#define R 1000 #define C 1000 #define NNZ 10004 const double val[10004] = { 658, 279, 587, 255, 359, 844, 905, 456, 897, 837, 652, 398, 885, 21, 669, 738, 365, 928, 713, 771, 536, 987, 917, 823, 544, 40, 80, 636, 263, 929, 757, 677, 151, 500, 875, 720, 205, 292, 859, 980, 97, 608, 813, 840, 397, 765, 294, 718, 751, 7, 482, 166, 653, 172, 187, 79, 228, 857, 540, 760, 509, 190, 396, 765, 37, 85, 866, 981, 999, 793, 921, 664, 208, 856, 528, 782, 318, 170, 521, 691, 726, 996, 947, 326, 825, 77, 823, 752, 266, 834, 196, 58, 430, 764, 807, 568, 665, 583, 178, 250, 273, 654, 487, 504, 729, 338, 866, 981, 852, 842, 785, 13, 588, 44, 432, 408, 374, 761, 653, 752, 684, 6, 357, 703, 447, 966, 457, 738, 646, 646, 217, 522, 839, 417, 506, 801, 233, 929, 487, 353, 660, 751, 738, 512, 566, 130, 61, 128, 698, 467, 362, 867, 639, 289, 371, 427, 650, 16, 878, 967, 369, 517, 161, 330, 294, 396, 606, 638, 171, 602, 531, 14, 968, 15, 193, 225, 863, 171, 254, 714, 256, 873, 353, 35, 910, 849, 658, 546, 389, 239, 355, 540, 494, 968, 319, 590, 608, 445, 806, 51, 117, 401, 314, 280, 334, 44, 17, 107, 108, 650, 807, 385, 748, 942, 719, 110, 630, 559, 717, 375, 963, 45, 403, 476, 408, 732, 87, 874, 635, 119, 190, 949, 777, 201, 503, 658, 777, 564, 830, 122, 929, 68, 11, 354, 395, 213, 766, 40, 995, 577, 514, 568, 56, 439, 91, 148, 612, 717, 157, 538, 682, 190, 571, 847, 275, 190, 824, 985, 29, 426, 173, 898, 297, 156, 936, 1, 455, 812, 173, 131, 376, 947, 596, 783, 800, 361, 798, 598, 710, 86, 149, 457, 129, 437, 352, 933, 320, 709, 167, 793, 46, 49, 305, 704, 577, 855, 336, 978, 206, 662, 230, 93, 898, 368, 422, 689, 351, 87, 465, 576, 33, 884, 675, 548, 116, 730, 385, 483, 340, 809, 938, 342, 576, 887, 479, 455, 820, 521, 320, 488, 506, 591, 901, 505, 525, 5, 133, 705, 561, 285, 95, 918, 410, 578, 347, 375, 735, 624, 491, 494, 931, 655, 819, 883, 328, 527, 194, 580, 584, 837, 700, 681, 249, 643, 958, 363, 316, 397, 638, 261, 459, 960, 636, 458, 84, 797, 696, 782, 831, 419, 393, 649, 312, 811, 703, 70, 688, 285, 39, 617, 935, 495, 392, 143, 734, 166, 406, 464, 732, 709, 379, 143, 527, 514, 709, 130, 965, 632, 448, 836, 62, 567, 600, 520, 519, 16, 394, 705, 438, 548, 696, 140, 573, 509, 968, 935, 165, 868, 577, 451, 865, 304, 777, 828, 147, 704, 821, 641, 783, 376, 757, 391, 170, 592, 235, 920, 846, 683, 249, 697, 253, 386, 244, 889, 607, 768, 88, 836, 259, 945, 33, 352, 70, 83, 996, 791, 18, 599, 488, 43, 582, 993, 692, 841, 558, 530, 350, 187, 295, 215, 869, 593, 385, 722, 724, 282, 681, 534, 788, 836, 378, 825, 93, 539, 120, 794, 384, 798, 505, 833, 27, 181, 951, 966, 498, 375, 22, 545, 62, 816, 119, 712, 813, 783, 655, 832, 143, 501, 519, 43, 760, 17, 896, 96, 390, 121, 458, 736, 649, 227, 778, 283, 657, 434, 214, 123, 929, 548, 206, 993, 463, 824, 369, 260, 868, 645, 857, 184, 198, 349, 652, 522, 23, 208, 968, 290, 770, 109, 978, 513, 298, 675, 306, 866, 927, 822, 495, 653, 134, 702, 147, 366, 947, 65, 586, 412, 638, 760, 541, 118, 551, 574, 85, 736, 999, 917, 478, 35, 629, 963, 898, 826, 113, 298, 606, 568, 152, 926, 277, 984, 549, 279, 839, 348, 672, 278, 94, 455, 590, 843, 85, 222, 901, 621, 30, 880, 914, 27, 974, 399, 873, 968, 870, 479, 696, 964, 929, 499, 121, 812, 933, 799, 506, 412, 712, 791, 426, 835, 488, 910, 522, 332, 967, 380, 61, 5, 282, 119, 22, 136, 436, 730, 341, 687, 371, 19, 893, 20, 327, 221, 221, 966, 354, 198, 985, 56, 305, 691, 980, 12, 790, 64, 484, 621, 214, 332, 898, 898, 318, 416, 445, 350, 317, 336, 714, 788, 541, 890, 42, 111, 596, 164, 424, 448, 666, 362, 429, 617, 910, 917, 970, 526, 321, 551, 481, 83, 46, 146, 569, 856, 85, 192, 724, 378, 299, 13, 422, 411, 552, 569, 100, 849, 484, 906, 47, 532, 742, 415, 228, 897, 715, 807, 329, 244, 312, 903, 758, 34, 172, 18, 917, 700, 108, 611, 567, 616, 572, 174, 925, 553, 903, 268, 544, 998, 708, 133, 717, 584, 517, 608, 680, 597, 316, 470, 764, 530, 221, 405, 133, 406, 506, 56, 458, 721, 935, 356, 130, 99, 395, 117, 34, 881, 231, 214, 248, 458, 246, 632, 471, 279, 385, 594, 855, 305, 30, 542, 144, 509, 548, 364, 171, 386, 382, 616, 997, 28, 361, 855, 449, 992, 956, 439, 569, 383, 523, 852, 337, 112, 24, 902, 352, 542, 231, 664, 411, 457, 572, 52, 760, 88, 907, 345, 284, 636, 219, 975, 713, 231, 888, 49, 624, 179, 579, 401, 694, 984, 905, 673, 414, 773, 165, 349, 436, 128, 186, 487, 17, 552, 833, 98, 424, 791, 220, 352, 75, 470, 405, 679, 939, 792, 653, 142, 226, 208, 629, 429, 55, 455, 362, 210, 765, 693, 113, 656, 824, 441, 191, 50, 957, 99, 27, 582, 461, 279, 299, 492, 678, 452, 640, 349, 758, 298, 903, 361, 333, 339, 60, 824, 773, 184, 621, 66, 49, 228, 608, 523, 591, 533, 234, 566, 291, 646, 93, 42, 810, 154, 846, 426, 32, 828, 360, 917, 182, 50, 40, 182, 19, 127, 614, 951, 662, 591, 140, 110, 685, 549, 6, 346, 766, 689, 743, 414, 135, 61, 548, 363, 915, 462, 526, 405, 524, 192, 754, 796, 616, 98, 341, 786, 778, 929, 6, 388, 293, 513, 148, 298, 311, 29, 456, 960, 560, 895, 121, 511, 141, 732, 762, 774, 261, 287, 314, 801, 320, 173, 616, 356, 783, 256, 129, 513, 212, 293, 168, 813, 279, 65, 784, 360, 921, 320, 177, 923, 385, 142, 380, 772, 929, 718, 277, 61, 620, 575, 772, 356, 414, 775, 392, 523, 760, 192, 905, 606, 134, 695, 784, 540, 63, 939, 941, 887, 217, 290, 893, 206, 662, 63, 102, 74, 943, 288, 8, 254, 131, 420, 841, 79, 139, 362, 221, 915, 6, 28, 417, 846, 996, 794, 522, 391, 513, 715, 87, 449, 801, 823, 16, 485, 874, 8, 601, 885, 146, 886, 318, 235, 390, 561, 869, 640, 860, 433, 651, 145, 149, 682, 612, 580, 946, 572, 155, 736, 898, 774, 81, 882, 286, 362, 982, 788, 658, 452, 889, 688, 384, 948, 342, 402, 777, 403, 547, 123, 187, 394, 470, 978, 234, 461, 127, 349, 476, 927, 837, 997, 494, 167, 920, 911, 84, 432, 339, 87, 841, 535, 972, 671, 395, 445, 681, 494, 737, 492, 96, 84, 261, 871, 91, 696, 960, 346, 430, 796, 326, 272, 982, 25, 927, 923, 528, 924, 215, 789, 691, 898, 811, 189, 284, 856, 200, 278, 436, 354, 114, 978, 648, 797, 437, 916, 220, 449, 740, 179, 484, 470, 332, 178, 65, 807, 860, 180, 421, 148, 563, 253, 691, 121, 837, 851, 341, 948, 563, 635, 780, 148, 567, 713, 118, 877, 505, 519, 975, 504, 745, 190, 958, 134, 898, 723, 546, 781, 46, 760, 530, 572, 163, 227, 886, 408, 586, 4, 901, 233, 753, 720, 203, 575, 748, 443, 207, 838, 492, 290, 223, 256, 715, 830, 432, 97, 99, 477, 725, 574, 91, 746, 731, 615, 629, 437, 320, 843, 559, 13, 902, 779, 564, 689, 207, 599, 726, 598, 606, 148, 58, 115, 536, 319, 279, 944, 485, 699, 948, 13, 895, 766, 582, 559, 998, 250, 788, 869, 877, 23, 647, 488, 164, 845, 344, 545, 307, 991, 0, 805, 152, 412, 534, 323, 614, 415, 865, 847, 210, 743, 122, 943, 594, 320, 268, 154, 253, 816, 347, 768, 953, 982, 606, 131, 813, 92, 339, 5, 707, 517, 526, 469, 537, 89, 141, 537, 557, 190, 659, 87, 659, 401, 367, 414, 460, 34, 96, 895, 740, 694, 352, 537, 592, 877, 137, 922, 915, 99, 216, 969, 716, 44, 869, 856, 853, 352, 556, 216, 426, 231, 259, 172, 67, 694, 488, 311, 712, 767, 279, 962, 265, 615, 141, 454, 711, 384, 452, 135, 90, 391, 787, 665, 528, 296, 824, 820, 455, 885, 301, 155, 647, 6, 973, 627, 663, 922, 969, 799, 698, 523, 404, 784, 422, 128, 103, 233, 601, 812, 281, 600, 336, 11, 743, 288, 925, 181, 228, 508, 308, 3, 141, 711, 602, 71, 868, 255, 307, 24, 862, 567, 134, 74, 755, 947, 111, 812, 42, 295, 650, 859, 78, 128, 462, 308, 290, 372, 166, 111, 364, 469, 591, 127, 56, 840, 758, 781, 756, 548, 658, 412, 851, 134, 233, 432, 257, 138, 210, 184, 986, 51, 806, 442, 711, 243, 571, 861, 550, 111, 798, 138, 316, 746, 549, 276, 458, 866, 335, 334, 178, 191, 473, 452, 764, 487, 525, 273, 457, 902, 888, 519, 203, 891, 497, 998, 535, 382, 673, 787, 112, 846, 836, 898, 681, 607, 546, 863, 639, 896, 281, 845, 305, 410, 835, 985, 245, 781, 208, 337, 248, 205, 264, 198, 305, 665, 351, 609, 186, 444, 589, 130, 292, 668, 617, 611, 111, 80, 9, 267, 275, 135, 201, 926, 789, 835, 221, 290, 297, 93, 437, 892, 921, 994, 748, 321, 23, 394, 725, 