 707]), (119, 10, 158, &[1, 1, 1, 7, 21, 13, 105, 89, 429, 965]), (120, 10, 161, &[1, 1, 5, 9, 17, 51, 45, 119, 157, 141]), (121, 10, 171, &[1, 3, 7, 7, 13, 45, 91, 9, 129, 741]), (122, 10, 181, &[1, 3, 7, 1, 23, 57, 67, 141, 151, 571]), (123, 10, 194, &[1, 1, 3, 11, 17, 47, 93, 107, 375, 157]), (124, 10, 199, &[1, 3, 3, 5, 11, 21, 43, 51, 169, 915]), (125, 10, 203, &[1, 1, 5, 3, 15, 55, 101, 67, 455, 625]), (126, 10, 208, &[1, 3, 5, 9, 1, 23, 29, 47, 345, 595]), (127, 10, 227, &[1, 3, 7, 7, 5, 49, 29, 155, 323, 589]), (128, 10, 242, &[1, 3, 3, 7, 5, 41, 127, 61, 261, 717]), (129, 10, 251, &[1, 3, 7, 7, 17, 23, 117, 67, 129, 1009]), (130, 10, 253, &[1, 1, 3, 13, 11, 39, 21, 207, 123, 305]), (131, 10, 265, &[1, 1, 3, 9, 29, 3, 95, 47, 231, 73]), (132, 10, 266, &[1, 3, 1, 9, 1, 29, 117, 21, 441, 259]), (133, 10, 274, &[1, 3, 1, 13, 21, 39, 125, 211, 439, 723]), (134, 10, 283, &[1, 1, 7, 3, 17, 63, 115, 89, 49, 773]), (135, 10, 289, &[1, 3, 7, 13, 11, 33, 101, 107, 63, 73]), (136, 10, 295, &[1, 1, 5, 5, 13, 57, 63, 135, 437, 177]), (137, 10, 301, &[1, 1, 3, 7, 27, 63, 93, 47, 417, 483]), (138, 10, 316, &[1, 1, 3, 1, 23, 29, 1, 191, 49, 23]), (139, 10, 319, &[1, 1, 3, 15, 25, 55, 9, 101, 219, 607]), (140, 10, 324, &[1, 3, 1, 7, 7, 19, 51, 251, 393, 307]), (141, 10, 346, &[1, 3, 3, 3, 25, 55, 17, 75, 337, 3]), (142, 10, 352, &[1, 1, 1, 13, 25, 17, 65, 45, 479, 413]), (143, 10, 361, &[1, 1, 7, 7, 27, 49, 99, 161, 213, 727]), (144, 10, 367, &[1, 3, 5, 1, 23, 5, 43, 41, 251, 857]), (145, 10, 382, &[1, 3, 3, 7, 11, 61, 39, 87, 383, 835]), (146, 10, 395, &[1, 1, 3, 15, 13, 7, 29, 7, 505, 923]), (147, 10, 398, &[1, 3, 7, 1, 5, 31, 47, 157, 445, 501]), (148, 10, 400, &[1, 1, 3, 7, 1, 43, 9, 147, 115, 605]), (149, 10, 412, &[1, 3, 3, 13, 5, 1, 119, 211, 455, 1001]), (150, 10, 419, &[1, 1, 3, 5, 13, 19, 3, 243, 75, 843]), (151, 10, 422, &[1, 3, 7, 7, 1, 19, 91, 249, 357, 589]), (152, 10, 426, &[1, 1, 1, 9, 1, 25, 109, 197, 279, 411]), (153, 10, 428, &[1, 3, 1, 15, 23, 57, 59, 135, 191, 75]), (154, 10, 433, &[1, 1, 5, 15, 29, 21, 39, 253, 383, 349]), (155, 10, 446, &[1, 3, 3, 5, 19, 45, 61, 151, 199, 981]), (156, 10, 454, &[1, 3, 5, 13, 9, 61, 107, 141, 141, 1]), (157, 10, 457, &[1, 3, 1, 11, 27, 25, 85, 105, 309, 979]), (158, 10, 472, &[1, 3, 3, 11, 19, 7, 115, 223, 349, 43]), (159, 10, 493, &[1, 1, 7, 9, 21, 39, 123, 21, 275, 927]), (160, 10, 505, &[1, 1, 7, 13, 15, 41, 47, 243, 303, 437]), (161, 10, 508, &[1, 1, 1, 7, 7, 3, 15, 99, 409, 719]), (162, 11, 2, &[1, 3, 3, 15, 27, 49, 113, 123, 113, 67, 469]), (163, 11, 11, &[1, 3, 7, 11, 3, 23, 87, 169, 119, 483, 199]), (164, 11, 21, &[1, 1, 5, 15, 7, 17, 109, 229, 179, 213, 741]), (165, 11, 22, &[1, 1, 5, 13, 11, 17, 25, 135, 403, 557, 1433]), (166, 11, 35, &[1, 3, 1, 1, 1, 61, 67, 215, 189, 945, 1243]), (167, 11, 49, &[1, 1, 7, 13, 17, 33, 9, 221, 429, 217, 1679]), (168, 11, 50, &[1, 1, 3, 11, 27, 3, 15, 93, 93, 865, 1049]), (169, 11, 56, &[1, 3, 7, 7, 25, 41, 121, 35, 373, 379, 1547]), (170, 11, 61, &[1, 3, 3, 9, 11, 35, 45, 205, 241, 9, 59]), (171, 11, 70, &[1, 3, 1, 7, 3, 51, 7, 177, 53, 975, 89]), (172, 11, 74, &[1, 1, 3, 5, 27, 1, 113, 231, 299, 759, 861]), (173, 11, 79, &[1, 3, 3, 15, 25, 29, 5, 255, 139, 891, 2031]), (174, 11, 84, &[1, 3, 1, 1, 13, 9, 109, 193, 419, 95, 17]), (175, 11, 88, &[1, 1, 7, 9, 3, 7, 29, 41, 135, 839, 867]), (176, 11, 103, &[1, 1, 7, 9, 25, 49, 123, 217, 113, 909, 215]), (177, 11, 