TopCoder Statistics - Problem Statement

Problem Statement

A faraway land is divided into n states, numbered 0 through n-1. You are given a int[] a with n elements. For each i, the value a[i] is the number of cities which lie in state i.

Each state has its own connected road network. (The topology of that network does not matter in this problem.) There are no roads between different states. The n states have now decided to form a federation. Therefore, they need to connect all their road networks. They will do so by building exactly n-1 federal roads. Each federal road will be a bidirectional road that connects two cities in different states.

Consider all possible ways of building a set of exactly n-1 federal roads in such a way that it will be possible to travel between any two cities in the federation. For each such set S of n-1 federal roads, compute a single integer V(S) by following the steps listed below:

For each i, let x[i] be the number of federal roads that have one endpoint in state i.
The integer V(S) is the product of all x[i].

Compute the sum of V(S) over all possible choices of the set S. Return the answer modulo 10^9 + 7.

Definition

Class:: ConnectedStates
Method:: getSum
Parameters:: int[]
Returns:: int
Method signature:: int getSum(int[] a)
(be sure your method is public)

Constraints

a will contain between 2 and 2000 elements, inclusive.
Each element of a will be between 1 and 1,000,000,000, inclusive.

Examples

{3, 10}

Returns: 30

There will be exactly one federal road, and there are 30 distinct ways to build it. For each of those ways we have x[0]=x[1]=1, so the integer we get is 1*1 = 1. Hence, the answer is 30 * 1 = 30.
{2, 2, 2}

Returns: 96

Here we have 48 distinct ways to choose the two federal roads. For each of those ways, one of the x[i] will be 2 and the other two will be 1. Hence, in each of the 48 ways the integer we'll compute will be 1*1*2 = 2. The final answer is therefore 48 * 2 = 96.
{1, 1, 1, 1}

Returns: 60

Here we have four states, each with a single city. Let's label the cities A, B, C, and D. One possible way of building three federal roads is to build the roads A-B, A-C, and A-D. In this case the values x[i] will be {3, 1, 1, 1}, so the integer we'll compute will be 3*1*1*1 = 3. There are four different sets of federal roads that produce the value 3. Another way is to build the roads A-B, A-C, and B-D. Here, the values x[i] are {2, 2, 1, 1}, and therefore the computed integer is 2*2*1*1 = 4. There are twelve sets of federal roads that look like this one. The final answer is the sum over all possible sets of roads: 4 * 3 + 12 * 4 = 60.
{205659656, 888625810}

Returns: 118040021

Watch out for integer overflow.
{2, 1, 2, 1, 2}

Returns: 27808
{14204721, 921856626, 804287587, 304606131, 277490604, 310739929, 900757841, 818413665, 155154829, 836327185, 602928524, 26132484, 587345385, 936362852, 92603422}

Returns: 376924431
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Returns: 722723378
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Returns: 144890926
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552991362, 687583153, 825994139, 666910598, 661805101, 117142222, 166553688, 995173554, 743004664, 803412413, 40692380, 341783306, 321626724, 814647214, 775931633, 180707235, 206812243, 468978214, 192351734, 524447942, 848103001, 167143030, 221763335, 419656957, 147846246, 330924785, 388724873, 12648726, 244322785, 677805671, 483291017, 954653022, 259909925, 914520330, 794356359, 670559450, 902062013, 154592203, 866589912, 707619998, 931537003, 17878175, 59287569, 12582712, 14854216, 780585243, 16578468, 530635209, 406742465, 149365961, 510657540, 649164157, 560868680, 815732976, 232154326, 956038849, 109278460, 902534601, 43558522, 345526310, 654080469, 799412074, 745277600, 258251777, 783993760, 143935920, 29786330, 773776958, 918305063, 400902698, 160430264, 262067839, 842770370, 45164298, 354427370, 482047248, 883928842, 210967984, 409563315, 924040819, 774173627, 527802452, 514036968, 319370023, 656370040, 758834905, 700257054, 210484962, 10501858, 989063664, 152108773, 654749780, 992099579, 576795996, 48336589, 391967197, 713952690, 370824872, 766394423, 860840588, 777612491, 178671245, 843689557, 226332827, 113932586}

