### Problem Statement

NOTE: This problem statement contains images that may not display properly if viewed outside of the applet.

Rabbit Taro wants to color the vertices of a cube. He thinks the cube will be beautiful if:
• Each vertex is colored by a color that is suitable for it.
• No two adjacent vertices have the same color.

There are N types of colors. You are given a String[] colors. The j-th color is suitable for the i-th vertex if the j-th character of the i-th element of colors is 'Y'. Return the number of different ways to color the cube.

### Definition

 Class: CubeColoring Method: theCount Parameters: String[] Returns: long Method signature: long theCount(String[] colors) (be sure your method is public)

### Notes

-Two ways are different if there exists an i such that the i-th vertex has a different color in one way than it does in the other way.

### Constraints

-colors will contain exactly 8 elements.
-Each element in colors will contain between 1 and 32 characters, inclusive.
-Each element in colors will contain the same number of characters.
-Each character in colors will be 'Y' or 'N'.

### Examples

0)

 `{"Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y"}`
`Returns: 0`
 It's impossible to color the cube by only 1 color.
1)

 `{"YNNNNNNN", "NYNNNNNN", "NNYNNNNN", "NNNYNNNN", "NNNNYNNN", "NNNNNYNN", "NNNNNNYN", "NNNNNNNY"}`
`Returns: 1`
 Color the i-th vertex by the i-th color.
2)

 `{"YNNYN", "YYYYY", "NYYNY", "YNYYN", "YNNYY", "YNNYY", "NNNYY", "NYYYY"}`
`Returns: 250`
3)

 `{"YNNYN", "YYYYY", "NNNNN", "YNYYN", "YNNYY", "YNNYY", "NNNYY", "NYYYY"}`
`Returns: 0`
 No color is suitable for vertex 2.
4)

 `{"YNNYNYYYYYNN", "NNNYNYYNYNNY", "YYNNYYNNNYYN", "YYYYYNNYYYNN", "NNNYYYNNYNYN", "YYYNYYYYNYNN", "NNNNNNYYNYYN", "NNYNYYNNYNYY"}`
`Returns: 611480`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=11130

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14237&pm=11130

rng_58

#### Testers:

PabloGilberto , ivan_metelsky , pieguy

#### Problem categories:

Brute Force, Graph Theory