CubeColoring

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

1. {"Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y"}

   Returns: 0

   It's impossible to color the cube by only 1 color.

2. {"YNNNNNNN", "NYNNNNNN", "NNYNNNNN", "NNNYNNNN", "NNNNYNNN", "NNNNNYNN", "NNNNNNYN", "NNNNNNNY"}

   Returns: 1

   Color the i-th vertex by the i-th color.

3. {"YNNYN", "YYYYY", "NYYNY", "YNYYN", "YNNYY", "YNNYY", "NNNYY", "NYYYY"}

   Returns: 250

4. {"YNNYN", "YYYYY", "NNNNN", "YNYYN", "YNNYY", "YNNYY", "NNNYY", "NYYYY"}

   Returns: 0

   No color is suitable for vertex 2.

5. {"YNNYNYYYYYNN", "NNNYNYYNYNNY", "YYNNYYNNNYYN", "YYYYYNNYYYNN", "NNNYYYNNYNYN", "YYYNYYYYNYNN", "NNNNNNYYNYYN", "NNYNYYNNYNYY"}

   Returns: 611480