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Problem B
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 $n$ ( $2 \leq n \leq 24$ ; $n$ 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

Problem BThis Ain't Your Grandpa's Checkerboard

Input

Output

Problem B
This Ain't Your Grandpa's Checkerboard