### Problem Statement

You are analyzing a communications network with at most 18 nodes. Character j in element i (both 0-based) 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

 Class: SeparateConnections Method: howMany Parameters: String[] Returns: int Method signature: int howMany(String[] mat) (be sure your method is public)

### 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

0)

 ```{ "NYYYY", "YNNNN", "YNNNN", "YNNNN", "YNNNN" }```
`Returns: 2`
 All communications must occur with node 0. Since node 0 can only communicate with 1 node at a time, the returned value is 2.
1)

 ```{ "NYYYY", "YNNNN", "YNNNY", "YNNNY", "YNYYN" }```
`Returns: 4`
 In this setup, we can let node 0 communicate with node 1, and node 3 communicate with node 4.
2)

 ```{ "NNYYYYYYYYYYYYYYYY", "NNYYYYYYYYYYYYYYYY", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN", "YYNNNNNNNNNNNNNNNN" }```
`Returns: 4`
3)

 ```{ "NNNNNNNNNYNNNNNYN", "NNNNNNNNNNNNNNNNN", "NNNNNNNYNNNNNNNNN", "NNNNNYNNNNNYNNYYY", "NNNNNNNNNNNNNNNYN", "NNNYNNNNNNNNNNYNN", "NNNNNNNNNYNNNNNNN", "NNYNNNNNNNNNNNNNN", "NNNNNNNNNYNNNNNNN", "YNNNNNYNYNNNNNNNY", "NNNNNNNNNNNNNNNNN", "NNNYNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNN", "NNNYNYNNNNNNNNNNN", "YNNYYNNNNNNNNNNNN", "NNNYNNNNNYNNNNNNN" }```
`Returns: 10`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=6095

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=9917&pm=6095