Grid Check

Problem Description

You are given an $n \times n$ grid in which each square is colored either black or white. The grid is correct if all of the following conditions hold:

• Each row contains the same number of black squares as white squares.
• Each column contains the same number of black squares as white squares.
• No row or column has $3$ or more consecutive squares of the same color.

Given the grid, determine whether it is correct.

Input Format

The first line contains an integer $n$ ($2 \leq n \leq 24$); $n$ is an even number.

The next $n$ lines each contain a string of length $n$ consisting of the characters B and W, representing the colors of the grid squares.

Output Format

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

Sample Input

4
WBBW
WBWB
BWWB
BWBW

Sample Output

1