Problem Statement

There is a grid with H rows and W columns, where each square is painted black or white.
You are given H strings S_1, S_2, ..., S_H, each of length W.
If the square at the i-th row from the top and the j-th column from the left is painted black, the j-th character in the string S_i is #; if that square is painted white, the j-th character in the string S_i is ..
Find the number of pairs of a black square c_1 and a white square c_2 that satisfy the following condition:

• There is a path from the square c_1 to the square c_2 where we repeatedly move to a vertically or horizontally adjacent square through an alternating sequence of black and white squares: black, white, black, white...

Input

Input is given from Standard Input in the following format:
H W
S_1
S_2
:
S_H

Output

Print the answer.

Constraints

• $1 \leq H, W \leq 400$
• $|S_i| = W (1 \leq i \leq H)$
• For each $i (1 \leq i \leq H)$, the string S_i consists of characters # and ..

Sample Input 1

3 3
.#.
..#

..

Sample Output 1

10

Some of the pairs satisfying the condition are ((1, 2), (3, 3)) and ((3, 1), (3, 2)), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

Sample Input 2

2 4
....
....

Sample Output 2

0

Sample Input 3

4 3

...

Sample Output 3

6

见题面 Input 部分

见题面 Output 部分