TopCoder Statistics - Problem Statement

Problem Statement

In a Bingo game, players have cards bearing a random selection of numbers ranging from 1 to 75. During the game, a blower containing exactly one ball for each of these numbers releases balls one at a time, without replacement, until a certain number of balls have been released. After each ball is released, the players will mark the cells on their cards that match the number on the ball. A player's objective in this game is to win prizes by matching the markings on his card with one or more predesignated patterns. Each pattern consists of the same number of cells as a card, and each cell in a pattern is either a 'X' or a '.'. A pattern is considered matched when all the cells on a card corresponding to its 'X's are marked. At the end of the game, each player wins all of the prizes corresponding to all the patterns matched by his card. For example, consider a card with four cells containing the numbers [1,10,2,3]. The winning patterns are given as "X...", "X..X", and "XXXX". If the balls released in a given game were 1, 2, 3, 4, and 5, you would mark the cells on the card containing the numbers 1, 2, and 3. The following two patterns would be matched by the card:

"X...", which represents a pattern that requires the first cell to be marked.
"X..X", a pattern that requires the cells at both ends of the card to be marked.

The card would not match the pattern "XXXX" because the second cell is not marked.

At the end of the game, one additional ball is released to give players a chance to win additional prizes. Determine the expected increase in your payout after this new ball is released. In other words, determine the expected payout of the patterns matched by the new ball, excluding all the patterns that were already matched before the new ball was released. In the example given above, there is a probability of 1/70 that the pattern "XXXX" will be matched after the additional ball is released (the additional ball would have to be 10). The expected increase in payout would therefore be 1/70 times the payout associated with that pattern.

You are given a int[] card containing the numbers on your card, and a int[] balls containing the sequence of balls that have already been released from the blower. You are also given a String[] patterns and a int[] prizes. The i-th element of prizes is the payout corresponding to the i-th element of patterns. As described above, one additional ball will be released from the blower. Return the expected increase in your payout after the new ball is released.

Definition

Class:: ExtraBall
Method:: expectedPayout
Parameters:: int[], int[], String[], int[]
Returns:: double
Method signature:: double expectedPayout(int[] card, int[] balls, String[] patterns, int[] prizes)
(be sure your method is public)

Notes

All available balls have the same probability of being released.
Your return value must have a relative or absolute error less than 1e-9.

Constraints

card will contain between 1 and 25 elements, inclusive.
balls will contain between 1 and 40 elements, inclusive.
Each element of card and balls will be between 1 and 75, inclusive.
No two elements of card will be equal.
No two elements of balls will be equal.
patterns will contain between 1 and 50 elements, inclusive.
prizes and patterns will contain the same number of elements.
The number of characters in each element of patterns will be equal to the number of elements in card.
Each element of patterns will contain only uppercase 'X' and '.' characters.
Each element of patterns will contain at least one 'X' character.
Each element of prizes will be between 1 and 10000, inclusive.

Examples

{1,2,3}

{1,2,4}

{"XXX"}

{10000}

Returns: 138.88888888888889

The full card pays a 10,000 jackpot. One of the 72 remaining balls will complete the pattern, thus (1/72)*10000 = 138.888888888 is the expected payout value.
{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}

{"X.X.X"}

{10}

Returns: 0.0

Three balls (1, 3, and 5) are needed to get the prize, but since only one additional ball is released, the prize cannot be won.
{29,16,2,35,75}

{75,4,16,3,21,44,2,38,11}

{"X....","X.X.X","XXX..","XXXXX"}

{10,100,300,1000}

Returns: 6.212121212121213
{1,2,3,4,5,6,7,8,9,10}

{75}

{"X.........",".X........","..X.......","...X......","....X.....","XXXXXXXXXX"}

{50,40,30,20,10,1000}

Returns: 2.027027027027027
{1,2,3,4}

{12,34,45,56,67,1,2,3,4}

{"X..X","XXXX"}

{10,100}

Returns: 0.0
{41,12,33,45,19,13,11,27,69,35,72,8,73,2,24,36,16,60,15,68,55,51,17,21,74}

{56,74,70,46,14,66,29,6,62,50,19,31,3,34,73,68,5,42,30,65,54,26,7,60,51,40,52,35,4,37,41,71,32,2,57,72,58,39,17,11}

{"..X...XXXX...X.X.X.XX.X..","X..XXXX.XXX.X.XX....X.XX.","X..X...XXXXXXXX..X.X...X.","XXXXXXX.XX.XXXX.X..X...XX","XXX.XX...XX...X.X...X...X","X.X.X.XXX.XX...X.XX.X.XXX","....XX....X.XX..X..XXX.XX","X..XXXXX.XXX...X.XXX..X.X",".X.X..XXX.XXX.XXXXXXXXXXX","XX.X..X..XX....XXXX..X.XX","XX.XX.....XXXXXX.X...XXXX","XXX.XXXXX...X..XX..XX..X.","XX....X.XXXXXX.XX.XX.XX..","XXXX.XX......X.X..XX..X..","XXXXX.XXX..XXXXX.X....X.X",".X.X.X.XXXX...XX.XXXX.XXX","XXXXXX.XXX..XX..X.XX.X...",".X...XXXXX...XXXXX.XXX.X.",".X..XXX.XX....XXX.XXXXX.X","XXXX...XX.....X.XXXXXXX..","...XXX...X..X...XXX.XX...","X.X.XXX.X..XX..XX.X...XXX","...XXXX.X.XXX...X.X......","....X..XX.X.X..XX.XXX...X","XX.X.X.....X.XX..X.X.X.X.","XXXX.....XX.....X....XXXX","X..XX.X.X.....XXXX..X..X.","X..XXXXXXXX......XXXX...X","XXXX.XX...X..X.XXXX......","X.X.XXXXXXX..X.X...XX.X.X","XX.XXX...X.X..X.X.X..X...","XXXXX.X.X.X.X...X..XX..XX",".XXXX.XXXXX.XX....XXXXX.X","XX..X.X.XXXX..XX...X..X..","XX.XXXX..X.X.X....XX..X..","XXXX..X.XXX.XX..X.XX..X..","X..XXXX...X......XXX.X..X","X...XX.XX..XX..X...XX.X..","...X.X..XX.....X..X..X.X.","X.X.X.XXX.XXXXX..XX.XX...","XXX..XX....X..X.X.XXX..X.","..XX..XXXXXX..XXXXXXX..X.","..XX.X.XXXXX..X.XXX..XX.X","X.XXXX.XXX..XX.X.XX.X.XX.",".XX.X...XX.XX..X.X..XX.XX","X..X.XXXXXX.XX.XXXX....XX",".XXX.X.X..XXXX.XX.X.....X",".X.XX......X.X..X....XXX.",".X.XX.....X......X.X.X...","XX.XXX.XXX.XXXX..XXXX...X"}

{2773,8879,2623,3,6957,7645,2341,3347,2535,1649,1394,5300,4127,2040,13,7743,106,2501,3121,6532,9561,305,2720,6731,7872,4322,2665,702,1511,8368,4630,261,8369,5124,841,2338,5740,5025,2184,7918,2712,4887,4502,7892,971,4053,2500,4973,8436,352}

Returns: 0.0
{36,41,64,51,75,27,16,61,71,12,2,30,50,31,3,56,67,60,22,43,45,23,49,73,11}

{42,68,53,29,41,60,33,56,26,45,11,7,70,2,62,39,20,15,25,17,6,55,52,73,18,43,16,50,35,59,65,32,1,24,3,34,36,19,49,12}

