Problem Statement
There is a country with N cities, numbered from 0 to N-1.
Your company has a warehouse in city 0. You want to distribute your wares from city 0 to all other cities.
In order to do that, you can hire one or more trucks. Each truck will visit some subset of the other cities and then return back to city 0.
You refuse to pay the truckers for useless work, so each of the cities 1 to N-1 must be visited only by one truck and only exactly once.
Additionally, you are limited by a demand made by the truckers' union: each trucker must receive an equal amount of work - more precisely, an equally long list of orders. In other words, each trucker must visit the same number of cities.
You are given the
Calculate and return the minimal total cost of distributing your wares to the entire country.
Definition
- Class:
- TruckUnion
- Method:
- optimize
- Parameters:
- int, int[]
- Returns:
- int
- Method signature:
- int optimize(int N, int[] C)
- (be sure your method is public)
Notes
- Each trucker may only return to city 0 at the end of their trip.
Constraints
- N will be between 2 and 18, inclusive.
- C will contain exactly N^2 values.
- For each i, C[i*N+i] will be 0.
- Each other element of C will be between 1 and 10^6, inclusive.
Examples
5
{0, 1, 1, 1, 1, 1, 0, 9, 9, 9, 1, 9, 0, 9, 9, 1, 9, 9, 0, 9, 1, 9, 9, 9, 0}
Returns: 8
We can send a single truck with wares for all four remaining cities. Regardless of which route we choose (e.g., 0-1-3-4-2-0), the total cost will be 1+9+9+9+1 = 29. We can send two trucks, each with wares for two cities. Again, each schedule (e.g., one truck goes 0-1-3-0 and the other 0-4-2-0) has the same cost: 1+9+1 + 1+9+1 = 22. We can send four trucks. Each will visit a single city and return back. This has the cost 4*(1+1) = 8 and this is the best option.
5
{0, 9, 9, 9, 8, 8, 0, 9, 9, 9, 9, 9, 0, 8, 9, 9, 8, 9, 0, 9, 9, 9, 8, 9, 0}
Returns: 40
Now that the travel costs are much more uniform, the optimal solution is to send a single truck. This time the exact route matters. The optimal truck route is 0-4-2-3-1-0. On this route each movement costs 8 and thus the total cost of the route is 5*8 = 40.
2
{0, 1000000, 1, 0}
Returns: 1000001
5
{0, 9, 9, 1, 1, 1, 0, 9, 9, 9, 1, 9, 0, 8, 9, 9, 8, 9, 0, 9, 9, 9, 8, 9, 0}
Returns: 20
Here's an example where it's optimal to use two trucks. An optimal solution: Send one truck along the route 0-3-1-0 (cost 1+8+1 = 10) and the other one along the route 0-4-2-0 (again, cost 1+8+1 = 10).
5
{0, 1, 1, 1000000, 1, 1, 0, 90000, 80000, 70000, 1, 60000, 0, 1, 50000, 900000, 40000, 1, 0, 1, 1, 30000, 20000, 1, 0}
Returns: 30004
Here the ideal solution would be to send one truck along 0-1-0 and the other along 0-2-3-4-0, only paying 6 for the whole distribution. However, the truck union rules forbid this solution, as the second trucker would have to visit more cities than the first trucker. The optimal valid solution is to send a single truck along the route 0-2-3-4-1-0.
3
{0, 65563, 451083, 580534, 0, 598518, 360155, 269933, 0}
Returns: 1024236
3
{0, 283591, 4289, 4, 0, 66733, 949, 94, 0}
Returns: 4387
4
{0, 253807, 34880, 588195, 392343, 0, 721003, 370622, 630169, 358523, 0, 603040, 798909, 205504, 250211, 0}
Returns: 1235767
4
{0, 612, 1809, 49337, 5, 0, 19993, 6988, 378, 99823, 0, 26614, 234744, 184, 321879, 0}
Returns: 28612
5
{0, 508978, 265436, 632837, 970733, 585151, 0, 465449, 15929, 178568, 573564, 657622, 0, 798460, 86797, 78229, 278659, 536069, 0, 652753, 573430, 499658, 820339, 840823, 0}
Returns: 946049
5
{0, 401087, 854582, 194778, 54, 5603, 0, 40, 5, 221263, 58481, 6, 0, 652608, 4646, 1066, 138, 10, 0, 63, 62494, 133690, 2, 13, 0}
Returns: 1133
6
{0, 652265, 245893, 746841, 64210, 397127, 129131, 0, 92893, 317434, 56510, 921961, 574469, 322611, 0, 642412, 940029, 769672, 560871, 158550, 576642, 0, 799464, 286430, 649056, 899995, 598564, 84624, 0, 515118, 359364, 583556, 54718, 999541, 120162, 0}
Returns: 941724
6
{0, 506, 335361, 2, 15626, 4638, 506, 0, 109, 682, 8562, 156810, 15737, 134, 0, 276, 251, 2328, 7, 112979, 212781, 0, 620175, 6, 3410, 112737, 4, 485557, 0, 1139, 3145, 181, 363, 13099, 15408, 0}
Returns: 3959
7
