Problem B
This Ain't Your Grandpa's Checkerboard
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 |
