### Problem Statement

You wish to share as many facts as possible with a group of N people, but you only have time to tell one fact to each person in the group. When you tell someone a fact, you also instruct them to tell all their friends. However, the friends do not tell their friends: if A and B are friends, B and C are friends, but A and C are not friends, then after telling the fact to A it will be passed on to B but not to C. You must tell each fact to enough people so that every person either hears the fact from you, or is a friend of someone who heard it from you.

friends contains N strings of N characters, each of which is either 'Y' or 'N'. The jth character of the ith element is 'Y' if members i and j are friends, and 'N' otherwise. Determine the maximum number of facts that can be shared with every person in the group.

### Definition

 Class: InformFriends Method: maximumGroups Parameters: String[] Returns: int Method signature: int maximumGroups(String[] friends) (be sure your method is public)

### Constraints

-friends will contain exactly N elements, where N is between 1 and 15, inclusive.
-Each element of friends will contain exactly N characters.
-Each character in friends will be either 'Y' or 'N'.
-For i and j between 0 and N - 1, inclusive, character j of element i of friends will be the same as character i of element j.
-For i between 0 and N - 1, inclusive, character i of element i of friends will be 'N'.

### Examples

0)

 ```{"NYYN", "YNYY", "YYNY", "NYYN"}```
`Returns: 3`
 Tell one fact to people 0 and 3, one fact to 1, and one fact to 2.
1)

 ```{"NYYN", "YNYN", "YYNN", "NNNN"}```
`Returns: 1`
 Person 3 has no friends, and so can learn only one fact directly from you.
2)

 ```{"NYNNNY", "YNYNNN", "NYNYNN", "NNYNYN", "NNNYNY", "YNNNYN"}```
`Returns: 3`
 Provide facts A, B, C, A, B, C to the six people in order. Each will receive one fact directly and one from each neighbor.
3)

 ```{"NYNY", "YNYN", "NYNY", "YNYN"}```
`Returns: 2`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8473

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=11122&pm=8473

bmerry

#### Testers:

PabloGilberto , Olexiy , marek.cygan , ivan_metelsky

#### Problem categories:

Dynamic Programming, Graph Theory