{0, 608475, 503002, 646, 28861, 443279, 908248, 479622, 0, 459149, 643888, 854209, 901659, 270242, 308242, 107487, 0, 129865, 978739, 177994, 443640, 353010, 521697, 446691, 0, 527807, 597970, 538167, 275882, 328194, 581741, 24188, 0, 638467, 705766, 915826, 397747, 897407, 958457, 623494, 0, 730632, 623737, 723361, 654322, 962061, 484260, 646952, 0}
Returns: 1969460
7
{0, 1, 357282, 303003, 29852, 1, 11074, 470754, 0, 3, 4093, 14306, 7, 4, 7470, 79201, 0, 31975, 9727, 3389, 5706, 918, 2, 27297, 0, 252, 3, 2381, 379709, 46581, 49655, 314, 0, 346, 24291, 3989, 235819, 385483, 916560, 6, 0, 158830, 87, 2, 43787, 18, 2, 234300, 0}
Returns: 6119
8
{0, 309199, 575935, 671652, 230210, 712077, 962405, 363769, 805970, 0, 672582, 329416, 106866, 37525, 211627, 850455, 586245, 142053, 0, 981946, 95309, 874215, 334841, 806085, 750150, 695620, 984107, 0, 960513, 449805, 530810, 572482, 600393, 789476, 807201, 713093, 0, 369260, 836235, 546648, 544715, 446169, 668836, 460453, 457222, 0, 433182, 763125, 514495, 23777, 204278, 342292, 51456, 628798, 0, 449343, 945022, 106024, 460424, 810917, 611113, 130058, 100971, 0}
Returns: 2380610
8
{0, 1, 29, 31948, 40600, 89, 551949, 130229, 657, 0, 2, 418749, 1, 216, 45, 1783, 11, 8757, 0, 5003, 7522, 2043, 139, 259730, 98, 2287, 2829, 0, 38582, 1718, 9302, 3, 144, 22, 118, 22854, 0, 4, 182, 114382, 23404, 922, 1, 864, 4, 0, 376792, 32988, 1, 3948, 37, 229, 55565, 1, 0, 1, 14856, 604, 235, 1225, 3594, 25, 181243, 0}
Returns: 436
9
{0, 7987, 443485, 448407, 436484, 741436, 443586, 606405, 769181, 133778, 0, 810713, 756707, 775820, 996596, 777567, 893517, 393962, 565068, 672544, 0, 482429, 275399, 671467, 865267, 672540, 154732, 78731, 41547, 618506, 0, 852632, 766501, 616321, 134498, 73930, 951812, 18384, 143629, 128598, 0, 817745, 133466, 641879, 895756, 976579, 991043, 306306, 597635, 631963, 0, 438638, 573956, 781653, 511777, 642218, 895342, 609165, 912899, 24600, 0, 819875, 843991, 626829, 568292, 606353, 863724, 664095, 759366, 152945, 0, 242461, 889783, 122981, 158874, 939381, 952301, 298991, 646693, 507856, 0}
Returns: 1594922
9
{0, 7780, 358341, 8088, 29754, 895, 105105, 457, 2193, 403032, 0, 2463, 4, 1720, 169736, 217, 17, 8035, 663, 193, 0, 5, 23, 381, 13777, 13, 5, 23, 107530, 740238, 0, 1, 2752, 21963, 57, 1, 588, 152, 11, 227, 0, 112420, 7, 1484, 384, 430344, 141119, 370911, 484, 628, 0, 215, 152, 362, 1, 375945, 63, 18921, 2143, 681472, 0, 368, 5650, 2, 758654, 77237, 120492, 417, 1267, 3, 0, 4, 110187, 258015, 71, 827, 3132, 146634, 3, 11800, 0}
Returns: 1319
10
{0, 333986, 457622, 541348, 260884, 639573, 713401, 893379, 736526, 673563, 922028, 0, 598106, 664833, 219918, 913075, 599337, 865292, 186090, 198605, 250899, 790266, 0, 30809, 728649, 637644, 892605, 534317, 902080, 942753, 852001, 635122, 273194, 0, 638649, 309013, 940469, 208203, 359978, 620684, 906774, 634049, 660544, 924763, 0, 353080, 528863, 182257, 783627, 813804, 889500, 343703, 390806, 193782, 164831, 0, 762426, 517401, 79203, 36897, 409868, 486768, 974861, 728236, 471919, 308568, 0, 98507, 828696, 670482, 729971, 516233, 849351, 657878, 900210, 283618, 349999, 0, 729074, 227534, 859912, 866127, 950263, 733299, 891393, 849096, 448252, 79144, 0, 641624, 401137, 339279, 482040, 306115, 168898, 253813, 191246, 380286, 241414, 0}
Returns: 2534222
10
{0, 62, 1042, 822489, 234, 48238, 15634, 1, 14, 11258, 69, 0, 78605, 69008, 124302, 129170, 173342, 23, 209, 63, 50773, 12376, 0, 96, 68, 11, 9580, 733, 608, 168, 220, 10, 2, 0, 315974, 277, 701, 3, 153, 356, 260816, 337639, 11, 97055, 0, 244, 352, 5523, 252, 60, 1530, 2781, 21, 288455, 52, 0, 838741, 151, 373, 1, 376, 489, 21, 105219, 12929, 282, 0, 3, 242479, 14, 2966, 59871, 11180, 230, 855, 7, 5247, 0, 94, 134, 918, 105234, 48, 2, 86, 446999, 1195, 24933, 0, 35, 252, 77, 52799, 28, 179, 51135, 21, 668, 251, 0}
Returns: 318
11
{0, 274103, 158344, 410038, 707221, 230002, 232579, 840673, 789641, 828259, 186767, 90421, 0, 304157, 541937, 152826, 855706, 487727, 815325, 309540, 33108, 990609, 111767, 930572, 0, 581869, 231602, 217400, 111465, 206509, 523653, 401873, 317122, 751415, 267745, 12762, 0, 351712, 377881, 440374, 101390, 92215, 345599, 972518, 272693, 559218, 875210, 242996, 0, 987421, 754326, 723613, 946211, 144429, 257894, 706147, 963144, 840209, 521425, 577617, 0, 662847, 210391, 809510, 35770, 776901, 175858, 24853, 597013, 912228, 912611, 328982, 0, 719397, 384608, 885186, 240199, 256568, 512372, 388488, 211579, 864534, 905561, 445301, 0, 486124, 624484, 644780, 233276, 37283, 806925, 426454, 488772, 977215, 243094, 444109, 0, 802854, 19066, 443298, 648243, 537553, 69144, 514439, 202760, 409830, 196628, 759683, 0, 251217, 516155, 545048, 12308, 877322, 577270, 982192, 309942, 502643, 329507, 321284, 0}