Returns: 596093004
{700166984, 664446800, 960034051, 518231435, 605424558, 73357617, 42420406, 263850255, 465921849, 273038620, 970092087, 569591643, 216418177, 688183844, 697219135, 747000850, 967450371, 246653253, 759151909, 337918109, 316880082, 787879482, 94985555, 230996415, 955333721, 313224329, 846794158, 72880738, 202811876, 932073054, 179042039, 845417760, 681800307, 432949826, 42142341, 61617734, 869678358, 917795879, 676281185, 929508991, 657492960, 973757274, 212871578, 365705148, 868115177, 379671415, 252275786, 789805100, 205112897, 969467829, 269947705, 794586153, 601062116, 968761911, 771574556, 648465503, 605896660, 246023883, 912273087, 778900892, 277014656, 640607695, 545496450, 582283446, 493255389, 732718187, 703602176, 852781480, 975321947, 154657852, 89267839, 207744092, 304698912, 156844972, 862891108, 178978179, 935980683, 123121192, 37770446, 288090713, 516348805, 653562229, 32852380, 918974034, 162505363, 592572978, 725080016, 806567447, 146230777, 543770273, 308993154, 369873024, 774807674, 602384353, 130671958, 153625655, 656747457, 601265811, 636061903, 925861277, 648458561, 246981009, 666365970, 806260552, 902461445, 340887541, 498079418, 124704016, 594565822, 635930280, 70763430, 122616790, 703432394, 967519938, 421297297, 29373495, 865356789, 158684641, 818201778, 744858043, 589647145, 746483636, 880599845, 828147394, 200814599, 753425430, 732613209, 878363557, 500153000, 889344505, 194766721, 583679433, 395462166, 847226808, 404420681, 175919, 734978647, 127776432, 782862039, 771868848, 31287564, 347580089, 213833338, 558169930, 327369936, 977033614, 652400999, 277032237, 251834775, 153688006, 177947246, 358500639, 815103653, 159520589, 777132400, 425720054, 190631405, 179216514, 332529092, 872900541, 753455987, 268684381, 542115515, 329508564, 873170511, 55184319, 994538833, 140521562, 538125062, 543283024, 541095312, 401013938, 407379009, 576032611, 333267703, 675046501, 147762635, 979349456, 219355792, 410221614, 776220792, 728638860, 60427959, 344389727, 948617215, 817902486, 912613020, 28823050, 473813585, 153014495, 895873706, 343581952, 308017281, 180945850, 841533999, 790709205, 645247698, 381611040, 948475334, 337010533, 380564935, 980999881, 177669162, 96817430, 472625270, 6827921, 232473246, 187091494, 798439862, 294438901, 526456077, 554395251, 81826989, 932703616, 627229614, 37176481, 31892626, 563519946, 246726585, 134043121, 932098365, 623807435, 850798788, 964843811, 738106068, 905114943, 823854629, 435444702, 971109480, 838317791, 824265357, 885208466, 742364237, 233579852, 948985049, 62433305, 209581058, 623927493, 436540223, 786532677, 607968642, 643674202, 135929308, 92038382, 421747791, 155474777, 164405253, 345313770, 113833920, 437333572, 680014832, 691788410, 320424310, 439034056, 456936460, 117695780, 296371031, 750104491, 496857644, 146706803, 352763830, 346333490, 721705244, 769209680, 15551447, 775393953, 315090066, 646201586, 395919577, 982253766, 592065682, 213628341, 486940704, 57255887, 483354651, 556672037, 535607796, 237443476, 558038837, 241614595, 272575048, 840037552, 221027037, 595534392, 115833139, 141842855, 41772129, 85846041, 489392929, 333193245, 621203053, 476921840, 447775720, 677305169, 710185123, 952653391, 586471073, 743330329, 389990562, 484586598, 633752077, 865655204, 437865395, 161937077, 356243711, 5006535, 829304512, 893500611, 209224104, 110822642, 879476519, 703484734, 412322287, 505272179, 644561285, 997610870, 447427449, 104648380, 471187161, 129466228, 884262303, 94944086, 766409387, 248520777, 716041705, 67425194, 69839337, 55955751, 713339558, 581092006, 880192625, 645485633, 491855026, 962286816, 334013345, 95942510, 89879442, 899862753, 112581610, 777601528, 435365886, 347961016, 550424009, 406003295, 153811469, 750392169, 339773013, 991618085, 914508990, 66832865, 649219197, 676630184, 652512990, 986030984, 911940463, 429155075, 639298330, 87941625, 328541864, 143858236, 619861765, 306900938, 47852547, 172159468, 429248335, 701764196, 294647825, 804531849, 552042574, 985106937, 134833156, 385193815, 15935716, 730278503, 538379043, 361525930, 944878634, 648507256, 943774015, 642495486, 799282549, 642286685, 658814756, 281988910, 38482676, 362442333, 991137355, 406457704, 112334217, 225998239}

Returns: 614473156
{729143285, 713532276, 796417621, 759053582, 211448024, 961990954, 552493707, 933712466, 38185499, 998992270, 710320027, 949181562, 104800391, 325647560, 753825464, 160133895, 536156732, 760662137, 682097012, 664906449, 622896802, 317606320, 467569933, 232344961, 973074436, 432793836, 450280280, 627885621, 322011888, 85232263, 116132103, 704706686, 491352061, 919083666, 151367879, 515267523, 349859290, 288674046, 966615047, 59953396, 902275766, 255012725, 780538598, 707713448, 779379964, 352508899, 518938740, 832660526, 290278004, 327878409, 709065842, 497994652, 683134892, 735758065, 776489436, 710776347, 565260660, 937083949, 335727856, 182513100, 942789338, 859089647, 989565735, 109963505, 348166364, 567294700, 684800930, 404716201, 314901482, 563090295, 235210383, 992363240, 992110783, 538504887, 992004957, 142031866, 880025882, 900460137, 190987366, 946923511, 996537732, 48880333, 457608445, 720335465, 424446917, 33860949, 298677465, 74937948, 235012031, 337738589, 638179474, 880498599, 157384923, 202771929, 288647991, 945569368, 175516467, 241192228, 18983769, 811111872, 318629065, 706713237, 364258334, 309274414, 365185524, 999356287, 628676662, 51526876, 168936485, 139477189, 77233991, 972462121, 279625154, 130238646, 714277023, 603792047, 376318261, 855668423, 142571385, 247374458, 274543003, 863485367, 769465028, 826658411, 811482004, 59864212, 766646245, 309042006, 956277655, 517070645, 148603792, 660227528, 160560160, 571227300, 96037269, 825803647, 485386079, 243820907, 186721585, 571660636, 873331325, 75208928, 650825871, 834830657, 39449945, 396688203, 19105243, 448444020, 474697939, 454402695, 276135782, 426794478, 26709361, 168822238, 312298320, 884555904, 965875225, 833541115, 919006178, 239712653, 723805205, 27712078, 619063332, 830432999, 943215132, 690315051, 177877635, 83879271, 775075672, 765844715, 695711133, 695067444, 417324809, 793527694, 105749248, 635586242, 793337871, 988452279, 5885093, 551057726, 116562205, 541811859, 918913215, 255013151, 582711234, 975287978, 56096092, 114986584, 686252589}

