TopCoder Statistics - Problem Statement

Problem Statement

This problem has a non-standard time limit: 5 seconds.

Alice and Bob play a game using an undirected weighted graph. The graph has no self-loops and no multiple edges. The graph has n nodes. The nodes are numbered 0 through n-1.

You are given the int n. You are also given three int[]s: a, b, and c, each with the same number of elements. For each valid i, there is an edge that connects nodes a[i] and b[i], and the weight of this edge is c[i].

In the first step of the game Alice chooses a nonempty subset of the nodes of the graph and paints them red. This subset must form a clique in the graph. (I.e., each pair of nodes selected by Alice must be connected by an edge. Specifically, Alice is allowed to select any single node. Alice is also allowed to select all nodes, if the entire graph is a clique.)

Next, Bob colors all the remaining nodes blue. These nodes are not required to form a clique.

Alice's score is the sum of weights of all edges that have both endpoints red. Similarly, Bob's score is the sum of weights of all edges that have both endpoints blue. The result of the game is computed as Alice's score minus Bob's score. Note that the result of the game may be negative.

Given the graph, consider all valid sets of vertices Alice can choose. For each of those sets we can compute the result of the game. Let S be the sum of all those results. Compute and return the value (S modulo 1,000,000,007).

Definition

Class:: CliqueCuts
Method:: sum
Parameters:: int, int[], int[], int[]
Returns:: int
Method signature:: int sum(int n, int[] a, int[] b, int[] c)
(be sure your method is public)

Constraints

n will be between 2 and 45, inclusive.
m will be between 0 and n*(n-1)/2, inclusive.
a,b,c will each have exactly m elements each.
Each element of a,b will be between 0 and n-1, inclusive.
Each element of c will be between 0 and 10^9, inclusive.
The edges (a[i], b[i]) form a simple undirected graph with no self-loops or multiple edges.

Examples

2

{0}

{1}

{100}

Returns: 100

The graph has 2 nodes and a single edge: the edge 0-1 with weight 100. Alice has three valid choices: she can choose either {0}, or {1}, or {0,1}. In the first case: Alice's score is 0, Bob's score is 0, hence the result of the game is 0-0 = 0. In the second case: Alice's score is 0, Bob's score is 0, hence the result of the game is 0-0 = 0. In the third case: Alice's score is 100, Bob's score is 0, hence the result of the game is 100-0 = 100. The sum of all possible results is S = 0 + 0 + 100 = 100.
5

{0,0,0,0,1,1,1,2,2,3}

{1,2,3,4,2,3,4,3,4,4}

{0,1,2,3,4,5,6,7,8,9}

Returns: 45
5

{0,1,2,3}

{1,2,3,4}

{9,2,4,3}

Returns: 999999941

This graph is the line 0-1-2-3-4. The edge weights are 9, 2, 4, and 3, respectively. As there is no triangle in this graph, Alice can only choose either a single vertex or two adjacent vertices. Thus, she has the following options: {0}, {1}, {2}, {3}, {4}, {0,1}, {1,2}, {2,3}, and {3,4}. Alice's scores in these cases are 0, 0, 0, 0, 0, 9, 2, 4, and 3. Bob's corresponding scores are 9, 7, 12, 11, 15, 7, 3, 9, and 11. Thus, there are nine possible results of the game: -9, -7, -12, -11, -15, 2, -1, -5, and -8, which gives us S = -66. As we are supposed to return S modulo 1,000,000,007, the correct return value is 999,999,941.
10

{0,1,2,9,5,3,4,7,3,4,1,5,2,3,0,7,8}

{6,7,4,5,6,2,6,3,1,8,2,0,9,9,8,2,5}

{10000,10000000,100000000,100,10,1,1000,100,10000,100,10000,1000,100,10,100,100000000,10}