Returns: 1359405
11
{0, 378760, 1, 63, 246687, 29488, 118245, 14, 1050, 55027, 79566, 451862, 0, 167, 1, 1, 173, 1789, 81, 77, 13, 1, 28, 144, 0, 105, 12495, 6, 130, 816962, 100613, 15843, 13, 11, 4, 4070, 0, 909869, 1, 96779, 32094, 4563, 24061, 54044, 47186, 3916, 10, 22, 0, 183499, 124233, 25, 61243, 122690, 29, 2180, 72012, 1, 62, 34, 0, 776, 25501, 4, 2013, 245, 11233, 6, 1978, 1, 1, 610176, 0, 46, 168612, 63, 39758, 306, 22746, 1, 49708, 12, 1324, 891, 0, 7427, 214332, 28, 7, 18, 5, 4, 33, 28, 4, 128650, 0, 646, 12, 81, 1, 29, 69362, 2, 60729, 36916, 1521, 1569, 0, 278, 17, 53167, 479, 560, 1539, 716239, 43485, 33, 126571, 97, 0}
Returns: 95
12
{0, 791032, 687141, 54763, 935467, 357714, 647257, 426758, 97307, 79527, 651515, 358517, 218856, 0, 358632, 726890, 126570, 652743, 159383, 624519, 472527, 935987, 984834, 397008, 609610, 352287, 0, 270300, 967901, 287682, 705047, 479839, 262109, 505623, 186003, 602135, 429182, 407320, 207921, 0, 339292, 46628, 893909, 246680, 70690, 122140, 287081, 251088, 505542, 462650, 792570, 146601, 0, 100663, 735170, 8672, 615133, 349306, 297429, 598012, 41991, 277682, 392482, 852870, 390716, 0, 165703, 954027, 990618, 92210, 784406, 269564, 94196, 505928, 562238, 530567, 489569, 699514, 0, 634795, 405903, 170806, 965824, 309360, 126530, 466955, 443721, 612783, 708669, 277781, 261293, 0, 252715, 847674, 798697, 48345, 164469, 34912, 802148, 966881, 319780, 678203, 863538, 439851, 0, 259555, 921160, 222269, 975601, 59141, 727122, 285694, 834142, 608088, 870003, 609806, 222993, 0, 40288, 337219, 287284, 139768, 436457, 125696, 121101, 239367, 556070, 951916, 188014, 730795, 0, 640140, 788636, 190333, 632160, 116713, 410437, 339563, 281329, 7342, 992200, 937570, 722769, 0}
Returns: 1335121
12
{0, 16, 846563, 209061, 7164, 762, 365, 925, 1457, 13, 34667, 10619, 111648, 0, 2, 120543, 42867, 21, 9327, 55, 2836, 18693, 35, 711, 2099, 14, 0, 5, 56, 246, 3772, 17514, 20, 54, 446082, 8, 562436, 10, 17, 0, 41502, 771, 468, 15, 10833, 29, 10, 20535, 7128, 251344, 51, 24, 0, 479922, 26, 6, 94736, 61, 11258, 99, 624676, 2244, 1149, 8830, 6, 0, 1044, 1478, 44, 26, 113, 1, 14, 884, 16154, 16318, 175423, 1, 0, 891, 5492, 47794, 29861, 1, 382, 24399, 37, 28742, 187989, 17157, 766, 0, 189806, 2214, 54678, 108416, 1965, 280476, 179477, 5, 3, 200835, 2162, 6, 0, 1571, 15, 82231, 341999, 400, 1, 1818, 492853, 65645, 200, 24722, 115992, 0, 3727, 1, 19543, 52460, 1527, 2, 1, 208, 4827, 50, 53, 5, 0, 3, 1, 3, 1, 2, 23323, 18, 18, 45, 22, 3970, 2204, 0}
Returns: 159
13
{0, 812490, 588108, 639419, 55965, 702731, 356999, 97131, 283776, 530776, 484638, 844858, 465521, 895539, 0, 236059, 509309, 218812, 271928, 652544, 535901, 178827, 690511, 815241, 857566, 847213, 406399, 317806, 0, 846814, 653981, 181956, 755824, 607564, 939566, 168030, 322790, 32581, 44248, 795892, 565075, 566472, 0, 931422, 743455, 199973, 207570, 617298, 86535, 673653, 457584, 884190, 584415, 231034, 580619, 4869, 0, 946110, 536965, 160489, 256701, 741652, 491495, 458452, 93004, 540219, 796772, 808520, 957610, 815031, 0, 54840, 851462, 647420, 632141, 824061, 176033, 696093, 769728, 401433, 301860, 359882, 314781, 855299, 0, 520476, 92988, 311558, 982991, 298312, 324175, 516834, 627984, 855541, 592594, 125303, 853212, 779082, 0, 846984, 548531, 344643, 360358, 467400, 210481, 42459, 639221, 4538, 25973, 770030, 517259, 533515, 0, 694393, 580860, 945225, 303059, 446925, 350461, 665852, 136407, 677196, 996395, 71944, 714654, 848860, 0, 385523, 222648, 292540, 948314, 880155, 508914, 952081, 766561, 302115, 629708, 385360, 755177, 890663, 0, 330895, 219808, 197162, 224782, 899674, 945388, 196191, 896127, 972315, 171159, 218354, 503709, 389280, 0, 318554, 165176, 872531, 419699, 700073, 335347, 616202, 895989, 401610, 120710, 855234, 123855, 441253, 0}
Returns: 1600701
13