377, 581, 57, 219, 461, 54, 183, 506, 889, 920, 714, 639, 836, 585, 787, 929, 597, 307, 678, 35, 296, 46, 459, 368, 342, 200, 609, 265, 11, 315, 10, 29, 32, 339, 250, 974, 736, 834, 281, 332, 656, 530, 384, 96, 544, 775, 208, 375, 230, 31, 589, 385, 130, 718, 82, 909, 267, 482, 503, 875, 824, 488, 837, 757, 19, 121, 129, 531, 712, 76, 183, 137, 764, 617, 846, 64, 65, 775, 593, 526, 53, 923, 142, 330, 153, 199, 71, 584, 423, 770, 318, 965, 493, 953, 238, 416, 471, 978, 436, 501, 505, 264, 789, 199, 241, 800, 168, 34, 291, 399, 972, 890, 462, 670, 628, 19, 204, 99, 751, 742, 231, 397, 5, 204, 886, 763, 706, 218, 775, 730, 231, 425, 118, 778, 886, 537, 364, 691, 19, 114, 195, 665, 675, 359, 653, 185, 76, 351, 221, 695, 147, 1, 109, 790, 749, 299, 358, 11, 581, 511, 614, 950, 916, 923, 764, 245, 487, 508, 471, 71, 482, 614, 660, 834, 875, 433, 470, 650, 753, 828, 360, 551, 946, 215, 358, 689, 468, 280, 98, 363, 451, 20, 842, 913, 105, 575, 798, 199, 612, 778, 959, 295, 322, 760, 963, 854, 191, 629, 165, 420, 127, 515, 858, 783, 487, 499, 534, 451, 373, 116, 973, 576, 184, 587, 765, 975, 945, 960, 801, 802, 793, 32, 608, 312, 533, 916, 92, 625, 661, 374, 967, 332, 554, 259, 838, 475, 765, 833, 74, 39, 780, 446, 132, 270, 583, 378, 677, 805, 921, 723, 624, 67, 434, 875, 847, 149, 881, 104, 729, 327, 239, 791, 22, 717, 647, 118, 353, 791, 129, 253, 60, 938, 533, 408, 994, 849, 789, 764, 797, 687, 892, 203, 880, 903, 946, 294, 830, 698, 297, 478, 305, 452, 258, 30, 799, 756, 793, 937, 775, 14, 383, 276, 481, 215, 317, 879, 52, 628, 654, 429, 753, 848, 606, 629, 748, 832, 335, 733, 90, 396, 690, 482, 54, 12, 306, 535, 750, 116, 524, 383, 475, 214, 178, 784, 798, 563, 935, 806, 949, 53, 694, 273, 124, 284, 619, 45, 521, 715, 851, 132, 424, 438, 319, 538, 981, 802, 986, 340, 600, 353, 980, 637, 505, 17, 280, 855, 237, 432, 184, 955, 538, 935, 480, 421, 580, 423, 928, 926, 930, 732, 210, 351, 346, 469, 100, 288, 353, 788, 232, 130, 79, 360, 870, 439, 47, 661, 595, 636, 52, 389, 986, 159, 454, 317, 961, 915, 76, 342, 895, 53, 396, 15, 66, 139, 310, 636, 549, 440, 926, 132, 734, 726, 696, 332, 229, 896, 486, 316, 840, 403, 557, 963, 67, 401, 318, 13, 109, 745, 296, 653, 711, 718, 2, 951, 853, 130, 22, 879, 878, 759, 466, 520, 25, 403, 952, 914, 29, 133, 156, 467, 435, 896, 78, 488, 55, 739, 861, 521, 904, 498, 748, 703, 489, 21, 377, 322, 248, 818, 176, 531, 564, 1, 694, 362, 876, 165, 881, 325, 475, 810, 181, 30, 455, 255, 673, 320, 600, 602, 568, 974, 350, 826, 212, 504, 91, 21, 317, 275, 775, 422, 278, 795, 826, 818, 377, 295, 165, 496, 753, 425, 554, 243, 964, 169, 281, 109, 884, 334, 692, 641, 411, 352, 66, 765, 196, 508, 696, 866, 369, 725, 838, 82, 62, 300, 637, 29, 108, 859, 222, 768, 442, 891, 38, 523, 158, 856, 949, 852, 145, 630, 686, 109, 577, 371, 673, 807, 224, 169, 148, 890, 329, 653, 720, 898, 771, 65, 712, 735, 606, 578, 836, 17, 498, 31, 275, 54, 494, 831, 255, 266, 574, 693, 418, 226, 351, 867, 287, 717, 708, 104, 131, 863, 474, 600, 323, 235, 80, 710, 719, 924, 168, 168, 979, 24, 755, 935, 78, 386, 41, 546, 155, 306, 366, 814, 445, 883, 504, 332, 920, 265, 484, 591, 98, 981, 576, 392, 905, 927, 715, 264, 598, 847, 753, 329, 350, 983, 179, 993, 810, 809, 155, 508, 564, 896, 733, 734, 714, 637, 560, 186, 751, 601, 636, 361, 916, 10, 542, 258, 286, 756, 471, 858, 97, 373, 699, 1, 707, 260, 900, 145, 979, 143, 487, 427, 863, 472, 638, 672, 309, 980, 332, 480, 26, 184, 40, 723, 102, 856, 785, 298, 816, 525, 160, 897, 421, 697, 122, 571, 372, 138, 892, 370, 805, 754, 113, 993, 448, 471, 423, 96, 331, 419, 144, 172, 987, 170, 788, 400, 346, 139, 676, 380, 257, 350, 89, 592, 501, 664, 19, 957, 462, 302, 430, 880, 869, 99, 70, 356, 931, 751, 43, 531, 790, 559, 455, 64, 846, 139, 685, 876, 166, 361, 28, 876, 223, 147, 928, 619, 734, 870, 738, 393, 293, 722, 301, 936, 566, 57, 881, 398, 796, 134, 566, 932, 756, 860, 638, 546, 33, 144, 29, 628, 254, 764, 604, 357, 987, 552, 400, 663, 874, 727, 586, 988, 684, 867, 343, 733, 349, 534, 976, 708, 998, 871, 564, 271, 105, 397, 40, 884, 62, 43, 361, 451, 188, 520, 953, 709, 796, 522, 365, 263, 807, 14, 439, 395, 800, 614, 831, 675, 532, 95, 332, 538, 318, 526, 1, 689, 111, 487, 370, 203, 211, 642, 549, 158, 206, 298, 846, 87, 717, 363, 83, 200, 769, 504, 670, 536, 349, 294, 441, 239, 721, 400, 355, 212, 120, 623, 664, 94, 116, 126, 904, 947, 938, 152, 542, 464, 735, 926, 112, 590, 1, 209, 102, 237, 258, 552, 427, 808, 319, 631, 769, 884, 24, 132, 697, 878, 344, 335, 391, 384, 27, 533, 900, 96, 279, 121, 998, 558, 987, 848, 426, 191, 925, 623, 850, 163, 184, 819, 881, 279, 850, 517, 178, 727, 603, 152, 657, 412, 17, 120, 241, 718, 785, 921, 237, 982, 936, 745, 810, 507, 207, 267, 17, 967, 133, 73, 627, 20, 158, 69, 829, 769, 457, 436, 986, 723, 248, 784, 704, 146, 408, 0, 170, 209, 720, 958, 149, 321, 919, 924, 223, 35, 326, 196, 513, 992, 884, 467, 877, 695, 432, 281, 722, 633, 209, 616, 140, 93, 274, 31, 401, 971, 177, 946, 782, 271, 934, 159, 416, 861, 9, 607, 415, 747, 444, 487, 701, 191, 88, 850, 580, 93, 59, 309, 477, 613, 974, 126, 348, 256, 573, 578, 865, 805, 280, 90, 858, 924, 455, 681, 307, 581, 714, 156, 224, 534, 198, 63, 489, 144, 123, 288, 500, 221, 618, 674, 233, 440, 788, 569, 70, 472, 166, 12, 979, 722, 929, 108, 736, 666, 525, 631, 554, 287, 742, 65, 324, 248, 710, 489, 834, 199, 338, 851, 793, 960, 761, 383, 891, 973, 943, 853, 422, 178, 600, 890, 732, 384, 431, 476, 237, 104, 622, 839, 904, 805, 512, 57, 17, 630, 378, 32, 996, 247, 209, 254, 119, 396, 565, 630, 782, 633, 138, 318, 112, 545, 743, 616, 663, 89, 367, 495, 845, 127, 597, 434, 129, 692, 109, 168, 953, 668, 590, 177, 578, 46, 707, 413, 115, 788, 513, 243, 935, 953, 58, 584, 64, 569, 367, 978, 249, 290, 125, 183, 852, 485, 847, 895, 835, 25, 289, 995, 226, 156, 980, 520, 656, 255, 37, 852, 719, 493, 473, 900, 417, 647, 363, 759, 778, 735, 349, 627, 525, 255, 13, 58, 399, 222, 70, 304, 663, 158, 152, 788, 103, 693, 274, 873, 116, 837, 876, 367, 272, 778, 65, 363, 625, 696, 809, 16, 491, 615, 196, 88, 0, 204, 418, 203, 952, 205, 240, 962, 899, 872, 222, 961, 363, 920, 659, 935, 943, 198, 385, 475, 298, 936, 22, 204, 947, 776, 911, 581, 661, 340, 433, 188, 622, 117, 154, 150, 388, 214, 513, 625, 875, 779, 262, 972, 396, 803, 396, 991, 976, 900, 387, 371, 522, 162, 234, 733, 314, 331, 666, 44, 205, 66, 422, 780, 978, 661, 775, 647, 511, 670, 515, 88, 714, 579, 133, 499, 837, 506, 904, 172, 248, 476, 836, 898, 514, 396, 852, 568, 706, 533, 54, 72, 167, 493, 809, 588, 792, 34, 325, 827, 878, 440, 708, 348, 589, 708, 271, 577, 857, 999, 547, 579, 502, 298, 330, 790, 687, 99, 245, 721, 264, 826, 487, 501, 783, 194, 469, 991, 653, 87, 946, 556, 707, 104, 879, 160, 15, 1, 95, 323, 870, 521, 897, 840, 699, 410, 751, 42, 342, 802, 547, 862, 168, 5, 561, 488, 170, 237, 655, 179, 909, 847, 536, 360, 44, 371, 9, 473, 253, 400, 563, 683, 471, 625, 823, 414, 590, 312, 407, 971, 929, 614, 705, 249, 69, 348, 527, 915, 978, 728, 593, 641, 627, 144, 653, 818, 763, 116, 676, 611, 451, 203, 589, 62, 984, 165, 631, 42, 873, 56, 256, 459, 134, 722, 235, 798, 291, 977, 646, 36, 156, 546, 113, 96, 964, 156, 570, 366, 718, 816, 726, 385, 188, 184, 154, 921, 821, 329, 928, 176, 688, 942, 204, 240, 423, 498, 422, 115, 696, 1, 850, 309, 733, 628, 595, 930, 467, 888, 638, 448, 895, 10, 938, 848, 116, 193, 390, 415, 330, 359, 115, 371, 432, 229, 264, 141, 162, 491, 397, 2, 141, 761, 471, 68, 55, 628, 593, 891, 84, 808, 740, 196, 196, 511, 901, 324, 464, 627, 461, 900, 995, 118, 486, 960, 709, 451, 432, 997, 785, 480, 20, 351, 25, 955, 40, 788, 56, 254, 329, 601, 293, 704, 639, 743, 983, 177, 722, 193, 708, 34, 202, 364, 404, 487, 436, 867, 906, 442, 472, 718, 610, 366, 991, 639, 821, 604, 618, 538, 266, 781, 958, 542, 744, 116, 604, 835, 310, 847, 277, 138, 979, 930, 962, 3, 641, 976, 673, 928, 851, 456, 963, 604, 336, 360, 467, 374, 536, 56, 729, 