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A. Not Shading

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere 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.

Example

Input

9 3 5 1 4 WBWWW BBBWB WWBBB 4 3 2 1 BWW BBW WBB WWB 2 3 2 2 WWW WWW 2 2 1 1 WW WB 5 9 5 9 WWWWWWWWW WBWBWBBBW WBBBWWBWW WBWBWBBBW WWWWWWWWW 1 1 1 1 B 1 1 1 1 W 1 2 1 1 WB 2 1 1 1 W B

Output

1 0 -1 2 2 0 -1 1 1

Note

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.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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