{"..X.X.X.....X...X.X....X.","XX.X.XXXX..XXX..XX..X.X.X","XXX....XXX.....XXX....XX.","X.X..X.X.X.XX.XX..X.XX..X",".X......XX.XXX..X.XXX.X.X","X..XX.....X..X.X...X.XX..","....XX.X...XXXXXXXXXX....","....X.XX..XXXXX.XX.XX..X.","...XX....XX.......X....XX","XX...XX.X.X...X..XX....X.","XXXX.X..X.X.XX.X.....XX..","X.XXXX..X..XX...XXXX.XX..",".....XX....XX.....X......","XX...X.XXX......X..XX..XX","X..X.XX.XX...X.XXX...XX.X","XX..X...XXX...XXX.XXX..XX","X.X.XX...XX.........XXX.X","X...X....XX.XXXX...XXXXX.","...X..X.X.XXX........X..X","XX.X..X...X.XX...X.XXXXX.","....X.XX....XXX.XXXX....X","X.X....X.X.X....X.X.XXX.X","X.XXX.X.X......XX..X....X","X..XXXX.XX.XXX.X..XX..X..","X......XXXX.XX.X.XX.....X","X..XX.XX..XXXXX....X.X.XX","XXX.XX..X.X..XXX.XXX..XX.","..X.......X.X....X.X..X..",".XX..XXXXX...XX...X.XX..X","XXXX..XX..X.X.XX.X.XX.XX.",".X.X....X.X.X.XXX...X.XX.","....X.X..X...X.X..XXX...X",".XX.XXX..XX.XXXX..X.X.XXX",".XX.X.........X...XXX....","XXXXXX..X...X.XXX.X.X.X.X","XX.X..X..XXXXX..X....XX..","X..XX...X.X....X...XX...X","X.XXXXXXX..X.X......XX..X",".XX.XX.XX..X...XXX.X.X.X.",".X.X..X..XXXX.XX.X.XXXX.X","X.X..X..X..X.X..X.X...X.X",".X.X..XXX.X.XXXX..XXXXX..","X.X..XX...XXXXXX..X.X.X..","X.XX..X...X...XXXX.XX.XX.","..X.XX.XXX.X.XXXX..X.X.X.","X.XXXX..XX.X.XXXXXXX...X.","...X..XX..XX....XXX....XX","...XX...XX.XXXX......X.X.",".X..X....X...X.X.XXXX..XX","XXX..X.XX...XX..XXX.X.X.."}

{2034,1477,4250,9247,9926,4873,74,9904,9828,3826,6564,8554,3466,9701,6384,7622,4061,9873,6063,4726,9709,5303,7820,7043,2664,7629,4084,3785,1565,644,551,4278,212,793,5391,8959,8044,8793,2320,1427,405,8265,7296,372,80,4981,4233,5219,6308,6471}

Returns: 108.14285714285714
{28,33,23,44,4,52,53,9,35,36,68,61,43,47,39,10,54,24,71,11,46,40,15,20,22}

{8,57,24,21,4,75,64,6,59,34,60,61,30,63,40,49,19,31,35,71,45,1,69,43,15,17,3,50,39,7,23,20,10,18,73,65,22,70,16,55}

{"XXX..XX....XXX..X.XXXX.XX","X..X..XXXXXX.X...X..X..XX","X...XX.X.XXXX...X.XXXXX.X","XXXX.XX.XXXX..XX....XXX..","X.XXX.......X.X.XX..X.XXX",".X..XXXX.X...XX.X.XXX.X.X","XX.XX..XXXXXXXX.X.XX...XX","XXX..XXXXXX.XX...X.X..XXX","X.XX.X.X.X.X....X..XXX..X",".XX..XX.XX..X...X.XX.X..X","X..X.X..X.X.X.....X...XXX","XXXXX.XX.XXXX......XX...X","X..X.X.X.....XX.XXX.XXX..",".X...XX.X.X.XX...XX..X.XX","X.XX...X.X......X.X.....X","..XX.X....X...XXX.X.....X","X..X.X.XXX..X..X......XXX","..XX..XX..X.X..X.X.X.XXX.",".........XXXX.X.XXX..X.X.","XXX.XX.XX.X.XX....X.XX..X","X.X.X.X.X..X....X.....X..",".....X.X..XX.XXX..XXXXXX.","XXX.....XX....XXXX.XXX..X","XXXXX..XXXXX...X.XX..X...",".X..XXXXXX....X..XX...XX.",".....XXX.X.....X.X..X.X.X","X.X..XX....X.XXX.XXXX.XXX","X...X..X.....XXXXXXXX..XX","XXX..X.X...X.X..XX.X.....","X....X..XXXXXX.X.X.XXX..X","XX..XX.XX...XX..XXXX.X.XX","..X.X.X.....XX...X....XXX","....X.X....XXXX..X..XX.X.","....X.......X..X.X.X..X.X","...X.XXXX..XXXXX...X.XX..","..X.XXXXX.XXX..X.XXXXX.X.","XXXX...XXX.XXX.X.XXX.X..X",".......X..X..XXXXXX..X.X.",".X....XXXX.XXXXX..X.....X",".X...X.XX..X.XXX.XXX.XX..","X.X..XX.X..X..X..XXXXX.XX","XXXXXX.XXXXX.X..X.XX.X...",".X....XXXX..X...X.......X","X.XX...X..X.X.....X.....X","X.X...XXX.X.X.X.XXX.XX..X",".XXXX...X.X.X.XX.XX.XXX.X",".X.X.X..XX..XX...X...X...","XXXXXXX..XXXX....X.....XX",".XXX.....XX...X.X.X.XXX..","..X....X.X..XXXXX...XXXXX"}

{2304,3637,4920,1207,4836,1410,7065,4748,6251,2377,8829,1782,8139,7835,50,1835,740,6822,3034,561,7894,284,5460,3615,2324,5028,1305,9658,2840,496,9765,3055,5622,5791,3127,6843,1173,1235,890,7523,6763,21,1892,6945,8920,567,2815,3949,2839,5595}

Returns: 165.45714285714286
{46,74,72,68,23,31,51,75,43,33,20,59,63,62,44,29,25,40,19,16,1,47,10,49,36}

{13,26,65,11,46,70,29,39,6,14,30,75,55,33,57,47,22,32,20,3,40,37,43,36,28,48,42,12,53,54,60,31,64,23,63,10,72,35,8,15}

{"X.XX.XXXXXXX..X.X.XX..X..",".....X.XX.....XXXX..XX...","........XXX...XX...XX.X.X",".X.XXX.XX.XXXX.XX.XX.X.XX","...X.X..XXXXXX.XX.X..X...","...XXXXX.X..XXXXX.....X.X",".X.X..XX.X..X....X.X...X.","XXXXX..X.X....X.XXXXX..X.","XX....XXXXX..X.....XXXX..","X.X.XX...X.X.XXXX.X....X.",".XXX.XXXX.XX....XX.XXX.X.",".XXX.X...X.X.XXX..X......","X.XXXXXX..X...........XX.",".X.XX..X.X.X.XX.X..X..XX.",".XXXX...X.XXXXXX..XX.....",".XX...XXXX..X..XXXX.X...X",".....X.X.XX..XXXX.X.XX...","XXXX.X.........X.XXXX.X.X","...X.XX.XXXXX....XXXXX...","XX..X........XXXXX..XXXXX","XXX....XX.X...X..X.XX.X.X",".XX.X..XXXXXXXX..X..XX..X","....X..XX.......XX.XXX.XX","XX..XXX...........X.XX.XX",".X..XXX.XX.XX.....X...X.X","X..XXXX.....XX.XX..X....X","...X.XXXX.X..XX.XX.XXX.X.",".XXX....X.XXXXXXXX..XX...","X.XXX.X...XXXXXX.X....XX.","X..X.X..XXXX..XX.XX..XXX.","XXXXX...X.XX.X..XX.XXX.X.",".X..XXXX.X..X..XXX.XX..XX","XX.....X...XX..XXX.X.X...","X..XXXX..X.X.X..XX..XXX.X",".XX...XX..X...X....XX.X.X","...X.XX....XXXX......XX..","X..X.X.XX...X.XXXX.XXX.XX","XXXXXX.X.XX..XXXXX...XXX.",".XXXXX..X.X..XXX.X...X.XX","XXXXX..XXX.X.....XXX..X.X","X...X.XXXXX.XX.XX..X.XXX.","XXXXXXX....XX..X.X...XX.X","..X.XX....XX...X.XX.....X","X.X...XXX...X.XX.XXX....X","XX.XXXX...XXXXXX.XXX.X.XX","XXX.XXX....XX.XXX.XXX...X",".X...X....XXX.X.....X..X.","X..XX.XX.XXX.X.X.XXX.X..X","XX..X.X.XX..X......XX..X.","XXXXX.XXX.XX..X...X.XXXX."}

