A14813. Not Shading

There is a grid with $n$ rows and $m$ columns. Some cells are colored black, and the rest of the cells are colored white.

In one operation, you can select some black cell and do exactly one of the following:

- color all cells in its row black, or
- color all cells in its column black.

You are given two integers $r$ and $c$ . Find the minimum number of operations required to make the cell in row $r$ and column $c$ black, or determine that it is impossible.

The input consists of multiple test cases. The first line contains an integer $t$ ( $1 \leq t \leq 100$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains four integers $n$ , $m$ , $r$ , and $c$ ( $1 \leq n, m \leq 50$ ; $1 \leq r \leq n$ ; $1 \leq c \leq m$ ) — the number of rows and the number of columns in the grid, and the row and column of the cell you need to turn black, respectively.

Then $n$ lines follow, each containing $m$ characters. Each of these characters is either 'B' or 'W' — a black and a white cell, respectively.

For each test case, if it is impossible to make the cell in row $r$ and column $c$ black, output $-1$ .

Otherwise, output a single integer — the minimum number of operations required to make the cell in row $r$ and column $c$ black.

The first test case is pictured below.

We can take the black cell in row $1$ and column $2$ , and make all cells in its row black. Therefore, the cell in row $1$ and column $4$ will become black.

In the second test case, the cell in row $2$ and column $1$ is already black.

In the third test case, it is impossible to make the cell in row $2$ and column $2$ black.

The fourth test case is pictured below.

We can take the black cell in row $2$ and column $2$ and make its column black.

Then, we can take the black cell in row $1$ and column $2$ and make its row black.

Therefore, the cell in row $1$ and column $1$ will become black.