Problem Statement   N people (where N is a power of 2) are taking part in a singleelimination tournament in cheese rolling.
The diagram below illustrates the structure of the tournament bracket.
The people entering the tournament are numbered from 0 to N1.
For each potential cheese rolling match you know who would win the match.
You are given this information encoded as a String[] wins with N elements, each containing N characters.
For each valid i and j, wins[i][j] is 'Y' if person i beats person j.
Otherwise, wins[i][j] is 'N'.
The relation is not necessarily transitive: it may be the case that person i beats person j, person j beats person k, and person k beats person i.
There are N! (N factorial) ways to assign the people to positions in the bracket.
Different assignments may produce a different winner of the tournament.
Return a long[] with N elements.
For each valid i, element i of the return value should be the exact number of assignments for which person i wins the tournament.   Definition   Class:  CheeseRolling  Method:  waysToWin  Parameters:  String[]  Returns:  long[]  Method signature:  long[] waysToWin(String[] wins)  (be sure your method is public) 
    Constraints    N will be between 2 and 16, inclusive.    N will be a power of 2.    wins will contain exactly N elements.    Each element of wins will have a length of exactly N.    Each element of wins will be composed of the characters 'Y' and 'N'.    For each i from 0 to N1, wins[i][i] = 'N'.    For all distinct integers i and j from 0 to N1, exactly one of wins[i][j] and wins[j][i] will be 'Y'.   Examples  0)     Returns: {0, 2 }  There are 2 ways to assign the players:
 Player 0 goes to position 0 and player 1 goes to position 1.
 Player 1 goes to position 0 and player 0 goes to position 1.
In both assignments, player 1 will win the match against player 0 because wins[1][0] = 'Y'. 

 1)    {"NYNY",
"NNYN",
"YNNY",
"NYNN"} 
 Returns: {8, 0, 16, 0 }  
 2)    {"NYNYNYNY",
"NNYNYNYY",
"YNNNNNNN",
"NYYNNYNY",
"YNYYNYYY",
"NYYNNNNN",
"YNYYNYNN",
"NNYNNYYN"} 
 Returns: {4096, 8960, 0, 2048, 23808, 0, 1408, 0 }  
 3)    {"NYNNNNYYNYYNNYNN",
"NNNNNNNNNYYNYYNY",
"YYNYYNNNNYYYYYYN",
"YYNNYYYNYNNYYYNY",
"YYNNNYYNYYNNNNYY",
"YYYNNNNYYNNYYNYN",
"NYYNNYNYNYNYYYYN",
"NYYYYNNNYYNYNYYY",
"YYYNNNYNNYYYYNNN",
"NNNYNYNNNNNNYYNY",
"NNNYYYYYNYNYYYNN",
"YYNNYNNNNYNNYNNY",
"YNNNYNNYNNNNNYNN",
"NNNNYYNNYNNYNNYY",
"YYNYNNNNYYYYYNNN",
"YNYNNYYNYNYNYNYN"} 
 Returns:
{331616878592, 37267079168, 2426798866432, 2606831599616, 994941665280, 1162501849088, 1888166674432, 4632734203904, 832881524736, 84707409920, 3007127748608, 55490052096, 17818550272, 254672666624, 629921447936, 1959311671296 }  
 4)    {"NYYYYYYYYYYYYYYY",
"NNYYYYYYYYYYYYYY",
"NNNYYYYYYYYYYYYY",
"NNNNYYYYYYYYYYYY",
"NNNNNYYYYYYYYYYY",
"NNNNNNYYYYYYYYYY",
"NNNNNNNYYYYYYYYY",
"NNNNNNNNYYYYYYYY",
"NNNNNNNNNYYYYYYY",
"NNNNNNNNNNYYYYYY",
"NNNNNNNNNNNYYYYY",
"NNNNNNNNNNNNYYYY",
"NNNNNNNNNNNNNYYY",
"NNNNNNNNNNNNNNYY",
"NNNNNNNNNNNNNNNY",
"NNNNNNNNNNNNNNNN"} 
 Returns: {20922789888000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }  Player 0 wins no matter how the positions are assigned, so the answer is 16! = 20922789888000. 


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