{9720,4472,396,8916,3317,5654,3830,8534,1927,2164,8880,9142,5447,3914,1868,3798,6058,4791,2831,8777,9401,868,2659,5397,4881,1028,2087,2440,8939,4255,5465,6409,8095,2224,7,8272,948,4219,9426,6697,8283,8562,8389,437,4285,3098,1589,338,338,1242}

Returns: 0.0
{57,4,61,13,16,20,10,34,44,36,1,53,11,30,68,26,32,58,2,42,73,7,9,8,45}

{68,24,33,38,2,47,30,37,5,31,4,75,50,34,52,29,22,36,67,65,57,42,51,13,19,69,71,35,46,6,63,54,26,12,49,72,17,55,16,32}

{".X...X.XX.X.........XX..X",".XX.XXXXXX.X.X.X.X...X.XX",".XXX..X..XXX.XX...X....XX","X.XXXXXX.X..XXX.XXXXX..XX",".X....XX.X.XX.XX....XXX.X","X..X..XXXXXXXXXXX.XX.X...","X.X..X.XXX..X.X.X.X..X.XX","XXXX..XXX...X.XX....X.X..",".XX.XXXX.XX.XX..XX..XXXX.","XX.X......XXX..X...XXX.XX","...X.X....XX.XX.XXXX.XX..","X.XX....X.XX..XX..XXXX..X","X......XXX.X.X...XXXXX.X.",".XXX.XXX.XX...XXX..X.....","XXX........X..X.XXXX.XXXX","........X...XXXXXXXX..X..","X.X..XXXX..X.XX..X.X...X.","..X.XXX.XXX......XX.X...X","..XXXXX.X.X..X...XX..XX..","...X.X.XX..X.XX....XXX.XX","..X.XXXX....X.X.X..XXX..X","XX.X..X.XX......X.X.X...X",".X.X.XXX.X..X.XX...X....X","X..X.XX...X.XX..X.XX...X.","XXX.X.XXXX....XXX...XX..X","X.X..X...XX.XX..XXXX.XXXX","XX...X..X.XX.X..X....X.XX","X...X..X.XXXX..X....X.XXX","XX.X...XXX...X..X.XXXXXX.","..X.XXXX.X.XXXX.XXXXX...X","...XXXXX.X....XX.XX...XX.","XXX.X..XX...XX..XXX.X.XXX","..XXXX...XX..X.XXXXXXXX..","...X..X..XXXXXXX.XXXXXX..","....XXX....XX....XXXXXX..","X..X.X.X.XX..X...XXXXXX.X",".XXXXX..XXX.X.XXX.XXX.XX.",".XX.X..X.X.XX...XX.X.....",".XX.X..XXXX.X...XXX.X.X.X","XX....X....XX.XX........X","..XX..X..X.X..XXX.XXXXX..","...XX.XXX.XX.X.X.XXX.XX.X","XX.......X.XX.XX..XX.X.X.","XXXXX....X.XXXXX..X...XXX","XXX.XXXXXXX..X......X...X","....X.X.X.XX.....XX.XXXX.","X..X...XXXXX...XXXX.XX...","X...X.....XX..XX.XXXX.X..",".X.X....X.X...XXXXXXX....","XX..X.XXXXXX.XX.X.X..XXX."}

{5567,9045,8583,5846,2665,4669,5561,602,2346,1772,114,5824,6185,6080,2421,8043,2521,5599,2830,122,1453,4366,9395,1483,9551,6703,1737,1419,2706,618,9643,2768,9446,4719,3862,8059,8509,666,6648,3256,396,8761,827,7224,1619,9306,8508,4337,736,9672}

Returns: 0.0
{64,67,61,19,71,36,24,68,57,26,58,18,13,4,35,20,37,40,15,2,46,11,32,6,22}

{40,45,38,62,31,16,53,17,43,26,72,29,4,9,32,33,36,69,66,10,75,15,58,52,51,48,67,11,64,34,13,30,35,61,12,25,73,7,57,49}

{"....X.XX..XX.XXX..XX.X.XX","...XXXX.XX.X...XX........",".XX...X..X.X...XXX.XXXX..",".XXXXX.X..X..X...XXX....X","XX....X.X.XX.XX.XX.X.XX.X",".XXX.X.XX..X....XXXX..XX.","XX...X.XXXXXXX....X..X.XX","X.XX..X..X.XX.X...X.X....","XXXXXXX..X....XX......XXX","XX...XX.X......XX.X.XX.XX","X.XX..XXXX...XXX.X.XXXX..","...XX...XXXX.X....XX.XXXX","X.XX.X.X.XX..XXX.XX.X..X.","X..X...XXX.X.X.XX.XXXXX..","XXXX..XX.X.X.XX.X.X..XXXX","..XXXXXX.X.XX...X..X.X.XX",".X.....XX..X.XXXX....XX.X",".X.X..X..XXX..X.X.....X.X","XX.XXXXXXX.XX..XXX...X.X.",".XX.X.XXXX...X..X..XX.XX.",".X.XXX.XXXXXXXX..X..XXX.X","X...X.X..X....XXXX.XXXX.X","X.XXXX...XXX.XX.X.XX.XX.X",".X..X.XX..X..X.X.X...XXXX","..XXXX.XXX...X..X..XXXXX.",".X.X..X..XX.X..XX...X.X.X",".X...XX.XX.X.XX....XXX.XX",".XXX.X.X...XXX.XX.X.XXXX.","X.XXX.XXXXXXX.X...XX.X.XX",".....XX..X..X.X...X..XX.X","X....X.XXXX..X..XXX.XXX..","..X.X..X.X.XXXX..X.X.XXX.","X.XXX...XX..X..XX.....XX.",".XXX..X.XXX..XX....XX.XXX","...XX..X.X..X..X.XX.XX...","...X....X..XXXX.....XXX.X","XXX.XXX.X.X..XXXX.X....X.","XXX..XXX...X...X.XXXXXXXX",".X.XX.XXXX...XXX...XX..XX",".XX.X..XXXX.XXX.XXX.X....","XXX...XXX.XX....X.......X","......X..X.X....XX.X.X...","XXXXX..X..XXX.X.X.XXXX.X.","..XXXX.XX.X.XXX.X...XX...","....XXXXX.XX..X.XX.XXX.XX",".X.XXX..X.XXXXX....XX.XX.","X.......X.XX.XXX..X...XXX",".X.XX.X.X.X...XX.X..XX...","..XXX..XX....X..XX.XX.X..","XX...X.XXXX..X.X.XX..X..X"}

{9687,7105,3762,2675,3906,956,9369,291,6867,3901,9632,6786,2428,9063,8076,795,2355,4095,2513,827,1070,5648,1930,7592,859,4912,8392,8580,6467,9619,704,3746,5135,7582,3822,1544,7899,1806,5710,773,2843,3130,6044,6853,2908,4902,4186,7539,6460,2442}

Returns: 0.0
{3,61,13,54,71,15,75,69,17,40,57,30,7,39,4,2,24,10,32,38,1,59,29,22,53}

{52,58,60,48,10,14,26,70,53,55,16,36,45,64,21,61,32,42,5,23,68,39,74,47,72,69,13,30,9,22,34,11,67,15,28,50,27,56,35,19}

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{4142,6124,2048,2421,5990,7657,8783,4735,4907,8643,2663,6104,1481,3093,5350,3178,4665,4922,6862,220,2144,9405,1228,5355,7624,8017,760,4429,3123,3683,8012,5570,2364,6653,7561,8843,5697,5724,4967,9616,4318,3941,4171,1708,219,723,333,4508,4266,4036}

Returns: 0.0
{58,29,54,49,48,43,67,32,56,62,21,16,72,41,57,66,27,36,71,44,46,50,42,31,18}

{37,45,18,73,38,65,64,9,10,50,20,62,30,12,63,75,56,58,11,28,29,2,16,66,8,59,42,54,48,36,1,71,46,21,40,44,51,32,41,5}