104, &[1, 1, 7, 3, 23, 15, 43, 133, 217, 327, 901]), (178, 11, 112, &[1, 1, 3, 3, 13, 53, 63, 123, 477, 711, 1387]), (179, 11, 115, &[1, 1, 3, 15, 7, 29, 75, 119, 181, 957, 247]), (180, 11, 117, &[1, 1, 1, 11, 27, 25, 109, 151, 267, 99, 1461]), (181, 11, 122, &[1, 3, 7, 15, 5, 5, 53, 145, 11, 725, 1501]), (182, 11, 134, &[1, 3, 7, 1, 9, 43, 71, 229, 157, 607, 1835]), (183, 11, 137, &[1, 3, 3, 13, 25, 1, 5, 27, 471, 349, 127]), (184, 11, 146, &[1, 1, 1, 1, 23, 37, 9, 221, 269, 897, 1685]), (185, 11, 148, &[1, 1, 3, 3, 31, 29, 51, 19, 311, 553, 1969]), (186, 11, 157, &[1, 3, 7, 5, 5, 55, 17, 39, 475, 671, 1529]), (187, 11, 158, &[1, 1, 7, 1, 1, 35, 47, 27, 437, 395, 1635]), (188, 11, 162, &[1, 1, 7, 3, 13, 23, 43, 135, 327, 139, 389]), (189, 11, 164, &[1, 3, 7, 3, 9, 25, 91, 25, 429, 219, 513]), (190, 11, 168, &[1, 1, 3, 5, 13, 29, 119, 201, 277, 157, 2043]), (191, 11, 173, &[1, 3, 5, 3, 29, 57, 13, 17, 167, 739, 1031]), (192, 11, 185, &[1, 3, 3, 5, 29, 21, 95, 27, 255, 679, 1531]), (193, 11, 186, &[1, 3, 7, 15, 9, 5, 21, 71, 61, 961, 1201]), (194, 11, 191, &[1, 3, 5, 13, 15, 57, 33, 93, 459, 867, 223]), (195, 11, 193, &[1, 1, 1, 15, 17, 43, 127, 191, 67, 177, 1073]), (196, 11, 199, &[1, 1, 1, 15, 23, 7, 21, 199, 75, 293, 1611]), (197, 11, 213, &[1, 3, 7, 13, 15, 39, 21, 149, 65, 741, 319]), (198, 11, 214, &[1, 3, 7, 11, 23, 13, 101, 89, 277, 519, 711]), (199, 11, 220, &[1, 3, 7, 15, 19, 27, 85, 203, 441, 97, 1895]), (200, 11, 227, &[1, 3, 1, 3, 29, 25, 21, 155, 11, 191, 197]), (201, 11, 236, &[1, 1, 7, 5, 27, 11, 81, 101, 457, 675, 1687]), (202, 11, 242, &[1, 3, 1, 5, 25, 5, 65, 193, 41, 567, 781]), (203, 11, 251, &[1, 3, 1, 5, 11, 15, 113, 77, 411, 695, 1111]), (204, 11, 256, &[1, 1, 3, 9, 11, 53, 119, 171, 55, 297, 509]), (205, 11, 259, &[1, 1, 1, 1, 11, 39, 113, 139, 165, 347, 595]), (206, 11, 265, &[1, 3, 7, 11, 9, 17, 101, 13, 81, 325, 1733]), (207, 11, 266, &[1, 3, 1, 1, 21, 43, 115, 9, 113, 907, 645]), (208, 11, 276, &[1, 1, 7, 3, 9, 25, 117, 197, 159, 471, 475]), (209, 11, 292, &[1, 3, 1, 9, 11, 21, 57, 207, 485, 613, 1661]), (210, 11, 304, &[1, 1, 7, 7, 27, 55, 49, 223, 89, 85, 1523]), (211, 11, 310, &[1, 1, 5, 3, 19, 41, 45, 51, 447, 299, 1355]), (212, 11, 316, &[1, 3, 1, 13, 1, 33, 117, 143, 313, 187, 1073]), (213, 11, 319, &[1, 1, 7, 7, 5, 11, 65, 97, 377, 377, 1501]), (214, 11, 322, &[1, 3, 1, 1, 21, 35, 95, 65, 99, 23, 1239]), (215, 11, 328, &[1, 1, 5, 9, 3, 37, 95, 167, 115, 425, 867]), (216, 11, 334, &[1, 3, 3, 13, 1, 37, 27, 189, 81, 679, 773]), (217, 11, 339, &[1, 1, 3, 11, 1, 61, 99, 233, 429, 969, 49]), (218, 11, 341, &[1, 1, 1, 7, 25, 63, 99, 165, 245, 793, 1143]), (219, 11, 345, &[1, 1, 5, 11, 11, 43, 55, 65, 71, 283, 273]), (220, 11, 346, &[1, 1, 5, 5, 9, 3, 101, 251, 355, 379, 1611]), (221, 11, 362, &[1, 1, 1, 15, 21, 63, 85, 99, 49, 749, 1335]), (222, 11, 367, &[1, 1, 5, 13, 27, 9, 121, 43, 255, 715, 289]), (223, 11, 372, &[1, 3, 1, 5, 27, 19, 17, 223, 77, 571, 1415]), (224, 11, 375, &[1, 1, 5, 3, 13, 59, 125, 251, 195, 551, 1737]), (225, 11, 376, &[1, 3, 3, 15, 13, 27, 49, 105, 389, 971, 755]), (226, 11, 381, &[1, 3, 5, 15, 23, 43, 35, 107, 447, 763, 253]), (227, 11, 385, &[1, 3, 5, 11, 21, 3, 17, 39, 497, 407, 611]), (228, 11, 388, &[1, 1, 7, 13, 15, 31, 113, 17, 23, 507, 1995]), (229, 11, 392, &[1, 1, 7, 15, 3, 15, 31, 153, 423, 79, 503]), (230, 11, 409, &[1, 1, 7, 9, 19, 25, 23, 171, 505, 923, 1989]), (231, 11, 415, &[1, 1, 