Alternating Path

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.

Examples

Input

3 3 .#. ..# #..

Output

10

Input

3 3 .#. ..# ..

Output

10

Input

2 4 .... ....

Output

0

Input

4 3

...

Output

6

inputFormat

Input

Input is given from Standard Input in the following format:

H W S_1 S_2 : S_H

outputFormat

Output

Print the answer.

Examples

Input

3 3 .#. ..# #..

Output

10

Input

3 3 .#. ..# ..

Output

10

Input

2 4 .... ....

Output

0

Input

4 3

...

Output

6

样例

3 3
.#.
..#
#..

10