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{3681,7948,7796,275,5573,4847,2687,149,2382,7205,7981,3931,7731,8950,4952,7330,2264,938,1383,181,2236,558,689,9998,7589,1402,1651,43,7369,1921,6353,894,638,4280,9418,455,4117,2954,8639,8261,5954,6859,4196,267,3311,284,1832,9536,2690,5166}

Returns: 561.2285714285715
{18,46,34,25,63,36,47,39,70,22,37,33,55,54,1,38,67,32,74,75,15,3,6,9,68}

{68,7,61,2,39,45,42,60,37,27,41,65,6,43,9,8,63,1,29,40,24,58,52,21,18,22,47,15,33,55,67,20,17,53,66,14,56,32,28,13}

{".X...XXXXX.X.X.X.X...X..X","X..XX.XXXX.XXXXX.XX....XX","XXX.XXX..X.X.XXXX..XX...X","..X..XX.XXXX..X.X.X....XX","..X..XXXX..X.XXX.XX..X.XX","..X..X..XXXX...X......XXX",".X..XX...XX.XX..XX..X...X","X.X.....X.X..XX.....X..X.",".X.X.X.X.X.XXX.XXXXX..XX.","XX...XXX..XX....X..X.X.XX","X..X...XX..XXXXXX..XXXXXX","X..X...XX.X.XXXXX..X.XXX.",".XX.XX.XXXX.XXX..XX.X.XX.","X.XX..XX.X...XX.XX..X.X..","XX.XXX..X.XXXXXX.XX.XXXX.","...XX.XXX.X.X..XXXX.XX.X.","....X.X.XX......X.X..X...",".XXX..X.XX.....X......X.X",".X...XX.XXX.XXX.XXXX..XXX","X...X..........XX.X..X..X","..X.XX.X.XX..X.XX.XXX.XX.",".X.XXX.XX..XX...X...X...X",".X.X.XXX.XX.X.XX.X.XX...X","X.XXXX.X...XX.XXX.X.X...X",".X.XX..XX..X.X.X.....X...","X.X....X.XX.X.XXXX..XXX..","XX..X.X.XXXX....XXX.....X","XX....XX.X.X..X.X.X.XX.XX","..X.XX..X.X......XX.XXX..","X.XXX.X.XX..XX.....X..X.X","...X.XX......XX.X...XXXXX","XXXXX........X.XX..XXXXX.","XX.XX..X....XX....XX.....","..X....XXXX...XX.X.X...X.",".XX....X.XXXX.X..X.X.XX.X",".....XX..X.XXXX..X..XX...","XXXX.XX.......XX....XX...","..X......XX...X.XXX......","X..XX..XXX..X.XX.XX...X.X","XX...XX.XXX..X...XXX...XX","X.XXX..XXX.X.XX...XX.....","....XXX.XX...X....XX.XXXX","...XXXXX....X..X.X.XXX...",".....X..XXX.X..X...X.XX..",".X.XXXXX.....X.XX....XXX.","XXXX....XX.X....X.X.X....","X.X.XXX.XX.XXX.X.X......X","X..X....XX..XXXX.XX.XXX.X","..XX..X..X......XXXX.XX.X",".XX.....XX..XX.XX..XXXXX."}

{5531,2155,8465,9598,3807,1184,3533,6572,9630,252,1954,1948,6253,5338,1732,5825,4665,8792,551,548,5267,5169,8316,1004,1320,523,1884,6414,6982,2401,1113,5926,6380,6083,1235,7639,2722,8141,1593,591,8793,2245,209,431,2308,4009,2698,9353,4695,9161}

Returns: 0.0
{65,12,72,52,66,24,15,71,55,21,14,29,10,19,13,5,50,68,60,42,48,62,70,39,36}

{35,60,47,43,64,41,46,12,26,9,21,63,49,34,5,61,51,52,16,32,62,19,58,30,24,6,31,39,37,66,70,25,13,50,75,27,2,42,59,4}

{"X.XX.....X.X..X...X.X..XX","X...X.XX.XXX..XX.XXXX..X.","X.XXX.XX.X.........X...XX","X....XXXXXX..X...X.XXX.X.","X.X.XXX.X..X..XXXXX..X...",".XX..X..XX...X.X....X...X","X...XX.XXXXXXX..X.X......","XX..X.XX.XX.XX..X...XXX.X",".X.X..X.X..X..XXXX.XX.X.X","XXX.XX.X..X..X..X.X..X.X.","..X.X.X.X..XXX.X.XXXX..XX","XXX..X.X..XX...XXXXXX..X.","X.X..X.XX..X...X...XXXX.X","X.XX...X.XX.XXX.X.XXXX..X",".X.X.X.XXXX..XX.X.XXXXXXX","...X....X..XX..XX....XXX.","...XX...XX...XX.XXXX.....",".X.X..X..X....X...X.X.XXX","X..XXXXX..X.XX...XX..XXX.","X.X..X.X.X.XXXXXXX.XX...X","..X.X.X..X.XX...X.X...XXX","...X...XXX.X.XX.XXX.X.XXX","..X.X.X.XX.XX..XX.XX.XXX.","X...XXXXX...X.XX.XX..X.XX",".XXXX..X....X.XX.XXX.XX.X",".XX.XX....XX.X...XX..X...","X....X.XX.X..XXX.X.X.X.X.","X.X....XXXX...X...XX.X..X",".........X.X..XXX...XXXX.","X...XXXX......X...XXX...X",".X...XX.X..X.X.XX.X..XX.X","....XXXX.XX.XX.XX.X...X..","XXX.XX..X.XXXXXXXX.....X.","X.XX..XXXXX...XXX...XXXXX","....X.XX.X..XXX..X..X..X.","XXX.XX...XXX...X.XX.X.XX.","XX...X...X.X..XXXXXXX..X.","X....XX.XX.X.X.X...XXXXX.",".X.X..X...XXXXXXX.XXX....","XXXX.XXX.......X..X...X..","..X.XXX.XX.X..X..XX.XX..X","..X.XXXXX.X..X.X.XX...X..","...X.XX.X.XXX....X.XX...X","X.XX.X..X..X.X.X...XX.XXX","XX...XX.XX..XX.XXX..XXX..","X.X......X.XX..XXX..X.X.X","XX.XX.X..X.X.X..XXXXXXXXX","..XX..XXXX.XX.X.X.XX.X.X.",".X..XXX.X...XX..X.XXX.X..","XXXX....X..X.XXX...XXX.XX"}

{7495,1444,52,4941,4441,2606,2981,3948,1668,197,181,9054,8497,9217,2458,197,9535,4962,6787,7457,7722,3301,5741,2360,3903,9044,4777,8027,7710,9932,4366,2807,5217,5235,7227,7801,9836,5849,4272,4166,1302,7214,7805,5498,6439,3013,4522,8879,5042,8647}

Returns: 0.0
{19}

{34,28,33,43,49,60,62,66,67,9,27,39,4,69,59,8,26,31,41,20,51,25,16,45,24,36,3,46,52,53,2,74,35,63,6,47,1,55,18,21}

{"X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X"}

{6414,1333,8415,3152,2865,6737,891,328,4609,2121,2663,5936,4795,1036,1999,303,9126,2239,3898,4594,8624,6410,1293,8524,2668,6834,1980,3214,3067,2360,9138,343,7068,6927,2610,7310,5135,2468,3455,8926,6958,7305,5993,3665,1501,6706,3706,9456,1168,1715}

Returns: 6285.171428571427
{1}

{33}

{"X"}

{5689}

Returns: 76.87837837837837
{55}

{5}

{"X"}

{6185}

Returns: 83.58108108108108
{47}

{7,63,16,34,42,58,10,67,61,73,59,60,11,2,18,25,52,28,62,24,13,74,64,20,51,27,45,3,41,23,30,37,75,39,9,40,1,47,46,36}

{"X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X","X"}

{3116,9873,8218,8259,1417,1873,9916,3126,90,1675,4813,5508,6857,6360,2642,735,3004,7918,1386,2778,926,3204,5343,3305,3869,759,3226,620,9334,3820,9388,1574,4685,5238,4682,2658,6274,6571,9624,3336,9072,9650,6362,3372,4936,767,855,3383,2286,850}