5, 9, 21, 27, 121, 223, 133, 87, 697]), (232, 11, 416, &[1, 1, 5, 5, 9, 19, 107, 99, 319, 765, 1461]), (233, 11, 421, &[1, 1, 3, 3, 19, 25, 3, 101, 171, 729, 187]), (234, 11, 428, &[1, 1, 3, 1, 13, 23, 85, 93, 291, 209, 37]), (235, 11, 431, &[1, 1, 1, 15, 25, 25, 77, 253, 333, 947, 1073]), (236, 11, 434, &[1, 1, 3, 9, 17, 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47, 491, 2143, 1797]), (759, 13, 1828, &[1, 3, 3, 3, 11, 39, 21, 135, 445, 259, 607, 3811, 5449]), (760, 13, 1831, &[1, 1, 7, 9, 11, 25, 113, 251, 395, 317, 317, 91, 1979]), (761, 13, 1837, &[1, 3, 1, 9, 3, 21, 103, 133, 389, 943, 1235, 1749, 7063]), (762, 13, 1838, &[1, 1, 3, 7, 1, 11, 5, 15, 497, 477, 479, 3079, 6969]), (763, 13, 1840, &[1, 1, 3, 3, 15, 39, 105, 131, 475, 465, 181, 865, 3813]), (764, 13, 1845, &[1, 1, 7, 9, 19, 63, 123, 131, 415, 525, 457, 2471, 3135]), (765, 13, 1863, &[1, 3, 7, 15, 25, 35, 123, 45, 341, 805, 485, 4049, 7065]), (766, 13, 1864, &[1, 1, 1, 5, 29, 9, 47, 227, 51, 867, 1873, 1593, 2271]), (767, 13, 1867, &[1, 1, 7, 15, 31, 9, 71, 117, 285, 711, 837, 1435, 6275]), (768, 13, 1870, &[1, 3, 1, 1, 5, 19, 79, 25, 301, 415, 1871, 645, 3251]), (769, 13, 1877, &[1, 3, 1, 3, 17, 51, 99, 185, 447, 43, 523, 219, 429]), (770, 13, 1881, &[1, 3, 1, 13, 29, 13, 51, 93, 7, 995, 757, 3017, 6865]), (771, 13, 1884, &[1, 1, 3, 15, 7, 25, 75, 17, 155, 981, 1231, 1229, 1995]), (772, 13, 1903, &[1, 3, 5, 3, 27, 45, 71, 73, 225, 763, 377, 1139, 2863]), (773, 13, 1917, &[1, 1, 3, 1, 1, 39, 69, 113, 29, 371, 1051, 793, 3749]), (774, 13, 1918, &[1, 1, 3, 13, 23, 61, 27, 183, 307, 431, 1345, 2757, 4031]), (775, 13, 1922, &[1, 3, 7, 5, 5, 59, 117, 197, 303, 721, 877, 723, 1601]), (776, 13, 1924, &[1, 3, 5, 1, 27, 33, 99, 237, 485, 711, 665, 3077, 5105]), (777, 13, 1928, &[1, 1, 3, 1, 13, 9, 103, 201, 23, 951, 2029, 165, 2093]), (778, 13, 1931, &[1, 3, 5, 13, 5, 29, 55, 85, 221, 677, 611, 3613, 4567]), (779, 13, 1951, &[1, 1, 1, 1, 7, 61, 9, 233, 261, 561, 953, 4023, 2443]), (780, 13, 1952, &[1, 3, 3, 13, 1, 17, 103, 71, 223, 213, 833, 1747, 6999]), (781, 13, 1957, &[1, 3, 5, 15, 25, 53, 57, 187, 25, 695, 1207, 4089, 2877]), (782, 13, 1958, &[1, 1, 7, 1, 7, 31, 87, 129, 493, 519, 1555, 1155, 4637]), (783, 13, 1964, &[1, 1, 1, 15, 21, 17, 23, 29, 19, 255, 927, 1791, 3093]), (784, 13, 1967, &[1, 1, 3, 9, 17, 33, 95, 129, 175, 461, 287, 2633, 2325]), (785, 13, 1970, &[1, 3, 5, 7, 23, 19, 63, 209, 249, 583, 1373, 2039, 2225]), (786, 13, 1972, &[1, 3, 3, 5, 5, 19, 79, 241, 459, 355, 1455, 3313, 3639]), (787, 13, 1994, &[1, 1, 7, 9, 21, 41, 97, 119, 129, 769, 1541, 3495, 7741]), (788, 13, 2002, &[1, 1, 7, 11, 9, 29, 35, 255, 141, 937, 1763, 41, 1393]), (789, 13, 2007, &[1, 3, 7, 1, 13, 51, 61, 157, 177, 847, 1829, 3539, 285]), (790, 13, 2008, &[1, 1, 1, 15, 21, 13, 9, 55, 397, 19, 1495, 1255, 7235]), (791, 13, 2023, &[1, 1, 7, 7, 25, 37, 53, 237, 319, 197, 269, 1205, 1485]), (792, 13, 2030, &[1, 1, 5, 15, 23, 17, 35, 247, 323, 807, 233, 3681, 4407]), (793, 13, 2035, &[1, 1, 3, 7, 9, 59, 85, 105, 493, 763, 1639, 391, 1451]), (794, 13, 2038, &[1, 3, 3, 9, 15, 33, 5, 253, 129, 625, 1527, 2793, 6057]), (795, 13, 2042, &[1, 3, 1, 1, 7, 47, 21, 161, 235, 83, 397, 3563, 5953]), (796, 13, 2047, &[1, 3, 7, 11, 3, 41, 25, 117, 375, 779, 1297, 3715, 8117]), (797, 13, 2051, &[1, 1, 3, 7, 31, 19, 103, 173, 475, 189, 2035, 2921, 1107]), (798, 13, 2058, &[1, 1, 7, 3, 25, 7, 93, 255, 307, 113, 1893, 