Consensus

A number of candidates are running for office. Each one has official positions on many issues, and these positions are given as a string, where the ithcharacter is a position on the ith issue. A position can be Yes ('Y'), No ('N'), or undecided ('?').

A consensus position is one where all candidates either agree or are undecided. While candidates can be undecided, a consensus position cannot be (i.e. it can’t contain a '?' position on any issue).

Given positions of the candidates, your job is to figure out in how many ways the candidates can reach consensus.

Example

• For candidate_positions = ["Y??", "??N"], the output should be Consensus(candidate_positions) = 2.
  
  There’re two consensus positions: "YYN" and "YNN".

• For candidate_positions = ["Y", "N"], the output should be Consensus(candidate_positions) = 0.
  
  It’s impossible to reach consensus in this example.

Input/Output

• [execution time limit] 0.5 seconds 

• [input] array.string candidate_positions

  Array of strings of the same length. Each string contain only characters 'Y', 'N' or '?'.

  Constraints:
  
  1 ≤ candidate_positions.length ≤ 16,
  
  1 ≤ candidate_positions[i].length ≤ 16.

• [output] integer

  • The number of the position sets that all candidates can agree upon.