Returns: 0.0
{14,49,73,75,1,43,60,52,9,3}

{9,59,3,2,7,50,20,55,43,31,52,6,58,66,44,32,38,23,24,51,22,42,13,35,33,46,74,27,54,47,67,73,26,69,61,30,19,25,49,16}

{".X...X...."}

{4683}

Returns: 0.0
{25}

{51,13,9,7,27,75,30,50,49,42,62,20,22,48,8,41,72,63,4,35,58,28,69,39,16,25,11,2,19,23,12,40,37,5,67,29,38,3,70,44}

{"X"}

{2505}

Returns: 0.0
{35,75,41,62,52,72,18,38,29,33,45,69,68,32,70,16,11,3,65,44,63,12,57,34,39}

{52}

{".X.....X.X.X..X.XX.....X.","......XXXX..XXXXX..XXXXX.","X.XX.XX....XX.X.XX.X....X","XXX..XX....X....XXXX....X",".X..X....X...X..XXX.XXXXX","X.X..X..XX.X.XX....X..X..","XX.X.X.XX.X..X.XXX....XXX",".X.XX.XXXXX...X.XX..XX.XX","X..XXX.XX..XXXX.XXX.XX.X.","X..X.X......X..X.X..X.XXX","..X..X..XX.X.....X...X..X","..XXXX.X.XX...X.X....XXX.",".XXX.X..XX.X...X.X......X","X....XX..X.XX.XXXXX.X...X","XX...XXX..X.XX.XXX.X.XX.X","XX..X...X.X.X...X.XXX..XX","..XX....XX.X.XX..XX.X...X","X....X..XX..XXX..XX.X....","XX...X.XX...XXX......X..X","X.X.X.X.X..X..XXX..X.X.XX",".XXXXXX.XXXXX.X.XXX..XX..","........XXX..XXXX..XXX..X","XX..X...X.X....XXXXX..X..","XX.....XXX..XXXXX..X...X.","..X....XXX.XXX..X...XX.XX","XXX..XXX..X.XXX.X.....X..","..X.X..XXX.X...X....XX.X.","XXXXX...X.XX.X...XX..XXX.","XXXX..X..XX.XXX.XXXX.X.XX","X...X.X..X...XX..XX.X..X.",".XX.XX..X...X....XXX..X.X","XX.XX..XXXX...X....X.X..X","X..XX...XXX.XXX..XXXX..X.","XXX....XXX...XXX....X.X.X","XXX.XXXX.XX.X.X..X.X..XXX","X..X.XXX..X..X.XX..XXX...",".XX.XX.XX.XXXX.XXXX..XX.X","XXXXXXXX...XX.X.XXX.XXXXX","X..XXX.XX.X...XXX.XX...X.","X.XX..X....XXX..X.XXXX.XX",".XXXX.X.XXX.XXXX.....X.XX","..XX.XXXX.X.XX.XXX..XX.XX","X.X..X...XXXXX.XX.XXX.X..","XX.X.X.X.X.XX.X.XXX...XX.","X.XXXXX..X.XX.XX.X..XX..X","X..XX.....XXXX.X..XXX.XXX",".XXXXX.XX.X.XXX..XX.XXXX.",".XXXXXX....X..XXX.X.XX.XX","X..X....X....XXX.......X.","X.X...XX.XXX..XXX....XXXX"}

{6814,4356,3837,2305,714,646,1980,6059,8327,9835,4677,2584,5735,8625,8910,8998,1010,7519,8616,6147,8958,467,4465,8050,7328,7167,4923,7681,6514,9524,6925,3544,2038,2989,5080,7188,6297,7327,4349,4404,3963,8767,637,5172,718,7029,1489,8041,1421,2383}

Returns: 0.0
{55,63,15,20,37,17,46,21,12,44,14,74,36,24,23,18,58,7,33,3,66,51,57,13,19}

{29,30}

{".X.XXX.X.XX.X.X..XXX.XXXX","X..XX....X.XXXXXXX..XX..X","XXXX.XXXXXXXX.XXX.XX.X.X.","X.X..XX.X.X.....XXXXXX.XX",".X...X..X....X..XXXXX..X.","X..XX..XXX..XXX.X..X.XXXX","XX.XXX..XX.X.X.XX..X.XX..","XXX.XX.XXXXX.X.....XX.XX.","X..XXXX.X..XX.X.X........",".X.X.....X.X.XXX.XXX...XX","X.......X....XXXXXXX.XXXX",".X...X.....X.X.....X.X...","..X..X..XXX..XXXXXX....X.","XXX.XX..X..X.XXXX..X.X.XX",".XX.XX.X.....X..XXX.X.X.X","X.XX..X.XX.X.....XXX.X.XX","XX..X.....X.XX.XX.XXX.XX.","XXX.X.XXX..XXX..XX.X.X.X.","X..X..X.XXXX.XX.XXX.X..X.","X...X.XX.......XX.....XXX","XXX.X...XXXXXX..XX....XXX","..XX.X.XXX.X.X.XXXX..XX..",".X..X..XX..X.X..XXXXXX...",".X....XX...X.XXXX....XX.X",".XXXXX..XXXXX.X.X.X.XX...","XX.X..X....X...XXXXXX....","X.XXXX.....XX......X.X...",".X.X.XXXX...XXXXX.X...XX.",".X.....X.X.XX.X....X.X...",".XXXXX.....X.X.X.XXXXX...","XXX..XXX...XXXXXX.X....X.",".XX...XX...XXX..X.XXX.X.X",".X..XX.XX.X..XX..X.XX..XX","XX...XX..XX...X...X.XXX.X","X..XXXXX.XXX.XXXX.X...XXX","XXXXXX....XX.XXXXX.XXX..X",".X.XXXXXXX.....X...X.X..X",".XX..XXXX..X..X...XXXXXX.",".XXXX..XX....X.XXXXX..X.X","..XX.X.XX..X...XXX.X.X.XX","X..XXX...XXXXX........X.X","XXXX..X...X.XX..XXX.XX..X",".XX.XXXXXXX...X..XX.X...X","..X...XX.XX.X..XX..XX..XX","XX..XX.X.XX.....XX..X.X..",".....X..X...XX..XX.X...XX","XX.XXXX..X..XX....XX.X.XX","X.XXX.X..XXX....X..XX.X.X","XXX..XX..XX.XXXXXXX.....X","XXXX.X.X...X.XXX..X.XXXXX"}

{4544,9373,6493,7706,9483,9344,84,9580,3817,8471,1115,1318,9280,9906,4224,9434,522,3680,8210,3661,5546,7175,6978,696,3874,1508,2379,688,3284,3088,1264,8007,8248,4100,6038,2628,8766,1790,2994,5809,5941,5220,5747,8371,4235,1064,9570,7311,8277,9885}

Returns: 0.0
{12,2,31,56,9,55,20,25,49,48,74,59,71,43,32,1,70,39,5,67,46,11,29,69,42}

{44,49,72}

{"X.XXXX..X.XX.X......X.XXX","..XX.XXXX....XXXX..XX.X.X","..X.XX.X.XXXX....XXXX.XX.","..XXXX..X....XXXXX..X.X..",".XXX.X..X.X.XX.X..XX..XXX",".XXXXX.XXXX..X.XXX..XX.X.","X...XX..X..X.XX...XX.X.XX",".XXX.X.XXX.X...XX...X...X","X...X.X..XX.X...X.XX..X.X",".X..X.X...X.....X..XXXXXX","...X...X.XXX...XX...X.XXX",".XX...XX..X..XX.XXXXXXXX.","X..X..XXX.....X...X......","....XX.X...X..XX....XX...",".XX.XX..X.XX.XXXXXXXXX..X","X..XXX....X.XXXX..XXXX..X","..X.XX.X..X..XXX....XX..X","XXX.XXXXXX......X.XXXX.X.",".XXXXX..X.X.XX.X.....X.X.",".X.XX.XX.X...XX...XX...XX","X.XX.X....XX.XX.X..X.....",".X.X.X.XX.X.XX.....XXX.XX",".XXX......X.XX..X..X.XXXX",".XX..XXXXX..XX..X......X.","X...XXX..XXXX..X.......X.","X..XXXXX.XXX.X...X.XXX.X.","XXX..XXX...X...X..X..X...","X.XX.X...XXX.X.XXXXX...X.","..X.XXX...X......X..XX.XX","XXXXX..X..XX...X..X......",".XX...XXX.XX.....XXX.XX..","X.X.XXX..XX..X.X....XXXXX","XXXX..X.XX..X.X.XXXXX..XX",".X..XX.X.....XXX..X.X..X.","XX...X...XXXX.X..XXX..XXX","..XXXX.X.X.XX..XX.X.XX...","XXXXX...X.XXX.X.....XX.XX","X..X.X.X...X...XXX.XXXX.X",".X.X.XX.X..XX.XX..XX.XX..","X.X..XXXXX.X......XX..XX.","XX.XXXXX..X.XXX.XX....X..",".XXX.X.XX..XXX......XX...","..X.X.XX....X.XXX.X.XXXXX","..XX.XX.XX.X.X..XXX....XX","XXXX.XX.X..X.XXX.X...X.XX","..X..XX.......XX.XX..XX.X","X.X.XXXXXXXX.XXX.XXXX..XX","XX.XX..XXX.XXX...X.X..XXX",".X.XXXX.X.X..XX...X...XX.","XXX.....XXX.X....XXXXX.X."}