2233, 6919]), (799, 13, 2060, &[1, 3, 5, 15, 9, 57, 79, 143, 165, 5, 1389, 193, 693]), (800, 13, 2071, &[1, 3, 5, 1, 29, 45, 91, 49, 189, 461, 439, 1283, 7835]), (801, 13, 2084, &[1, 1, 3, 13, 11, 61, 41, 231, 373, 695, 395, 915, 5393]), (802, 13, 2087, &[1, 3, 7, 11, 5, 51, 67, 53, 483, 95, 1943, 247, 5653]), (803, 13, 2099, &[1, 3, 7, 5, 5, 57, 45, 235, 137, 793, 1069, 1661, 1557]), (804, 13, 2108, &[1, 3, 5, 3, 25, 55, 103, 177, 81, 861, 1151, 143, 7655]), (805, 13, 2111, &[1, 1, 3, 1, 21, 41, 67, 131, 253, 431, 1269, 3181, 3429]), (806, 13, 2120, &[1, 3, 1, 1, 21, 7, 77, 221, 257, 663, 71, 2949, 2481]), (807, 13, 2128, &[1, 3, 5, 3, 3, 23, 45, 107, 299, 739, 1013, 3, 3165]), (808, 13, 2138, &[1, 1, 5, 1, 3, 37, 109, 37, 243, 983, 1221, 1691, 3869]), (809, 13, 2143, &[1, 1, 5, 5, 31, 7, 5, 193, 397, 867, 1495, 3435, 7441]), (810, 13, 2144, &[1, 1, 1, 1, 17, 59, 97, 233, 389, 597, 1013, 1631, 483]), (811, 13, 2153, &[1, 1, 1, 11, 7, 41, 107, 53, 111, 125, 1513, 1921, 7647]), (812, 13, 2156, &[1, 3, 3, 3, 31, 29, 117, 3, 365, 971, 1139, 2123, 5913]), (813, 13, 2162, &[1, 1, 1, 13, 23, 3, 1, 167, 475, 639, 1811, 3841, 3081]), (814, 13, 2167, &[1, 1, 5, 3, 5, 47, 65, 123, 275, 783, 95, 119, 7591]), (815, 13, 2178, &[1, 3, 1, 15, 13, 33, 93, 237, 467, 431, 705, 4013, 4035]), (816, 13, 2183, &[1, 3, 5, 1, 19, 7, 101, 231, 155, 737, 1381, 3343, 2051]), (817, 13, 2202, &[1, 1, 5, 9, 15, 49, 45, 163, 433, 765, 2031, 201, 2589]), (818, 13, 2211, &[1, 3, 7, 9, 19, 41, 31, 89, 93, 623, 105, 745, 4409]), (819, 13, 2214, &[1, 1, 5, 1, 11, 45, 127, 85, 389, 439, 829, 477, 7965]), (820, 13, 2223, &[1, 3, 3, 15, 13, 41, 1, 207, 435, 585, 311, 1725, 2737]), (821, 13, 2225, &[1, 3, 3, 3, 13, 49, 21, 31, 197, 799, 1411, 2959, 7133]), (822, 13, 2232, &[1, 3, 1, 3, 7, 43, 9, 141, 133, 579, 1059, 93, 957]), (823, 13, 2237, &[1, 3, 7, 1, 15, 51, 23, 213, 381, 851, 699, 2261, 3419]), (824, 13, 2257, &[1, 3, 5, 9, 25, 35, 67, 141, 35, 409, 1423, 365, 1645]), (825, 13, 2260, &[1, 3, 3, 11, 15, 33, 27, 181, 93, 87, 1761, 3511, 1353]), (826, 13, 2267, &[1, 3, 5, 3, 25, 63, 111, 137, 321, 819, 705, 1547, 7271]), (827, 13, 2274, &[1, 3, 1, 1, 5, 57, 99, 59, 411, 757, 1371, 3953, 3695]), (828, 13, 2276, &[1, 3, 5, 11, 11, 21, 25, 147, 239, 455, 709, 953, 7175]), (829, 13, 2285, &[1, 3, 3, 15, 5, 53, 91, 205, 341, 63, 723, 1565, 7135]), (830, 13, 2288, &[1, 1, 7, 15, 11, 21, 99, 79, 63, 593, 2007, 3629, 5271]), (831, 13, 2293, &[1, 3, 3, 1, 9, 21, 45, 175, 453, 435, 1855, 2649, 6959]), (832, 13, 2294, &[1, 1, 3, 15, 15, 33, 121, 121, 251, 431, 1127, 3305, 4199]), (833, 13, 2297, &[1, 1, 1, 9, 31, 15, 71, 29, 345, 391, 1159, 2809, 345]), (834, 13, 2303, &[1, 3, 7, 1, 23, 29, 95, 151, 327, 727, 647, 1623, 2971]), (835, 13, 2308, &[1, 1, 7, 7, 9, 29, 79, 91, 127, 909, 1293, 1315, 5315]), (836, 13, 2311, &[1, 1, 5, 11, 13, 37, 89, 73, 149, 477, 1909, 3343, 525]), (837, 13, 2318, &[1, 3, 5, 7, 5, 59, 55, 255, 223, 459, 2027, 237, 4205]), (838, 13, 2323, &[1, 1, 1, 7, 27, 11, 95, 65, 325, 835, 907, 3801, 3787]), (839, 13, 2332, &[1, 1, 1, 11, 27, 33, 99, 175, 51, 913, 331, 1851, 4133]), (840, 13, 2341, &[1, 3, 5, 5, 13, 37, 31, 99, 273, 409, 1827, 3845, 5491]), (841, 13, 2345, &[1, 1, 3, 7, 23, 19, 107, 85, 283, 523, 509, 451, 421]), (842, 13, 2348, &[1, 3, 5, 7, 13, 9, 51, 81, 87, 619, 61, 2803, 5271]), (843, 13, 2354, &[1, 1, 1, 15, 9, 45, 35, 219, 401, 271, 953, 649, 6847]), (844, 