{0, 31, 4, 66, 36, 7464, 46, 167103, 31108, 2, 296, 7386, 347, 11, 0, 147, 9, 103, 1962, 696384, 987458, 490900, 5, 70762, 15, 424473, 475811, 14907, 0, 47848, 50430, 29, 320827, 6, 2821, 115, 1, 2, 1747, 975717, 286, 15312, 0, 1, 1, 80202, 97480, 84333, 501, 3, 22479, 45, 598, 523298, 4, 15480, 0, 11583, 7, 946, 1349, 468, 24512, 488, 906, 53233, 6794, 8242, 11, 450049, 0, 297, 27073, 6, 2868, 50657, 97896, 8, 1, 15, 52409, 7, 5691, 5019, 0, 11216, 201, 1, 68, 430, 28971, 235, 354515, 4, 3577, 2, 246497, 42904, 0, 128241, 942424, 1888, 458, 21, 63, 1548, 7034, 3127, 28, 1, 3853, 549, 0, 2974, 2972, 1074, 6, 4, 7346, 222, 3538, 1, 5476, 695009, 4320, 194, 0, 258419, 76, 292, 8081, 115335, 1420, 56, 27572, 113, 229, 2454, 1028, 99, 0, 13643, 12109, 4158, 241, 3380, 27, 893, 1503, 776, 4358, 50, 73414, 352391, 0, 249, 4, 1, 343, 29013, 38307, 127, 951, 47408, 101, 316, 15, 2, 0}
Returns: 207
14
{0, 554700, 443869, 705222, 221510, 923598, 271075, 264573, 944943, 47490, 401402, 638028, 396778, 295763, 839499, 0, 540751, 554880, 713404, 690978, 819788, 742531, 906106, 902699, 178790, 15339, 433512, 848733, 328297, 75675, 0, 786906, 265549, 437273, 895605, 179967, 160291, 735827, 134765, 463689, 198874, 220368, 811867, 828924, 937065, 0, 587141, 403781, 453164, 883715, 282462, 130569, 926208, 296343, 309156, 682218, 486087, 523611, 64150, 29017, 0, 212809, 4269, 457387, 19373, 108862, 563554, 438524, 786746, 687370, 178188, 464740, 303752, 480508, 934768, 0, 333642, 434146, 840674, 480154, 465611, 796184, 118576, 637516, 513730, 920221, 577609, 230596, 273882, 62188, 0, 2200, 603973, 977082, 419625, 60150, 678270, 701359, 536973, 832812, 29931, 699044, 526341, 101025, 797699, 0, 632516, 38141, 598024, 486409, 257963, 334828, 489571, 382602, 770970, 469420, 390397, 71957, 697016, 789042, 0, 922509, 436069, 465537, 567712, 282747, 129331, 735645, 343483, 12031, 515124, 597950, 544405, 556990, 715407, 0, 575512, 490750, 116607, 700133, 868318, 196908, 462881, 880980, 869659, 996504, 72133, 987687, 259349, 209763, 0, 666171, 294676, 184922, 804493, 519898, 724030, 464215, 226295, 888806, 925221, 947002, 476865, 329485, 285819, 0, 759535, 540190, 185261, 973047, 855391, 730371, 470112, 386240, 239035, 57963, 540894, 9322, 309489, 192277, 0, 880518, 194421, 513000, 304828, 535325, 161479, 678469, 764678, 570705, 685805, 670927, 723820, 468556, 980413, 0}
Returns: 1621296
14
{0, 732667, 2, 4961, 104, 1, 4, 287028, 13709, 65405, 1291, 5, 8, 2, 161, 0, 6, 917, 7406, 2875, 115, 6244, 167760, 5530, 23984, 30, 8, 1, 52, 710130, 0, 726, 7, 1348, 3, 2466, 45628, 6, 101298, 87081, 443102, 836445, 224, 131, 419327, 0, 151, 945, 16106, 54398, 13, 4, 26, 456, 600888, 325060, 278246, 511540, 64097, 1339, 0, 217185, 28, 92358, 64, 11549, 77203, 108034, 2, 2, 39385, 28783, 82733, 443063, 261, 0, 8015, 8, 322173, 390, 74752, 1, 301597, 4, 157539, 314, 16032, 215082, 61, 756, 0, 1, 16, 3, 252805, 125, 479, 12, 214763, 6210, 3, 1387, 1133, 1464, 1, 0, 202530, 4, 61, 771398, 113, 7024, 1596, 12354, 385, 177711, 837910, 69, 166, 107693, 0, 2, 148470, 379, 46, 4, 695, 50752, 24, 4799, 3769, 310, 2, 43, 64770, 0, 955, 143, 545, 1, 6578, 29768, 3634, 200, 343197, 372, 114, 1967, 15580, 13435, 0, 530, 558, 50814, 2, 232047, 127342, 24742, 3888, 1174, 909608, 3156, 7, 15, 13, 0, 32501, 20, 17552, 114, 411155, 139, 9038, 154, 86467, 273910, 979, 11548, 8839, 7617, 0, 833, 31, 60441, 209399, 868, 35692, 32577, 293, 991265, 22, 142, 55534, 1647, 19, 0}
Returns: 391
15
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Returns: 1347230
15
{0, 221, 18, 788, 30, 7410, 8103, 119383, 23341, 61324, 1, 747272, 3892, 398, 1370, 600733, 0, 471, 587884, 20379, 60214, 1, 22, 5, 117885, 6, 88, 21747, 22451, 141, 1, 87269, 0, 31, 14, 46, 82421, 47451, 161, 11, 56332, 8898, 6, 283, 3, 1451, 11561, 42, 0, 40719, 434525, 50, 294, 900, 14, 18, 14251, 6, 108, 344300, 945, 174152, 34, 20842, 0, 265842, 144333, 7, 317, 5985, 1, 7, 13, 10816, 15032, 368921, 28, 46740, 7603, 112, 0, 582346, 11379, 394, 14, 3, 5, 206984, 456395, 53, 90, 1, 168469, 201, 67, 217969, 0, 2041, 97877, 156, 257336, 43934, 7, 1, 217259, 35525, 902, 19105, 6340, 150143, 698, 960165, 0, 10571, 3497, 971929, 30437, 22, 7074, 71, 70974, 3, 182755, 227, 1693, 194, 99876, 2456, 0, 12378, 110, 11540, 1, 3, 2914, 286769, 421206, 5, 5871, 90, 46724, 2, 37, 3, 0, 10792, 115738, 14092, 8406, 1568, 128493, 3, 24959, 800629, 29720, 206716, 144736, 13883, 2103, 8103, 0, 703, 51, 2459, 5, 1709, 700, 32, 1, 314241, 8387, 2, 3, 45, 191, 12417, 0, 47295, 2852, 317093, 238, 2777, 40, 122901, 6, 511328, 36549, 4, 113, 144914, 25, 145584, 0, 2764, 27, 3, 16426, 7, 1, 483171, 49, 7762, 2, 394971, 4170, 653, 727863, 3, 0, 15123, 751, 26107, 73, 1591, 53175, 3528, 19, 506171, 62859, 99783, 1625, 786235, 53193, 114, 0}