{3648,7938,2011,7976,7032,3826,901,2266,6810,9931,4216,629,7827,2284,7674,2562,1841,596,6137,5097,9292,7021,5901,868,6425,5705,5659,5074,2333,3212,1035,2985,4543,7323,8876,8623,8610,2147,1734,5803,8625,5804,880,6007,5372,9855,7379,8137,9026,7815}

Returns: 0.0
{16,22,1,40,35,54,67,11,45,47,73,20,42,2,32,33,49,6,10,19,41,51,60,64,26}

{5,65,4,47,64,42,7,45,74,52,58,12,26,73,11,24,75,43,35,38,69,25,20,31,72,10,22,1,34,2}

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Returns: 0.0
{63,68}

{5,23}

{".X",".X"}

{1703,6214}

Returns: 108.45205479452055
{71,50,53,22,40,30,24,1,25,29,42,44,34,43,14,69,39,55,5,10,64,61,74,27,51}

{66,1,59,74,20,43,44,8,62,68,52,40,12,36,24,72,34,15,17,45,26,13,22,48,63}

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{4436,5249,9453,5089,383,2369,2359,579,90,9843,3096,7911,4256,790,3045,9268,3586,501,9416,8886,4139,8559,8714,5923,3446}

Returns: 0.0
{73,65,40,31,4,18,10,24,20,30,9,68,75,70,56,43,28,35,25,41,23,66}

{51,4,20,24,69,50,66,22,14,71,8,64,75,7,3,15,35,63,67,21,48,45}

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{37,9399,2645,6221,2145,4239,1256,2016,7867,3749,3622,6680,4002,5966,4400,3097,3853,2580,9031,5783,2047,2639}

Returns: 0.0
{41,12,33,45,19,13}

{11,27,69,19,35,72,8,73,2,24,36,16,60,15,68,55,51,33,17,21}

{".X...X","XX....","XXXXXX","X...X.","XX..XX","..X...","XX..X.","X...X.","XXX.X.",".X...X","XXX...","X.X.X.","XX.X..","X..XXX","X.XXX.","X.XX..","..X.XX",".X..X.","..XXXX","XXXX..","X.X...","X.XXXX","XXX.XX",".XXXX.","X..X..",".XXXXX",".XX...","XX...X",".X...X","...XX.","X.X.XX","X.XX..",".X.XX.","X.XXX.","...XX.","...X.X","X..X..","XXX.XX","X..XXX","XX.XXX","...X.X","XX..X.","X.X.X.",".XXX.X","XX.XXX","XXXXXX","XXXX.X","..X..X","X....X","XXX..X"}

{183,4462,9924,8358,5664,6623,4028,620,8465,5681,1157,7777,7621,340,6480,4546,5758,448,7494,5569,268,5207,6705,7059,750,7306,2252,6822,2600,2814,1256,8359,9878,5648,4352,1140,720,8151,9743,7405,1646,7849,3185,3584,8046,1121,9831,8182,9956,175}

Returns: 800.2545454545453
{39,52,38,7,57,64}

{4,54,31,69,55,68,53,51,25,30,9,48,65,58,33,3,46,41,32,2}

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{2598,1971,2,8910,8590,948,2721,5357,7545,9637,1859,9926,8486,9405,2887,9417,2833,2607,8016,2351,3631,5413,3525,3616,2042,4492,1018,2260,4041,7871,2174,5560,1235,8488,2359,3604,3365,7797,4347,267,7939,1800,2624,370,2236,2129,9335,2116,545,8207}

Returns: 154.74545454545455
{45,34,59,42,8,9}

{31,21,50,16,71,74,19,15,75,47}

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{3010,3536,7379,4617,1302,8316,2869,3322,2698,7389,7243,7279,636,860,2106,8901,2739,5950,7870,8793,5559,8749,7739,2078,547,1913,1876,6429,6586,6251,2492,5980,3656,9803,1563,578,2347,4211,4515,3914,8690,115,3267,1702,276,5398,5372,1750,6980,9701}

Returns: 218.9076923076923
{71,18,6,29,61,39}

{43,25,28,40,36,14,49,8,66,64,6,53,74,51,30,48,1,4,26,63,72,70,16,65,9,69,24,47,32,50,5,57,19,22,33,46,34,58,54,56}

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{1899,1629,4934,8115,2240,5112,9441,708,5107,7424,8460,2054,2188,8507,5035,2900,8858,236,1017,597,934,7924,4707,3905,748,8983,9198,547,5576,7870,3104,8512,4045,9275,6381,1591,4188,1458,2064,2121,1507,5509,8765,2667,9044,2016,4116,7465,7367,4743}

Returns: 1051.5714285714287
{20,52,36,27,49,74}

{60,61}

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{7518,3689,217,7314,8457,517,6525,2976,6406,5524,8587,4141,8245,8436,9566,4718,2469,3948,2476,7966,7075,5589,3774,4068,8176,1609,7188,9119,8630,6634,2055,597,4859,790,4686,973,9463,8329,2565,6681,8867,5155,2651,7689,1026,8524,1290,2539,548,2598}

Returns: 718.8767123287671
{49,23,5,24,11,62}

{19}

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{1288,8154,7615,5183,1556,8039,742,2287,5670,1390,3241,3504,9267,5010,1470,9505,4548,8022,9579,8767,3244,6451,1608,5201,8971,8103,3029,5030,6611,1744,7999,7884,8441,9578,8096,5298,189,5957,2213,5136,4413,90,3828,6645,9015,1999,4237,7617,8126,7177}

Returns: 562.081081081081
{55,20,16,22,28,47}

{35}

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{4815,8611,5306,6252,416,6230,4465,282,82,4851,5412,5706,7869,451,8949,8146,449,7716,2044,1533,3900,7788,776,5681,2094,3181,8656,4338,874,3978,4239,3525,8880,4201,1232,3767,3210,9705,1638,1999,4628,9254,9440,7826,7119,2891,1674,2246,7111,1592}

Returns: 257.41891891891896
{74,41,66,60,3,6}

{43,33,73,50,27,31,20,29,56,13}

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{7708,4462,3672,8107,1855,2255,264,411,2425,1551,2382,2826,9761,9320,2571,2655,7968,2661,1083,4887,4621,9289,887,2327,859,6913,9738,5809,7830,9671,3763,1814,6634,5176,4395,8715,9445,2472,2488,670,638,8293,3584,5915,3909,4249,6658,9098,3148,5556}

Returns: 126.0923076923077
{62,60,27,32,14,34}

{29,45,13}

{".XXX..",".X.X..",".XX.X.",".X.X.X","X.X..X","X.X...",".XXXX.","XX.XX.","XX.X..",".X..XX","X.XX..","X.XXXX","XXXX..","...X.X",".XX..X","XXXX..",".XXX..",".XXXXX","....X.","XX.X..","XXX..X","..X..X",".XXX.X","X...XX","X...X.","XX.X.X","X.XX..",".X...X",".X..XX","XXXXX.",".X.X..","..XX.X","X.X.X.","X...XX","XXX..X",".X..X.","..XXXX","XXX.XX","X....X","XXX.XX","X.....","..X..X","...X..","..X.XX","X.XX.X","..X..X","X.XX..","X..X.X","XXXX.X","..X.X."}