13, 2368, &[1, 1, 7, 11, 9, 45, 17, 219, 169, 837, 1483, 1605, 2901]), (845, 13, 2377, &[1, 1, 7, 7, 21, 43, 37, 33, 291, 359, 71, 2899, 7037]), (846, 13, 2380, &[1, 3, 3, 13, 31, 53, 37, 15, 149, 949, 551, 3445, 5455]), (847, 13, 2383, &[1, 3, 1, 5, 19, 45, 81, 223, 193, 439, 2047, 3879, 789]), (848, 13, 2388, &[1, 1, 7, 3, 11, 63, 35, 61, 255, 563, 459, 2991, 3359]), (849, 13, 2395, &[1, 1, 5, 9, 13, 49, 47, 185, 239, 221, 1533, 3635, 2045]), (850, 13, 2397, &[1, 3, 7, 3, 25, 37, 127, 223, 51, 357, 483, 3837, 6873]), (851, 13, 2401, &[1, 1, 7, 9, 31, 37, 113, 31, 387, 833, 1243, 1543, 5535]), (852, 13, 2411, &[1, 3, 1, 9, 23, 59, 119, 221, 73, 185, 2007, 2885, 2563]), (853, 13, 2413, &[1, 1, 1, 13, 7, 33, 53, 179, 67, 185, 1541, 1807, 4659]), (854, 13, 2419, &[1, 3, 1, 11, 31, 37, 23, 215, 269, 357, 207, 645, 4219]), (855, 13, 2435, &[1, 3, 3, 13, 19, 27, 107, 55, 91, 71, 1695, 1815, 89]), (856, 13, 2442, &[1, 1, 3, 15, 3, 19, 35, 247, 49, 529, 1523, 3317, 6151]), (857, 13, 2455, &[1, 1, 7, 7, 23, 25, 107, 139, 483, 503, 1277, 243, 7879]), (858, 13, 2472, &[1, 3, 3, 13, 3, 15, 11, 197, 135, 839, 985, 275, 5527]), (859, 13, 2478, &[1, 3, 5, 3, 25, 47, 95, 21, 113, 307, 1001, 3065, 295]), (860, 13, 2490, &[1, 1, 3, 9, 19, 19, 99, 213, 363, 449, 735, 2851, 2521]), (861, 13, 2507, &[1, 1, 3, 9, 5, 49, 63, 61, 157, 857, 497, 2801, 6987]), (862, 13, 2509, &[1, 1, 1, 9, 1, 41, 109, 119, 499, 939, 867, 3675, 8023]), (863, 13, 2517, &[1, 3, 1, 1, 13, 33, 109, 123, 289, 3, 1271, 2773, 4265]), (864, 13, 2524, &[1, 3, 1, 11, 9, 57, 83, 221, 95, 43, 1189, 457, 7133]), (865, 13, 2528, &[1, 1, 7, 3, 11, 49, 33, 219, 229, 289, 685, 3359, 4495]), (866, 13, 2531, &[1, 3, 1, 3, 19, 43, 67, 193, 41, 771, 407, 81, 3891]), (867, 13, 2538, &[1, 1, 7, 11, 5, 29, 51, 175, 297, 539, 1, 2245, 6439]), (868, 13, 2545, &[1, 3, 7, 15, 21, 33, 117, 183, 511, 489, 1283, 3281, 5979]), (869, 13, 2546, &[1, 3, 7, 5, 9, 3, 125, 147, 359, 549, 369, 3049, 2405]), (870, 13, 2555, &[1, 3, 5, 7, 19, 5, 65, 97, 483, 377, 1523, 1457, 2995]), (871, 13, 2557, &[1, 1, 5, 1, 11, 21, 41, 113, 277, 131, 1475, 1043, 2367]), (872, 13, 2564, &[1, 3, 3, 1, 15, 17, 101, 69, 443, 865, 817, 1421, 5231]), (873, 13, 2573, &[1, 1, 3, 3, 3, 55, 95, 99, 75, 195, 1929, 3931, 5855]), (874, 13, 2579, &[1, 3, 1, 3, 19, 23, 93, 213, 241, 551, 1307, 585, 7729]), (875, 13, 2592, &[1, 3, 1, 11, 23, 15, 53, 249, 467, 519, 95, 741, 409]), (876, 13, 2598, &[1, 1, 1, 15, 29, 37, 43, 203, 233, 877, 77, 1933, 2729]), (877, 13, 2607, &[1, 3, 7, 11, 27, 39, 43, 161, 255, 15, 1463, 833, 495]), (878, 13, 2612, &[1, 1, 7, 11, 3, 53, 81, 67, 375, 823, 1903, 3061, 395]), (879, 13, 2619, &[1, 1, 1, 1, 15, 37, 93, 233, 247, 501, 1321, 3275, 5409]), (880, 13, 2621, &[1, 3, 3, 7, 7, 11, 5, 105, 139, 983, 1239, 531, 3881]), (881, 13, 2627, &[1, 1, 5, 3, 19, 49, 107, 227, 361, 101, 355, 2649, 7383]), (882, 13, 2633, &[1, 1, 7, 5, 25, 41, 101, 121, 209, 293, 1937, 2259, 5557]), (883, 13, 2636, &[1, 1, 3, 7, 7, 1, 9, 13, 463, 1019, 995, 3159, 107]), (884, 13, 2642, &[1, 3, 5, 11, 5, 35, 127, 97, 261, 789, 807, 807, 6257]), (885, 13, 2654, &[1, 1, 7, 5, 11, 13, 45, 91, 417, 101, 1973, 3645, 2107]), (886, 13, 2660, &[1, 1, 3, 7, 5, 63, 57, 49, 203, 157, 115, 1393, 8117]), (887, 13, 2669, &[1, 3, 5, 5, 3, 43, 15, 155, 127, 489, 1165, 3701, 4867]), (888, 13, 2675, &[1, 1, 7, 7, 29, 29, 69, 215, 415, 367, 371, 1901, 6075]), (889, 13, 2684, &[1, 