Returns: 465874913
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88, 24, 51, 32, 25, 27, 14, 23, 25, 20, 63, 54, 53, 59, 33, 60, 50, 10, 60, 87, 72, 97, 92, 5, 28, 24, 39, 19, 1, 47, 65, 10, 51, 11, 93, 93, 18, 13, 85, 16, 63, 24, 77, 19, 80, 49, 45, 60, 53, 75, 9, 27, 17, 48, 95, 78, 27, 43, 8, 94, 4, 78, 48, 85, 80, 90, 71, 83, 4, 97, 8, 95, 75, 71, 24, 71, 79, 37, 95, 85, 44, 9, 99, 97, 27, 23, 66, 10, 6, 43, 18, 15, 62, 55, 12, 95, 26, 93, 83, 49, 7, 21, 97, 46, 56, 72, 2, 58, 31, 99, 30, 24, 99, 51, 76, 81, 20, 5, 24, 78, 62, 4, 11, 48, 61, 89, 60, 97, 17, 15, 60, 95, 84, 39, 79, 55, 39, 64, 22, 37, 36, 42, 91, 67, 83, 59, 78, 30, 80, 95, 48, 28, 74, 12, 7, 86, 97, 90, 77, 91, 87, 69, 29, 90, 67, 28, 74, 94, 90, 34, 62, 14, 21, 79, 35, 38, 84, 42, 25, 79, 56, 74, 30, 79, 69, 83, 72, 97, 37, 52, 98, 43, 39, 17, 39, 44, 41, 94, 96, 42, 80, 60, 43, 64, 92, 65, 57, 39, 86, 17, 100, 85, 33, 94, 19, 40, 45, 16, 67, 86, 59, 40, 5, 3, 4, 34, 31, 48, 39, 31, 91, 63, 45, 50, 30, 35, 19, 27, 35, 73, 100, 34, 86, 22, 30, 46, 42, 51, 18, 78, 55, 83, 22, 94, 8, 17, 49, 48, 14, 16, 90, 61, 23, 34, 37, 5, 63, 79, 22, 8, 60, 66, 24, 97, 88, 57, 55, 40, 53, 14, 86, 7, 44, 61, 18, 36, 99, 79, 48, 82, 29, 75, 76, 6, 7, 18, 69, 91, 89, 22, 36, 72, 73, 45, 84, 66, 99, 29, 95, 96, 11, 84, 54, 96, 41, 42, 77, 6, 81, 56, 60, 82, 99, 43, 16, 3, 37, 11, 58, 100, 33, 66, 37, 7, 55, 16, 32, 67, 100, 91, 83, 42, 59, 27, 60, 22, 27, 44, 78, 75, 58, 60, 66, 16, 78, 5, 55, 96, 70, 35, 4, 38, 66, 30, 54, 13, 18, 30, 68, 65, 13, 7, 81, 19, 31, 32, 86, 14, 49, 70, 2, 10, 99, 15, 19, 17, 8, 69, 88, 32, 20, 75, 49, 78, 23, 12, 57, 49, 40, 18, 14, 86, 93, 22, 87, 35, 2, 31, 56, 58, 17, 57, 26, 100, 69, 22, 58, 84, 72, 73, 51, 17, 89, 68, 77, 86, 20, 51, 2, 41, 25, 73, 30, 76, 53, 28, 54, 99, 27, 98, 50, 64, 36, 25, 39, 7, 32, 41, 99, 46, 95, 4, 23, 49, 57, 93, 30, 49, 30, 15, 95, 7, 23, 49, 10, 11, 92, 8, 46, 9, 51, 8, 11, 56, 45, 40, 29, 69, 16, 100, 42, 36, 37, 86, 62, 59, 100, 93, 73, 92, 20, 57, 82, 61, 94, 7, 27, 65, 50, 14, 76, 19, 63, 11, 64, 75, 81, 100, 93, 64, 54, 46, 98, 93, 13, 62, 95, 45, 62, 32, 75, 68, 94, 1, 66, 9, 49, 34, 88, 40, 1, 45, 96, 33, 58, 36, 90, 97, 54, 53, 94, 47, 74, 91, 32, 52, 81, 48, 28, 26, 3, 32, 76, 7, 51, 12, 19, 96, 100, 89, 86, 62, 72, 95, 99, 92, 5, 71, 6, 84, 58, 15, 56, 5, 15, 30, 53, 5, 95, 46, 98, 21, 62, 9, 89, 98, 13, 89, 33, 87, 39, 46, 84, 27, 91, 31, 8, 43, 4, 97, 17, 50, 72, 28, 21, 17, 80, 32, 78, 29, 13, 58, 4, 44, 67, 4, 70, 22, 8, 84, 83, 89, 2, 10, 31, 88, 19, 54, 19, 59, 100, 89, 31, 50, 93, 27, 22, 33, 38, 26, 33, 19, 22, 43, 34, 90, 99, 85, 34, 57, 62, 17, 92, 65, 94, 33, 89, 2, 64, 25, 12, 40, 59, 85, 54, 48, 7, 23, 47, 96, 86, 99, 97, 29, 76, 34, 73, 87, 82, 85, 95, 97, 28, 75, 77, 12, 13, 11, 79, 41, 32, 81, 11, 56, 96, 73, 31, 20, 37, 65, 55, 58, 34, 86, 47, 34, 87, 80, 97, 80, 35, 3, 94, 70, 55, 100, 7, 83, 79, 30, 38, 59, 49, 16, 38, 63, 31, 75, 91, 70, 98, 69, 99, 27, 43, 94, 97, 11, 66, 89, 58, 1, 10, 59, 34, 89, 61, 27, 10, 79, 81, 58, 48, 62, 87, 78, 91, 29, 82, 65, 14, 74, 41, 62, 17, 46, 37, 20, 2, 64, 3, 44, 90, 56, 7, 75, 25, 41, 80, 8, 42, 44, 9, 39, 64, 78, 42, 79, 37, 1, 86, 89, 12, 74, 59, 24, 78, 22, 31, 51, 53, 9, 15, 32, 87, 75, 69, 85, 77, 62, 19, 67, 75, 44, 45, 87, 65, 68, 19, 35, 8, 25, 6, 58, 17, 42, 61, 41, 58, 44, 57, 32, 88, 34, 54, 21, 89, 2, 23, 51, 100, 22, 30, 21, 98, 61, 64, 81, 1, 46, 63, 96, 17, 16, 66, 83, 83, 82, 28, 5, 21, 6, 72, 15, 73, 85, 57, 77, 54, 79, 32, 11, 33, 10, 90, 7, 89, 10, 66, 21, 16, 98, 74, 91, 74, 21, 49, 1, 34, 97, 48, 82, 34, 47, 16, 88, 32, 78, 66, 79, 99, 89, 8, 59, 9, 62, 26, 52, 58, 49, 56, 65, 70, 87, 64, 15, 13, 91}