272, 563, 205, 301, 583, 329, 632, 151, 678, 100, 234, 74, 315, 289, 759, 313, 854, 558, 997, 905, 186, 261, 863, 607, 41, 70, 234, 147, 448, 619, 179, 65, 716, 309, 858, 408, 143, 61, 760, 308, 115, 116, 233, 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802, 879, 316, 909, 85, 530, 162, 819, 420, 995, 655, 546, 83, 666, 491, 224, 436, 981, 473, 206, 574, 977, 573, 905, 370, 928, 524, 974, 177, 667, 662, 121, 514, 916, 830, 801, 455, 43, 986, 364, 479, 667, 157, 546, 927, 120, 882, 184, 769, 480, 892, 324, 822, 947, 608, 704, 503, 888, 28, 741, 735, 189, 673, 549, 13, 594, 331, 965, 430, 323, 625, 845, 487, 704, 232, 774, 239, 323, 458, 415, 843, 822, 500, 699, 940, 198, 205, 274, 723, 728, 817, 307, 500, 942, 294, 475, 840, 245, 863, 692, 884, 15, 43, 589, 639, 584, 66, 194, 473, 487, 382, 984, 855, 19, 764, 751, 420, 783, 774, 692, 537, 467, 185, 506, 348, 617, 961, 109, 118, 833, 725, 706, 47, 641, 69, 382, 892, 613, 168, 546, 72, 287, 658, 280, 961, 11, 786, 468, 65, 25, 145, 746, 846, 911, 574, 392, 779, 746, 711, 935, 796, 482, 506, 772, 873, 712, 546, 93, 546, 28, 757, 858, 313, 663, 914, 858, 508, 945, 912, 223, 945, 200, 313, 367, 309, 487, 637, 824, 869, 534, 699, 79, 510, 860, 34, 420, 255, 493, 790, 310, 444, 113, 719, 695, 358, 148, 947, 483, 821, 59, 835, 434, 903, 41, 634, 592, 594, 150, 410, 598, 14, 961, 97, 942, 79, 466, 17, 112, 830, 751, 454, 84, 374, 264, 624, 963, 372, 81, 536, 775, 159, 372, 174, 707, 399, 984, 57, 648, 923, 258, 417, 86, 978, 982, 414, 147, 403, 610, 251, 571, 656, 151, 156, 812, 621, 669, 21, 148, 31, 74, 77, 49, 175, 263, 527, 797, 797, 775, 553, 981, 898, 725, 357, 116, 678, 297, 357, 496, 159, 750, 979, 145, 331, 691, 711, 921, 829, 284, 217, 581, 203, 124, 670, 62, 544, 289, 240, 308, 333, 829, 758, 48, 339, 468, 795, 844, 212, 623, 954, 946, 951, 531, 119, 806, 153, 382, 632, 472, 665, 241, 794, 786, 436, 323, 840, 594, 95, 175, 134, 796, 940, 747, 997, 360, 755, 467, 711, 275, 449, 291, 217, 677, 446, 422, 225, 302, 8, 957, 836, 901, 37, 919, 426, 623, 94, 105, 654, 752, 464, 323, 877, 954, 228, 375, 752, 743, 349, 350, 181, 532, 97, 777, 935, 148, 433, 153, 973, 525, 131, 947, 752, 692, 927, 84, 270, 152, 62, 676, 772, 301, 542, 874, 841, 976, 442, 540, 397, 922, 430, 729, 328, 779, 624, 430, 783, 852, 691, 657, 553, 216, 941, 965, 248, 656, 952, 514, 250, 890, 502, 392, 951, 357, 453, 744, 557, 940, 738, 207, 960, 612, 410, 688, 517, 612, 723, 773, 269, 176, 305, 210, 455, 178, 764, 414, 918, 958, 727, 54, 74, 191, 371, 376, 770, 275, 82, 913, 527, 249, 800, 675, 387, 810, 388, 503, 240, 491, 28, 491, 110, 133, 734, 720, 476, 943, 315, 810, 672, 761, 421, 269, 449, 677, 98, 912, 873, 36, 313, 585, 401, 35, 248, 301, 668, 136, 88, 514, 765, 68, 160, 267, 325, 663, 511, 927, 524, 243, 22, 126, 193, 846, 233, 289, 676, 783, 957, 845, 673, 692, 285, 763, 575, 742, 791, 744, 630, 650, 435, 748, 128, 612, 892, 729, 230, 818, 271, 634, 875, 930, 576, 333, 589, 849, 116, 143, 383, 705, 321, 218, 620, 142, 602, 477, 31, 550, 407, 552, 766, 851, 17, 123, 828, 678, 986, 66, 629, 393, 595, 319, 404, 352, 95, 140, 329, 357, 197, 571, 46, 8, 251, 628, 0, 327, 965, 938, 187, 95, 925, 514, 566, 95, 301, 153, 166, 526, 648, 41, 663, 145, 534, 712, 452, 770, 326, 518, 767, 743, 726, 560, 301, 198, 253, 702, 177, 619, 698, 645, 696, 622, 686, 401, 644, 124, 276, 707, 746, 136, 48, 275, 263, 285, 301, 59, 367, 802, 225, 719, 334, 91, 899, 836, 39, 801, 797, 52, 769, 941, 404, 667, 842, 726, 652, 538, 68, 780, 305, 694, 212, 208, 576, 35, 505, 26, 939, 402, 977, 342, 4, 436, 287, 861, 465, 898, 593, 691, 341, 595, 526, 722, 464, 273, 301, 51, 148, 888, 16, 548, 760, 252, 855, 690, 754, 886, 625, 404, 861, 546, 558, 201, 715, 800, 24, 464, 763, 181, 111, 42, 899, 398, 995, 166, 769, 737, 196, 1, 99, 136, 62, 335, 351, 346, 289, 899, 124, 607, 468, 686, 775, 991, 561, 335, 250, 880, 252, 56, 390, 363, 965, 233, 98, 954, 669, 596, 836, 912, 645, 516, 891, 340, 529, 722, 391, 580, 212, 501, 961, 154, 117, 877, 956, 245, 543, 749, 229, 959, 415, 3, 886, 430, 294, 501, 957, 218, 686, 825, 508, 746, 186, 624, 450, 123, 310, 161, 775, 581, 541, 630, 788, 652, 849, 101, 81, 872, 316, 621, 8, 17, 934, 555, 326, 252, 104, 720, 706, 130, 364, 56, 558, 83, 928, 538, 227, 366, 463, 527, 769, 19, 815, 801, 899, 72, 970, 25, 993, 340, 724, 765, 167, 347, 803, 148, 363, 967, 325, 927, 588, 791, 579, 647, 245, 767, 522, 989, 49, 619, 794, 385, 865, 665, 136, 426, 849, 354, 982, 870, 328, 181, 922, 304, 822, 665, 956, 324, 168, 412, 785, 919, 486, 340, 677, 751, 646, 857, 629, 108, 650, 366, 931, 195, 684, 498, 266, 669, 73, 103, 512, 456, 187, 190, 356, 146, 361, 597, 277, 261, 993, 479, 850, 883, 950, 622, 192, 351, 293, 375, 86, 141, 824, 714, 492, 48, 589, 564, 266, 359, 425, 75, 797, 538, 550, 885, 404, 863, 468, 301, 321, 475, 876, 916, 666, 927, 31, 256, 839, 177, 61, 875, 23, 348, 257, 939, 931, 533, 473, 865, 108, 130, 772, 296, 768, 721, 908, 108, 727, 659, 811, 821, 971, 652, 546, 727, 678, 767, 229, 606, 503, 298, 186, 539, 4, 203, 752, 630, 179, 182, 476, 366, 651, 924, 38, 925, 37, 177, 658, 489, 816, 322, 963, 928, 818, 169, 602, 403, 506, 127, 844, 749, 674, 845, 529, 865, 635, 791, 776, 334, 136, 342, 593, 512, 660, 640, 787, 139, 544, 181, 43, 46, 413, 337, 854, 986, 815, 121, 877, 294, 218, 4, 136, 225, 766, 992, 910, 530, 646, 213, 695, 271, 967, 986, 628, 777, 180, 866, 599, 664, 46, 994, 396, 56, 256, 739, 481, 608, 360, 134, 970, 282, 898, 417, 948, 956, 230, 884, 748, 74, 938, 224, 920, 974, 475, 405, 442, 630, 596, 118, 398, 439, 969, 188, 169, 251, 630, 835, 480, 557, 904, 461, 371, 885, 197, 305, 678, 12, 663, 960, 311, 877, 747, 20, 271, 622, 48, 621, 135, 59, 179, 377, 684, 861, 760, 38, 780, 91, 18, 23, 432, 37, 443, 450, 508, 193, 960, 986, 761, 605, 788, 86, 436, 23, 581, 605, 128, 84, 979, 732, 230, 787, 836, 261, 677, 117, 292, 477, 388, 20, 962, 707, 979, 933, 662, 112, 234, 771, 167, 31, 673, 42, 705, 675, 151, 452, 875, 655, 399, 59, 702, 502, 444, 892, 290, 856, 53, 260, 19, 221, 987, 330, 80, 665, 551, 377, 540, 188, 920, 680, 133, 77, 466, 439, 258, 570, 659, 56, 10, 615, 504, 336, 655, 720, 156, 289, 354, 637, 184, 853, 944, 177, 973, 177, 537, 934, 78, 267, 209, 898, 115, 986, 920, 926, 393, 217, 204, 312, 989, 655, 214, 47, 231, 278, 866, 734, 707, 605, 208, 232, 506, 116, 383, 662, 151, 92, 785, 431, 614, 585, 682, 781, 343, 590, 458, 232, 360, 187, 18, 769, 704, 620, 67, 109, 88, 353, 401, 228, 508, 406, 255, 989, 151, 702, 277, 376, 381, 409, 932, 31, 761, 783, 233, 154, 871, 55, 648, 5, 12, 465, 96, 904, 169, 325, 428, 572, 47, 78, 258, 525, 276, 502, 972, 488, 763, 798, 973, 186, 490, 362, 205, 154, 245, 784, 493, 76, 975, 459, 598, 227, 161, 752, 243, 858, 931, 996, 543, 488, 560, 240, 49, 318, 374, 914, 52, 693, 762, 329, 691, 193, 122, 925, 577, 748, 236, 8, 591, 640, 61, 77, 295, 117, 323, 732, 493, 811, 67, 694, 158, 589, 247, 115, 184, 682, 927, 918, 353, 217, 904, 834, 107, 728, 683, 908, 596, 721, 44, 412, 780, 882, 682, 497, 832, 559, 126, 303, 100, 214, 829, 344, 654, 679, 336, 148, 213, 982, 859, 558, 855, 999, 698, 38, 490, 340, 846, 852, 26, 942, 575, 383, 1, 198, 836, 570, 893, 950, 7, 527, 628, 753, 660, 180, 354, 819, 775, 271, 187, 374, 532, 374, 900 }; const int idx[10004] = { 13, 111, 124, 218, 316, 502, 34, 119, 167, 180, 186, 346, 511, 543, 755, 788, 833, 929, 46, 109, 154, 220, 248, 448, 509, 517, 530, 557, 639, 643, 720, 137, 189, 424, 480, 570, 642, 849, 896, 968, 117, 136, 208, 248, 347, 410, 433, 515, 747, 144, 148, 375, 405, 444, 532, 788, 808, 987, 110, 112, 403, 415, 596, 612, 669, 794, 851, 80, 285, 288, 433, 500, 628, 982, 999, 57, 237, 252, 304, 469, 600, 609, 621, 741, 798, 251, 322, 369, 374, 376, 507, 623, 666, 669, 677, 707, 823, 919, 63, 187, 266, 360, 396, 439, 459, 526, 623, 804, 857, 881, 948, 160, 165, 226, 446, 538, 585, 