1, 1, 3, 11, 33, 89, 149, 433, 705, 1437, 1597, 505]), (890, 13, 2694, &[1, 3, 5, 1, 13, 37, 19, 119, 5, 581, 2037, 1633, 2099]), (891, 13, 2703, &[1, 3, 7, 13, 5, 49, 103, 245, 215, 515, 133, 2007, 1933]), (892, 13, 2706, &[1, 3, 1, 9, 1, 3, 25, 197, 253, 387, 1683, 2267, 221]), (893, 13, 2712, &[1, 3, 5, 15, 21, 9, 73, 201, 405, 999, 437, 3877, 6045]), (894, 13, 2715, &[1, 1, 3, 1, 31, 55, 25, 83, 421, 395, 1807, 2129, 7797]), (895, 13, 2722, &[1, 1, 3, 1, 23, 21, 121, 183, 125, 347, 143, 3685, 4317]), (896, 13, 2727, &[1, 3, 3, 3, 17, 45, 17, 223, 267, 795, 1815, 1309, 155]), (897, 13, 2734, &[1, 1, 1, 15, 17, 59, 5, 133, 15, 715, 1503, 153, 2887]), (898, 13, 2742, &[1, 1, 1, 1, 27, 13, 119, 77, 243, 995, 1851, 3719, 4695]), (899, 13, 2745, &[1, 3, 1, 5, 31, 49, 43, 165, 49, 609, 1265, 1141, 505]), (900, 13, 2751, &[1, 1, 7, 13, 11, 63, 21, 253, 229, 585, 1543, 3719, 4141]), (901, 13, 2766, &[1, 3, 7, 11, 23, 27, 17, 131, 295, 895, 1493, 1411, 3247]), (902, 13, 2768, &[1, 1, 5, 9, 29, 7, 97, 15, 113, 445, 859, 1483, 1121]), (903, 13, 2780, &[1, 3, 1, 9, 13, 49, 99, 107, 323, 201, 681, 3071, 5281]), (904, 13, 2790, &[1, 1, 1, 15, 9, 19, 61, 161, 7, 87, 587, 2199, 2811]), (905, 13, 2794, &[1, 3, 3, 15, 15, 19, 95, 45, 299, 829, 981, 3479, 487]), (906, 13, 2796, &[1, 1, 1, 9, 3, 37, 7, 19, 227, 13, 397, 513, 1257]), (907, 13, 2801, &[1, 1, 5, 15, 15, 13, 17, 111, 135, 929, 1145, 811, 1801]), (908, 13, 2804, &[1, 3, 1, 3, 27, 57, 31, 19, 279, 103, 693, 631, 3409]), (909, 13, 2807, &[1, 1, 1, 1, 15, 13, 67, 83, 23, 799, 1735, 2063, 3363]), (910, 13, 2816, &[1, 3, 3, 7, 3, 1, 61, 31, 41, 533, 2025, 4067, 6963]), (911, 13, 2821, &[1, 1, 5, 7, 17, 27, 81, 79, 107, 205, 29, 97, 4883]), (912, 13, 2831, &[1, 1, 1, 5, 19, 49, 91, 201, 283, 949, 651, 3819, 5073]), (913, 13, 2834, &[1, 1, 7, 9, 11, 13, 73, 197, 37, 219, 1931, 3369, 6017]), (914, 13, 2839, &[1, 1, 7, 15, 11, 7, 75, 205, 7, 819, 399, 661, 6487]), (915, 13, 2845, &[1, 3, 3, 3, 27, 37, 95, 41, 307, 165, 1077, 3485, 563]), (916, 13, 2852, &[1, 3, 5, 3, 21, 49, 57, 179, 109, 627, 1789, 431, 2941]), (917, 13, 2856, &[1, 1, 7, 5, 11, 19, 43, 137, 149, 679, 1543, 245, 1381]), (918, 13, 2861, &[1, 3, 5, 5, 15, 3, 69, 81, 135, 159, 1363, 3401, 6355]), (919, 13, 2873, &[1, 3, 5, 1, 9, 61, 49, 53, 319, 25, 1647, 1297, 615]), (920, 13, 2874, &[1, 3, 5, 11, 31, 43, 9, 101, 71, 919, 335, 3147, 5823]), (921, 13, 2888, &[1, 3, 1, 1, 15, 5, 29, 109, 511, 945, 867, 3677, 6915]), (922, 13, 2893, &[1, 3, 3, 15, 17, 49, 91, 111, 215, 29, 1879, 97, 2505]), (923, 13, 2894, &[1, 3, 1, 13, 19, 61, 11, 111, 163, 777, 533, 1113, 5339]), (924, 13, 2902, &[1, 1, 7, 9, 17, 55, 117, 91, 455, 289, 557, 913, 4455]), (925, 13, 2917, &[1, 3, 1, 7, 25, 19, 123, 37, 1, 277, 717, 2965, 4469]), (926, 13, 2921, &[1, 3, 7, 3, 19, 23, 87, 235, 209, 457, 2041, 2893, 1805]), (927, 13, 2922, &[1, 3, 3, 5, 5, 43, 23, 61, 351, 791, 59, 2009, 2909]), (928, 13, 2929, &[1, 1, 3, 7, 5, 1, 27, 231, 385, 257, 1261, 2701, 1807]), (929, 13, 2935, &[1, 3, 1, 1, 27, 19, 87, 253, 131, 685, 1743, 3983, 2651]), (930, 13, 2946, &[1, 3, 7, 11, 21, 17, 11, 81, 191, 641, 1821, 3005, 7251]), (931, 13, 2951, &[1, 3, 3, 5, 15, 31, 41, 213, 55, 931, 1953, 49, 6037]), (932, 13, 2957, &[1, 1, 7, 15, 7, 27, 65, 223, 113, 79, 1875, 911, 5445]), (933, 13, 2960, &[1, 3, 7, 7, 23, 55, 51, 167, 495, 25, 1585, 3447, 799]), (934, 13, 2966, &[1, 1, 3, 7, 27, 15, 95, 193, 