{6110,2144,8553,5387,895,778,1783,2945,1937,3801,955,9396,327,2788,1662,8301,588,6475,2082,6210,648,7033,5929,8769,6385,1814,8085,8578,9556,7921,1615,2039,3924,892,2395,872,4386,6743,9420,1661,7933,5090,5061,1723,5084,429,2544,1619,4458,3795}

Returns: 209.3888888888889
{58,13,57,28,38,42}

{74,43,4,75,55,22,62,69,5,20,25,54,72,64,15,73,6,45,9,12}

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{6712,2146,1332,5371,34,5860,4396,5053,353,1454,3869,1233,2401,3335,1551,4286,2864,4235,8980,5102,1261,2184,7596,837,9168,8027,8838,7634,1450,9819,4360,7476,7262,2692,5056,2254,6800,5000,7115,1582,9868,3328,6391,5291,2250,873,373,5005,5937,8525}

Returns: 651.2727272727274
{29,35,60,21,59,63,20,26,71,44,11,39,34,15,70,23,75,49,9,3}

{15,65,40,17,25,41,5,67,62,23,38,27,14,36,10,71,52,28,50,63,2,72,29,55,58,51,60,26,3,18,45,24,35,32,42,70,34,20,11,6}

{".....X.X.XX.X.XX..X.","..X...X.X..X.XXXX.XX","XXX.XX.X.XX.X.XX....","XXXX.XX....X..XX.XX.","XXX...X..X.XX..XX.XX","....XXX..X.XX.XX.X.X",".X.....XX..XX..XX..X","XX.X.XX..XXX..XXXX.X",".XXXX....XX.XX.....X","X.X...XXX..X.XX.XXXX","XX....XXXXXX.XXXX.XX","XXXXX...XX....X....X","X...X..XXX.XX..X..X.","......XXXX....XXXXX.","..XX...X.XXX...XX..X","....X.XX.X.X.XX..XX.","XXXX..XXX.XXX.....X.","X..XXX.XXXXX.X.X.X..","XXX.XXX.X.XX.X..X.XX","XX.XX.XX.XXX.XX.XX..",".X.X..XX...X.X....X.","..X.........XX.X.X.X","X..X.X.XXX.X.X.X.XX.","X..X..XX.XX...XXX...","..X.......X...XXXXXX","X.XXX...X.XXXX.X.X..","...X.X.X..X.XX.....X",".......XXXX..XXXXX..","XXXXX.X.XX.XX....XX.","X.XX.X....XXXX..XX..","..X....XXXX....X.X..","X....X...X..XXX.XXXX","XX.X..X..XX.X.XX....","X..X..XX.X.X.XX.X..X",".XXX....XXX.X.XX.XXX","XX...X.XX..XX.XXX..X","XX.XX..XXXX.XXX.XX.X",".X..X.X......X..X.X.",".X.XXX..X..X..XX.X..","...X...X..X..XXXX.X.","XX...X.X....XXX..XXX",".X..XX.X...X.X......","XX....XX..X.XX.XXXXX",".X...XXX...XXX..X.XX",".XXX.X.XX.XXX..X...X",".X.X...X.XXX..XX..XX","....XX.X.XX..XX.X...","XX....X..XX..XXX..XX",".X....XX...X.XX...XX","X......X..XX.X.X.X.X"}

{4135,2487,3804,2643,1367,3936,684,816,1673,9041,5360,923,3668,4713,8000,3562,8009,9716,9250,926,1494,2230,4778,3189,5838,5708,372,770,3286,6337,8288,8065,6304,4014,9486,7237,6893,4886,6730,8309,5343,7073,2121,6439,5421,7463,4661,4155,6699,5664}

Returns: 74.34285714285714
{65,7,48,70,39,72,34,46,18,30,28,22,35,43,10,8,24,6,73,58}

{58,46,33,2,50,21,31,71,13,52,1,34,60,29,37,28,70,57,36,9,55,15,44,12,41,67,22,49,30,26,35,56,40,54,10,45,5,8,53,66}

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{879,3817,5227,9524,8315,422,6179,5871,991,8177,3349,9676,5901,5340,6815,5939,2123,5597,2953,1740,13,1609,1304,3351,9689,7714,6708,938,2519,1023,1644,1852,9384,9884,4472,7794,1561,641,2191,4983,312,871,1882,7890,9958,6967,3912,7154,3741,4725}

Returns: 0.0
{22,65,44,49,48,63,72,68,57,32,47,69,34,70,46,74,42,2,27,53}

{52,18,14,72,49,47,69,34,60,45,48,11,75,65,51,1,67,16,36,32,15,35,3,10,20,39,43,63,19,56,29,9,54,33,58,53,28,68,22,27}

{".XX.XXX.XX.XXX.X.XXX","..XXX..XX.X.X.X.X..X","..X.XXXX.XX.XXX.X..X",".X...X.XX.......XX..","...XXXXXX.X...XXXXXX"}

{1801,1431,1632,4408,1607}

Returns: 0.0
{57,74,61,66,7,45,46,59,53,67,52,9,43,23,1,51,18,56,71,54}

{61,1,6,25,43,67,58,21,63,14,18,47,29,71,20,32,30,28,42,7,24,31,23,22,48,2,12,69,45,37,4,38,57,8,34,33,56,60,46,9}

{"....XX.X.XXXXX..XXXX","X.X.X.X.XX...XX.X..X","....X...XXXXXX....X.","XXXX.....XX......X.X","....X.X.XXXX...XXXXX",".X...XX..X.....X.X.X","X.X....X.X....XXXXX.","....X.X.X.XXXXX...XX","X..XXX...XXXXXX.X...",".X..XX...XX...XXX..X",".XXX.X.X.X..XX.XX.X.",".XX..X.XX..XXXX...XX","..XX...X...X.XXX.XX.",".XXXXX.XXX.XXXX.X...","XXXXXXXXX....XX.XXXX","X.XXX..X.X.XXXXXXX..","...X...X.X..X.XX..XX","XX..X..X...XXXXXX..X","XXX..XX....X.XXXXX..","X.X..XX.X.XX..X...XX","X.X.X.XXX..XXX...XXX","XX........X.XXXXX..X","...X.XX..XXX.XX..X.X","X.XXXXXXX...X..XX.X.","..X..X...XX.XX.X..XX","..XX..XXXX..XX.X.XX.","....XX..X.X.......X.",".X...XX..XX.X...XXXX",".XXXX..X..XX....XX.X",".XXX.XXX.X..XXX....X","..XX.X.XXXX..XX..XX.","XXXXXXX.....XXXXX.X.","X...X.XXX..X.XXXXXX.",".X.XXX...XXXXXXXX.X.","XXXX.XXXX.XXXXXXX..X","...XX.........XX.X.X",".XX.XXXX..XXXXX...XX","XX.XXXX..X.XX.X.....",".X.XXX..XX.XXXX....X","XXX..XX.X.X..X.XX.X.","XXXX....XXXX.XX...XX","XX..X....XXXXX..X.X.","..XXX.X..X.X.XX.X..X","X..XXX.XXXXX.XXXX..X",".XXX..XX.X.X...XX..X","..X.XX...XX.X.XX.XXX",".X.XXX.X...XX...X...","XX...X.X..XX.X...X.X","X..X.X.X..X.X...X...","..X..XXXXXX...X...X."}

{4378,1678,1930,7171,1871,1025,8296,266,9281,8241,6931,7192,7001,4502,3008,5918,9009,8272,8192,231,315,9655,7880,3016,7413,8405,606,8903,2075,1362,4502,7937,9134,6784,3102,2054,4116,888,6182,6856,9055,9604,2853,261,5922,4703,1319,6688,5634,4522}

Returns: 0.0
{8,22,45,3,21,7,52,71,18,64,1,5,35,15,16,9,19,37,58,51}

{30,55,62,15,64,1,10,40,26,43,41,51,33,39,74,21,56,35,9,16,54,32,18,8,7,48,38,34,3,2,45,12,66,20,4,52,47,75,42,72}

