Statistics

Problem Statement for "CollectAllCoins"

Problem Statement

R * C coins are arranged into a grid with R rows and C columns. The coins are numbered in row major order, starting from zero. (That is, top row from left to right has coins 0 to C-1, second row has coins C to 2C-1, and so on.)

Coin 0 is heads up, all other coins are tails up.

You want to remove all coins, one after another. There are two rules:

  • You can only remove a coin if it's heads up.
  • Whenever you remove a coin, you must flip all coins that are horizontally or vertically adjacent.

Return a int[] containing the numbers of coins in an order in which they can be removed. Any valid solution will be accepted. If there is no solution, return an empty int[] instead.

Definition

Class:
CollectAllCoins
Method:
collect
Parameters:
int, int
Returns:
int[]
Method signature:
int[] collect(int R, int C)
(be sure your method is public)

Constraints

  • R will be between 1 and 30, inclusive.
  • C will be between 1 and 30, inclusive.

Examples

  1. 3

    3

    Returns: {0, 3, 4, 6, 5, 2, 8, 7, 1 }

    The nine coins are numbered as follows: 012 345 678 Below we illustrate the example return value by showing the state of the board at the beginning and also after each step. ('H' denotes a coin that's heads, 'T' denotes a coin that's tails, and '.' a coin that has already been removed.) 0: 1: 2: 3: 4: 5: 6: 7: 8: 9: HTT .HT .HT .TT .TT .TH .H. .H. .H. ... TTT HTT .HT ..H ..H ... ... ... ... ... TTT TTT HTT HHT .TT .TH .TH .H. ... ... There are other valid solutions, too.