Returns: 209370454
45

{}

{}

{}

Returns: 0
45

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

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

{783,247,447,571,192,863,75,100,841,352,762,205,185,748,202,704,84,110,803,60,651,463,253,932,926,215,549,413,784,270,617,500,592,462,690,835,353,727,292,131,455,636,7,963,693,536,238,835,941,569,777,494,678,234,339,487,632,46,188,880,927,28,562,825,469,460,950,469,790,333,136,228,192,427,571,77,846,804,852,888,422,752,999,222,973,920,788,238,21,451,588,525,230,414,67,754,630,733,600,2,79,109,466,486,526,136,692,240,726,950,959,938,191,223,100,697,587,295,535,160,243,532,480,611,152,750,854,159,624,697,604,262,779,118,604,6,176,915,373,564,164,242,600,228,23,186,862,237,529,814,3,381,379,7,334,44,788,431,196,883,695,438,456,831,202,465,189,503,279,717,147,346,316,535,599,87,788,858,789,107,169,642,572,416,234,895,742,765,67,262,198,282,403,710,374,737,433,945,273,161,825,611,72,81,502,233,476,97,697,93,924,843,875,932,303,648,396,451,44,384,217,51,336,20,480,182,742,415,601,950,671,743,325,334,993,720,284,509,610,515,787,248,915,823,916,353,915,57,534,349,215,74,469,450,242,112,951,933,803,896,398,620,559,944,743,106,44,187,802,766,646,940,658,311,335,97,601,867,2,203,951,118,987,701,17,45,742,222,493,202,600,267,853,249,321,996,671,687,402,140,356,359,161,232,470,271,245,461,681,762,513,459,386,827,233,218,227,699,140,199,55,384,169,363,347,935,651,531,757,688,294,985,239,554,572,680,174,741,18,781,991,924,474,489,63,18,599,300,90,138,755,879,715,275,982,724,891,487,899,681,379,128,251,138,821,751,297,427,8,825,397,566,342,370,960,981,997,892,376,231,936,797,708,123,802,572,639,789,638,574,670,437,576,249,612,536,881,941,167,128,229,250,824,802,675,25,318,631,544,742,640,42,390,909,957,115,254,620,810,352,662,133,675,254,221,567,281,401,190,433,87,880,111,726,997,14,449,750,645,372,201,641,625,900,577,844,582,904,235,406,427,259,970,19,826,912,450,192,729,256,345,807,950,383,176,580,692,605,291,620,507,852,660,371,353,747,585,701,325,199,0,809,130,357,780,909,586,616,335,379,252,180,848,142,790,364,688,618,832,420,888,453,915,174,110,613,519,182,169,152,371,410,9,96,952,698,38,456,570,357,818,340,474,329,448,474,204,243,393,255,802,577,135,587,548,870,786,378,614,605,710,527,388,947,288,670,269,986,186,693,390,517,880,306,102,693,713,513,4,54,504,880,15,542,531,912,227,134,774,692,312,600,426,160,813,760,47,64,988,279,190,683,756,724,973,836,930,111,871,613,133,611,943,484,732,452,822,143,638,306,61,535,94,578,825,975,386,133,544,194,992,936,802,426,824,963,694,372,96,535,890,982,825,930,831,529,129,692,899,353,306,603,835,18,130,657,417,332,937,730,197,849,829,824,85,12,794,926,714,55,588,538,810,152,16,897,226,70,615,719,941,747,818,96,42,823,411,808,670,114,422,890,951,444,658,761,185,22,759,623,952,780,993,82,328,692,5,187,111,129,395,138,812,696,299,948,183,886,126,237,219,69,211,164,889,12,438,219,346,182,804,238,3,507,507,528,632,178,364,431,637,315,293,26,707,9,132,890,367,333,291,25,322,401,621,119,99,456,374,275,188,269,357,235,816,822,191,898,481,402,103,638,608,697,818,510,48,466,934,956,614,661,634,16,572,611,705,375,787,43,607,811,219,259,780,712,620,745,469,391,537,847,77,862,223,926,479,589,626,594,780,463,405,177,720,951,851,588,286,898,643,150,155,962,614,737,227,11,99,789,891,141,954,392,649,123,65,608,353,211,0,696,676,241,485,679,331,861,539,949,244,552,451,266,110,820,228,545,736,573,821,271,133,234,206,288,599,572,338,924,905,597,142,130,280,118,914,392,100,704,975,629,53,883,960,234,77,380,872,687,582,45,915,871,253,969,170,368,291,913,360,503,53,818,331,836,880,649,370,153,388,247,160,724,565,171,991,750,866,743,830,483,871,634,995,440,194,369,463,513,76,73,300,545,485,618,300,114,617,96,699,845,412,210,719,581,48,717,806,110,435,566,633,973,393,717,340,65,545,947,21,370,960,118,165,193,228,490,631,654,953,664,719,81,628,651,108,138,472,395,721,208,86,762,74,567,720,696,317,370,538,715,931,316,511,423,45,152,467,4,399,815,404,978,267,140,361,605,70,516}

