题目描述

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.

  </ul>

  Given a grid, determine whether it is correct.

  输入格式

  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.

  输出格式

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

  样例

  输入样例1

  4
  WBBW
  WBWB
  BWWB
  BWBW
  

  输出样例1

  1
  

  输入样例2

  4
  BWWB
  BWBB
  WBBW
  WBWW
  

  输出样例2

  0
  

  输入样例3

  6
  BWBWWB
  WBWBWB
  WBBWBW
  BBWBWW
  BWWBBW
  WWBWBB
  

  输出样例3

  0
  

  输入样例4

  6
  WWBBWB
  BBWWBW
  WBWBWB
  BWBWBW
  BWBBWW
  WBWWBB
  

  输出样例4

  1