Returns: 169
16
{0, 415373, 589995, 256407, 228723, 58557, 215296, 262902, 315194, 248122, 712524, 142254, 941502, 392777, 301468, 720209, 586574, 0, 381881, 912424, 495403, 934209, 802906, 194325, 76948, 812510, 40174, 315320, 715078, 537258, 306724, 786684, 601176, 124323, 0, 253907, 920479, 975485, 264720, 930636, 112823, 648936, 78557, 302480, 857707, 523816, 399601, 213831, 158830, 816342, 691341, 0, 154344, 109786, 3219, 246271, 599176, 627701, 796409, 710514, 347395, 242970, 160394, 362458, 875329, 909155, 901090, 842910, 0, 137632, 607761, 749629, 841103, 448514, 695073, 357392, 276472, 528342, 503685, 792637, 977253, 458936, 648813, 444634, 459760, 0, 535215, 274360, 595600, 902351, 176172, 778758, 806611, 234435, 143463, 657391, 861023, 410999, 646984, 922997, 881328, 527094, 0, 135411, 622509, 318755, 80173, 651925, 187976, 866135, 128524, 558551, 707644, 799367, 817686, 85277, 49352, 500985, 473932, 0, 943333, 940245, 401982, 136949, 479635, 18725, 913058, 503483, 361129, 417065, 531283, 812739, 829689, 650760, 849547, 5603, 0, 651718, 644799, 400709, 435310, 907079, 792979, 933638, 429409, 48318, 236662, 323062, 978215, 69596, 424760, 783868, 71996, 0, 407514, 237749, 72770, 18811, 215760, 986451, 606936, 952339, 301706, 599380, 988775, 971355, 722336, 496269, 628832, 587836, 0, 102587, 786743, 880350, 141830, 463549, 982041, 784798, 318030, 734921, 257288, 394079, 115208, 599148, 21408, 199359, 594863, 0, 212833, 15107, 362516, 150184, 297348, 778477, 797255, 496958, 747896, 789174, 49881, 622688, 836057, 232035, 643311, 221882, 0, 659994, 456546, 822514, 181691, 217240, 337158, 490971, 21291, 526597, 192275, 632963, 419890, 964760, 141485, 307967, 475823, 0, 254076, 864975, 170600, 258782, 434970, 803148, 508008, 575600, 939127, 882981, 856811, 895440, 134294, 179585, 773377, 939938, 0, 156556, 837263, 210470, 326015, 255702, 796163, 761872, 335208, 780081, 701747, 199758, 264586, 411717, 929905, 260039, 784500, 0}
Returns: 1771572
16
{0, 9, 14, 3961, 2562, 11315, 57677, 3399, 10904, 11, 11, 1, 5, 28365, 304896, 5562, 7, 0, 3341, 3603, 15, 5, 703804, 27840, 3, 852, 12355, 72, 18, 8719, 339, 2570, 228901, 439053, 0, 866, 3466, 864, 848, 12, 41479, 59836, 793, 676, 4, 25, 582, 1, 147572, 613, 31, 0, 12206, 6269, 4256, 74733, 44425, 96, 9, 829468, 13, 47449, 2926, 83, 10464, 137, 22446, 32694, 0, 71422, 1696, 5451, 1387, 236999, 99, 499503, 940686, 10, 31, 6593, 21, 492463, 765, 604908, 256, 0, 16, 3771, 66, 41, 69, 1, 74766, 936, 79, 1, 3, 12, 3792, 937, 171234, 56226, 0, 1936, 211, 11585, 651, 5264, 486618, 495715, 262138, 141, 4, 57116, 1, 39, 256956, 22375, 1427, 0, 18, 234, 9288, 1, 52953, 6, 886, 657288, 792128, 1, 4590, 404756, 268, 24, 10, 942140, 0, 571, 573, 191476, 844715, 1, 27052, 1776, 17, 23, 42720, 7, 329973, 6397, 451, 76417, 202, 0, 14, 38872, 87417, 25, 419842, 52, 113050, 436940, 201488, 3375, 3425, 5949, 916, 51324, 769657, 911751, 0, 6701, 13514, 1, 367579, 150, 4, 94, 2965, 5, 86449, 68654, 1, 185111, 94, 289, 63, 0, 749037, 235623, 732848, 47336, 7, 26503, 74, 231435, 2740, 24, 1420, 3982, 1, 490217, 3, 17575, 0, 9471, 21244, 5671, 63446, 415, 34386, 165, 99647, 8, 167715, 295325, 190541, 670, 850176, 279015, 15699, 0, 412, 1, 240, 49054, 63416, 1, 33640, 115, 1433, 140, 216059, 56108, 5885, 374, 649626, 96, 0, 1, 69, 15, 813951, 8, 393545, 21748, 1, 686430, 237, 91917, 20, 19, 545, 3440, 73, 0}
Returns: 179
17