Returns: 486687
45

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

{2277016,388,516,6069,1,1884317,15367,88,96333,3,110701753,7734,49541281,13898,353,1,25564695,190604,13,7,1523,81352,816144,37915,3,177833587,256191,13312,8,529715505,813234030,1935016,476668699,2653,198,9,17807,387277107,43,72395275,2,2,4,1047456,22,21844,4197,383397,4,8,625,297091501,57097,3885227,16393691,25081,228472555,170290863,10639,20,100468,3724594,39728146,713,11624095,66978,23330,3383,5,34524188,8251015,69,334428,1555,12953258,299,262889550,43010530,716,566076931,4036,353,5863911,311,401401,1283275,198193561,302354977,1214049,56,10644,359242,129071,267,1868131,48677834,896784673,14,232652552,707105326,45273,14,1103290,254986219,1216911,12975666,9288,270,3977478,135412,184472,811,86952,23043,856006170,166,388423,365844446,842490811,3,11596662,32,2012,1,17,11,162009772,357,554,269523,2669027,580624250,943504,958652768,1,49777,1,44,27470771,3508241,36,93,9,16,9374,1134448,34123,2756,7248463,44148,328762,21313,1662981,40239654,14927,825163,206264497,8499,33,420206,1970,179589,5,6,142805715,68202944,1821,24,40,797096974,463744289,19731109,91444536,56033,5877,135521822,1,2840874,11,10776,583,392,2,2,745515791,1423,112,86028,2232,775,52684,137426,128,7,33,644730,1520921,54,557273483,448755,14103,2,1112873,53938985,864837,10528,29,11559,74,1550,131,634402381,129328,98644,205367627,386,858967742,6554,16192747,1959,3,1377,16233656,97253502,28,1,912737710,29954,33,1,254997209,226485801,93606,4144,24250327,224602,382538527,20651,1018,89473174,3199231,228187791,766609406,5124253,2753,5912414,10317,1,344,1473,660427,397690,2,3752,762002033,8,7244,376970233,725497,24316629,8518,2,810514,18153,771333,553243,393,88,3,14,2463,155,7294,1072346,98488,18514,182558,16016,35367,65263,30530,43130,17,6888267,454794,404633,7,18631,27237340,2318595,668,636,35,176,3245335,52,102825,1,9,327,203592,28,3217415,733459662,8,146,467326,2,3392439,3,1719,14,254,229,64248330,561008451,1929532,1660697,12,20,184,10250,366792384,336799,46884861,1101110,102238644,13278645,13,1,127573,3984,26075719,4,476,225609185,2546812,6032824,292,557970256,42,3853,119,937171,3171,1206055,5,732525189,10471,41858258,392,13,2164370,6530897,1,160822923,304951,161548,883028433,21332,693,2,17,10,457,2041352,26,1547425,152803,81039,261,11,1230065,870,355,4361,909750318,5646183,217656021,437,240996,2818678,2035054,142413,1223726,33,167,7,3,109320,9102522,1,87,84217,46187,526221,46977241,9,2173171,7,3,126928,144917617,329098264,4,407,1235354,458683529,217750108,14047102,3433,1712,18382361,136069628,15098300,58170,1438858,205381,15,64367,36,10881695,322721,2,24,75927,365163,12800,88497910,1191,453,32204497,172,158,35,26148958,25,112,4,187970176,457509,54687,608424140,2150222,4316390,4,27000969,122426,41846,7,639282,88,7951,2034,4,1,97502,111,361,2374294,12,1,538,27,15049893,968625,902,349721,17227,49877782,148,6403,102138,7,80711737,2573,181615,282425632,46,91267865,381,3,287446681,1,2,202,1883425,22268856,7,12127606,27,3422,324281219,2042371,106612997,11648895,27124119,49,34960,26,23408,11938913,5,54663,398,489916937,1611,16,1117,308328529,78,66231,194681717,13,63,225,55404,27567,363058,941,57,6748331,1098,492078,63648536,36,26,25,47,1,597324,62244,215,1,118989258,397,2,543228,11166,30736659,55559,149,2479708,18,419245,1,11248105,1,70292695,22,13085030,56,150577,93387,161252798,12486441,123057677,7,1,11407372,195800500,1387,128309,148,1296193,51,1312,10720586,6612084,6268057,73626693,141702066,260,83,100,5,159299,64553263,207080985,18,322,25,3250373,21,7866612,1002,4292,350814,2940446,44880000,45429528,13,9,23,155,666,401914,24638355,173,11,1993736,11122313,3185444,352,9452519,5067679,478099954,485505,2963,92095238,590609,265451,323,10676,17023,2,8749,3,1075239,36900,3232,85,294432110,33168519,38986862,1247,5217711,46059,17049,899490,2,296834,147986274,7,3,154018667,37019,3110552,270628345,3526554,390623,50311517,3582,360,48346,1291,955176576,312615685,10693801,3430,8537,13511,155440911,277596,3443676,3139,61087,203781663,10677,16,94745703,688802,12,1409653,682,3316,279583,45251281,14,12702254,13291,57361283,3130,15229776,16982712,38702,237,906,4426,2916,1,1161940,17774,3322760,45756,391,10,713719700,44559,4348,48,559,443368019,126,200836,14953273,122,9,976544,24738742,12161021,35137,1,1,7910,12425453,2090949,19678128,221,52,93358213,90,273,4485,160297,96,1,583786396,22681755,3562123,35486,4927185,30,5,4,3210,6162646,2,19216,10,17,513724277,644238,5454,95,15169,3546,45,567870699,8315319,8059968,129311,312,174754,57068,11246,1042,56810482,1249973,49741008,5,56692324,4450555,61653514,8,9562669}