624, 866, 975, 979, 18, 54, 151, 180, 230, 298, 480, 678, 688, 696, 742, 757, 889, 979, 100, 245, 513, 925, 162, 413, 427, 588, 645, 807, 853, 194, 313, 339, 466, 539, 581, 732, 791, 832, 927, 954, 962, 966, 42, 45, 138, 141, 239, 338, 584, 696, 912, 929, 269, 352, 443, 463, 896, 962, 60, 92, 273, 568, 591, 851, 38, 77, 281, 362, 544, 614, 651, 836, 871, 873, 45, 61, 140, 153, 234, 439, 472, 509, 588, 675, 760, 777, 178, 198, 248, 517, 566, 679, 700, 289, 455, 602, 695, 711, 853, 923, 179, 199, 214, 280, 343, 405, 435, 504, 898, 910, 939, 130, 219, 296, 445, 508, 634, 763, 918, 922, 978, 87, 285, 614, 667, 679, 739, 834, 192, 347, 549, 557, 724, 764, 928, 929, 976, 17, 283, 413, 429, 612, 683, 707, 725, 743, 833, 856, 165, 267, 304, 361, 397, 410, 570, 683, 766, 788, 849, 882, 885, 30, 58, 221, 254, 453, 457, 470, 674, 687, 745, 809, 819, 55, 121, 231, 538, 604, 718, 768, 960, 71, 77, 104, 186, 205, 234, 456, 467, 579, 682, 733, 767, 947, 66, 86, 157, 290, 422, 441, 473, 560, 607, 640, 682, 888, 37, 296, 439, 629, 642, 733, 824, 917, 969, 4, 25, 580, 622, 636, 666, 672, 732, 802, 921, 943, 130, 194, 245, 273, 323, 344, 603, 740, 795, 974, 189, 422, 445, 446, 831, 905, 912, 36, 60, 218, 428, 455, 627, 743, 796, 801, 903, 136, 152, 166, 352, 364, 369, 382, 466, 521, 577, 665, 746, 910, 294, 345, 445, 645, 686, 718, 757, 762, 796, 817, 832, 836, 997, 127, 258, 259, 449, 541, 643, 665, 756, 817, 854, 870, 89, 134, 188, 362, 408, 531, 566, 816, 127, 170, 302, 336, 426, 434, 601, 708, 774, 780, 900, 935, 377, 469, 618, 650, 790, 809, 78, 253, 340, 382, 586, 673, 684, 282, 354, 363, 398, 636, 655, 729, 885, 911, 10, 175, 195, 229, 273, 339, 380, 531, 660, 681, 794, 800, 236, 416, 646, 679, 685, 885, 7, 116, 299, 481, 702, 747, 922, 64, 153, 374, 391, 532, 558, 602, 655, 662, 804, 847, 867, 998, 45, 66, 97, 106, 236, 240, 247, 453, 641, 646, 711, 712, 715, 855, 906, 923, 37, 65, 122, 331, 578, 589, 610, 139, 293, 354, 395, 430, 486, 589, 614, 661, 699, 846, 910, 18, 53, 78, 234, 296, 690, 828, 923, 87, 115, 156, 161, 173, 201, 400, 474, 501, 526, 782, 861, 63, 271, 427, 552, 590, 657, 920, 41, 194, 281, 571, 640, 681, 696, 301, 306, 514, 553, 560, 641, 683, 762, 812, 818, 876, 904, 932, 978, 38, 62, 98, 103, 370, 390, 531, 559, 693, 813, 924, 943, 955, 973, 13, 40, 62, 75, 396, 419, 615, 773, 968, 989, 150, 183, 241, 261, 407, 476, 492, 524, 541, 863, 994, 156, 195, 197, 278, 457, 467, 610, 621, 956, 49, 343, 454, 477, 572, 600, 700, 759, 804, 923, 92, 194, 455, 842, 968, 160, 211, 461, 463, 467, 622, 854, 972, 333, 469, 563, 571, 639, 838, 977, 18, 105, 133, 258, 572, 720, 804, 851, 930, 19, 139, 158, 301, 354, 407, 589, 726, 846, 904, 26, 54, 155, 212, 216, 418, 534, 647, 792, 862, 889, 101, 216, 228, 396, 470, 473, 592, 706, 799, 913, 922, 98, 324, 524, 672, 685, 856, 213, 224, 228, 300, 395, 604, 631, 651, 835, 944, 289, 574, 613, 657, 671, 748, 763, 768, 815, 843, 908, 74, 79, 203, 218, 245, 249, 390, 548, 616, 804, 986, 49, 196, 585, 591, 608, 728, 750, 810, 836, 920, 980, 38, 41, 93, 94, 320, 360, 502, 555, 729, 742, 814, 984, 89, 131, 499, 677, 825, 846, 919, 966, 17, 37, 121, 168, 560, 585, 691, 788, 892, 925, 951, 995, 13, 69, 124, 229, 308, 554, 643, 668, 717, 747, 813, 814, 864, 298, 327, 386, 425, 586, 600, 725, 730, 832, 12, 38, 94, 150, 175, 501, 538, 552, 571, 606, 624, 650, 686, 728, 157, 605, 630, 713, 784, 850, 954, 181, 234, 610, 612, 661, 663, 677, 688, 726, 809, 818, 67, 77, 164, 193, 214, 345, 352, 551, 696, 919, 994, 12, 311, 404, 454, 473, 521, 581, 651, 677, 717, 850, 873, 880, 892, 945, 54, 138, 210, 219, 248, 413, 480, 491, 639, 652, 773, 807, 824, 962, 79, 211, 499, 560, 561, 759, 774, 800, 865, 35, 146, 619, 746, 754, 81, 237, 258, 388, 477, 658, 704, 712, 781, 109, 720, 758, 98, 209, 252, 311, 410, 532, 611, 656, 722, 772, 822, 828, 912, 980, 95, 107, 167, 287, 289, 303, 441, 446, 580, 600, 630, 632, 658, 682, 847, 92, 137, 177, 238, 262, 324, 438, 479, 534, 539, 689, 846, 956, 962, 200, 496, 521, 656, 714, 785, 814, 857, 184, 204, 455, 702, 754, 803, 887, 928, 993, 42, 51, 189, 204, 358, 572, 601, 665, 867, 71, 108, 208, 243, 263, 314, 359, 418, 482, 556, 680, 945, 958, 964, 97, 200, 202, 223, 230, 428, 447, 537, 574, 635, 663, 728, 737, 858, 861, 930, 71, 84, 85, 196, 199, 242, 513, 761, 48, 98, 127, 194, 233, 283, 334, 420, 627, 632, 931, 34, 82, 176, 197, 217, 235, 237, 358, 462, 947, 10, 178, 265, 350, 396, 468, 539, 586, 612, 628, 644, 791, 40, 234, 292, 299, 375, 396, 410, 429, 728, 36, 360, 475, 562, 962, 5, 60, 169, 509, 558, 594, 613, 648, 654, 726, 769, 773, 777, 40, 49, 403, 446, 524, 548, 730, 774, 938, 978, 997, 221, 248, 407, 447, 585, 756, 824, 894, 972, 121, 189, 364, 537, 563, 179, 328, 344, 692, 711, 750, 760, 780, 810, 929, 942, 106, 336, 551, 616, 640, 654, 726, 890, 74, 200, 233, 254, 382, 396, 895, 971, 283, 614, 898, 87, 122, 172, 255, 324, 383, 498, 525, 699, 817, 825, 3, 41, 104, 280, 399, 617, 641, 769, 789, 817, 891, 937, 143, 175, 185, 217, 222, 362, 391, 465, 515, 544, 818, 868, 35, 44, 122, 235, 345, 415, 479, 569, 575, 740, 765, 867, 967, 78, 107, 265, 358, 524, 646, 716, 720, 840, 76, 77, 353, 406, 533, 648, 726, 733, 906, 979, 65, 133, 182, 187, 191, 424, 430, 520, 674, 776, 945, 975, 18, 242, 393, 458, 468, 530, 599, 717, 933, 278, 297, 465, 476, 579, 591, 633, 643, 937, 271, 481, 618, 890, 5, 126, 171, 192, 209, 259, 367, 840, 861, 6, 26, 47, 90, 225, 239, 385, 577, 782, 795, 797, 893, 76, 82, 309, 348, 450, 583, 677, 696, 752, 785, 800, 991, 2, 191, 211, 279, 280, 556, 591, 774, 785, 822, 913, 34, 117, 159, 204, 266, 418, 547, 565, 962, 992, 33, 72, 140, 141, 157, 254, 513, 558, 643, 695, 779, 791, 882, 978, 13, 53, 65, 479, 513, 674, 687, 711, 785, 811, 830, 4, 5, 9, 34, 77, 137, 265, 270, 542, 552, 622, 632, 634, 647, 783, 895, 951, 995, 89, 113, 174, 225, 231, 258, 294, 347, 383, 414, 444, 463, 467, 493, 535, 612, 688, 107, 111, 213, 238, 494, 555, 572, 676, 40, 50, 59, 119, 291, 365, 416, 565, 607, 613, 631, 902, 908, 998, 63, 495, 534, 581, 601, 694, 719, 731, 790, 969, 176, 262, 481, 545, 694, 737, 853, 202, 267, 269, 302, 466, 727, 786, 816, 858, 923, 14, 241, 387, 416, 468, 501, 513, 599, 48, 157, 318, 426, 589, 632, 871, 882, 87, 444, 486, 558, 618, 773, 794, 73, 116, 199, 229, 233, 255, 360, 400, 425, 468, 474, 540, 589, 786, 834, 868, 888, 85, 112, 162, 185, 316, 331, 346, 410, 611, 729, 798, 863, 234, 591, 637, 933, 8, 12, 32, 43, 101, 339, 436, 708, 88, 111, 115, 790, 841, 935, 976, 12, 175, 245, 447, 449, 548, 581, 652, 743, 763, 773, 776, 828, 951, 58, 62, 68, 277, 297, 401, 418, 460, 482, 561, 656, 734, 812, 818, 837, 861, 118, 192, 254, 267, 270, 276, 347, 463, 509, 514, 714, 717, 788, 905, 924, 100, 256, 334, 335, 465, 627, 803, 815, 884, 996, 15, 140, 172, 197, 227, 300, 310, 466, 530, 560, 567, 784, 860, 15, 108, 132, 188, 310, 621, 838, 839, 988, 8, 130, 289, 462, 472, 549, 557, 561, 643, 753, 755, 841, 955, 40, 325, 334, 371, 375, 417, 573, 872, 921, 989, 25, 94, 138, 217, 312, 370, 528, 585, 603, 630, 729, 803, 810, 73, 424, 570, 624, 630, 642, 671, 697, 873, 935, 987, 94, 174, 318, 415, 507, 516, 676, 779, 821, 941, 973, 73, 78, 97, 148, 237, 269, 293, 304, 483, 575, 591, 916, 64, 228, 238, 269, 287, 400, 633, 749, 114, 173, 311, 400, 454, 634, 644, 726, 731, 860, 921, 224, 262, 367, 401, 504, 589, 630, 727, 848, 161, 392, 401, 410, 530, 548, 787, 894, 989, 121, 372, 437, 676, 929, 976, 980, 111, 365, 706, 954, 82, 379, 563, 728, 949, 124, 227, 540, 671, 767, 861, 484, 678, 840, 864, 916, 304, 348, 502, 599, 617, 657, 82, 149, 163, 216, 229, 449, 612, 620, 636, 673, 679, 756, 802, 859, 953, 142, 176, 215, 273, 335, 415, 586, 658, 682, 764, 865, 896, 923, 76, 283, 284, 464, 481, 588, 625, 742, 790, 947, 119, 186, 309, 320, 404, 407, 440, 496, 692, 853, 884, 901, 980, 990, 345, 493, 503, 691, 738, 743, 890, 929, 993, 998, 45, 272, 313, 350, 384, 452, 