Returns: 633339361
{90, 79, 49, 59, 53, 64, 3, 37, 17, 84, 71, 79, 6, 49, 100, 55, 51, 76, 78, 21, 34, 50, 86, 14, 70, 35, 51, 35, 38, 73, 100, 26, 82, 93, 97, 38, 68, 74, 84, 9, 57, 43, 7, 84, 93, 51, 54, 11, 25, 5, 99, 9, 8, 87, 14, 18, 19, 68, 72, 59, 99, 81, 62, 75, 81, 83, 71, 44, 71, 45, 67, 68, 75, 99, 49, 20, 28, 69, 19, 57, 75, 96, 62, 67, 89, 55, 88, 92, 88, 14, 65, 78, 49, 63, 13, 21, 37, 52, 22, 51, 17, 35, 29, 70, 23, 88, 1, 11, 69, 98, 94, 1, 20, 89, 81, 50, 42, 26, 25, 67, 55, 43, 17, 9, 75, 60, 33, 12, 48, 63, 2, 84, 17, 9, 41, 3, 23, 53, 65, 8, 33, 85, 40, 11, 98, 43, 67, 22, 30, 32, 64, 37, 18, 4, 1, 2, 34, 26, 59, 89, 62, 64, 9, 93, 70, 12, 16, 55, 62, 85, 76, 100, 4, 18, 54, 49, 88, 35, 19, 27, 38, 8, 10, 38, 66, 33, 8, 53, 88, 27, 64, 86, 61, 40, 14, 85, 98, 22, 42, 85, 13, 52, 59, 15, 22, 95, 7, 60, 73, 37, 96, 11, 7, 33, 18, 85, 12, 9, 23, 80, 17, 64, 32, 81, 92, 70, 47, 4, 31, 16, 51, 2, 48, 38, 28, 34, 45, 82, 35, 8, 22, 19, 44, 20, 82, 68, 37, 99, 96, 80, 44, 31, 43, 61, 86, 25, 21, 33, 5, 46, 97, 62, 22, 47, 95, 59, 18, 86, 97, 55, 41, 57, 12, 61, 31, 43, 34, 94, 17, 13, 26, 20, 51, 46, 38, 70, 34}