{0, 529873, 317682, 663466, 464427, 368328, 485751, 670689, 829532, 383526, 64612, 84360, 987732, 242893, 406838, 246501, 304056, 949636, 0, 517292, 189900, 5562, 493132, 766627, 977494, 406211, 976741, 633787, 272123, 949306, 9891, 308991, 405493, 780821, 444871, 342086, 0, 809823, 574920, 102624, 566546, 347277, 512849, 95011, 217841, 195778, 87846, 822584, 633181, 198531, 78699, 403372, 167447, 699097, 0, 250446, 976714, 945894, 248131, 904585, 769152, 463072, 785467, 886549, 514701, 672314, 804333, 458376, 38282, 751322, 268417, 322445, 0, 502223, 614902, 849151, 834016, 238301, 292407, 531567, 840005, 78979, 962010, 49884, 141812, 970601, 601140, 324601, 573676, 816397, 0, 851005, 623463, 272413, 761670, 339393, 938376, 897443, 836628, 616882, 365071, 461122, 219368, 463565, 414172, 453894, 158481, 745807, 0, 590441, 557921, 67741, 903188, 119828, 235163, 213574, 443409, 934508, 156793, 803630, 713426, 262860, 953946, 225612, 540443, 781606, 0, 709655, 444973, 891903, 225532, 285727, 142860, 326409, 792049, 785644, 438574, 540186, 142833, 794134, 635980, 318685, 425348, 47487, 0, 74209, 734479, 477444, 555645, 12938, 157501, 423721, 27902, 383912, 226828, 730357, 538341, 559021, 842375, 252723, 305201, 947593, 0, 868785, 720620, 928570, 785088, 469196, 429459, 198547, 761971, 62329, 964354, 191707, 359633, 632324, 443877, 408593, 961484, 427281, 0, 516250, 484508, 569121, 157934, 524974, 921125, 663956, 125488, 552143, 150851, 566317, 323984, 429263, 929778, 42227, 77910, 798437, 0, 206167, 438317, 470494, 96547, 471784, 207569, 714017, 145923, 297709, 700740, 635399, 678239, 642310, 488071, 442489, 583965, 589807, 0, 349624, 657584, 925715, 357887, 45288, 952282, 856949, 916738, 771667, 100611, 842793, 190585, 18495, 134401, 929933, 934684, 903396, 0, 990551, 554939, 789350, 346891, 286578, 906787, 383060, 218579, 317705, 69287, 5165, 511829, 559879, 306229, 145516, 406094, 387082, 0, 239731, 552803, 556168, 857576, 115982, 175706, 475815, 202289, 518737, 183727, 851081, 536819, 574450, 92652, 4779, 574083, 776770, 0, 211984, 71546, 714476, 115294, 759130, 502798, 741443, 975626, 284423, 597734, 11585, 226688, 741557, 864856, 26933, 656762, 272782, 0}
Returns: 1814461
17
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Returns: 54
18
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Returns: 1192933
18
{0, 88, 445982, 14, 2, 3611, 20, 13, 6744, 92870, 757, 2908, 354, 247, 77112, 864, 24966, 9, 2, 0, 106, 910121, 13, 251902, 245377, 37087, 55201, 60781, 7, 32, 5732, 152234, 181166, 300792, 236926, 765, 37, 48, 0, 114, 120400, 42, 63530, 7, 31, 4, 13145, 1, 563835, 20002, 9, 2, 263, 1818, 7476, 1664, 72744, 0, 25293, 32715, 326, 7190, 35, 2, 398, 1, 121026, 28215, 44, 24, 72, 77257, 23, 1778, 7, 19, 0, 369390, 1, 241053, 153, 2, 156275, 114951, 34538, 613365, 47419, 237581, 57, 7125, 4454, 631123, 690418, 237965, 5922, 0, 373, 930643, 26456, 403676, 12446, 3, 387783, 125257, 571203, 262, 56, 10300, 10, 13025, 52, 416, 2352, 37, 0, 89, 1439, 143, 2125, 64562, 6, 12, 63, 7892, 1, 7270, 93049, 465134, 14, 2142, 305241, 3420, 22, 0, 1, 24, 8219, 13690, 8535, 2, 25251, 286479, 75, 6021, 1, 117528, 481141, 1047, 246, 1233, 40013, 301, 0, 91, 3, 1589, 2719, 9243, 24, 7553, 191798, 7, 358, 376, 25, 574724, 441, 354512, 111, 895, 9687, 0, 4512, 3, 4, 47209, 167, 13098, 4598, 16588, 16996, 626567, 326017, 2553, 13, 716385, 53338, 3, 1336, 14, 0, 94, 3, 366, 15, 25594, 5, 3251, 37, 1, 225220, 1020, 256, 1641, 40, 305, 151, 338, 46, 0, 252901, 468545, 363483, 39889, 461733, 419728, 222, 1, 467527, 77, 742, 13253, 26394, 2575, 14, 230822, 59477, 1, 0, 881, 100895, 946974, 67, 1, 155210, 294, 5919, 91, 14, 1, 545, 14636, 105, 5, 6594, 686, 40434, 0, 1892, 101752, 52215, 11, 14840, 86226, 96311, 668, 590, 69102, 108, 27, 4109, 352, 3013, 2672, 1, 40561, 0, 98902, 111, 37949, 796, 1, 398, 29561, 33724, 10371, 16935, 91, 28322, 868, 609066, 72, 5, 77, 24306, 0, 98, 7495, 3620, 1148, 15, 66481, 4, 2566, 31, 389, 18343, 4, 48070, 171, 804, 13917, 1062, 912, 0, 13436, 4, 55354, 1, 3, 10888, 24, 485228, 80, 28174, 572, 2010, 1734, 1357, 15578, 2, 42524, 30, 0}
Returns: 111
3
{0, 3655, 4289, 283591, 0, 598518, 4, 269933, 0}
Returns: 291539
4
{0, 56300, 1, 91223, 12157, 0, 9580, 961968, 1724, 942396, 0, 595139, 68, 241222, 249291, 0}
Returns: 161473
5
{0, 447243, 99823, 26614, 184, 378, 0, 566366, 852478, 265117, 1106, 680325, 0, 923913, 237983, 234744, 733174, 886703, 0, 229171, 321879, 780329, 115497, 810628, 0}
Returns: 876953
6
{0, 509508, 194778, 5603, 40, 221263, 854582, 0, 585151, 156450, 465449, 15929, 54, 573564, 0, 843404, 798460, 86797, 31, 278659, 536069, 0, 652753, 573430, 5, 820339, 840823, 456774, 0, 963097, 58481, 34794, 637315, 277887, 942873, 0}
Returns: 1118935
7