499, 569, 248, 346, 515, 676, 751, 755, 775, 778, 17, 491, 522, 538, 622, 672, 919, 961, 54, 126, 207, 301, 375, 447, 500, 599, 651, 683, 890, 947, 93, 317, 482, 656, 774, 865, 904, 96, 224, 260, 313, 340, 372, 410, 437, 452, 511, 512, 718, 911, 77, 100, 176, 232, 418, 661, 689, 805, 956, 51, 262, 280, 352, 380, 413, 461, 538, 616, 769, 783, 821, 855, 946, 956, 73, 169, 238, 246, 319, 391, 392, 669, 769, 770, 786, 946, 415, 453, 590, 628, 630, 684, 852, 52, 258, 318, 322, 535, 545, 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702, 959, 29, 71, 163, 196, 197, 416, 756, 851, 890, 921, 926, 65, 443, 507, 514, 531, 581, 649, 674, 855, 861, 865, 957, 35, 94, 113, 505, 660, 821, 208, 229, 246, 324, 327, 446, 470, 494, 518, 526, 600, 659, 886, 897, 103, 402, 403, 460, 541, 709, 815, 816, 973, 128, 236, 378, 398, 561, 602, 609, 659, 677, 688, 741, 815, 59, 82, 122, 162, 233, 265, 335, 407, 452, 489, 495, 542, 642, 696, 825, 902, 262, 524, 738, 166, 389, 408, 564, 603, 639, 942, 16, 51, 87, 211, 336, 371, 404, 449, 538, 560, 594, 612, 849, 953, 23, 64, 432, 559, 802, 813, 874, 919, 89, 341, 355, 383, 509, 650, 778, 972, 998, 13, 208, 407, 419, 465, 582, 595, 825, 909, 83, 110, 184, 240, 362, 559, 684, 815, 840, 881, 269, 670, 675, 680, 793, 794, 804, 805, 807, 830, 2, 20, 491, 581, 676, 9, 231, 243, 294, 464, 513, 544, 703, 763, 813, 862, 880, 943, 114, 115, 131, 145, 191, 357, 380, 391, 394, 399, 548, 651, 654, 805, 82, 152, 163, 241, 250, 331, 430, 467, 474, 536, 598, 634, 722, 778, 857, 951, 954, 104, 131, 190, 354, 475, 511, 574, 656, 778, 801, 902, 100, 296, 462, 928, 9, 231, 239, 263, 311, 485, 614, 713, 139, 238, 307, 343, 349, 395, 499, 678, 821, 912, 166, 181, 312, 491, 520, 710, 752, 871, 108, 306, 511, 652, 679, 777, 799, 19, 23, 80, 92, 261, 466, 558, 606, 781, 844, 941, 11, 89, 94, 178, 257, 381, 398, 586, 610, 646, 817, 903, 952, 988, 107, 176, 296, 332, 430, 434, 531, 669, 807, 888, 997, 124, 246, 537, 650, 786, 979, 194, 535, 548, 560, 566, 711, 760, 930, 947, 143, 151, 395, 872, 981, 95, 107, 380, 475, 552, 597, 757, 804, 810, 914, 96, 210, 329, 445, 516, 575, 609, 690, 860, 913, 963, 134, 197, 307, 313, 414, 465, 560, 639, 780, 854, 946, 103, 353, 413, 532, 657, 689, 904, 958, 990, 43, 131, 142, 217, 236, 406, 597, 859, 61, 153, 437, 468, 586, 635, 670, 701, 117, 138, 237, 305, 358, 528, 605, 613, 628, 759, 771, 836, 896, 968, 988, 34, 82, 347, 448, 461, 575, 761, 910, 977, 50, 103, 173, 185, 287, 308, 406, 462, 671, 767, 789, 890, 905, 548, 562, 606, 653, 692, 846, 114, 170, 477, 549, 607, 696, 945, 130, 172, 175, 319, 443, 480, 869, 44, 65, 111, 324, 413, 474, 610, 627, 642, 685, 807, 824, 265, 465, 558, 564, 614, 628, 833, 916, 942, 26, 70, 136, 208, 492, 641, 803, 912, 914, 74, 168, 198, 368, 376, 558, 737, 783, 816, 845, 959, 126, 246, 406, 444, 449, 517, 579, 665, 772, 789, 906, 988, 189, 235, 374, 387, 446, 456, 554, 643, 685, 826, 848, 893, 944, 972, 21, 134, 141, 304, 360, 385, 409, 498, 523, 659, 8, 111, 156, 256, 276, 342, 449, 480, 543, 686, 691, 863, 205, 281, 302, 375, 439, 492, 605, 675, 707, 741, 933, 966, 971, 42, 381, 569, 899, 902, 980, 217, 321, 374, 416, 482, 560, 563, 626, 677, 690, 780, 788, 963, 57, 58, 61, 77, 110, 255, 326, 389, 466, 476, 557, 744, 791, 846, 861, 967, 980, 31, 99, 213, 234, 282, 362, 396, 702, 861, 51, 102, 209, 308, 335, 408, 418, 511, 567, 726, 758, 899, 927, 940, 992, 69, 132, 185, 261, 358, 396, 684, 872, 986, 116, 149, 204, 691, 814, 892, 895, 914, 916, 154, 224, 243, 253, 282, 368, 579, 654, 661, 703, 735, 868, 930, 29, 164, 253, 277, 290, 340, 626, 765, 852, 173, 203, 225, 282, 415, 587, 595, 643, 858, 874, 83, 238, 314, 462, 803, 822, 960, 83, 362, 467, 497, 666, 748, 814, 76, 210, 256, 374, 538, 759, 833, 881, 8, 57, 74, 92, 117, 142, 383, 649, 738, 815, 821, 836, 919, 13, 18, 218, 342, 474, 664, 723, 827, 866, 147, 153, 240, 404, 557, 567, 591, 656, 721, 757, 822, 12, 98, 205, 241, 376, 394, 487, 494, 823, 919, 74, 272, 285, 362, 575, 598, 873, 880, 894, 119, 221, 227, 291, 338, 447, 507, 541, 559, 620, 721, 752, 802, 819, 835, 843, 849, 90, 130, 258, 417, 481, 576, 611, 826, 859, 893, 950, 321, 476, 528, 664, 679, 752, 789, 940, 951, 51, 97, 144, 274, 341, 384, 466, 627, 642, 682, 753, 766, 140, 301, 310, 340, 480, 669, 793, 885, 887, 917, 83, 115, 188, 269, 272, 418, 534, 546, 746, 810, 869, 109, 126, 185, 245, 345, 750, 759, 815, 854, 492, 514, 609, 647, 706, 726, 760, 106, 176, 289, 544, 753, 861, 901, 47, 145, 234, 253, 308, 466, 467, 826, 38, 89, 147, 210, 254, 270, 283, 453, 607, 727, 828, 874, 912, 915, 921, 17, 201, 303, 338, 815, 880, 984, 100, 296, 475, 490, 567, 963, 979, 72, 110, 120, 308, 451, 622, 670, 695, 696, 720, 912, 981, 23, 239, 255, 344, 397, 847, 950, 45, 141, 311, 607, 626, 877, 58, 87, 106, 132, 210, 232, 265, 373, 447, 476, 621, 887, 959, 134, 135, 187, 189, 345, 346, 411, 603, 626, 901, 21, 158, 177, 263, 344, 408, 458, 851, 855, 856, 942, 971, 978, 6, 23, 129, 235, 368, 400, 617, 962, 311, 445, 457, 530, 540, 650, 722, 18, 118, 176, 177, 337, 350, 510, 771, 787, 804, 839, 193, 229, 261, 434, 523, 528, 553, 559, 660, 673, 197, 400, 436, 481, 556, 566, 569, 627, 642, 662, 866, 101, 247, 354, 423, 611, 669, 714, 923, 323, 447, 531, 561, 668, 674, 700, 816, 921, 27, 243, 270, 324, 341, 380, 546, 594, 730, 877, 889, 367, 683, 847, 889, 897, 166, 535, 574, 680, 819, 949, 185, 261, 266, 637, 639, 669, 836, 963, 990, 72, 233, 450, 675, 815, 826, 996, 93, 129, 278, 355, 405, 422, 430, 550, 585, 727, 783, 795, 882, 51, 79, 303, 308, 311, 354, 449, 469, 530, 553, 572, 731, 757, 900, 933, 255, 359, 382, 405, 426, 453, 680, 727, 757, 195, 287, 342, 445, 687, 693, 824, 875, 955, 986, 29, 61, 154, 200, 236, 287, 359, 497, 568, 761, 843, 965, 140, 217, 301, 459, 518, 647, 698, 870, 880, 24, 60, 158, 202, 223, 333, 477, 746, 749, 826, 930, 265, 431, 539, 588, 610, 620, 900, 901, 929, 13, 117, 140, 170, 287, 390, 438, 580, 611, 659, 806, 916, 930, 940, 159, 296, 467, 534, 639, 679, 706, 878, 989, 147, 533, 545, 685, 741, 846, 2, 34, 251, 331, 424, 440, 647, 694, 733, 808, 866, 929, 423, 571, 667, 692, 996, 74, 347, 424, 565, 581, 618, 638, 658, 681, 833, 919, 936, 965, 128, 307, 357, 367, 412, 468, 523, 571, 616, 667, 683, 57, 137, 197, 337, 398, 606, 781, 840, 850, 864, 880, 948, 115, 177, 229, 265, 293, 303, 479, 659, 667, 813, 844, 953, 22, 95, 274, 308, 423, 485, 608, 632, 688, 820, 875, 945, 952, 71, 234, 248, 250, 497, 951, 141, 170, 236, 265, 394, 471, 567, 703, 854, 896, 897, 37, 164, 271, 395, 524, 793, 943, 5, 109, 156, 183, 293, 349, 383, 533, 679, 743, 114, 138, 236, 316, 334, 352, 489, 569, 699, 755, 904, 993, 314, 489, 568, 658, 736, 748, 848, 156, 160, 252, 472, 531, 613, 687, 701, 740, 767, 780, 841, 882, 975, 990, 47, 195, 363, 506, 654, 767, 792, 802, 150, 204, 319, 379, 455, 574, 843, 869, 84, 116, 190, 191, 193, 268, 366, 409, 579, 628, 767, 794, 801, 823, 887, 107, 176, 361, 465, 467, 647, 666, 700, 708, 720, 754, 784, 932, 959, 66, 167, 196, 213, 261, 319, 330, 398, 416, 534, 598, 677, 787, 800, 910, 961, 999, 404, 411, 452, 536, 786, 886, 940, 84, 116, 236, 334, 374, 433, 701, 870, 73, 184, 341, 367, 412, 423, 673, 678, 981, 258, 269, 313, 360, 423, 561, 602, 854, 985, 112, 227, 253, 256, 326, 327, 517, 624, 736, 891, 38, 79, 361, 369, 581, 583, 700, 43, 100, 329, 391, 722, 926, 967, 972, 82, 224, 254, 366, 389, 755, 756, 820, 942, 54, 393, 405, 464, 596, 663, 864, 966, 108, 297, 305, 368, 832, 878, 903, 918, 995, 324, 797, 823, 871, 298, 535, 642, 720, 803, 910, 961, 33, 319, 442, 492, 568, 803, 8, 84, 197, 359, 435, 791, 922, 949, 969, 984, 210, 220, 380, 904, 949, 977, 984, 22, 68, 83, 190, 333, 468, 648, 683, 783, 807, 856, 959, 54, 95, 180, 213, 353, 417, 721, 744, 888, 331, 388, 441, 951, 5, 86, 132, 167, 224, 366, 553, 655, 812, 815, 989, 33, 34, 183, 239, 270, 529, 811, 105, 117, 126, 220, 280, 315, 353, 201, 294, 364, 511, 