2, -1, -1   2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607,
2, -1, +1   1, 2, 4, 8, 16,
2, +1, -1   1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, 94, 103, 143, 206, 216, 306, 324, 391, 458, 470, 827,
2, +1, +1   1, 2, 5, 6, 8, 12, 18, 30, 36, 41, 66, 189, 201, 209, 276, 353, 408, 438, 534,


3, -1, -1   1, 2, 3, 7, 8, 12, 20, 23, 27, 35, 56, 62, 68, 131, 222, 384, 387, 579, 644,
3, -1, +1   1, 2, 4, 5, 6, 9, 16, 17, 30, 54, 57, 60, 65, 132, 180, 320, 696, 782, 822, 897,
3, +1, -1   1, 3, 5, 7, 15, 45, 95, 235, 463, 733,
3, +1, +1   1, 2, 3, 6, 14, 15, 39, 201, 249, 885, 1005,


4, -1, -1   1, 2, 3, 9, 17, 19, 32, 38, 47, 103, 108, 153, 162, 229, 235, 637,
4, -1, +1   1, 3, 4, 6, 9, 15, 18, 33, 138, 204, 219, 267,
4, +1, -1   1, 2, 4, 5, 6, 7, 9, 16, 24, 27, 36, 74, 92, 124, 135, 137, 210, 670, 719, 761, 819, 877, 942, 1007,


5, -1, -1   1, 3, 9, 13, 15, 25, 39, 69, 165, 171, 209, 339,
5, -1, +1   2, 6, 18, 50, 290,
5, +1, -1   1, 2, 5, 11, 28, 65, 72, 361, 479, 494, 599,
5, +1, +1   1, 2, 3, 23, 27, 33, 63, 158, 278, 290, 351, 471, 797,


6, -1, -1   1, 2, 6, 7, 11, 23, 33, 48, 68, 79, 116, 151, 205, 1016,
6, -1, +1   1, 2, 4, 17, 136, 147, 203, 590, 754, 964, 970,
6, +1, -1   1, 2, 3, 13, 21, 28, 30, 32, 36, 48, 52, 76, 734,
6, +1, +1   1, 6, 17, 38, 50, 80, 207, 236, 264, 309, 555,


7, -1, -1   1, 2, 7, 18, 55, 69, 87, 119, 141, 189, 249, 354,
7, -1, +1   1, 4, 9, 99, 412,
7, +1, -1   4, 7, 10, 14, 23, 59,


8, -1, -1   3, 7, 15, 59,
8, -1, +1   2, 40, 58, 60, 130, 144, 752,
8, +1, -1   1, 5, 7, 21, 33, 53, 103, 313, 517,
8, +1, +1   1, 2, 11, 14, 21, 27, 54, 122, 221, 435, 498, 942,


9, -1, -1   1, 2, 5, 25, 85, 92, 97, 649,
9, -1, +1   1, 4, 5, 11, 26, 29, 38, 65, 166, 490, 641,
9, +1, -1   1, 2, 4, 5, 7, 10, 11, 13, 15, 19, 27, 29, 35, 42, 51, 70, 112, 164, 179, 180, 242, 454, 621,
9, +1, +1   2, 6, 9, 11, 51, 56, 81, 941,


10, -1, -1   1, 3, 7, 19, 29, 37, 93, 935,
10, -1, +1   3, 4, 5, 9, 22, 27, 36, 57, 62, 78, 201, 537, 696, 790, 905,
10, +1, -1   1, 9, 11, 17, 22, 29, 36, 37, 52, 166, 448,


11, -1, -1   1, 3, 37, 119, 255, 355, 371, 497,
11, -1, +1   10, 24, 864,
11, +1, -1   1, 2, 3, 4, 11, 13, 22, 27, 48, 51, 103, 147, 280, 908,
11, +1, +1   2, 3, 6, 8, 138, 149, 222, 363, 995,


12, -1, -1   1, 2, 21, 25, 33, 54, 78, 235,
12, -1, +1   3, 4, 35, 119, 476, 507,
12, +1, -1   2, 6, 11, 66, 196, 478,
12, +1, +1   1, 2, 8, 9, 17, 26, 62, 86, 152, 365,


13, -1, -1   2, 7, 11, 36, 164, 216, 302, 311, 455, 738,
13, -1, +1   1, 2, 4, 21, 34, 48, 53, 160, 198, 417, 773,
13, +1, -1   1, 3, 4, 9, 11, 17, 19, 21, 24, 84, 93, 564, 817, 864, 961, 1009,