Returns: 101289342
{56, 52, 15, 38, 41, 45, 63, 100, 7, 25, 3, 71, 44, 21, 23, 14, 91, 12, 13, 92, 30, 70, 93, 36, 68, 2, 76, 98, 12, 97, 100, 68, 77, 42, 27, 78, 91, 40, 97, 1, 16, 15, 69, 85, 53, 95, 93, 9, 2, 76, 29, 23, 75, 17, 35, 67, 91, 11, 5, 92, 75, 14, 84, 6, 16, 21, 39, 8, 51, 33, 90, 80, 77, 80, 90, 93, 75, 63, 7, 41, 7, 40, 8, 78, 27, 30, 4, 7, 61, 6, 88, 31, 7, 57, 66, 19, 77, 79, 64, 54, 80, 7, 31, 52, 61, 18, 36, 45, 24, 2, 46, 3, 48, 58, 61, 51, 76, 30, 59, 70, 4, 42, 36, 99, 74, 39, 89, 39, 22, 76, 61, 20, 3, 93, 98, 53, 22, 86, 47, 20, 67, 58, 64, 85, 15, 64, 60, 73, 78, 15, 69, 88, 46, 87, 55, 75, 54, 23, 100, 13, 84, 66, 28, 60, 14, 38, 71, 24, 88, 75, 21, 97, 73, 62, 71, 89, 90, 13, 51, 86, 97, 72, 9, 60, 11, 83, 93, 8, 86, 8, 78, 74, 65, 51, 65, 19, 27, 96, 69, 97, 56, 66, 15, 79, 38, 42, 14, 6, 91, 91, 72, 44, 12, 100, 5, 64, 55, 68, 17, 1, 88, 82, 71, 20, 68, 39, 23, 67, 58, 45, 97, 18, 11, 56, 42, 67, 3, 22, 61, 35, 74, 100, 6, 29, 44, 70, 78, 34, 22, 88, 25, 40, 83, 36, 75, 71, 1, 75, 35, 29, 17, 2, 22, 9, 44, 16, 55, 33, 39, 39, 73, 9, 54, 49, 15, 1, 37, 80, 50, 97, 19, 86, 22, 38, 28, 11, 71, 100, 12, 42, 91, 89, 45, 86, 63, 30, 22, 77, 41, 60, 12, 66, 99, 22, 60, 50, 57, 49, 75, 29, 26, 87, 63, 68, 10, 85, 96, 87, 28, 13, 11, 42, 24, 85, 49, 36, 58, 18, 22, 46, 50, 32, 23, 7, 14, 51, 100, 54, 63, 18, 12, 8, 60, 29, 67, 35, 78, 59, 88, 64, 37, 80, 86, 23, 53, 50, 96, 3, 65, 42, 60, 4, 9, 33, 77, 81, 89, 98, 79, 32, 83, 96, 92, 9, 65, 12, 38, 3, 82, 8, 97, 46, 55, 83, 12, 72, 75, 87, 76, 1, 19, 92, 42, 69, 25, 47, 42, 32, 42, 36, 3, 7, 77, 60, 98, 62, 38, 92, 56, 29, 74, 94, 23, 14, 90, 16, 69, 45, 84, 23, 59, 62, 30, 36, 32, 50, 51, 56, 26, 48, 37, 35, 94, 2, 12, 13, 1, 57, 68, 62, 34, 58, 54, 93, 24, 29, 65, 58, 18, 45, 85, 28, 38, 60, 51, 72, 64, 97, 25, 67, 65, 17, 82, 29, 64, 52, 2, 97, 8, 99, 87, 57, 93, 88, 39, 64, 7, 62, 83, 44, 95, 30, 33, 17, 100, 33, 7, 25, 6, 16, 95, 42, 56, 89, 10, 63, 89, 96, 16, 49, 74, 76, 37, 57, 39, 39, 46, 80, 73, 1, 24, 61, 7, 87, 54, 18, 58, 17, 56, 81, 39, 59, 96, 92, 95, 30, 93, 34, 60, 27, 72, 61, 88, 26, 69, 34, 13, 27, 73, 28, 40, 2, 4, 5, 74, 48, 89, 88, 10, 93, 9, 38, 36, 49, 95, 65, 15, 40, 92, 76, 98, 9, 100, 32, 10, 70, 70, 55, 98, 64, 38, 43, 67, 33, 20, 36, 15, 85, 87, 61, 83, 56, 43, 23, 51, 78, 64, 86, 35, 3, 65, 70, 69, 3, 41, 87, 24, 11, 96, 98, 50, 48, 30, 68, 94, 39, 70, 80, 52, 10, 46, 55, 9, 50, 90, 45, 46, 60, 12, 68, 75, 37, 62, 2, 34, 35, 56, 69, 40, 82, 33, 73, 27, 82, 85, 46, 10, 52, 82, 65, 11, 7, 56, 66, 45, 15, 29, 53, 48, 75, 91, 32, 60, 62, 11, 35, 29, 8, 38, 24, 11, 39, 77, 11, 90, 24, 39, 57, 11, 25, 62, 42, 81, 43, 44, 49, 69, 10, 70, 40, 98, 61, 46, 22, 12, 15, 17, 38, 36, 19, 28, 82, 58, 42, 27, 74, 6, 26, 17, 11, 14, 49, 85, 40, 74, 15, 35, 14, 38, 73, 15, 16, 4, 83, 61, 75, 35, 81, 96, 17, 99, 17, 12, 52, 43, 34, 25, 60, 23, 6, 14, 73, 92, 23, 22, 90, 87, 50, 16, 67, 54, 1, 54, 32, 86, 89, 12, 72, 48, 43, 71, 55, 54, 66, 54, 69, 41, 90, 80, 79, 4, 84, 88, 58, 31, 68, 56, 1, 55, 56, 13, 4, 53, 48, 28, 23, 36, 52, 57, 14, 98, 13, 51, 92, 13, 66, 26, 12, 11, 64, 91, 91, 95, 75, 78, 37, 76, 13, 90, 31, 22, 56, 37, 38, 2, 87, 32, 26, 9, 38, 72, 85, 31, 75, 91, 91, 72, 41, 28, 98, 98, 5, 60, 56, 9, 61, 71, 65, 98, 85, 26, 16, 83, 61, 46, 43, 30, 9, 52, 72, 53, 16, 26, 20, 95, 27, 12, 31, 68, 88, 2, 95, 74, 77, 28, 97, 96, 44, 61, 36, 47, 94, 53, 84, 8, 89, 4, 79, 18, 4, 80, 42, 85, 66, 8, 54, 54, 7, 100, 73, 65, 42, 86, 92, 26, 25, 5, 10, 35, 45, 10, 56, 1, 99, 85, 42, 65, 94, 57, 67, 64, 95, 13, 63, 79, 59, 26, 58, 32, 82, 6, 22, 58, 50, 99, 47, 30, 51, 53, 29, 91, 25, 32, 62, 88, 61, 6, 3, 61, 90, 1, 6, 85, 46, 51, 31, 31, 81, 8, 24, 69, 74, 58, 45, 19, 57, 91, 58, 86, 33, 57, 49, 75, 38, 52, 54, 14, 44, 32, 26, 82, 8, 13, 51, 50, 72, 54, 42, 15, 18, 51, 48, 78, 43, 11, 66, 92, 35, 70, 86, 66, 52, 96, 71, 42, 16, 21, 61, 91, 38, 100, 82, 98, 4, 22, 79, 34, 40, 30, 2, 70, 56, 63, 16, 68, 74, 8, 99, 62, 39, 57, 59, 40, 47, 22, 89, 94, 21, 1, 66, 64, 16, 54, 29, 24, 33, 64, 10, 27, 37, 44, 55, 5, 11, 29, 69, 32, 78, 44, 21, 83, 83, 21, 79, 73, 25, 40, 54, 16, 63, 11, 62, 7, 93, 46, 77, 35, 70, 17, 79, 20, 53, 22, 69, 97, 67, 61, 70, 8, 37, 95, 50, 6, 57, 67, 44, 34, 53, 21, 76, 72, 68, 45, 4, 81, 87, 97, 24, 52, 24, 3, 63, 89, 65, 26, 91, 46, 41, 17, 79, 61, 56, 32, 12, 56, 31, 63, 26, 99, 44, 37, 14, 33, 24, 13, 19, 94, 22, 99, 74, 41, 61, 17, 11, 35, 78, 30, 72, 7, 96, 72, 25, 10, 51, 74, 80, 75, 92, 70, 78, 48, 41, 19, 7, 12, 5, 76, 84, 46, 12, 36, 51, 61, 16, 44, 34, 27, 30, 1, 63, 38, 36, 100, 74, 82, 74, 36, 53, 83, 33, 20, 10, 31, 100, 30, 38, 70, 2, 23, 31, 11, 93, 35, 70, 48, 57, 27, 77, 18, 96, 24, 90, 29, 83, 89, 64, 60, 73, 64, 59, 78, 72, 46, 6, 23, 55, 15, 99, 39, 47, 25, 44, 19, 23, 79, 59, 31, 70, 54, 44, 96, 83, 94, 21, 51, 37, 69, 18, 9, 45, 49, 67, 94, 16, 40, 61, 93, 17, 16, 18, 19, 96, 7, 83, 25, 99, 22, 66, 54, 99, 23, 69, 88, 10, 88, 24, 34, 47, 3, 53, 73, 77, 37, 65, 44, 72, 58, 60, 98, 26, 30, 99, 57, 70, 41, 24, 91, 72, 76, 12, 70, 6, 71, 17, 82, 55, 42, 23, 24, 89, 7, 34, 8, 80, 89, 79, 97, 93, 4, 4, 73, 10, 16, 80, 21, 67, 88, 94, 55, 99, 95, 39, 18, 6, 21, 44, 70, 4, 76, 42, 55, 42, 93, 57, 4, 41, 86, 97, 31, 31, 42, 11, 94, 35, 37, 33, 39, 53, 72, 80, 64, 17, 54, 66, 36, 58, 64, 98, 98, 36, 27, 21, 8, 66, 48, 100, 57, 93, 71, 85, 69, 59, 79, 92, 81, 69, 85, 96, 79, 67, 81, 72, 12, 12, 10, 90, 95, 17, 6, 1, 30, 5, 91, 22, 60, 60, 66, 39, 4, 90, 6, 100, 8, 70, 20, 19, 95, 55, 1, 94, 90, 27, 8, 10, 83, 46, 45, 87, 35, 88, 96, 29, 93, 64, 55, 96, 16, 8, 36, 61, 74, 98, 76, 99, 48, 10, 73, 21, 97, 21, 88, 73, 91, 46, 64, 49, 15, 49, 53, 9, 6, 49, 92, 72, 53, 57, 8, 59, 89, 79, 99, 17, 88, 92, 16, 23, 90, 54, 41, 19, 10, 93, 24, 1, 32, 22, 37, 20, 28, 7, 73, 28, 17, 72, 69, 98, 34, 90, 44, 61, 44, 37, 56, 95, 50, 18, 68, 75, 17, 29, 49, 96, 36, 93, 9, 1, 44, 14, 25, 96, 17, 33, 25, 14, 64, 11, 56, 7, 88, 100, 85, 9, 54, 24, 75, 9, 11, 65, 30, 14, 89, 8, 32, 45, 61, 71, 95, 72, 21, 84, 96, 61, 49, 75, 98, 78, 55, 31}