521, 532, 557, 744, 756, 846, 173, 199, 436, 511, 712, 725, 27, 244, 262, 274, 347, 404, 486, 623, 857, 858, 34, 126, 217, 618, 674, 813, 818, 830, 876, 885, 63, 134, 200, 269, 427, 448, 486, 646, 774, 778, 928, 162, 229, 251, 273, 277, 281, 372, 448, 563, 606, 641, 845, 997, 81, 93, 153, 516, 592, 603, 641, 706, 929, 945, 17, 25, 109, 140, 440, 524, 803, 309, 494, 513, 542, 778, 809, 93, 161, 360, 405, 507, 556, 559, 734, 881, 986, 53, 238, 271, 320, 367, 600, 768, 940, 315, 351, 521, 530, 548, 549, 628, 881, 909, 917, 246, 296, 318, 324, 339, 359, 393, 511, 557, 690, 696, 764, 777, 810, 954, 73, 337, 473, 526, 601, 620, 668, 689, 698, 768, 782, 859, 930, 937, 942, 954, 162, 279, 410, 454, 958, 29, 36, 77, 109, 139, 185, 224, 270, 512, 601, 657, 664, 669, 683, 695, 734, 947, 146, 193, 464, 491, 767, 771, 818, 911, 947, 981, 56, 102, 291, 434, 527, 601, 613, 646, 731, 777, 3, 90, 179, 196, 270, 380, 458, 638, 680, 854, 883, 956, 72, 104, 272, 518, 755, 33, 387, 450, 519, 528, 576, 607, 637, 786, 228, 298, 355, 377, 414, 560, 847, 853, 927, 47, 191, 304, 328, 371, 424, 441, 555, 658, 837, 902, 132, 215, 252, 278, 293, 339, 390, 729, 754, 855, 896, 11, 115, 159, 173, 351, 407, 412, 438, 996, 87, 104, 164, 212, 213, 329, 419, 668, 683, 847, 940, 134, 245, 296, 306, 346, 369, 382, 417, 495, 555, 578, 662, 712, 844, 850, 885, 988, 58, 212, 347, 886, 925, 60, 132, 301, 377, 933, 26, 38, 49, 94, 176, 206, 344, 416, 686, 719, 734, 837, 32, 160, 194, 481, 567, 653, 711, 813, 871, 946, 980, 48, 53, 124, 170, 281, 370, 414, 501, 938, 943, 951, 115, 386, 540, 583, 678, 729, 901, 28, 105, 153, 177, 178, 443, 494, 496, 591, 609, 628, 683, 22, 144, 185, 234, 306, 323, 704, 830, 838, 923, 940, 29, 75, 140, 393, 625, 760, 916, 919, 15, 109, 266, 846, 107, 129, 278, 279, 323, 438, 461, 543, 567, 648, 713, 866, 908, 277, 320, 390, 421, 549, 564, 620, 885, 935, 58, 322, 330, 432, 435, 517, 578, 704, 941, 952, 89, 172, 420, 511, 542, 607, 654, 921, 103, 240, 287, 289, 302, 324, 399, 415, 657, 680, 764, 781, 799, 824, 835, 911, 36, 148, 156, 170, 241, 478, 600, 672, 685, 764, 936, 979, 106, 285, 492, 493, 834, 839, 873, 948, 956, 35, 50, 122, 176, 261, 597, 621, 628, 654, 935, 190, 244, 301, 337, 473, 646, 886, 76, 193, 213, 313, 331, 356, 408, 449, 511, 848, 853, 876, 19, 109, 168, 262, 269, 320, 467, 642, 650, 687, 703, 921, 936, 973, 43, 68, 305, 395, 433, 534, 746, 812, 815, 986, 998, 165, 240, 323, 346, 459, 468, 474, 650, 834, 919, 991, 993, 36, 40, 46, 195, 331, 346, 844, 852, 7, 216, 248, 548, 637, 733, 788, 810, 909, 151, 205, 248, 297, 381, 501, 589, 601, 610, 693, 851, 211, 379, 508, 770, 955, 17, 216, 372, 471, 804, 838, 934, 977, 16, 119, 332, 338, 478, 628, 803, 911, 8, 132, 144, 169, 192, 713, 748, 808, 824, 13, 19, 31, 78, 94, 513, 561, 587, 825, 953, 248, 254, 470, 520, 594, 634, 636, 647, 830, 862, 869, 17, 37, 62, 138, 270, 337, 449, 474, 540, 566, 583, 721, 929, 935, 954, 221, 273, 315, 397, 447, 641, 725, 830, 885, 928, 7, 175, 188, 464, 482, 493, 519, 612, 615, 666, 758, 807, 915, 70, 133, 350, 438, 479, 522, 564, 893, 120, 273, 384, 424, 446, 447, 467, 585, 633, 792, 948, 997, 7, 51, 151, 197, 232, 348, 581, 596, 628, 833, 890, 32, 96, 265, 272, 387, 691, 694, 17, 322, 369, 457, 499, 611, 735, 813, 885, 72, 84, 130, 210, 228, 334, 349, 396, 443, 483, 498, 508, 509, 762, 105, 127, 157, 198, 206, 286, 298, 371, 380, 516, 698, 738, 837, 840, 946, 982, 359, 436, 687, 802, 805, 950, 112, 113, 141, 282, 290, 524, 527, 624, 642, 762, 840, 858, 997, 30, 257, 465, 573, 605, 661, 752, 783, 795, 880, 907, 8, 101, 145, 253, 375, 459, 556, 559, 584, 748, 999, 50, 180, 388, 638, 902, 122, 192, 405, 468, 486, 562, 604, 841, 844, 134, 197, 381, 382, 414, 430, 431, 655, 666, 807, 958, 81, 210, 496, 538, 724, 903, 947, 51, 118, 243, 326, 537, 597, 836, 966, 11, 139, 147, 204, 214, 269, 288, 290, 304, 307, 334, 451, 575, 600, 661, 775, 800, 969, 986, 64, 206, 269, 403, 461, 508, 548, 581, 596, 692, 777, 124, 232, 312, 322, 447, 498, 526, 543, 656, 670, 712, 751, 907, 923, 71, 94, 114, 148, 201, 249, 293, 296, 331, 336, 505, 607, 768, 933, 217, 260, 296, 302, 311, 581, 625, 655, 781, 892, 926, 23, 43, 100, 156, 273, 337, 572, 673, 741, 980, 52, 156, 164, 336, 373, 400, 470, 951, 20, 30, 73, 179, 351, 566, 636, 872, 883, 944, 11, 62, 460, 482, 486, 495, 512, 651, 868, 917, 997, 16, 74, 417, 496, 590, 639, 692, 778, 781, 855, 928, 930, 259, 275, 477, 637, 748, 807, 957, 999, 38, 184, 260, 266, 268, 323, 391, 598, 628, 881, 947, 54, 62, 219, 270, 471, 473, 491, 673, 859, 892, 947, 72, 218, 309, 331, 372, 573, 741, 822, 825, 966, 48, 200, 205, 237, 261, 265, 338, 353, 666, 928, 967, 53, 74, 259, 284, 507, 615, 886, 905, 955, 10, 21, 44, 406, 460, 684, 782, 816, 826, 907, 34, 189, 260, 332, 356, 444, 460, 758, 781, 838, 842, 905, 967, 6, 7, 169, 220, 295, 384, 399, 442, 739, 922, 969, 286, 300, 401, 460, 503, 659, 686, 727, 749, 785, 974, 993, 998, 183, 210, 328, 450, 453, 480, 496, 517, 525, 549, 635, 716, 732, 748, 749, 832, 959, 95, 107, 121, 258, 326, 416, 588, 654, 753, 831, 34, 83, 101, 181, 224, 552, 623, 671, 866, 983, 997, 104, 129, 143, 198, 213, 420, 438, 612, 674, 910, 943, 210, 212, 218, 321, 330, 455, 692, 794, 839, 960, 965, 17, 101, 124, 395, 476, 513, 514, 566, 692, 846, 856, 859, 862, 908, 920, 947, 958, 8, 200, 373, 462, 556, 739, 796, 932, 951, 958, 44, 56, 186, 262, 310, 355, 380, 470, 593, 714, 906, 964, 989, 65, 114, 195, 306, 307, 355, 403, 469, 513, 654, 685, 800, 812, 816, 825, 843, 925, 3, 328, 425, 486, 730, 773, 789, 824, 943, 966, 967, 981, 984, 83, 156, 311, 439, 545, 565, 650, 682, 769, 299, 341, 409, 782, 943, 5, 52, 57, 123, 146, 175, 409, 443, 532, 989, 120, 158, 430, 436, 449, 640, 659, 734, 749, 834, 882, 911, 952, 22, 226, 442, 591, 879, 51, 69, 86, 97, 178, 263, 316, 425, 534, 554, 565, 888, 988, 991, 24, 352, 511, 522, 555, 570, 603, 696, 887, 960, 39, 133, 260, 401, 465, 526, 609, 732, 131, 206, 305, 669, 809, 877, 986, 439, 520, 567, 588, 617, 712, 891, 998, 274, 358, 425, 495, 715, 872, 918, 923, 951, 980, 983, 119, 123, 316, 324, 349, 644, 705, 718, 769, 781, 795, 884, 110, 133, 140, 152, 157, 495, 569, 608, 629, 803, 827, 909, 942, 9, 230, 268, 423, 626, 707, 724, 748, 828, 996, 274, 308, 436, 722, 879, 213, 259, 324, 329, 377, 534, 588, 827, 896, 149, 261, 591, 597, 785, 813, 883, 920, 996, 10, 64, 237, 417, 535, 686, 709, 717, 744, 41, 67, 260, 370, 405, 407, 520, 632, 893, 955, 127, 250, 336, 354, 388, 474, 591, 703, 805, 811, 833, 871, 881, 991, 994, 17, 91, 113, 122, 300, 301, 463, 716, 741, 776, 784, 906, 994, 33, 57, 206, 448, 520, 612, 769, 834, 282, 393, 441, 461, 503, 796, 72, 206, 304, 381, 565, 723, 114, 121, 130, 259, 346, 386, 432, 538, 575, 595, 855, 945 }; const double x[1000] = { 602, 730, 528, 886, 890, 755, 124, 435, 24, 245, 112, 144, 171, 746, 547, 172, 905, 97, 70, 133, 117, 951, 783, 271, 174, 263, 769, 889, 920, 698, 644, 138, 34, 866, 831, 249, 611, 672, 502, 450, 225, 557, 793, 244, 336, 942, 604, 135, 507, 328, 36, 299, 769, 323, 957, 171, 455, 627, 701, 624, 383, 354, 675, 971, 562, 945, 354, 90, 495, 269, 684, 468, 832, 38, 189, 103, 509, 754, 85, 70, 727, 897, 441, 745, 443, 561, 23, 796, 104, 178, 388, 178, 663, 652, 533, 738, 423, 500, 390, 567, 834, 806, 97, 517, 352, 636, 158, 839, 822, 68, 707, 838, 778, 15, 201, 364, 397, 166, 372, 39, 525, 360, 596, 664, 606, 182, 684, 147, 941, 695, 815, 721, 377, 215, 386, 265, 598, 890, 241, 302, 423, 623, 610, 26, 311, 887, 496, 968, 549, 581, 421, 638, 154, 471, 768, 953, 7, 906, 894, 155, 687, 813, 376, 463, 815, 436, 817, 5, 366, 412, 435, 825, 437, 614, 437, 14, 492, 117, 610, 0, 837, 665, 464, 847, 513, 606, 532, 503, 566, 270, 559, 509, 634, 339, 535, 708, 663, 1, 837, 508, 499, 216, 758, 36, 242, 351, 432, 439, 562, 307, 643, 498, 659, 16, 265, 653, 105, 527, 595, 448, 832, 381, 714, 533, 178, 644, 455, 667, 7, 378, 639, 19, 50, 