337, 415, 975, 3085, 967]), (935, 13, 2972, &[1, 1, 7, 15, 19, 7, 93, 41, 433, 551, 401, 3169, 3971]), (936, 13, 2976, &[1, 1, 7, 11, 13, 15, 53, 69, 433, 59, 1117, 3359, 6231]), (937, 13, 2979, &[1, 1, 7, 3, 23, 5, 115, 201, 225, 109, 1903, 3897, 6265]), (938, 13, 2985, &[1, 1, 1, 11, 17, 1, 39, 143, 361, 659, 1105, 23, 4923]), (939, 13, 3000, &[1, 1, 1, 9, 27, 57, 85, 227, 261, 119, 1881, 3965, 6999]), (940, 13, 3003, &[1, 3, 7, 7, 15, 7, 107, 17, 315, 49, 1591, 905, 7789]), (941, 13, 3013, &[1, 3, 1, 7, 29, 3, 47, 237, 157, 769, 839, 3199, 3195]), (942, 13, 3018, &[1, 1, 3, 15, 25, 39, 63, 15, 111, 857, 881, 1505, 7671]), (943, 13, 3020, &[1, 1, 7, 1, 3, 35, 41, 215, 99, 895, 1025, 1483, 4707]), (944, 13, 3025, &[1, 3, 5, 1, 1, 31, 25, 247, 113, 841, 397, 1825, 6969]), (945, 13, 3042, &[1, 1, 3, 5, 19, 41, 49, 243, 225, 973, 241, 175, 1041]), (946, 13, 3047, &[1, 1, 1, 7, 15, 15, 105, 141, 83, 75, 1675, 3523, 5219]), (947, 13, 3048, &[1, 1, 7, 5, 13, 27, 47, 199, 445, 841, 959, 1157, 2209]), (948, 13, 3051, &[1, 3, 5, 15, 23, 31, 31, 81, 85, 33, 785, 2639, 7799]), (949, 13, 3054, &[1, 1, 5, 13, 21, 3, 47, 99, 235, 943, 1731, 2467, 7891]), (950, 13, 3056, &[1, 1, 1, 3, 17, 53, 85, 219, 73, 131, 1339, 875, 1191]), (951, 13, 3065, &[1, 1, 5, 7, 17, 63, 113, 7, 185, 557, 749, 3563, 4973]), (952, 13, 3073, &[1, 3, 3, 15, 15, 21, 43, 111, 155, 689, 345, 423, 3597]), (953, 13, 3074, &[1, 1, 5, 1, 15, 29, 93, 5, 361, 713, 695, 3937, 425]), (954, 13, 3083, &[1, 3, 7, 7, 13, 41, 115, 175, 315, 937, 123, 2841, 4457]), (955, 13, 3086, &[1, 1, 3, 11, 25, 5, 103, 53, 423, 811, 657, 399, 7257]), (956, 13, 3091, &[1, 1, 1, 1, 1, 13, 101, 211, 383, 325, 97, 1703, 4429]), (957, 13, 3097, &[1, 3, 7, 9, 31, 45, 83, 157, 509, 701, 841, 1105, 3643]), (958, 13, 3109, &[1, 1, 1, 7, 1, 9, 69, 17, 129, 281, 1161, 2945, 7693]), (959, 13, 3116, &[1, 3, 7, 1, 11, 29, 51, 143, 77, 433, 1723, 2317, 5641]), (960, 13, 3124, &[1, 1, 1, 1, 21, 43, 13, 67, 177, 505, 1629, 1267, 4885]), (961, 13, 3128, &[1, 1, 3, 11, 27, 63, 111, 47, 233, 781, 453, 1679, 3209]), (962, 13, 3153, &[1, 1, 3, 13, 29, 27, 119, 141, 493, 971, 461, 1159, 633]), (963, 13, 3160, &[1, 1, 3, 15, 23, 5, 79, 215, 163, 149, 1805, 2399, 61]), (964, 13, 3165, &[1, 3, 5, 13, 19, 5, 1, 39, 409, 561, 709, 829, 1357]), (965, 13, 3172, &[1, 3, 3, 13, 19, 43, 9, 177, 449, 447, 73, 2107, 5669]), (966, 13, 3175, &[1, 3, 5, 1, 23, 13, 63, 109, 203, 593, 829, 4017, 6881]), (967, 13, 3184, &[1, 1, 5, 7, 3, 9, 53, 175, 391, 169, 1283, 3793, 4451]), (968, 13, 3193, &[1, 1, 5, 7, 29, 43, 9, 5, 209, 77, 927, 2941, 8145]), (969, 13, 3196, &[1, 3, 5, 15, 17, 49, 5, 143, 131, 771, 1685, 925, 2175]), (970, 13, 3200, &[1, 1, 3, 11, 27, 27, 27, 159, 161, 1015, 1587, 4049, 1983]), (971, 13, 3203, &[1, 3, 1, 3, 23, 57, 119, 67, 481, 577, 389, 3319, 5325]), (972, 13, 3205, &[1, 3, 5, 1, 19, 39, 87, 61, 329, 657, 1773, 31, 1707]), (973, 13, 3209, &[1, 1, 3, 1, 5, 25, 15, 241, 131, 815, 1751, 3029, 8039]), (974, 13, 3224, &[1, 3, 3, 13, 27, 13, 77, 87, 437, 57, 621, 1031, 7891]), (975, 13, 3239, &[1, 3, 1, 13, 23, 51, 117, 37, 331, 745, 605, 3179, 4713]), (976, 13, 3251, &[1, 1, 5, 5, 19, 17, 99, 167, 87, 721, 737, 789, 2165]), (977, 13, 3254, &[1, 3, 5, 13, 1, 51, 119, 211, 165, 299, 1327, 3053, 3343]), (978, 13, 3265, &[1, 1, 5, 15, 29, 45, 17, 129, 67, 345, 1553, 2705, 7369]), (979, 13, 3266, &[1, 1, 1, 9, 23, 7, 13, 209, 7, 407, 317, 