Returns: 853015488
{98, 69, 58, 79, 94, 87, 99, 9, 25, 54, 14, 70, 56, 22, 28, 68, 90, 9, 4, 100, 59, 20, 17, 72, 8, 7, 68, 80, 95, 7, 50, 19, 73, 75, 45, 98, 26, 78, 53, 79, 45, 5, 1, 80, 26, 18, 19, 23, 8, 25, 82, 67, 9, 71, 71, 98, 85, 11, 38, 44, 23, 90, 87, 88, 67, 74, 72, 95, 89, 12, 30, 89, 50, 87, 6, 48, 65, 39, 71, 81, 83, 72, 54, 63, 27, 82, 23, 56, 57, 18, 56, 3, 97, 93, 82, 61, 83, 6, 85, 73, 20, 39, 57, 12, 39, 67, 13, 50, 63, 55, 40, 89, 10, 47, 13, 26, 49, 60, 52, 90, 23, 28, 10, 67, 50, 72, 32, 58, 85, 90, 99, 100, 10, 40, 32, 39, 69, 72, 58, 18, 55, 88, 98, 24, 34, 41, 98, 27, 12, 28, 47, 18, 87, 19, 98, 84, 40, 19, 61, 15, 47, 97, 71, 65, 91, 4, 15, 100, 57, 47, 18, 61, 21, 83, 12, 41, 76, 58, 65, 55, 68, 29, 9, 74, 76, 91, 61, 8, 58, 95, 22, 10, 85, 40, 32, 45, 77, 6, 43, 34, 45, 48, 63, 84, 72, 44, 81, 86, 50, 5, 77, 12, 99, 72, 86, 5, 70, 84, 57, 77, 46, 27, 99, 66, 58, 95, 18, 59, 84, 25, 42, 72, 84, 31, 25, 45, 5, 99, 98, 95, 46, 3, 28, 74, 31, 33, 6, 26, 39, 53, 91, 90, 23, 48, 31, 100, 64, 15, 67, 14, 46, 24, 56, 97, 72, 97}