{0, 1, 101339, 259851, 7, 506, 2, 83, 0, 21729, 277084, 43732, 147261, 189981, 304455, 536513, 0, 514834, 210920, 821123, 810417, 565, 518726, 553937, 0, 590984, 594896, 10473, 6993, 77433, 183630, 876372, 0, 966638, 569843, 335361, 666397, 909210, 48954, 920168, 0, 245893, 15626, 64210, 397127, 129131, 23294, 92893, 0}
Returns: 315202
8
{0, 466, 6, 112737, 485557, 1139, 181, 13099, 37, 0, 301601, 821817, 738991, 514015, 526799, 119673, 3410, 257027, 0, 834931, 347194, 175026, 485031, 23692, 4, 102956, 703528, 0, 985345, 482900, 290233, 669025, 1126, 719341, 729054, 722653, 0, 24940, 587411, 198481, 3145, 712613, 300999, 42873, 809296, 0, 568594, 506130, 363, 71792, 757515, 824177, 114332, 921906, 0, 743505, 15408, 628011, 500505, 563250, 780490, 829200, 379546, 0}
Returns: 625983
9
{0, 4093, 7, 7470, 353805, 9727, 5706, 2, 634223, 14306, 0, 479622, 545494, 459149, 643888, 854209, 901659, 270242, 4, 107487, 0, 129865, 978739, 177994, 443640, 353010, 521697, 79201, 245900, 527807, 0, 538167, 275882, 328194, 581741, 24188, 31975, 638467, 705766, 915826, 0, 897407, 958457, 623494, 617929, 3389, 623737, 723361, 654322, 962061, 0, 646952, 585435, 188220, 918, 735995, 395329, 854056, 44876, 190458, 0, 974243, 190277, 27297, 81719, 508512, 430985, 63199, 235322, 484152, 0, 975848, 252, 417222, 4682, 654779, 145847, 779351, 76322, 587404, 0}
Returns: 391884
10
{0, 223386, 984740, 17127, 1, 163586, 4579, 7936, 40600, 551949, 60653, 0, 532465, 270197, 747916, 899633, 800971, 321467, 524357, 634967, 7480, 957678, 0, 65483, 300841, 754593, 185879, 511992, 729357, 253034, 52, 640285, 497092, 0, 617725, 915278, 418991, 638639, 246680, 655694, 7, 392273, 840080, 825732, 0, 354262, 67416, 164706, 618535, 111034, 6, 885605, 907491, 192128, 83857, 0, 539995, 176318, 753698, 173445, 703, 97192, 132069, 617728, 412914, 904153, 0, 127712, 434810, 309199, 63896, 671652, 230210, 712077, 962405, 363769, 805970, 0, 672582, 329416, 89, 37525, 211627, 850455, 586245, 142053, 346248, 981946, 0, 874215, 130229, 806085, 750150, 695620, 984107, 990988, 960513, 449805, 530810, 0}
Returns: 1015270
11
{0, 1039, 280, 32988, 3948, 229, 1, 1, 604, 1225, 25, 4, 0, 313211, 46363, 673114, 647376, 894104, 701839, 6609, 268627, 361410, 376792, 201563, 0, 225506, 387318, 945884, 388692, 140101, 212230, 469133, 646128, 1, 835134, 777725, 0, 316261, 631909, 702046, 314138, 442265, 116178, 443158, 37, 438632, 364385, 793549, 0, 269300, 47601, 759227, 592391, 756801, 722938, 55565, 514635, 240885, 283717, 425229, 0, 915071, 25168, 412212, 200006, 802817, 415, 384657, 545471, 93025, 361918, 757666, 0, 654972, 929150, 658080, 355471, 14856, 908050, 877012, 71072, 923964, 68635, 496149, 0, 67483, 170144, 214672, 235, 974010, 442603, 495601, 831855, 207045, 311127, 6228, 0, 633879, 591833, 3594, 12440, 263304, 559313, 223346, 558161, 390773, 493891, 960975, 0, 348572, 181243, 955573, 40198, 705702, 677872, 614965, 434866, 341260, 850336, 843438, 0}
Returns: 656077
12
{0, 8, 17, 663, 930, 23, 13777, 5, 107530, 785564, 2752, 57, 217, 0, 810713, 756707, 775820, 996596, 777567, 893517, 393962, 565068, 672544, 950668, 8035, 275399, 0, 865267, 672540, 154732, 78731, 41547, 618506, 253204, 852632, 766501, 193, 134498, 73930, 0, 18384, 143629, 128598, 543689, 817745, 133466, 641879, 895756, 5, 991043, 306306, 597635, 0, 923197, 438638, 573956, 781653, 511777, 642218, 895342, 381, 912899, 24600, 175537, 819875, 0, 626829, 568292, 606353, 863724, 664095, 759366, 13, 975148, 242461, 889783, 122981, 158874, 0, 952301, 298991, 646693, 507856, 941078, 23, 681993, 513857, 483000, 864130, 895413, 634412, 0, 429623, 790458, 970916, 471555, 740238, 192395, 13415, 448735, 847869, 826342, 979683, 914566, 0, 513421, 767607, 427860, 1, 393154, 582720, 316555, 838565, 940931, 322228, 413635, 872615, 0, 394758, 37284, 21963, 800071, 551914, 281778, 148524, 490070, 411442, 106266, 876445, 924841, 0, 691545, 1, 621611, 35597, 385635, 983418, 669520, 860591, 934171, 356727, 696091, 710650, 0}
Returns: 1682396
13