Returns: 43362813
45

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

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

{398204,4455,6247100,17943,89,306028,47,800762104,16284746,1040667,59999941,115569714,261,16,47280,10,3753,337687948,30,2,2080,69,13,2420,12657621,170485,82,7013,86701,30976148,10940325,36,29134584,2206504,14408577,7,16484,21128,228185483,28,3,333,1543,1993,51068,143,2,1519951,799657,2,845086,139,9,880122,105738183,4,106660106,13269212,127069,267187,1002699,301743924,79,7584,151671,175,193377244,14186,94079175,4341931,261580535,29,2378704,171610,2754,3,913,954788,52168923,4,6863,7,518341,23744,4403523,1504,76,533,2079763,114388,61338,11,3,55063,3405500,355312,1181693,92916,17263366,152331469,857479818,163270,5562649,454759579,7166234,227,5,38950,313491274,679288,402192,9240,4,42,897397,523,5,92114227,87,67,16652,1854,55,971,11880,9974533,74130503,48232016,93192,263872,417,17,4004,5874123,27,82649869,357509,28932,749868,94916,120,1249,8921,21,280,6,26,685182,51958743,113077,2623,2090,2,123056372,245711463,533870397,4177665,3,887337841,23357887,145490838,8,1577468,8,24482521,5754641,42,382021691,2356,75966,195,6586121,20079,404580159,81088,19877,2041,14,768,408818310,110291940,449772,4909,448,631,376767496,14324,44167595,252950,71374,265213510,515,290,1437,431702136,75478361,1559,378318,2531871,1809232,24054611,1274,16485544,1,33,261123664,22,2876830,5121,1986,145538,12227363,19980,96800,11086,19,582,277831481,147867,74157746,1250,24644,6667810,51758,916445546,215375433,255,202944122,9,5531252,40262456,22222998,409670335,782981,13,836771,660470,15,52,2,92656,258,5092,862,708633063,172,261,8777786,328127,491117,117478,766643,4520208,5,34610404,1940,1,310473128,2,374436160,59269,193,127712,668,49418,608631494,1,331021,37516,411,9,37197697,2,177271,269,16703,118443234,147413152,47860,378323032,415,1067,147961,55043,603695,135793392,4,347094157,851129,211235,3373,54757,198,31882375,18,19,683799542,618,237,175777237,20781,10,242,14263,1,13798,171286,772,10,28959735,36567542,314717,88520,31139,62223,19,19,267820232,28774758,29958320,6933498,5022326,9,263,57,558954,3115,54152084,3,9523,52077392,320334821,27342566,2,568547731,118099449,586502,5563859,23464,60,321465535,59718464,21,1153587,258,464576,209890387,5451394,625880,30756767,34,12,2452395,585,14978836,14,11088119,9599,2,4686840,463,13098089,892778076,24217,4420722,250157763,510351150,33,782713537,3197929,20753,606864,2565371,2654,1,4,2,203847,521,6922694,58910,34252,85,10,438322628,175,13583320,4278238,44894,438012,2751,214,2581136,2122,28695524,2,251822,11269,360741461,150,1074,18,262891,63615,1075,5,24708,29576,145061,693732,6,460213018,173,11,735,1,71880,6509730,33543,286620208,1102,24518,16953590,431,5,1,153,1,20341,558780,4272748,98,1,56,132,94,4106625,163156,35016562,255,433,598445078,230571673,42123610,1,628,158718,577790,86275733,4,328270,3890,7264568,438726,928765797,6676989,554,48547,33,35,2185,85906,4795011,1,1041894,319,41,22743,46202,4191419,21678930,24140586,274254,27159,1248,3120055,248140862,308189809,257,17347317,935,108775,1554,25406,382,17,79949,5,2,4706841,1,1,839,7204045,57,483,16388,43,1013242,2748,5189357,461,1015,100,9,751134,176207,13606,5620697,4836938,707,36,2639,554055,111,18,27996,35,95,219392023,2,577077582,359643,5109,4341,136,13,1120,4127959,25129,5,2437944,64667,898360,397519,89441062,65167227,389,530668,53,3,698741271,15,3,352,116205546,13090352,1295,146567,9088172,20521,16213,335229293,432,715,9,6722584,30,1,30108800,1,3,47336839,2384960,10694411,291,400915}