  2. 7

    1

    Returns: {0, 1, 2, 3, 4, 5, 6 }

    This is the only correct answer

  3. 2

    3

    Returns: {0, 1, 2, 3, 5, 4 }

    The coins on the board are numbered as follows: 012 345

  4. 14

    28

    Returns: { }

  5. 1

    1

    Returns: {0 }

  6. 1

    2

    Returns: {0, 1 }

  7. 2

    1

    Returns: {0, 1 }

  8. 2

    2

    Returns: { }

  9. 3

    2

    Returns: {0, 2, 4, 1, 5, 3 }

  10. 1

    3

    Returns: {0, 1, 2 }

  11. 3

    1

    Returns: {0, 1, 2 }

  12. 30

    30

    Returns: { }

  13. 30

    29

    Returns: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200, 202, 175, 177, 179, 181, 183, 185, 187, 189, 191, 193, 195, 197, 199, 201, 203, 205, 207, 209, 211, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 204, 206, 208, 210, 212, 214, 216, 218, 220, 222, 224, 226, 228, 230, 232, 234, 236, 238, 240, 242, 244, 246, 248, 250, 252, 254, 256, 258, 260, 233, 235, 237, 239, 241, 243, 245, 247, 249, 251, 253, 255, 257, 259, 261, 263, 265, 267, 269, 271, 273, 275, 277, 279, 281, 283, 285, 287, 289, 262, 264, 266, 268, 270, 272, 274, 276, 278, 280, 282, 284, 286, 288, 290, 292, 294, 296, 298, 300, 302, 304, 306, 308, 310, 312, 314, 316, 318, 291, 293, 295, 297, 299, 301, 303, 305, 307, 309, 311, 313, 315, 317, 319, 321, 323, 325, 327, 329, 331, 333, 335, 337, 339, 341, 343, 345, 347, 320, 322, 324, 326, 328, 330, 332, 334, 336, 338, 340, 342, 344, 346, 348, 350, 352, 354, 356, 358, 360, 362, 364, 366, 368, 370, 372, 374, 376, 349, 351, 353, 355, 357, 359, 361, 363, 365, 367, 369, 371, 373, 375, 377, 379, 381, 383, 385, 387, 389, 391, 393, 395, 397, 399, 401, 403, 405, 378, 380, 382, 384, 386, 388, 390, 392, 394, 396, 398, 400, 402, 404, 406, 408, 410, 412, 414, 416, 418, 420, 422, 424, 426, 428, 430, 432, 434, 407, 409, 411, 413, 415, 417, 419, 421, 423, 425, 427, 429, 431, 433, 435, 437, 439, 441, 443, 445, 447, 449, 451, 453, 455, 457, 459, 461, 463, 436, 438, 440, 442, 444, 446, 448, 450, 452, 454, 456, 458, 460, 462, 464, 466, 468, 470, 472, 474, 476, 478, 480, 482, 484, 486, 488, 490, 492, 465, 467, 469, 471, 473, 475, 477, 479, 481, 483, 485, 487, 489, 491, 493, 495, 497, 499, 501, 503, 505, 507, 509, 511, 513, 515, 517, 519, 521, 494, 496, 498, 500, 502, 504, 506, 508, 510, 512, 514, 516, 518, 520, 522, 524, 526, 528, 530, 532, 534, 536, 538, 540, 542, 544, 546, 548, 550, 523, 525, 527, 529, 531, 533, 535, 537, 539, 541, 543, 545, 547, 549, 551, 553, 555, 557, 559, 561, 563, 565, 567, 569, 571, 573, 575, 577, 579, 552, 554, 556, 558, 560, 562, 564, 566, 568, 570, 572, 574, 576, 578, 580, 582, 584, 586, 588, 590, 592, 594, 596, 598, 600, 602, 604, 606, 608, 581, 583, 585, 587, 589, 591, 593, 595, 597, 599, 601, 603, 605, 607, 609, 611, 613, 615, 617, 619, 621, 623, 625, 627, 629, 631, 633, 635, 637, 610, 612, 614, 616, 618, 620, 622, 624, 626, 628, 630, 632, 634, 636, 638, 640, 642, 644, 646, 648, 650, 652, 654, 656, 658, 660, 662, 664, 666, 639, 641, 643, 645, 647, 649, 651, 653, 655, 657, 659, 661, 663, 665, 667, 669, 671, 673, 675, 677, 679, 681, 683, 685, 687, 689, 691, 693, 695, 668, 670, 672, 674, 676, 678, 680, 682, 684, 686, 688, 690, 692, 694, 696, 698, 700, 702, 704, 706, 708, 710, 712, 714, 716, 718, 720, 722, 724, 697, 699, 701, 703, 705, 707, 709, 711, 713, 715, 717, 719, 721, 723, 725, 727, 729, 731, 733, 735, 737, 739, 741, 743, 745, 747, 749, 751, 753, 726, 728, 730, 732, 734, 736, 738, 740, 742, 744, 746, 748, 750, 752, 754, 756, 758, 760, 762, 764, 766, 768, 770, 772, 774, 776, 778, 780, 782, 755, 757, 759, 761, 763, 765, 767, 769, 771, 773, 775, 777, 779, 781, 783, 785, 787, 789, 791, 793, 795, 797, 799, 801, 803, 805, 807, 809, 811, 784, 786, 788, 790, 792, 794, 796, 798, 800, 802, 804, 806, 808, 810, 812, 814, 816, 818, 820, 822, 824, 826, 828, 830, 832, 834, 836, 838, 840, 813, 815, 817, 819, 821, 823, 825, 827, 829, 831, 833, 835, 837, 839, 841, 843, 845, 847, 849, 851, 853, 855, 857, 859, 861, 863, 865, 867, 869, 842, 844, 846, 848, 850, 852, 854, 856, 858, 860, 862, 864, 866, 868 }