415, 591, 827, 956, 69, 712, 767, 368, 552, 230, 288, 146, 676, 651, 333, 284, 782, 283, 774, 791, 451, 795, 991, 618, 620, 547, 769, 226, 563, 117, 524, 287, 615, 322, 41, 582, 156, 664, 261, 368, 702, 25, 439, 382, 123, 682, 970, 511, 928, 870, 453, 865, 724, 255, 504, 567, 105, 465, 146, 349, 616, 419, 389, 629, 964, 482, 483, 252, 183, 300, 578, 255, 825, 702, 650, 468, 808, 939, 360, 830, 281, 969, 139, 488, 603, 449, 731, 941, 172, 643, 569, 90, 966, 468, 818, 249, 649, 661, 661, 955, 52, 17, 364, 472, 854, 154, 543, 110, 327, 905, 715, 940, 612, 248, 634, 690, 326, 622, 52, 935, 244, 406, 604, 351, 303, 268, 717, 247, 475, 718, 835, 885, 534, 842, 942, 929, 713, 786, 72, 122, 443, 64, 512, 38, 189, 552, 935, 778, 832, 569, 144, 810, 634, 399, 261, 918, 728, 648, 340, 730, 358, 496, 928, 344, 929, 572, 876, 667, 933, 584, 122, 739, 978, 37, 250, 192, 113, 763, 214, 852, 365, 638, 570, 82, 861, 448, 649, 813, 950, 843, 154, 527, 12, 953, 153, 311, 177, 490, 754, 973, 511, 777, 649, 605, 311, 539, 133, 245, 940, 717, 851, 189, 905, 410, 214, 170, 983, 998, 404, 599, 843, 41, 955, 505, 916, 947, 851, 397, 194, 288, 781, 897, 546, 305, 113, 356, 454, 679, 774, 314, 897, 452, 169, 391, 344, 880, 840, 327, 404, 29, 353, 688, 196, 135, 860, 878, 288, 523, 335, 1, 680, 923, 480, 108, 10, 188, 165, 500, 331, 668, 279, 939, 797, 203, 925, 768, 310, 453, 213, 909, 769, 136, 93, 501, 926, 249, 888, 591, 628, 317, 668, 364, 375, 951, 432, 217, 765, 469, 458, 25, 330, 279, 734, 995, 187, 150, 739, 179, 551, 844, 920, 871, 906, 397, 540, 376, 123, 233, 19, 227, 109, 158, 20, 11, 899, 462, 655, 837, 756, 930, 580, 304, 655, 419, 695, 319, 496, 856, 575, 700, 223, 793, 462, 666, 274, 967, 650, 287, 521, 69, 898, 684, 759, 31, 373, 515, 56, 966, 971, 836, 950, 94, 647, 948, 766, 988, 556, 458, 415, 46, 741, 519, 186, 393, 409, 658, 349, 833, 339, 61, 250, 49, 63, 503, 21, 951, 809, 391, 242, 739, 823, 9, 548, 876, 431, 920, 451, 967, 291, 529, 37, 133, 656, 240, 981, 223, 167, 458, 624, 473, 570, 942, 260, 808, 16, 792, 699, 537, 84, 906, 429, 728, 320, 785, 301, 9, 679, 882, 98, 431, 223, 920, 173, 895, 605, 68, 698, 696, 987, 855, 191, 657, 533, 478, 321, 846, 921, 490, 278, 145, 500, 274, 974, 505, 33, 936, 691, 922, 140, 846, 951, 745, 893, 803, 316, 689, 960, 509, 518, 911, 121, 12, 477, 702, 94, 521, 751, 840, 492, 666, 922, 714, 43, 683, 871, 531, 774, 137, 914, 745, 722, 78, 398, 384, 536, 365, 245, 807, 925, 201, 917, 368, 214, 246, 143, 388, 937, 483, 480, 793, 415, 835, 554, 514, 838, 655, 837, 481, 483, 777, 447, 963, 596, 248, 819, 696, 540, 163, 333, 589, 863, 603, 835, 952, 253, 329, 552, 207, 684, 593, 618, 742, 53, 90, 27, 955, 217, 955, 20, 520, 221, 316, 45, 948, 552, 110, 594, 774, 517, 880, 32, 575, 852, 463, 685, 10, 58, 945, 572, 875, 633, 942, 880, 426, 283, 491, 848, 491, 280, 412, 1, 819, 199, 190, 577, 488, 936, 678, 79, 317, 408, 689, 353, 889, 294, 561, 501, 411, 554, 321, 193, 748, 309, 110, 454, 33, 28, 193, 166, 804, 710, 581, 70, 726, 805, 673, 751, 147, 793, 395, 151, 129, 143, 610, 700, 590, 577, 814, 104, 990, 56, 254, 816, 278, 108, 765, 31, 208, 804, 730, 960, 323, 152, 202, 449, 238, 907, 532, 618, 377, 295, 625, 252, 383, 345, 46, 934, 908, 851, 304, 235, 623, 808, 363, 80, 373, 858, 839, 385, 426, 727, 615, 675, 860, 602, 623, 780, 246, 22, 681, 623, 293, 421, 908, 419, 811, 631, 155, 139, 861, 262, 789, 344, 507, 14, 445, 995, 316, 74, 32, 239, 932, 586, 167, 578, 555, 8, 720, 804, 18, 185, 637, 185, 21, 121, 993, 457, 0, 911, 330, 214, 343, 600, 720, 645, 542, 991, 704, 261, 481, 242, 949, 909, 745, 799, 644, 858, 132, 886, 194, 886, 695, 912, 980, 956, 51, 885, 410, 88, 578, 636, 698, 636, 532, 579, 389, 124, 386, 54, 616, 203, 838, 732, 152, 775, 749, 373 }; const int ptr[1001] = { 0, 6, 18, 31, 40, 49, 58, 67, 75, 85, 98, 111, 121, 135, 139, 146, 159, 169, 175, 181, 191, 203, 210, 217, 228, 238, 245, 254, 265, 278, 290, 298, 311, 323, 332, 343, 353, 360, 370, 383, 396, 407, 415, 427, 433, 440, 449, 461, 467, 474, 487, 503, 510, 522, 530, 542, 549, 556, 570, 584, 594, 605, 614, 624, 629, 637, 644, 653, 663, 674, 685, 691, 701, 712, 723, 734, 746, 754, 766, 779, 788, 802, 809, 820, 831, 846, 860, 869, 874, 883, 886, 900, 915, 929, 937, 946, 955, 969, 985, 993, 1004, 1014, 1026, 1035, 1040, 1053, 1064, 1073, 1078, 1089, 1097, 1105, 1108, 1119, 1131, 1143, 1156, 1165, 1175, 1187, 1196, 1205, 1209, 1218, 1230, 1242, 1253, 1263, 1277, 1288, 1306, 1323, 1331, 1345, 1355, 1362, 1372, 1380, 1388, 1395, 1412, 1424, 1428, 1436, 1443, 1457, 1473, 1488, 1498, 1511, 1520, 1533, 1543, 1556, 1567, 1578, 1590, 1598, 1609, 1618, 1627, 1634, 1638, 1643, 1649, 1654, 1660, 1675, 1688, 1698, 1712, 1722, 1730, 1738, 1746, 1758, 1765, 1778, 1787, 1802, 1814, 1821, 1833, 1842, 1851, 1864, 1877, 1886, 1890, 1898, 1904, 1916, 1931, 1942, 1953, 1966, 1975, 1988, 1999, 2008, 2021, 2027, 2036, 2049, 2058, 2069, 2078, 2086, 2099, 2109, 2115, 2123, 2133, 2142, 2155, 2166, 2175, 2185, 2191, 2202, 2215, 2220, 2234, 2248, 2260, 2271, 2277, 2285, 2297, 2310, 2318, 2328, 2337, 2352, 2358, 2370, 2378, 2391, 2397, 2407, 2413, 2425, 2434, 2442, 2452, 2462, 2476, 2480, 2487, 2500, 2512, 2525, 2533, 2545, 2552, 2563, 2576, 2585, 2591, 2599, 2608, 2619, 2629, 2643, 2658, 2664, 2675, 2682, 2696, 2705, 2715, 2718, 2736, 2746, 2765, 2771, 2787, 2793, 2802, 2813, 2826, 2837, 2849, 2863, 2870, 2885, 2895, 2904, 2914, 2925, 2931, 2944, 2949, 2957, 2973, 2982, 2995, 3009, 3025, 3031, 3046, 3061, 3069, 3082, 3089, 3100, 3106, 3116, 3119, 3123, 3130, 3136, 3144, 3153, 3162, 3180, 3185, 3200, 3205, 3215, 3225, 3234, 3246, 3255, 3266, 3273, 3283, 3293, 3303, 3312, 3320, 3331, 3342, 3349, 3357, 3367, 3372, 3380, 3387, 3398, 3405, 3417, 3425, 3432, 3443, 3449, 3456, 3461, 3471, 3480, 3491, 3498, 3521, 3530, 3539, 3554, 3562, 3569, 3579, 3585, 3597, 3604, 3613, 3628, 3646, 3657, 3673, 3681, 3691, 3696, 3709, 3717, 3731, 3745, 3756, 3763, 3769, 3774, 3786, 3799, 3810, 3819, 3827, 3838, 3854, 3867, 3876, 3885, 3902, 3911, 3926, 3936, 3948, 3959, 3970, 3983, 3991, 4002, 4009, 4023, 4032, 4043, 4058, 4065, 4078, 4087, 4099, 4106, 4114, 4120, 4132, 4146, 4155, 4168, 4177, 4189, 4199, 4212, 4219, 4231, 4241, 4253, 4260, 4266, 4278, 4287, 4303, 4310, 4322, 4334, 4344, 4354, 4368, 4376, 4383, 4399, 4408, 4416, 4431, 4444, 4458, 4467, 4474, 4486, 4495, 4506, 4515, 4521, 4536, 4549, 4564, 4571, 4580, 4593, 4602, 4613, 4618, 4627, 4635, 4644, 4659, 4664, 4675, 4684, 4690, 4702, 4713, 4723, 4735, 4743, 4751, 4759, 4768, 4779, 4790, 4799, 4811, 4818, 4823, 4830, 4838, 4850, 4861, 4870, 4878, 4890, 4897, 4908, 4916, 4930, 4939, 4950, 4959, 4971, 4977, 4985, 4996, 4999, 5003, 5012, 5018, 5026, 5041, 5048, 5058, 5071, 5081, 5086, 5094, 5099, 5109, 5114, 5127, 5137, 5147, 5162, 5172, 5179, 5187, 5197, 5209, 5226, 5231, 5239, 5248, 5263, 5270, 5283, 5293, 5301, 5308, 5318, 5327, 5342, 5349, 5357, 5367, 5374, 5381, 5395, 5406, 5418, 5428, 5435, 5440, 5452, 5464, 5477, 5490, 5497, 5504, 5510, 5518, 5529, 5542, 5561, 5579, 5588, 5599, 5601, 5609, 5618, 5627, 5631, 5640, 5646, 5654, 5661, 5672, 5690, 5699, 5712, 5723, 5733, 5742, 5752, 5759, 5766, 5776, 5788, 5799, 5801, 5813, 5825, 5829, 5841, 5846, 5858, 5867, 5878, 5892, 5902, 5910, 5921, 5933, 5941, 5957, 5964, 5975, 5988, 6000, 6007, 6019, 6027, 6036, 6046, 6055, 6065, 6080, 6090, 6098, 6110, 6122, 6139, 6151, 6160, 6168, 6181, 6190, 6202, 6209, 6221, 6228, 6238, 6249, 6260, 6266, 6274, 6289, 6302, 6310, 6325, 6334, 6349, 6367, 6370, 6382, 6391, 6399, 6414, 6423, 6435, 6442, 6452, 6461, 6469, 6479, 6493, 6502, 6517, 6524, 6539, 6549, 6555, 6561, 6568, 6575, 6594, 6605, 6613, 6620, 6626, 6637, 6643, 6656, 6669, 6679, 6687, 6698, 6706, 6715, 6730, 6739, 6746, 6762, 6768, 6776, 6785, 6791, 6798, 6805, 6818, 6827, 6836, 6846, 6853, 6861, 6877, 6885, 6894, 6901, 6912, 6924, 6937, 6947, 6951, 6966, 6975, 6985, 6996, 7003, 7019, 