Returns: 41266882
45

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

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

{22146080,185,214658506,40882640,16042356,185443749,2263,21,4830748,62916,1,532793,28927,1012797,141,294,304268843,2577771,122776622,7,29926,216861,178104219,18254478,4728582,30470,20,1025,6541595,5546516,22,151,391840,1,24,66168,1309,2095,749528017,8,8,1859975,561666931,5978,10,28325817,267,157,10255,84203942,1076,454988991,6257040,112,221,608768,148005,1467,11645,81038521,683223900,11093,180935,1106,32409881,52916,849766,303615554,88,208,20,14848171,34726,24316,74197,43303,68281,3814,8637,37207,66383170,8,2042986,149370,2,469,16995,4230,982,38996290,9856,131787,3,494828,905,538355,171750,2701,623157703,23,2912643,2200,3474,26257,236654541,86011940,598284,21304809,21,189236,1040148,54056446,13873279,7891979,157,224,549545,243,2,22,97,35633479,1089,909,3,4199754,727003,11,4940076,375199,40160,1,2728075,60940,57064733,2,126500,9824,231,16623,107,15175,129,109,167049,588234174,7034183,651,1357514,275491,9113,15,243735,1354193,8,18914433,930,1,272,1436166,4163,19,8989,1586922,52370747,10,3,517559700,3696653,1,2,45787,372504877,190763433,342205,127737,93,35075380,15669,361,208,1,44374,51380679,30,43,1380409,4567,2,3231174,11148,2104,151105,26175,5,5,16355,275982905,820860,471,1601910,1960426,12,22682,617262807,1303805,11146727,31958982,54479,662679,3,98444,61,1563002,16329792,45,24002845,278933,308289,42826,41214,4,87,11778,58657,3,2,1,377837253,504682001,6419,19390,22867,5,55901,16,119536160,20,35278503,34387,12736523,57,2353823,266366399,37307,524124,399,1280,142409,53286,40851,31665,5486126,848428494,68471,15471401,13712771,59,716595045,185,2,2934,172,645401,1,478781398,5842554,73714,156794,4347761,47844739,586159,56741,11932692,591680,25602974,31,212,88594763,10237,30846,454,434356,2383,134,533952,53,70500491,1755,119941606,6517943,74130832,1,43994294,2,144088,2319284,2,417566617,41,190,73990,24510691,34692923,242073,35423,276240948,7750667,1,452737364,428427,3,13264017,28287242,3416882,272335748,19861,681639,14,2768,9,1270469,157512,1016753,384641,141,5,25543,20871,465,16,60376722,5537,91648,794941,1747717,36648,985,720848022,4436349,797569,376742655,11253143,1476340,6552800,3,1,3939684,12078229,124122,17808,548,10,5,51527402,2147422,5871,3300,1311,11466,20533,29203,1697496,6735,1,177652,49,123752158,983,981263,1846559,4681609,144840618,18477,215,65886390,25249192,2420406,1325646,421,1,4077,18797010,61759,73196956,33255581,3213,21,13602687,2657703}

