This Ain't Your Grandpa's Checkerboard

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You are given an $n$-by-$n$ grid where each square is colored either black or white. A grid is correct if all of the following conditions are satisfied:

  • Every row has the same number of black squares as it has white squares.

  • Every column has the same number of black squares as it has white squares.

  • No row or column has $3$ or more consecutive squares of the same color.

Given a grid, determine whether it is correct.

Input

The first line contains an integer $n$ ($2\le n\le 24$; $n$ is even). Each of the next $n$ lines contains a string of length $n$ consisting solely of the characters ‘B’ and ‘W’, representing the colors of the grid squares.

Output

If the grid is correct, print the number $1$ on a single line. Otherwise, print the number $0$ on a single line.

Sample Input 1 Sample Output 1
4
WBBW
WBWB
BWWB
BWBW
1
Sample Input 2 Sample Output 2
4
BWWB
BWBB
WBBW
WBWW
0
Sample Input 3 Sample Output 3
6
BWBWWB
WBWBWB
WBBWBW
BBWBWW
BWWBBW
WWBWBB
0
Sample Input 4 Sample Output 4
6
WWBBWB
BBWWBW
WBWBWB
BWBWBW
BWBBWW
WBWWBB
1