14, -1, -1   1, 3, 5, 27, 35, 165, 209,
14, -1, +1   2, 40, 402,
14, +1, -1   2, 8, 172, 357, 918,
14, +1, +1   1, 3, 24, 29, 44, 48,


15, -1, -1   14, 33, 43,
15, -1, +1   1, 3, 4, 9, 11, 14, 23, 122, 141, 591,
15, +1, -1   1, 9, 15, 57, 79, 221,
15, +1, +1   1, 3, 5, 21, 35, 101, 860,


16, -1, -1   1, 20, 29, 43, 56, 251,
16, -1, +1   1, 3, 11, 12, 28, 42, 225, 702, 782, 972,
16, +1, -1   1, 4, 5, 9, 15, 24, 31, 63, 89, 115, 153, 166, 243, 297, 328,


17, -1, -1   1, 3, 71, 139, 265, 793,
17, -1, +1   4, 20, 320, 736,
17, +1, -1   4, 6, 15, 18, 23, 83, 359, 420, 711, 723, 864,
17, +1, +1   1, 6, 204,


18, -1, -1   2, 6, 26, 79, 91, 96, 416, 554,
18, -1, +1   1, 6, 9, 12, 22, 30, 102, 154, 600,
18, +1, -1   3, 4, 5, 7, 476, 572, 684, 865,
18, +1, +1   9,


19, -1, -1   6, 9, 20, 43, 174, 273, 428,
19, -1, +1   29, 32, 59, 65, 303,
19, +1, -1   1, 2, 503, 806,


20, -1, -1   1, 219, 223,
20, -1, +1   14, 18, 20, 38, 108, 150, 640,
20, +1, -1   1, 10, 26, 30, 33, 73, 80, 120, 282, 331, 662, 859,
20, +1, +1   1, 6, 191, 468, 644,


21, -1, -1   1, 2, 7, 24, 31, 60, 230, 307, 750,
21, -1, +1   1, 2, 3, 4, 12, 17, 38, 54, 56, 123, 165, 876,
21, +1, -1   1, 8, 13, 26, 355, 985,
21, +1, +1   1, 5, 26, 206, 350,


22, -1, -1   1, 2, 5, 19, 141, 302, 337,
22, -1, +1   1, 9, 53, 261,
22, +1, -1   2, 18, 252,


23, -1, -1   55, 103, 115, 131, 535,
23, -1, +1   14, 62, 84,
23, +1, -1   7, 35, 79, 117, 137, 144, 157, 481, 529,
23, +1, +1   2, 11, 18, 27, 57, 362, 383, 651,


24, -1, -1   12, 18, 63, 153, 221,
24, -1, +1   2, 4, 9, 42, 47, 54, 89, 102, 118, 269, 273, 316, 698,
24, +1, -1   1, 3, 11, 29, 171, 249, 569, 735, 1019,
24, +1, +1   1, 2, 3, 8, 66, 968,


25, -1, -1   1, 5, 7, 30, 75, 371, 383, 609, 819, 855,
25, -1, +1   1, 4, 162,
25, +1, -1   2, 17, 18, 118, 220, 290, 988,


26, -1, -1   133, 205, 215,
26, -1, +1   2, 18, 100,
26, +1, -1   1, 2, 4, 14, 26, 49, 226,
26, +1, +1   2, 5, 179, 377, 425, 491,


27, -1, -1   1, 3, 5, 13, 15, 31, 55, 151, 259, 479, 734,
27, -1, +1   4, 5, 167, 408, 416, 701, 707,
27, +1, -1   2, 4, 6, 8, 46, 56, 79, 571,
27, +1, +1   1, 5, 6, 165, 825,


28, -1, -1   20,
28, -1, +1   1, 2, 136, 154, 524,
28, +1, -1   1, 72, 153,


29, -1, -1   1, 7, 11, 57, 69, 235,
29, -1, +1   2, 4, 6, 44, 334,
29, +1, -1   2, 4, 13, 17, 27, 189, 200, 340, 449, 1024,
29, +1, +1   5, 41, 42, 44, 125,


30, -1, -1   2, 83, 566, 938,
30, -1, +1   4, 5, 9, 18, 71, 124, 165, 172, 888,
30, +1, -1   1, 5, 11, 15, 21, 22, 129, 153, 217, 411, 855,
30, +1, +1   2, 36, 282, 425, 918,