Returns: 475518983
45

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

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

{17291505,825,196991268,6983909,298711298,337360,229,1,219375,6110,305412381,13,307497833,7550,60,35434815,124944410,900,272730,112806,342999948,124911,7256,543,188706,242190,380700706,37669238,139100,19,2815,7992960,227,6895416,21,27353175,4821,15174,608917,25950349,124,302,481,1135,70,1049301,3560384,6402,475651,1,4708,2633,178989,303,451489417,500933,4,12636992,49455,7,2,208416946,3582,796320,7023,30512601,33,9623068,75437,37594,6,1841495,12,465938,152,18796,182,23914465,123802,3726145,54605,904673,1,757464,758375883,545055239,6110,7,834214,150282,5989023,997994,3895,419,1,4,51709,1541,3,702782505,14,49391,75,1203,13,101311,11243059,61110944,44,3546,1090195,15188,46440569,883991,13791166,2,9,1233,48,5358,5326588,375254762,949,1697,534933,313,4499999,95883,142015,34856,72689070,900245,486580980,157402,90756,2249,32,600,5,3577,8871,278995,17355298,172579968,44,5565,6,253481693,24,36,37394,212348179,2297586,59201187,11,2675,3650308,27362821,111,17787,814318,19376,2825,28554,55563,10985995,35760,1776,251,895889,56,2638278,97,34924,123,560192510,99605,6807478,616102116,106691,13523,7044586,5509,1,424,135132,26,8973,3,3686475,243391152,10446,36618722,2,107977,13158652,949458227,129128,328,13689,1382,27505,12105}