Returns: 635932025
{12, 89, 25, 9, 88, 100, 84, 81, 10, 5, 44, 57, 46, 45, 65, 20, 95, 33, 78, 23, 53, 75, 80, 40, 16, 45, 4, 6, 24, 8, 59, 34, 7, 30, 68, 8, 4, 71, 68, 60, 91, 82, 38, 4, 94, 32, 22, 46, 16, 8, 31, 96, 8, 58, 86, 36, 88, 85, 57, 70, 80, 59, 87, 81, 65, 74, 64, 13, 18, 21, 85, 77, 1, 71, 78, 8, 18, 74, 29, 15, 74, 29, 45, 68, 36, 15, 49, 52, 90, 54, 49, 94, 81, 39, 24, 86, 65, 61, 87, 33, 44, 93, 96, 69, 30, 40, 26, 91, 10, 4, 28, 100, 85, 73, 76, 7, 72, 21, 23, 80, 40, 12, 98, 25, 94, 40, 45, 61, 62, 1, 62, 47, 53, 62, 72, 56, 24, 95, 64, 3, 69, 66, 83, 93, 85, 60, 17, 84, 80, 80, 5, 33, 18, 68, 13, 55, 31, 24, 77, 96, 54, 86, 43, 99, 52, 47, 78, 84, 62, 44, 49, 16, 96, 74, 88, 71, 89, 99, 68, 21, 3, 31, 1, 30, 96, 28, 72, 49, 35, 61, 55, 58, 83, 97, 74, 99, 45, 19, 98, 42, 2, 74, 81, 95, 76, 86, 14, 9, 54, 9, 26, 16, 95, 100, 59, 64, 44, 69, 63, 24, 50, 29, 16, 13, 59, 30, 57, 81, 42, 71, 20, 95, 66, 43, 82, 34, 59, 20, 34, 84, 86, 27, 90, 18, 81, 24, 91, 71, 20, 81, 75, 48, 79, 25, 73, 92, 12, 45, 65, 51, 75, 31, 1, 29, 59, 80, 15, 91, 91, 66, 49, 48, 79, 88, 58, 2, 56, 8, 38, 34, 89, 83, 18, 9, 12, 17, 61, 45, 59, 15, 14, 79, 32, 11, 81, 54, 38, 7, 90, 24, 82, 98, 66, 23, 4, 10, 73, 70, 25, 47, 90, 8, 1, 70, 90, 29, 34, 53, 15, 7, 26, 9, 7, 4, 11, 28, 40, 88, 62, 60, 72, 90, 6, 82, 58, 61, 65, 87, 77, 36, 38, 51, 78, 5, 46, 69, 63, 13, 95, 14, 2, 71, 81, 64, 91, 35, 22, 55, 96, 53, 8, 45, 33, 32, 92, 69, 1, 80, 24, 13, 53, 96, 76, 18, 30, 99, 47, 100, 71, 57, 66, 80, 87, 56, 44, 7, 49, 3, 5, 39, 14, 80, 74, 37, 22, 39, 21, 35, 87, 2, 95, 78, 11, 70, 92, 32, 37, 52, 84, 39, 72, 12, 98, 17, 26, 70, 100, 40, 47, 52, 11, 84, 70, 31, 47, 55, 37, 69, 50, 21, 39, 97, 22, 67, 12, 25, 58, 86, 15, 4, 30, 15, 73, 79, 100, 61, 15, 41, 39, 95, 4, 9, 34, 74, 84, 37, 14, 58, 51, 35, 20, 100, 36, 13, 14, 35, 16, 23, 47, 77, 8, 95, 66, 70, 4, 28, 17, 86, 15, 55, 91, 51, 77, 66, 15, 8, 29, 50, 59, 82, 1, 18, 67, 3, 51, 45, 74, 63, 62, 21, 21, 43, 2, 14, 65, 1, 36, 23, 47, 22, 59, 25, 42, 66, 24, 92, 36, 47, 90, 7, 66, 72, 64, 1, 42, 73, 86, 24, 72, 52, 34, 16, 61, 5, 18, 85, 54, 45, 55, 17, 89, 93, 16, 7, 2, 47, 4, 29, 32, 19, 80, 66, 99, 66, 49, 77, 94, 46, 58, 78, 42, 65, 93, 19, 6, 84, 20, 15, 21, 29, 56, 51, 31, 32, 35, 77, 33, 44, 62, 65, 87, 90, 89, 83, 87, 76, 44, 14, 48, 27, 96, 12, 25, 29, 46, 35, 21, 70, 35, 50, 37, 91, 14, 85, 47, 80, 26, 81, 67, 34, 88, 65, 43, 60, 94, 79, 51, 30, 44, 22, 15, 33, 5, 71, 22, 18, 94, 50, 69, 2, 41, 24, 7, 89, 29, 89, 39, 22, 31, 88, 14, 60, 38, 90, 44, 60, 52, 5, 17, 100, 33, 67, 22, 15, 84, 65, 4, 22, 45, 17, 32, 23, 24, 12, 60, 77, 73, 64, 55, 99, 54, 17, 71, 63, 98, 24, 63, 8, 63, 97, 15, 87, 97, 71, 49, 27, 84, 87, 57, 47, 84, 77, 99, 97, 100, 26, 95, 41, 93, 59, 24, 36, 49, 66, 55, 95, 74, 60, 13, 31, 15, 91, 48, 76, 53, 84, 20, 81, 78, 40, 8, 71, 99, 19, 8, 66, 16, 42, 36, 93, 61, 47, 9, 43, 82, 79, 93, 84, 90, 67, 12, 43, 43, 88, 66, 40, 20, 22, 37, 6, 98, 75, 51, 13, 91, 74, 15, 78, 23, 18, 89, 49, 100, 28, 62, 48, 20, 98, 43, 4, 33, 74, 99, 94, 4, 89, 67, 2, 56, 31, 25, 78, 64, 70, 96, 27, 19, 92, 18, 24, 21, 7, 48, 26, 83, 10, 32, 14, 49, 31, 96, 85, 12, 82, 27, 60, 92, 22, 77, 71, 61, 46, 5, 71, 85, 27, 41, 80, 4, 19, 54, 95, 3, 60, 96, 5, 99, 47, 72, 51, 60, 22, 86, 82, 29, 74, 8, 41, 28, 67, 88, 24, 57, 16, 3, 19, 74, 28, 28, 9, 12, 32, 35, 41, 20, 50, 13, 23, 84, 35, 2, 20, 45, 18, 69, 69, 29, 77, 2, 42, 95, 11, 35, 94, 4, 68, 45, 4, 29, 2, 14, 85, 52, 27, 37, 97, 62, 70, 36, 41, 11, 60, 100, 3, 98, 10, 84, 61, 50, 93, 71, 11, 3, 100, 8, 57, 52, 84, 93, 79, 48, 65, 91, 88, 4, 78, 60, 47}

