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문제

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.

입력

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.

출력

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

예제 입력 1

4
WBBW
WBWB
BWWB
BWBW

예제 출력 1

1

예제 입력 2

4
BWWB
BWBB
WBBW
WBWW

예제 출력 2

0

예제 입력 3

6
BWBWWB
WBWBWB
WBBWBW
BBWBWW
BWWBBW
WWBWBB

예제 출력 3

0

예제 입력 4

6
WWBBWB
BBWWBW
WBWBWB
BWBWBW
BWBBWW
WBWWBB

예제 출력 4

1