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:
from sys import setrecursionlimit


def dfs(i, j, c):
    visited[i][j] = 1
    current.append((i, j))
    for di, dj in (1, 0), (-1, 0), (0, 1), (0, -1):
        ni, nj = i + di, j + dj
        if not (0 <= ni < H and 0 <= nj < W and not visited[ni][nj]):
            continue
        if S[ni][nj] == c:
            continue
        dfs(ni, nj, not c)


setrecursionlimit(2 * 10 ** 5)
H, W = map(int, input().split())
S = [[c == "#" for c in input()] for _ in range(H)]

ans = 0
visited = [[0] * W for _ in range(H)]
for i in range(H):
    for j in range(W):
        if S[i][j] and not visited[i][j]:
            current = []
            dfs(i, j, True)
            b, w = 0, 0
            for k, l in current:
                if S[k][l]:
                    b += 1
                else:
                    w += 1
            ans += b * w
print(ans)