Returns: 929291481
45

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

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

{60319,678939,2,675109653,88491,5456892,1,26856,25,303499882,269,1592585,27182337,63228773,1683,197647899,1487,442810,168,2,1493685,15484583,3,1242229,764906,53301470,549656,65,86258341,21846,2,550737,58358,14,1164,38770969,11178,507,61809339,14539,10,22689155,79,1,643,95,818558,98437168,4,474053,28,11053,25,169001345,602,72247350,66539,137,173,733875883,16081007,1,366089046,666000707,2033679,2669,13728522,52223973,43608,155217,286,329141,230881296,8,10010,3463,5287204,6,528709,2344766,3837,2095538,8887,9541017,6955998,383324,81,13908,150988095,748,6,3,2119,77783,608,3,74857626,23153,513,269,212960099,113186,32511,21547272,2701798,21202583,18034,542268,76188345,519841,1254,110157369,525459,229585,138480,10862,137289,1,273103,3828,453660851,131,14861034,386022841,85904630,20895357,160821269,45835904,514751599,164561406,108,4,1149,2163,3,328717736,57445516,2015276,1,1110497,543601991,311,942311,688883296,67,25233,851264,12,318,2,1659547,490485,35139,52940,225,325096988,14,3618535,415728,2103769,41874,24,80846,1242659,4,1443,307943,12,4455391,34251514,23843,340,189010811,360,87170610,12519453,19639632,25581596,400695,742921,41413191,22846727,616524,302129,3709102,168539987,720,61615386,4,93825193,1684414,25,2,138865,7335734,1,509867311,92436,13,116689489,83689132,13,107,34498264,159840,124820932,23857,125390408,32011721,1060960,65,220,26775,5600353,910,247,101,735118929,5762814,168905,5650,23358,68549663,4051,4,23881985,220,116673065,302547,74173242,44,55211448,3000,210643,105441,1217269,53774530,932297,949667627,91148524,15,472065,162120,102698,14,611906610,58,11285441,11113,1289,4,4,2073927,491,47,5,10933,2372,21721334,131813,133,7636,86,7890,23145,14385663,698065531,20725,908,146260,546,7,14,232556676,1582527,690066,1733,230336528,225915983,253442182,243505214,107,20412454,1,620,360885,10124,116526107,12,590,2020577,4596802,46,2475,1263252,6,2451,37,101249283,17718,191010,2778471,11,287042139,1,278,369831,3506647,304754352,252,218342,1,315710523,567,60222370,1799643,2040829,261,545828,49,16629577,35,69451069,203,118645,10430,135119,8381728,15735404,18932025,299085,35752,2193052,7387828,10319,123,17,1377481,1,836192,325577,60,91377,442,172,782,1,725546,5899930,10922,3841588,297699378,1771,10785,128428345,345612,44,13,668,150332204,5445,59,46,5,9981,7614794,78713039,572092487,179641899,7,118811238,197590,41634102,978,1529132,69076041,29284,27421,16823037,45,7,1,2,5877362,9143,8351,1,69,318490,4511050,22,1086,1,6554,890,3049277,112889,254608,13,126,69,30982704,5566000,35826,1,5956021,963616369,9301070,310847,47785,5326,18757285,3,1883,2,2652,18211829,91598,1209940,27661,10748887,5260617,16,1656,48952,28116,29397678,319,123,251003730,947,1393208,10659965,722309639,506,228,459,50733969,68,7900,41,142172,9,49,98780,73666150,81,11,3447,4169,10839,199959,65,13,1,4,142216688,255627058,58948,1092943,99,272,14351,1405,4538637,17589,6,1,9,14038246,63,2999076,427,12,101679751,951,188018731,654180508,6,2,11315,32,2348189,2358,727134,9,714547772,91378413,2648723,3970,19037,915664,11823129,48771,3461,1662,23576,950891078,4,547920,151,72671177,194382317,3965,102159,100691143,103385568,449470,34,7,270913926,135095,33,24738185,60705179,849,2,30,1305,33492,850795075,34,7,10371,984661911,14488670,28,5650,61,1050907,1,2,22755,13492,44,110253,8131,166410,53,111087,723,114672,3435,6,131891667,85,6,290,468337,406,1,3791430,12485,9,20,196,2299,16296469,95353743,171074,107383136,13987904,2781,13613,438837,38851756,376,21533153,325,227803335,202,108,14551,5063,106454477,1055537,82,5189,220701254,52757548,3550513,864987130,39,54,2269206,355154810,11863409,22895,1477,2672,365172,8,12126,139925628,1,4077814,64506,41,1916264,11,3,729416,32432979,131,56021,21607411,24,71743319,110158,3,43407,248,542,4,988216708,362336,3640356,636793,6,85669,90,28,6726715,26192847,374260678,116,13063489,3,6,568,1120,106178532,50061446,102865957,14688,9,29,354,13090173,517450649,49322,1268939,254245028,291216612,490110,25580,4,116,787,3,16,262204,21548863,6,2845720,4148768,525,3029310,11,2,5562774,1340544}

Returns: 457715905
45

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

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Returns: 878440513
45

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Returns: 297277921
22

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

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

{65637596,16651646,169739,207459095,7,21014207,6503,3609,3,2997824,9238580,24999367,404858946,24333222,1384140,1111,9,798,23366472,381402322,15,649431,1,19,12755016,97571,2846606,333622650,368,2351,12,896687208,5439,75632,127,177,15685133,18,20,1,12,28762,705053,40948668,680,47933152,134406215,483629217,195,788,8,1,1570,2534,9796,4214991,93,10816147,2,10,77,685406816,26135799,16,95455,960,204,171,498,2,177062614,70,50984,83522,35701704,6,1,6202,50828928,6401534,3,20,1,42,371527522,44,760,397,32149118,716931,713572,2536,55215974,2,2,825384857,63,513,2,420,4741464,360666,229013,78284,1586,12965757,12450786,168434620,1,605,112473946,2,1296494,121437496,40,13137,133816785,28,7615,25006,1,10634552,189000189,4551431,446721,22,5514056,4366,2259071,2551446,115,87630723,249643663,125345,836,45977,45091784,10399,1989642,27794,588136664,7384,8,54748,794681,949686512,71640488,2415,5737619,1201,3298939,935869043,144,20102,1,805694,441,82,9893,1497978,251857,1070,104,42,231,6,8,106,13,105239,1947509,121,684,242028664,3557,44202746,7410200,131868,349,295,12659,4,110256541,39890016}

