JOIN

 Problem Statement

### Problem Statement

John and Brus have become very famous people all over the world, especially in Bolivia. Once they decided to visit their fan club in Bolivia. John has an old map of Bolivia which shows all of its cities and the roads connecting them. All roads are bidirectional, meaning they can be traversed in both directions. Since the map is old, it's possible that some additional roads have been built since the map was produced. However, roads are never destroyed in Bolivia, so all the roads on the map still exist.

Brus has discovered on the Internet that each pair of Bolivian cities now has exactly one simple path connecting them. A path between cities A and B is a sequence of cities starting with A and ending with B such that there's a road between each pair of consecutive cities in the sequence. The path is considered simple if it consists of distinct cities.

You are given a String[] map. The j-th character of the i-th element of map will be 'Y' if there is a road between the i-th and j-th cities on the old map, or 'N' otherwise. Return the number of ways John and Brus can add new roads to the old map. Two ways are considered different if the sets of added roads are distinct. The order in which roads are added does not matter.

### Definition

 Class: TheCitiesAndRoadsDivTwo Method: find Parameters: String[] Returns: int Method signature: int find(String[] map) (be sure your method is public)

### Notes

-The answer will always fit in signed 32-bit integer.

### Constraints

-map will contain between 1 and 9 elements, inclusive.
-Each element of map will contain exactly n characters, where n is the number of elements in map.
-Each character of map will be either 'Y' of 'N'.
-The j-th character of the i-th element of map will be equal to the j-th character of the i-th element of map.
-The i-th character of the i-th element of map will be 'N'.
-There will be at least one way for John and Brus to add new roads to the old map.

### Examples

0)

 ```{"NN", "NN"}```
`Returns: 1`
 The only way is to connect two cities with a road.
1)

 ```{"NY", "YN"}```
`Returns: 1`
2)

 ```{"NNY", "NNN", "YNN"}```
`Returns: 2`
 There are two possible ways - connect the second city with the first one or with the third one.
3)

 ```{"NYNN", "YNNN", "NNNY", "NNYN"}```
`Returns: 4`

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This problem was used for:
Single Round Match 460 Round 1 - Division II, Level Three