Returns: 674822760
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Returns: 775552852
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Returns: 309839473
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Returns: 852755203
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Returns: 76958900
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13786008, 279184250, 115839439, 706721971, 677996084, 649165210, 541854279, 373324562, 147796416, 559842883, 794575336, 499402676, 633604302, 390876487, 266726811, 663638926, 761647834, 81138552, 261196834, 43748360, 918073831, 721800200, 357462117, 796113498, 600726999, 679505328, 152320761, 342403977, 665593011, 252029806, 354835368, 533000180, 868249484, 920696907, 346420690, 609959027, 366459170, 162713296, 136327574, 835010476, 266015379, 217291971, 738834730, 417337979, 976822514, 63954730, 281642424, 188312536, 356571606, 71632486, 206256324, 215065140, 666285687, 240842887, 851943098, 817314538, 771162215, 370423384, 794452791, 55161201, 500025223, 325072695, 27742392, 720160365, 549950150, 504232827, 235200133, 340384894, 853210745, 670535948, 387883011, 40173807, 315670499, 808847069, 876561547, 330162815, 25507796}

Returns: 256336340
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1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000}

Returns: 304882317
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Returns: 714638742
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1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000}

Returns: 304882317
{2, 1, 2, 1, 2 }

Returns: 27808

Statistics

Problem Statement for "ConnectedStates"

Problem Statement

Definition

Constraints

Examples