3077, 7287]), (980, 13, 3275, &[1, 1, 1, 5, 9, 59, 89, 3, 487, 451, 505, 2499, 7563]), (981, 13, 3280, &[1, 3, 1, 7, 21, 1, 21, 203, 101, 417, 1389, 2751, 1397]), (982, 13, 3283, &[1, 3, 7, 13, 7, 31, 3, 247, 349, 485, 1259, 549, 6321]), (983, 13, 3286, &[1, 1, 7, 7, 27, 33, 107, 197, 293, 729, 1753, 2571, 103]), (984, 13, 3301, &[1, 3, 5, 9, 25, 35, 5, 253, 137, 213, 2041, 3387, 1809]), (985, 13, 3302, &[1, 1, 7, 13, 15, 35, 67, 83, 295, 175, 839, 2831, 839]), (986, 13, 3305, &[1, 3, 3, 11, 3, 17, 55, 141, 247, 991, 117, 3799, 1221]), (987, 13, 3319, &[1, 1, 5, 1, 11, 37, 87, 233, 457, 653, 899, 2933, 3105]), (988, 13, 3323, &[1, 1, 3, 15, 3, 31, 67, 167, 437, 9, 651, 1109, 1139]), (989, 13, 3326, &[1, 1, 3, 1, 7, 63, 67, 17, 11, 883, 1855, 1941, 4751]), (990, 13, 3331, &[1, 3, 7, 9, 19, 33, 113, 117, 495, 39, 1795, 2561, 5519]), (991, 13, 3348, &[1, 1, 7, 5, 1, 3, 103, 37, 201, 223, 1101, 877, 6483]), (992, 13, 3351, &[1, 1, 5, 9, 29, 49, 51, 33, 439, 917, 861, 1321, 2135]), (993, 13, 3358, &[1, 1, 3, 3, 1, 5, 17, 93, 217, 619, 613, 1357, 6095]), (994, 13, 3368, &[1, 3, 1, 11, 3, 21, 5, 41, 15, 175, 843, 2937, 6849]), (995, 13, 3374, &[1, 3, 3, 7, 9, 57, 55, 127, 79, 287, 445, 2205, 7989]), (996, 13, 3376, &[1, 1, 7, 13, 23, 17, 93, 129, 157, 135, 1747, 1813, 4183]), (997, 13, 3379, &[1, 1, 1, 5, 31, 59, 99, 33, 425, 329, 887, 367, 1761]), (998, 13, 3385, &[1, 1, 7, 9, 17, 53, 77, 139, 435, 387, 49, 3649, 1773]), (999, 13, 3386, &[1, 3, 3, 15, 21, 57, 45, 161, 331, 719, 273, 3479, 4173]), (1000, 13, 3396, &[1, 1, 3, 9, 3, 3, 105, 201, 373, 877, 919, 1263, 6649]), (1001, 13, 3420, &[1, 3, 1, 15, 13, 43, 13, 99, 73, 163, 353, 3569, 5601]), (1002, 13, 3423, &[1, 3, 7, 3, 5, 9, 69, 177, 449, 47, 781, 1125, 4245]), (1003, 13, 3430, &[1, 1, 1, 5, 3, 45, 1, 123, 409, 903, 205, 2057, 7637]), (1004, 13, 3433, &[1, 3, 5, 9, 19, 47, 87, 135, 481, 799, 101, 3409, 2241]), (1005, 13, 3434, &[1, 3, 1, 13, 3, 25, 15, 27, 181, 967, 669, 2577, 7249]), (1006, 13, 3439, &[1, 1, 7, 3, 31, 5, 103, 53, 1, 911, 1209, 3697, 6685]), (1007, 13, 3442, &[1, 1, 3, 1, 5, 5, 49, 135, 281, 747, 761, 2973, 7963]), (1008, 13, 3444, &[1, 3, 3, 5, 19, 61, 125, 199, 299, 515, 1365, 369, 7027]), (1009, 13, 3453, &[1, 3, 1, 7, 5, 41, 63, 229, 283, 571, 147, 447, 657]), (1010, 13, 3464, &[1, 3, 1, 11, 5, 15, 55, 7, 259, 61, 27, 1429, 5631]), (1011, 13, 3477, &[1, 1, 5, 1, 3, 53, 51, 253, 155, 553, 1293, 3735, 6567]), (1012, 13, 3478, &[1, 3, 5, 9, 5, 41, 21, 159, 101, 785, 1981, 3799, 7693]), (1013, 13, 3482, &[1, 3, 7, 7, 9, 3, 95, 105, 129, 213, 1215, 1027, 5699]), (1014, 13, 3487, &[1, 1, 3, 3, 29, 13, 9, 253, 449, 321, 341, 2879, 171]), (1015, 13, 3497, &[1, 3, 7, 11, 21, 11, 75, 35, 43, 965, 675, 2217, 7175]), (1016, 13, 3500, &[1, 1, 5, 15, 31, 5, 29, 137, 311, 751, 47, 1367, 5921]), (1017, 13, 3505, &[1, 1, 3, 15, 17, 1, 45, 69, 55, 649, 835, 569, 7615]), (1018, 13, 3506, &[1, 3, 1, 13, 31, 7, 23, 15, 391, 145, 1845, 1825, 1403]), (1019, 13, 3511, &[1, 1, 3, 15, 5, 9, 79, 77, 105, 399, 1933, 2503, 4781]), (1020, 13, 3512, &[1, 3, 1, 3, 17, 47, 19, 13, 107, 475, 759, 2933, 3761]), (1021, 13, 3515, &[1, 1, 7, 11, 3, 7, 121, 209, 397, 877, 293, 847, 7039]), (1022, 13, 3525, &[1, 1, 1, 15, 29, 45, 5, 109, 335, 461, 143, 931, 4045]), (1023, 13, 3532, &[1, 3, 1, 7, 11, 57, 73, 89, 201, 173, 803, 3953, 5205]), (1024, 13, 3538, &[1, 1, 5, 11, 11, 33, 37, 29, 263, 1019, 657, 1453, 7807]), ];