7029, 7037, 7046, 7053, 7060, 7068, 7075, 7081, 7088, 7094, 7108, 7117, 7123, 7139, 7150, 7162, 7168, 7182, 7191, 7203, 7219, 7222, 7229, 7243, 7251, 7260, 7269, 7279, 7289, 7294, 7307, 7321, 7338, 7349, 7353, 7361, 7371, 7379, 7386, 7397, 7411, 7422, 7428, 7437, 7442, 7452, 7463, 7474, 7483, 7491, 7499, 7514, 7523, 7536, 7542, 7549, 7556, 7568, 7577, 7586, 7597, 7609, 7623, 7633, 7645, 7658, 7664, 7677, 7694, 7703, 7718, 7727, 7736, 7749, 7758, 7768, 7775, 7782, 7790, 7803, 7812, 7823, 7833, 7842, 7859, 7870, 7879, 7891, 7901, 7912, 7921, 7928, 7935, 7943, 7958, 7965, 7972, 7984, 7991, 7997, 8010, 8020, 8033, 8041, 8048, 8059, 8069, 8080, 8088, 8097, 8108, 8113, 8119, 8128, 8135, 8148, 8163, 8172, 8182, 8194, 8203, 8214, 8223, 8237, 8246, 8252, 8264, 8269, 8282, 8293, 8305, 8317, 8330, 8336, 8347, 8354, 8364, 8376, 8383, 8398, 8406, 8414, 8429, 8443, 8460, 8467, 8475, 8484, 8493, 8503, 8510, 8518, 8527, 8535, 8544, 8548, 8555, 8561, 8571, 8578, 8590, 8599, 8603, 8614, 8621, 8628, 8638, 8644, 8654, 8664, 8675, 8688, 8698, 8705, 8711, 8721, 8729, 8739, 8754, 8770, 8775, 8792, 8802, 8812, 8824, 8829, 8838, 8847, 8858, 8869, 8878, 8889, 8906, 8911, 8916, 8928, 8939, 8950, 8957, 8969, 8980, 8988, 8992, 9005, 9014, 9024, 9032, 9048, 9060, 9069, 9079, 9086, 9098, 9112, 9123, 9135, 9143, 9152, 9163, 9168, 9176, 9184, 9193, 9203, 9214, 9229, 9239, 9252, 9260, 9272, 9283, 9290, 9299, 9313, 9329, 9335, 9348, 9359, 9370, 9375, 9384, 9395, 9402, 9410, 9429, 9440, 9454, 9468, 9479, 9489, 9497, 9507, 9518, 9530, 9538, 9549, 9560, 9570, 9581, 9590, 9600, 9613, 9624, 9637, 9654, 9664, 9675, 9686, 9697, 9714, 9724, 9737, 9754, 9767, 9776, 9781, 9791, 9804, 9809, 9823, 9833, 9841, 9848, 9856, 9867, 9879, 9892, 9902, 9907, 9916, 9925, 9934, 9944, 9959, 9972, 9980, 9986, 9992, 10004 }; const double verify_data[1000] = { 1971101, 3601995, 3608374, 3068439, 2756891, 1644445, 2326970, 3571797, 2167311, 3272467, 5257490, 2287052, 5507394, 1707471, 1181529, 2596954, 2999820, 1456597, 1755714, 2783599, 2224880, 953747, 1863442, 2375479, 3838149, 1472958, 2613759, 1412651, 2454897, 4139599, 1540527, 2373885, 2371153, 2496043, 2946006, 3041837, 2102841, 3413598, 3937131, 3428786, 2323528, 1657458, 3358521, 1821261, 937257, 2638848, 3351703, 2436591, 1387045, 3372777, 4422352, 2696491, 2775768, 1711500, 2463910, 1906176, 2655972, 2176802, 4025605, 1836921, 2902963, 1950818, 2553243, 2012524, 2449182, 1632320, 2628093, 1093587, 3089207, 3020390, 1485696, 1932818, 3334949, 1610563, 2076427, 3114683, 1548840, 3339439, 3335032, 1366398, 1685659, 1668385, 2510712, 2871270, 3270369, 4311377, 1982006, 1326681, 1381634, 398901, 3333661, 3352243, 2878790, 1577319, 2415255, 1191188, 3219765, 3467850, 1940862, 2056258, 1786527, 2278347, 2077897, 1457888, 3707208, 1405999, 952210, 1600564, 2343319, 1781556, 2474389, 522450, 3674982, 3619187, 3211390, 3586103, 1475431, 3546147, 3698208, 2049193, 1979189, 1111515, 2790498, 3439083, 4279066, 2774436, 2077245, 4390617, 3149593, 5326535, 3848199, 2772446, 2682304, 2277814, 1222790, 2067874, 1982666, 2371257, 1270393, 3228410, 2598823, 2428645, 904561, 2100006, 2337148, 3164102, 3908197, 1529402, 3084375, 1927419, 3196639, 2303890, 4265937, 2061281, 2212135, 2407656, 1723976, 2903704, 3276733, 1491735, 1684162, 1307018, 1201185, 636997, 1186016, 1774809, 2607471, 2619840, 3493545, 3226129, 1737347, 2380184, 1201957, 983240, 2529069, 2689857, 3022018, 2223714, 3625235, 3008732, 2417998, 4428750, 2270952, 2186948, 4812008, 2233927, 3334976, 1264519, 1626345, 1123879, 3098605, 4036407, 3104973, 2897790, 3788865, 2422217, 3611590, 1749696, 2447434, 2977777, 1573650, 2620107, 2319242, 2902283, 1882200, 1787017, 2436605, 3467551, 2413830, 187567, 2242075, 1754385, 1836061, 4245412, 3751015, 2715151, 1557751, 421948, 2963355, 2050843, 1758567, 2680768, 4076059, 4484640, 3293151, 1433126, 1649435, 4409656, 2223098, 2455979, 1874200, 2098066, 4020158, 1312572, 2801068, 3341899, 3785087, 1569098, 2778159, 1992179, 2669866, 1914494, 1619868, 2274333, 1857912, 3099797, 809499, 1679713, 3531350, 2599926, 1970143, 2920228, 2883295, 1394658, 3554897, 3534392, 1625041, 1492274, 1451033, 2248274, 2910569, 2341827, 2768016, 3567361, 781606, 2434644, 1782504, 4124675, 3646132, 2864945, 512560, 3618571, 2223074, 4315721, 1195043, 4737421, 1748427, 3474050, 1798506, 4916152, 2411793, 3382242, 5132409, 810557, 4870878, 1368859, 2955757, 1940419, 3146202, 880792, 3448573, 1017493, 2481321, 3652309, 3475252, 2845994, 3182841, 5898263, 1771223, 3346757, 2512678, 1778448, 3432671, 2814247, 3403195, 812303, 2104162, 85040, 989115, 1897384, 1248980, 2002961, 1371732, 2373820, 5178478, 1511192, 5127654, 1468260, 2185303, 2436412, 2978141, 2230665, 1707852, 2529167, 1152196, 3239187, 2498749, 2707774, 1502699, 1633289, 2782744, 4089832, 1548833, 1704769, 2712629, 992084, 1369606, 2480517, 2846051, 3100172, 2371224, 1173652, 1837754, 3822172, 1417367, 1538908, 1146694, 2528965, 2800885, 3461160, 786155, 6573509, 3071638, 1511640, 3652853, 1475533, 1525596, 2695806, 1277883, 3278333, 2226936, 2030339, 3914645, 4318373, 2059669, 3961569, 1772074, 3135802, 1261862, 4771438, 1587528, 2435428, 2869031, 2629400, 1533986, 1866116, 1203541, 2007311, 4295134, 3082652, 2127515, 3110833, 2895900, 4701588, 2727753, 2324739, 2142817, 4359375, 2762710, 2675084, 2776056, 2906201, 2859945, 1471060, 3224362, 2455374, 2030195, 909337, 2716237, 2230075, 3070171, 4476596, 2646370, 3421732, 2163616, 4043766, 2111374, 2016619, 1318843, 3586217, 3000490, 2914687, 2728187, 3496083, 3137438, 1555757, 2975780, 864871, 3568793, 3273559, 4362169, 1225951, 1858409, 1867854, 2081582, 4028493, 1772236, 2634979, 3563733, 1734270, 2430471, 3597625, 1010411, 1086456, 3717761, 3038402, 1630224, 4565438, 3347069, 2543316, 3034145, 1190307, 3710367, 2894919, 4122408, 1917891, 1308296, 1847812, 2799933, 5544619, 990734, 2302389, 2828494, 2767749, 2734181, 1584801, 2096227, 2132396, 1605917, 3953389, 489065, 3370917, 1246610, 1859633, 3905768, 2375583, 2352791, 3066605, 3023804, 1714567, 1630198, 3244096, 3311209, 2837076, 1806523, 3111912, 924345, 891749, 1710635, 2779972, 2288984, 2104226, 2726511, 2994247, 4159385, 927922, 3372483, 2093351, 3228595, 1549615, 3203118, 1566786, 2046013, 1122663, 902592, 2101848, 633763, 1382735, 2235887, 1595380, 1684910, 4534882, 1927642, 3881319, 4091228, 3489550, 1186206, 1089968, 1673520, 2908231, 1060251, 4422500, 2814892, 2014163, 3954105, 2685902, 1427353, 1040905, 2481509, 2984177, 5050926, 1266027, 2158372, 2317752, 4020554, 1226253, 3034218, 3335936, 3282626, 1782262, 3007006, 2399815, 4116453, 1101525, 2175742, 1919181, 1935647, 3021439, 2975812, 1409385, 3435714, 2843659, 2535310, 973352, 4051148, 3198667, 3025227, 3821291, 2634495, 1066026, 1015860, 2374721, 1893315, 2896157, 5768610, 4638503, 1096525, 2521763, 201516, 1885950, 2456554, 2395576, 1805310, 3539192, 706652, 3652867, 1803915, 2740108, 4902727, 2480670, 4763486, 2831231, 2804267, 2958655, 1180330, 1377988, 1967048, 3251495, 3641699, 2327118, 518996, 3627226, 4512513, 821503, 4513458, 1746977, 3396668, 2072470, 3064446, 4435618, 2734309, 2193304, 4275484, 3468741, 2498396, 3068739, 1699359, 2816909, 2705770, 2392503, 1288021, 2667346, 1722567, 2924017, 3160472, 1098169, 3756129, 5913618, 3768712, 2089078, 2340072, 2483109, 4368798, 2778403, 1706517, 2503001, 2633764, 2488649, 3759253, 1596753, 1671868, 1377167, 2721074, 2026518, 3148597, 1753515, 2407030, 3191030, 3974792, 1798541, 4805468, 2569249, 4324091, 3385093, 745588, 2231981, 2000465, 2339460, 3327609, 3719613, 4276833, 1018769, 2495582, 2942706, 2035953, 2227503, 3631249, 2988856, 2784977, 1822310, 4621193, 2352625, 1249877, 1540945, 1241921, 1994350, 5628798, 1620488, 1897543, 952310, 1052254, 3358187, 2994928, 2959189, 2720309, 2875425, 2144130, 4548462, 2048162, 1339841, 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