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.

Input

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.

Output

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.

Note

The first test case is pictured below.

$\text{[math]}$

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.

$\text{[math]}$

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.

$\text{[math]}$

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

$\text{[math]}$

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

$\text{[math]}$

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

Not Shading

Examples