{0, 1, 416650, 219341, 893, 18859, 15565, 807905, 59, 462712, 338, 1495, 62, 398740, 0, 991055, 218373, 286990, 626286, 408414, 911920, 116381, 267977, 579761, 375080, 125435, 53, 390328, 0, 558946, 235915, 305071, 263129, 638166, 709845, 732990, 682209, 336402, 597343, 44159, 796632, 648330, 0, 310618, 467715, 810328, 968674, 914948, 341001, 790846, 119767, 153362, 21, 191967, 924846, 916907, 0, 273084, 359712, 287300, 99272, 308874, 218106, 39706, 802496, 1, 283693, 642967, 682241, 227603, 0, 716131, 516265, 519257, 81204, 400292, 680573, 24413, 304, 804231, 990363, 621626, 157185, 111598, 0, 439686, 315619, 969437, 231031, 894367, 434159, 801, 199010, 90342, 224621, 673524, 665123, 918377, 0, 234367, 574663, 93614, 582542, 439650, 3, 330683, 392070, 956125, 124514, 95497, 725746, 329532, 0, 222150, 806908, 123171, 685017, 982, 561847, 696586, 357212, 796947, 594201, 722419, 507775, 833563, 0, 62249, 334463, 323390, 87, 766241, 772386, 699553, 828969, 397402, 277693, 803418, 620658, 62249, 0, 268499, 479436, 274, 230957, 537836, 535888, 508919, 297159, 333986, 457622, 541348, 260884, 639573, 0, 893379, 1042, 673563, 922028, 344562, 598106, 664833, 219918, 913075, 599337, 865292, 186090, 198605, 0}
Returns: 1147841
14
{0, 26412, 11126, 12929, 275, 242479, 2966, 11180, 855, 5247, 94, 918, 48, 86, 101, 0, 136452, 769694, 421945, 464771, 196286, 259920, 48137, 421241, 705380, 474121, 558026, 549319, 25, 584990, 0, 570971, 470129, 566720, 509074, 882257, 617535, 169082, 166233, 826283, 794228, 995607, 282, 289000, 704088, 0, 203071, 584330, 708061, 893494, 517026, 533352, 839785, 778648, 288087, 482114, 3, 353381, 550609, 122189, 0, 798115, 266585, 822613, 994642, 236972, 34275, 819574, 144596, 256418, 14, 772716, 923418, 970583, 747250, 0, 469658, 771615, 748931, 912294, 815023, 88890, 339862, 763737, 59871, 774018, 677656, 687497, 998386, 226557, 0, 657215, 98653, 830689, 272888, 543707, 164706, 291494, 230, 146301, 784860, 172625, 82559, 914122, 193209, 0, 58505, 894354, 810754, 533883, 188279, 633193, 7, 961065, 678271, 849553, 582468, 641649, 643664, 107661, 0, 44010, 841473, 336136, 194481, 90626, 3, 289192, 103428, 312942, 204847, 621459, 790674, 790523, 518977, 0, 981060, 757085, 150991, 809014, 134, 142878, 255114, 746279, 564571, 890158, 252155, 638134, 327662, 269322, 0, 775269, 941962, 476437, 105234, 27568, 324076, 960403, 197653, 781469, 958348, 26670, 451699, 182746, 281764, 0, 733065, 510567, 2, 470306, 13478, 387486, 666945, 259377, 420932, 531892, 187765, 824710, 184944, 187705, 0, 52624, 446999, 330464, 639609, 422148, 687272, 314454, 768398, 280634, 656186, 97346, 317477, 241253, 45589, 0}
Returns: 927520
15
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Returns: 972924
16
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Returns: 623281
17
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Returns: 676231
18
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Returns: 1185530
17
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Returns: 1336462
18
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Returns: 1282873
17
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Returns: 734956
18
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Returns: 1778410
17
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Returns: 1070613
18
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Returns: 1209558
17
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Returns: 927258
18
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Returns: 1513847
17
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Returns: 647617
18
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Returns: 1684956
17
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Returns: 832181
18
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Returns: 1321845
17
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Returns: 835228
18
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Returns: 747953
17
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Returns: 729390
18
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Returns: 1438319
16
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Returns: 14539587
17
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Returns: 15508072
18
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Returns: 16437150
17
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Returns: 17
18
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Returns: 1340233
17
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Returns: 1625863
6
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Returns: 5000001
18
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Returns: 1216374