Returns: 268057280
22

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

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

{234583410,24158547,1,1,561220,151,52781,1677,180,13048,1597821,38308,2,275218,1,660,404,422077,52648232,20,3912028,24544,742804,937,13034929,1682212,66868,230725268,29226,1537,4866,16809517,96720,26033009,6543999,55976,9201,944,433478,22,1642394,12,119233583,580,127982,2,1071235,75423,162924,62,811147,80,187460962,2072,307249,51490,103,49,145327496,62736,656767,14,1310,300758,165,248726192,963817635,881104,8160,403,58432,8927855,3,11371,985336490,3462860,3946,1917,2169,2254228,18,1370880,807508,571092,162,138476811,471144,183038721,16511514,1601,157823601,44652999,1069926,47777,6126111,2937,97,27,445198,2,4,4764,200282502,29870515,620118790,5647175,16285,10738,51210902,957,15,4192,38,1144251,1519722,3229987,10693708,34807450,323033260,7213,1880,12,215692,2307,2,452084,7,5,8,268197,4670983,2,3,9418448,1,122380,17655121,350,187966,2,355353,56222046,9,203775356,8701860,3266,2111964,305083087,128,7797,676852740,198,7249,144629572,25854275,32120,5826586,463051717,1224,78599,6325,4822455,2943,513,304704,1296709,231002070,81517162,10886,3694565,7755,15691,319,66975308,724554531,347741554,1148463,37984923,7931,391892513,14,31,115056,418278763,627,35514,1261933,107810,550767414,6323,1219,28,13551109,2,6,1,261,288,2934,34975750,217524,2391,21,175778,10090885,9040401,106,555603,760,18408319,17131772,4938,287884657,4947220,8698,1802,1357,10,2790,5212,134223842,1,186267,2310595,1023413,5}

Returns: 192255953
45

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Returns: 442831623
45

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Returns: 990
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Returns: 4929430
45

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798000285, 140479115, 593447123, 572300292, 82880253, 69219492, 143564855, 881148191, 288554612, 984092565, 305420925, 505652666, 563832786, 555354270, 890357494, 111296825, 16487053, 508869060, 986629696, 392229170, 708349871, 544804452, 300434930, 849620801, 921395014, 498052617, 629125252, 678643551, 518187799, 199393598, 117310771, 238133443, 440556178, 475369736, 584183210, 866098160, 991930396, 153800109, 11074127, 415400342, 254570846, 636130184, 17777793, 984306572, 241021929, 37012076, 429048008, 360032777, 671522841, 311346250, 964934961, 724318956, 625718485, 990285692, 713724680, 265621064, 109566017, 887373520, 487216035, 449368552, 106555984, 395833440, 33220740, 779210935, 401729565, 915408943, 798404194, 252995795, 841491216, 604739165, 133423336, 444310468, 584326881, 342105295, 706566501, 719671896, 60172845, 22437643, 330306780, 395715426, 31970363, 670916805, 625779376, 764652352, 766771907, 752210106, 135715876, 408994576, 927845316, 33084924, 594291903, 614818259, 24313877, 587292608, 303064482, 896818341, 578368490, 109294039, 103863687, 173791344, 720232071, 953737431, 284462660, 286842337, 49542258, 230778509, 658091164, 72115667, 17879612, 676743600, 156301062, 689669690, 704110342, 107369291, 251649462, 67868293, 588050981 }

Returns: 85538484

Statistics

Problem Statement for "CliqueCuts"

Problem Statement

Definition

Constraints

Examples