31, -1, -1   1, 5, 27, 41, 48, 177, 398, 536, 608, 618,
31, -1, +1   5, 18, 93, 269, 488,
31, +1, -1   1, 4, 9, 11, 22, 34, 59, 89, 117, 127, 172, 223,


32, -1, -1   1, 7, 23, 41, 47, 693,
32, -1, +1   12, 28,
32, +1, -1   2, 7, 38, 66, 72, 163, 371,
32, +1, +1   5, 105, 284, 326,


33, -1, -1   2, 3, 146,
33, -1, +1   2, 4, 6, 9, 29, 292, 377, 444, 581,
33, +1, -1   4, 13, 48, 216, 859,
33, +1, +1   1, 629, 699,


34, -1, -1   15, 25, 99, 188,
34, -1, +1   1, 2, 4, 9, 32, 33, 50, 56, 168, 315,
34, +1, -1   2, 3, 4, 5, 24, 59, 64, 91, 171, 731, 784,


35, -1, -1   3, 5, 7, 13, 31, 69, 341, 437, 485,
35, -1, +1   2,
35, +1, -1   1, 19, 23, 45, 103, 113,
35, +1, +1   2, 3, 6, 8, 29, 185, 492,


36, -1, -1   1, 9, 11, 15, 27, 145, 417, 762,
36, -1, +1   2, 9, 11, 21, 50, 96, 137, 210, 345,
36, +1, -1   2, 5, 7, 9, 13, 23, 35, 110, 137, 345, 712, 927,
36, +1, +1   3, 8,


37, -1, -1   7, 325, 439,
37, -1, +1   9, 16, 36, 72, 299, 532, 681,
37, +1, -1   2, 22, 92, 172, 712,


38, -1, -1
38, -1, +1   16, 32, 72,
38, +1, -1   1, 3, 4, 12, 16, 157, 361, 419, 427, 523, 647,
38, +1, +1   1, 21, 63, 87, 122, 206,


39, -1, -1   1, 3, 5, 8, 90, 272, 290, 767,
39, -1, +1   1, 4, 45,
39, +1, -1   1, 3, 4, 6, 69, 101, 139, 163, 188, 432, 473, 512, 606,
39, +1, +1   3, 9, 44, 89, 356,


40, -1, -1   1, 19, 218, 767,
40, -1, +1   2, 4, 11, 17, 60, 69, 96, 159, 310, 330, 994,
40, +1, -1   2, 4, 10, 88, 134, 644, 712,


41, -1, -1   7, 295,
41, -1, +1   80, 120, 170,
41, +1, -1   1, 5, 7, 49, 100, 134, 167, 542,
41, +1, +1   1, 6, 11, 39, 636,


42, -1, -1   1, 3, 6, 9, 11, 47, 61, 105, 263, 517,
42, -1, +1   1, 4, 5, 15, 20, 39,
42, +1, -1   8, 14, 26, 72, 80, 160, 455, 484,
42, +1, +1   2, 17, 114, 501,


43, -1, -1   7, 39, 71, 639,
43, -1, +1   2, 9, 14, 40, 81, 156, 221, 252, 569,
43, +1, -1   3, 4, 24, 67,


44, -1, -1   7, 17, 43, 731,
44, -1, +1   4, 108, 174, 272,
44, +1, -1   1, 2, 16, 40, 108, 119, 295, 468, 986,
44, +1, +1   2, 3, 24, 26, 32, 134,


45, -1, -1   1, 13, 72, 83, 132, 144,
45, -1, +1   2, 5, 15, 17, 28, 84, 390, 778,
45, +1, -1   1, 6, 40, 49, 58, 78, 366, 1009,
45, +1, +1   2, 15, 21, 39, 183, 255, 849,


46, -1, -1   1, 2, 3, 9, 12, 24, 68, 108, 476, 619, 839,
46, -1, +1   3, 18, 27, 28, 66, 129, 189, 399, 550, 714,
46, +1, -1   1, 6, 36, 79, 107, 475,


47, -1, -1   1, 9, 15, 45, 211,
47, -1, +1   16,
47, +1, -1   2, 4, 12, 19,
47, +1, +1   2, 41, 129,


48, -1, -1   2, 3, 14, 48, 215, 324, 518,
48, -1, +1   2, 5, 6, 40, 986,
48, +1, -1   1, 5, 11, 35, 39,
48, +1, +1   6, 14, 15, 87, 231,