Problem Statement  
In a chess tournament, each pair of distinct players played a single match against each other. Each match resulted in one of three outcomes: the first player won, the second player won, or there was a draw. The ambiguity number of the tournament is defined as the number of distinct triples of players (a, b, c) such that player a defeated b, player b defeated player c, and player c defeated player a. You are given the results of all the matches as a String[] table. The jth character of the ith element of table is '1' (one) if player i defeated player j, '0' (zero) if player j defeated player i, or '' if the match between players i and j resulted in a draw. Return the ambiguity number of the given tournament.  
Definition  
 
Constraints  
  table will contain between 1 and 50 elements, inclusive.  
  Each element of table will contain exactly n characters, where n is the number of elements in table.  
  Each character in each element of table will be '1' (one), '0' (zero), or ''.  
  The ith character of the jth element of table will be '1' if and only if the jth character of the ith element of table is '0'.  
  The ith character of the jth element of table will be '' if and only if the jth character of the ith element of table is ''.  
  The ith character of the ith element of table will be ''.  
Examples  
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