Problem: 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

Solution (in PYTHON3):

Solution:
import sys
sys.setrecursionlimit(100000000)

def trace(i, j, S, col, num_color):
    next_col = 1 - col
    num_color[col] += 1
    S[i][j] = 2
    if S[i-1][j] == next_col:
        trace(i-1, j, S, next_col, num_color)
    if S[i][j-1] == next_col:
        trace(i, j-1, S, next_col, num_color)
    if S[i+1][j] == next_col:
        trace(i+1, j, S, next_col, num_color)
    if S[i][j+1] == next_col:
        trace(i, j+1, S, next_col, num_color)
    return num_color[0] * num_color[1]

def main():
    H, W = map(int, input().split())
    # 黒0，白1，padding2
    S = [[2] * (W+2)]
    for _ in range(H):
        S.append([2] + [0 if s == '#' else 1 for s in input()] + [2])
    S.append([2] * (W+2))
    num_comb = 0
    for i in range(1, H+1):
        for j in range(1, W+1):
            if S[i][j] == 0:
                num_color = [0, 0]
                num_comb += trace(i, j, S, 0, num_color)
    print(num_comb)

main()