Problem Statement  
You are analyzing a communications network with at most 18 nodes. Character j in element i (both 0based) of mat denotes whether nodes i and j can communicate ('Y' for yes, 'N' for no). Assuming a node cannot communicate with two nodes at once, return the maximum number of nodes that can communicate simultaneously.  
Definition  
 
Notes  
  If node S is communicating with node T then node T is communicating with node S.  
Constraints  
  mat will contain between 1 and 18 elements inclusive.  
  Each element of mat will contain exactly N characters, where N is the number of elements in mat.  
  Each character in mat will be 'Y' or 'N'.  
  Character i of element i of mat will be 'N'.  
  Character i of element j will be the same as character j of element i.  
Examples  
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