This problem shares some similarities with A1, with key differences in bold.

Atari 2600? More like Atari 2600 BCE!

The classic board game Go is a two-player game played on an (R \times C) board. One player places white stones while the other places black stones. On a player's turn, they may place a stone in any empty space. A curiosity of Go is that stones are placed on the intersections of grid lines rather than between the lines, so an in-progress (5 \times 5) game looks like this:

An orthogonally contiguous set of stones of the same color is called a group. A group of stones is captured (and removed from the board) once no stones in the group has an adjacent empty space.

You're playing as Black and it's your turn. Given a valid board (i.e. no groups have (0) adjacent empty spaces), what’s the maximum number of white stones you can capture with a single black stone?

Here are some examples of captures. If a black stone is placed at the point marked with a triangle, a single white stone will be captured:

Here, Black can capture a group of (3) white stones. Note that this move is valid even though the new black stone has no adjacent empty spaces at the moment it's placed:

Black can even capture multiple groups at once. Here, Black captures a group of (2) stones and a group of (3) stones:

The Go board is represented as a character array (A) where (A_{i, j}) is one of:

B for a black stone
W for a white stone
. for an empty space

Constraints

(1 \leq T \leq 150) (1 \leq R, C \leq \textbf{3{,}000}) (A_{i, j} \in {)'.', 'B', 'W'(})

Input Format

Input begins with an integer (T), the number of test cases. Each case begins with a line containing two integers (R) and (C). Then, (R) lines follow, the (i)th of which contains (C) characters (A_{i, 1}) through (A_{i,C}).

Output Format

For the (i)th test case, print "Case #i: " followed by a single integer, the maximum number of white stones you can capture on your turn.

Sample Explanation

In the first case, Black can capture 3 white stones by playing in the bottom-right corner.

In the second case, there are no white stones that can be captured.

In the third case, Black can capture both white groups at once, for a total of 6 + 3 = 9 white stones.

In the fourth case, there are 6 different white stones that can be captured, but Black can capture at most 4 of them at once (by playing in the center of the board).