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...

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 ..

Input

Input is given from Standard Input in the following format:

$H$ $W$ $S_1$ $S_2$ $:$ $S_H$

Output

Print the answer.

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