  14. 29

    30

    Returns: {0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 480, 510, 540, 570, 600, 630, 660, 690, 720, 750, 780, 810, 840, 1, 61, 121, 181, 241, 301, 361, 421, 481, 541, 601, 661, 721, 781, 841, 31, 91, 151, 211, 271, 331, 391, 451, 511, 571, 631, 691, 751, 811, 2, 62, 122, 182, 242, 302, 362, 422, 482, 542, 602, 662, 722, 782, 842, 32, 92, 152, 212, 272, 332, 392, 452, 512, 572, 632, 692, 752, 812, 3, 63, 123, 183, 243, 303, 363, 423, 483, 543, 603, 663, 723, 783, 843, 33, 93, 153, 213, 273, 333, 393, 453, 513, 573, 633, 693, 753, 813, 4, 64, 124, 184, 244, 304, 364, 424, 484, 544, 604, 664, 724, 784, 844, 34, 94, 154, 214, 274, 334, 394, 454, 514, 574, 634, 694, 754, 814, 5, 65, 125, 185, 245, 305, 365, 425, 485, 545, 605, 665, 725, 785, 845, 35, 95, 155, 215, 275, 335, 395, 455, 515, 575, 635, 695, 755, 815, 6, 66, 126, 186, 246, 306, 366, 426, 486, 546, 606, 666, 726, 786, 846, 36, 96, 156, 216, 276, 336, 396, 456, 516, 576, 636, 696, 756, 816, 7, 67, 127, 187, 247, 307, 367, 427, 487, 547, 607, 667, 727, 787, 847, 37, 97, 157, 217, 277, 337, 397, 457, 517, 577, 637, 697, 757, 817, 8, 68, 128, 188, 248, 308, 368, 428, 488, 548, 608, 668, 728, 788, 848, 38, 98, 158, 218, 278, 338, 398, 458, 518, 578, 638, 698, 758, 818, 9, 69, 129, 189, 249, 309, 369, 429, 489, 549, 609, 669, 729, 789, 849, 39, 99, 159, 219, 279, 339, 399, 459, 519, 579, 639, 699, 759, 819, 10, 70, 130, 190, 250, 310, 370, 430, 490, 550, 610, 670, 730, 790, 850, 40, 100, 160, 220, 280, 340, 400, 460, 520, 580, 640, 700, 760, 820, 11, 71, 131, 191, 251, 311, 371, 431, 491, 551, 611, 671, 731, 791, 851, 41, 101, 161, 221, 281, 341, 401, 461, 521, 581, 641, 701, 761, 821, 12, 72, 132, 192, 252, 312, 372, 432, 492, 552, 612, 672, 732, 792, 852, 42, 102, 162, 222, 282, 342, 402, 462, 522, 582, 642, 702, 762, 822, 13, 73, 133, 193, 253, 313, 373, 433, 493, 553, 613, 673, 733, 793, 853, 43, 103, 163, 223, 283, 343, 403, 463, 523, 583, 643, 703, 763, 823, 14, 74, 134, 194, 254, 314, 374, 434, 494, 554, 614, 674, 734, 794, 854, 44, 104, 164, 224, 284, 344, 404, 464, 524, 584, 644, 704, 764, 824, 15, 75, 135, 195, 255, 315, 375, 435, 495, 555, 615, 675, 735, 795, 855, 45, 105, 165, 225, 285, 345, 405, 465, 525, 585, 645, 705, 765, 825, 16, 76, 136, 196, 256, 316, 376, 436, 496, 556, 616, 676, 736, 796, 856, 46, 106, 166, 226, 286, 346, 406, 466, 526, 586, 646, 706, 766, 826, 17, 77, 137, 197, 257, 317, 377, 437, 497, 557, 617, 677, 737, 797, 857, 47, 107, 167, 227, 287, 347, 407, 467, 527, 587, 647, 707, 767, 827, 18, 78, 138, 198, 258, 318, 378, 438, 498, 558, 618, 678, 738, 798, 858, 48, 108, 168, 228, 288, 348, 408, 468, 528, 588, 648, 708, 768, 828, 19, 79, 139, 199, 259, 319, 379, 439, 499, 559, 619, 679, 739, 799, 859, 49, 109, 169, 229, 289, 349, 409, 469, 529, 589, 649, 709, 769, 829, 20, 80, 140, 200, 260, 320, 380, 440, 500, 560, 620, 680, 740, 800, 860, 50, 110, 170, 230, 290, 350, 410, 470, 530, 590, 650, 710, 770, 830, 21, 81, 141, 201, 261, 321, 381, 441, 501, 561, 621, 681, 741, 801, 861, 51, 111, 171, 231, 291, 351, 411, 471, 531, 591, 651, 711, 771, 831, 22, 82, 142, 202, 262, 322, 382, 442, 502, 562, 622, 682, 742, 802, 862, 52, 112, 172, 232, 292, 352, 412, 472, 532, 592, 652, 712, 772, 832, 23, 83, 143, 203, 263, 323, 383, 443, 503, 563, 623, 683, 743, 803, 863, 53, 113, 173, 233, 293, 353, 413, 473, 533, 593, 653, 713, 773, 833, 24, 84, 144, 204, 264, 324, 384, 444, 504, 564, 624, 684, 744, 804, 864, 54, 114, 174, 234, 294, 354, 414, 474, 534, 594, 654, 714, 774, 834, 25, 85, 145, 205, 265, 325, 385, 445, 505, 565, 625, 685, 745, 805, 865, 55, 115, 175, 235, 295, 355, 415, 475, 535, 595, 655, 715, 775, 835, 26, 86, 146, 206, 266, 326, 386, 446, 506, 566, 626, 686, 746, 806, 866, 56, 116, 176, 236, 296, 356, 416, 476, 536, 596, 656, 716, 776, 836, 27, 87, 147, 207, 267, 327, 387, 447, 507, 567, 627, 687, 747, 807, 867, 57, 117, 177, 237, 297, 357, 417, 477, 537, 597, 657, 717, 777, 837, 28, 88, 148, 208, 268, 328, 388, 448, 508, 568, 628, 688, 748, 808, 868, 58, 118, 178, 238, 298, 358, 418, 478, 538, 598, 658, 718, 778, 838, 29, 89, 149, 209, 269, 329, 389, 449, 509, 569, 629, 689, 749, 809, 869, 59, 119, 179, 239, 299, 359, 419, 479, 539, 599, 659, 719, 779, 839 }