{"....X.XXXX..XXXX..X.",".X.XX.X..X..XXX....X","X..XXXX.XXXXXX......","X.XXXX.X..XXXXX..X.X",".XX.X.....X.X..X.XX.","XX.X...XX...XX...XXX",".XX.X....XX.XX.X..X.",".....X.X.X.XX.X.XX..","...XXX.XX.XXX......X",".XX..X..X.XXXX.XX..X","XXXX..XX..X......X.X","...XXX..XXXX..X.....","..X.X..XXXXX.XXX.X..",".X.XXX.X.XXX..XXX...","X...X..X..X...X.XX.X","...XXX.X.XXXXX...X..",".X.XXX...X......X..X","X.XXXXXXX..X..XX...X","..X.......XX...XXX.X","X.....XXX.XX..X.X.XX","X..XX..X.X....XXXXXX","XXX..X.XX..X.X.XXXXX","..XX.X..XX.X.....XXX","..X.X..X.XX...X...XX","XX.X..XXX..XXX..XXXX",".X.X.XX..XX.X.XX...X","XXXX...X.XXX.X.....X","X.XXX..X.X.X...X...X","XX.XXXX.X.X.X.XX.X..","XX.XX..XX.XX..X.X..X","XXXX.X......XX..XX.X","X.XXXXX..X.XXX.XX...",".X...XXX.X.XX..XXX..","....XX.....X.X.XX...",".X.XXX.X.XXXXX..XX.X","X.XX.X.X..XXX....XXX","XXX.XX.X..X.XXX.X...","X.XX..X..XX.......XX",".XX..XX.XX.X.XXXXXXX","X.XXX.XXXX..XXXX.XX.",".XXX.XXX...X.X..XXX.","X.XXXX.X.X..XX...X..",".XX.XXX.....XXX.X...",".XXXXX.X.XX.XXX.XX.X","..XXX.X..X..X...X.X.","...X.X.X..XX.X...X..","..X.XX.X.X.X..XXX...","..X..X.X.X..X.XX.X..","XXX.X.X..X....X..X..","XXX.XXXXXX..XXXX.XX."}

{9017,5782,2305,7898,2405,476,1505,1800,4926,8490,6145,6860,8357,6775,4713,876,4204,8405,6891,5750,9683,8976,5264,6441,1712,4627,676,3301,6180,7983,2741,3728,7036,9790,6487,3387,1861,4245,3452,8276,1236,2585,8178,846,3636,9987,5677,1886,3009,2662}

Returns: 680.5428571428571
{4,23,57,64,68,73,72,48,31,59,19,9,22,45,38,27,11,16,21,6}

{72,31,51,53,69,41,49,26,24,21,71,28,46,17,7,5,32,57,66,58,10,54,6,40,55,20,68,30,47,19,70,22,44,8,59,13,4,52,23,38}

{"X...X.X.XX.XX...XX.X","...X.XX.XXXX..X.X.X.","X..XXXX.X.XX...XXX..",".XXX.X.XXXXXXX..X.XX","XXX...XXX.XXXX.XXXXX","X..XXX.....XXXX.X.X.","XXX.X.XX.XXXXX.X....",".XX..X..X..XX...X...",".XX..X.XX.XXX...X..X","....X..XXXXXX.......",".XXX.X...X.XXXX..X.X","XXX.XX..XXX.XX..X...","X.XX.XXX..X.XX...X..",".X...X.XX.X.X.XXXXXX",".XX..X.X.XX...X.X..X","..X....X.X...X...XXX",".XX.XXX..X...X...XXX",".X...XXXXX..X...X.XX","X..X..X...XX...XXXXX","..XXX.X.X.X......XX.","..XX.XXXX.XXX.X...X.","XX.XX.XXX.XX..XX..XX","X..XXXX.X.X.X.XX.X..","X.XXXX...XXXX..X.X.X",".XX.X......X.X..X.X.","XXX.X.XX.X..X.XX..X.",".XX.X.XX.X..X..X.X..",".XXXX.XXXXXX.XXX....","XX.X.XX.......X...X.","..XX..X.X.XXXXXXXX.X","XX..X.....X.X...X...","XXX......X.X....X...",".XXX.XX.X..X.XX..X.X","...XX..X.X..X.X....X",".X.X.XXXXXXX.X.X.X.X","X.XX..X...X.X.X..X..",".XX.XX.........X...X","..XX..X..XXXXXXXX.X.","......X..XX..XXXXXXX","X.XX.....X.X...XXXXX","X.XX..XXXX.XXX.X.XXX",".X.X.X..XX.X........",".X.X.X.XXXX.XX.....X","XXXX...XXXXXXX.XXXXX",".X.XX.....X.X.X.X...","......X..XX......X.X","X...XX..XXXXX...XXX.",".X...X.XXXX....XXXXX","...X....XX..X.X..XX.","XX.XXXX..X..X....X.."}

{3229,3156,7962,4613,5036,8893,5276,811,1977,8841,191,8259,275,205,6638,3816,4403,4170,9166,8083,4358,9883,7613,102,9422,8955,696,6682,9446,9097,5583,540,3205,2974,1372,9684,9492,269,4882,1174,5411,8604,6866,9980,1817,3443,3844,980,2251,8163}

Returns: 257.88571428571424
{29, 16, 2, 35, 75 }

{75, 4, 16, 3, 21, 44, 2, 38, 11 }

{"X....", "X.X.X", "XXX..", "XXXXX" }

{10, 100, 300, 1000 }

Returns: 6.212121212121213
{1, 2, 3 }

{1, 2, 4 }

{"XXX" }

{10000 }

Returns: 138.88888888888889
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

{75 }

{"X.........", ".X........", "..X.......", "...X......", "....X.....", "XXXXXXXXXX" }

{50, 40, 30, 20, 10, 1000 }

Returns: 2.027027027027027
{3, 5, 7, 45, 34, 23, 67, 75, 12, 24 }

{71, 50, 49, 3, 66, 67, 70, 12, 55, 34 }

{"X.X.X.X.X.", "XXXXX.....", "XXXX..XXXX", "XXXXXXXXXX" }

{128, 578, 2753, 10000 }

Returns: 1.9692307692307693
{1, 2, 3, 4, 5, 6, 7, 8, 75, 22 }

{75, 22 }

{"X.........", ".X........", "..X.......", "...X......", "....X.....", "XXXXXXXXXX", "..X.....X.", "..X.....XX", "..X......X", ".X......X." }

{50, 40, 17, 20, 31, 1000, 23, 2, 5674, 34 }

Returns: 80.6986301369863
{1, 2, 3, 4 }

{1, 2, 3 }

{"...X" }

{100 }

Returns: 1.3888888888888888
{1, 2, 3 }

{1, 2, 4, 5, 6, 7, 67 }

{"XXX" }

{10000 }

Returns: 147.05882352941177
{1, 2, 3, 4 }

{12, 34, 45, 56, 67, 1, 2, 4 }

{"X..X", "XXXX" }

{10, 100 }

Returns: 1.492537313432836
{1, 2, 3, 4, 5 }

{12, 34, 45, 56, 67, 1, 2, 3, 4 }

{"X..X.", "XXXX." }

{10, 100 }

Returns: 0.0
{1 }

{1 }

{"X" }

{1234 }

Returns: 0.0
{1, 2, 3 }

{1, 2, 3 }

{"XXX", "X.X", "..X" }

{100, 1000, 50 }

Returns: 0.0
{1, 2, 3 }

{3, 2, 1 }

{"..X", ".X.", "X.." }

{10000, 10000, 10000 }

Returns: 0.0
{75 }

{1 }

{"X" }

{10000 }

Returns: 135.13513513513513
{75 }

{1 }

{"X", "X" }

{10000, 10000 }

Returns: 270.27027027027026
{1, 2 }

{1 }

{"X.", "XX" }

{100, 100 }

Returns: 1.3513513513513513

Statistics

Problem Statement for "ExtraBall"

Problem Statement

Definition

Notes

Constraints

Examples