  15. 29

    29

    Returns: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200, 202, 175, 177, 179, 181, 183, 185, 187, 189, 191, 193, 195, 197, 199, 201, 203, 205, 207, 209, 211, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 204, 206, 208, 210, 212, 214, 216, 218, 220, 222, 224, 226, 228, 230, 232, 234, 236, 238, 240, 242, 244, 246, 248, 250, 252, 254, 256, 258, 260, 233, 235, 237, 239, 241, 243, 245, 247, 249, 251, 253, 255, 257, 259, 261, 263, 265, 267, 269, 271, 273, 275, 277, 279, 281, 283, 285, 287, 289, 262, 264, 266, 268, 270, 272, 274, 276, 278, 280, 282, 284, 286, 288, 290, 292, 294, 296, 298, 300, 302, 304, 306, 308, 310, 312, 314, 316, 318, 291, 293, 295, 297, 299, 301, 303, 305, 307, 309, 311, 313, 315, 317, 319, 321, 323, 325, 327, 329, 331, 333, 335, 337, 339, 341, 343, 345, 347, 320, 322, 324, 326, 328, 330, 332, 334, 336, 338, 340, 342, 344, 346, 348, 350, 352, 354, 356, 358, 360, 362, 364, 366, 368, 370, 372, 374, 376, 349, 351, 353, 355, 357, 359, 361, 363, 365, 367, 369, 371, 373, 375, 377, 379, 381, 383, 385, 387, 389, 391, 393, 395, 397, 399, 401, 403, 405, 378, 380, 382, 384, 386, 388, 390, 392, 394, 396, 398, 400, 402, 404, 406, 408, 410, 412, 414, 416, 418, 420, 422, 424, 426, 428, 430, 432, 434, 407, 409, 411, 413, 415, 417, 419, 421, 423, 425, 427, 429, 431, 433, 435, 437, 439, 441, 443, 445, 447, 449, 451, 453, 455, 457, 459, 461, 463, 436, 438, 440, 442, 444, 446, 448, 450, 452, 454, 456, 458, 460, 462, 464, 466, 468, 470, 472, 474, 476, 478, 480, 482, 484, 486, 488, 490, 492, 465, 467, 469, 471, 473, 475, 477, 479, 481, 483, 485, 487, 489, 491, 493, 495, 497, 499, 501, 503, 505, 507, 509, 511, 513, 515, 517, 519, 521, 494, 496, 498, 500, 502, 504, 506, 508, 510, 512, 514, 516, 518, 520, 522, 524, 526, 528, 530, 532, 534, 536, 538, 540, 542, 544, 546, 548, 550, 523, 525, 527, 529, 531, 533, 535, 537, 539, 541, 543, 545, 547, 549, 551, 553, 555, 557, 559, 561, 563, 565, 567, 569, 571, 573, 575, 577, 579, 552, 554, 556, 558, 560, 562, 564, 566, 568, 570, 572, 574, 576, 578, 580, 582, 584, 586, 588, 590, 592, 594, 596, 598, 600, 602, 604, 606, 608, 581, 583, 585, 587, 589, 591, 593, 595, 597, 599, 601, 603, 605, 607, 609, 611, 613, 615, 617, 619, 621, 623, 625, 627, 629, 631, 633, 635, 637, 610, 612, 614, 616, 618, 620, 622, 624, 626, 628, 630, 632, 634, 636, 638, 640, 642, 644, 646, 648, 650, 652, 654, 656, 658, 660, 662, 664, 666, 639, 641, 643, 645, 647, 649, 651, 653, 655, 657, 659, 661, 663, 665, 667, 669, 671, 673, 675, 677, 679, 681, 683, 685, 687, 689, 691, 693, 695, 668, 670, 672, 674, 676, 678, 680, 682, 684, 686, 688, 690, 692, 694, 696, 698, 700, 702, 704, 706, 708, 710, 712, 714, 716, 718, 720, 722, 724, 697, 699, 701, 703, 705, 707, 709, 711, 713, 715, 717, 719, 721, 723, 725, 727, 729, 731, 733, 735, 737, 739, 741, 743, 745, 747, 749, 751, 753, 726, 728, 730, 732, 734, 736, 738, 740, 742, 744, 746, 748, 750, 752, 754, 756, 758, 760, 762, 764, 766, 768, 770, 772, 774, 776, 778, 780, 782, 755, 757, 759, 761, 763, 765, 767, 769, 771, 773, 775, 777, 779, 781, 783, 785, 787, 789, 791, 793, 795, 797, 799, 801, 803, 805, 807, 809, 811, 784, 786, 788, 790, 792, 794, 796, 798, 800, 802, 804, 806, 808, 810, 812, 814, 816, 818, 820, 822, 824, 826, 828, 830, 832, 834, 836, 838, 840, 813, 815, 817, 819, 821, 823, 825, 827, 829, 831, 833, 835, 837, 839 }

  16. 17

    27

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

  17. 27

    17

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

  18. 2

    27

    Returns: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52 }

  19. 2

    28

    Returns: { }

  20. 26

    2

    Returns: { }

  21. 25

    2

    Returns: {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47 }

  22. 1

    23

    Returns: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 }

  23. 24

    1

    Returns: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 }

  24. 7

    18

    Returns: {0, 18, 36, 54, 72, 90, 108, 1, 37, 73, 109, 19, 55, 91, 2, 38, 74, 110, 20, 56, 92, 3, 39, 75, 111, 21, 57, 93, 4, 40, 76, 112, 22, 58, 94, 5, 41, 77, 113, 23, 59, 95, 6, 42, 78, 114, 24, 60, 96, 7, 43, 79, 115, 25, 61, 97, 8, 44, 80, 116, 26, 62, 98, 9, 45, 81, 117, 27, 63, 99, 10, 46, 82, 118, 28, 64, 100, 11, 47, 83, 119, 29, 65, 101, 12, 48, 84, 120, 30, 66, 102, 13, 49, 85, 121, 31, 67, 103, 14, 50, 86, 122, 32, 68, 104, 15, 51, 87, 123, 33, 69, 105, 16, 52, 88, 124, 34, 70, 106, 17, 53, 89, 125, 35, 71, 107 }

  25. 22

    5

    Returns: {0, 1, 2, 3, 4, 5, 7, 9, 6, 8, 10, 12, 14, 11, 13, 15, 17, 19, 16, 18, 20, 22, 24, 21, 23, 25, 27, 29, 26, 28, 30, 32, 34, 31, 33, 35, 37, 39, 36, 38, 40, 42, 44, 41, 43, 45, 47, 49, 46, 48, 50, 52, 54, 51, 53, 55, 57, 59, 56, 58, 60, 62, 64, 61, 63, 65, 67, 69, 66, 68, 70, 72, 74, 71, 73, 75, 77, 79, 76, 78, 80, 82, 84, 81, 83, 85, 87, 89, 86, 88, 90, 92, 94, 91, 93, 95, 97, 99, 96, 98, 100, 102, 104, 101, 103, 105, 107, 109, 106, 108 }

  26. 18

    12

    Returns: { }

  27. 7

    8

    Returns: {0, 8, 16, 24, 32, 40, 48, 1, 17, 33, 49, 9, 25, 41, 2, 18, 34, 50, 10, 26, 42, 3, 19, 35, 51, 11, 27, 43, 4, 20, 36, 52, 12, 28, 44, 5, 21, 37, 53, 13, 29, 45, 6, 22, 38, 54, 14, 30, 46, 7, 23, 39, 55, 15, 31, 47 }

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