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 collections import deque
H, W = map(int, input().split())
S = []
for _ in range(H):
    S.append(list(input()))

ans = 0
for h in range(H):
    for w in range(W):
        if S[h][w] == "x":
            continue
        q = deque()
        q.append((h, w))
        shw = S[h][w]
        bl = wh = 0
        while len(q):
            i, j = q.popleft()
            if not 0 <= i < H or not 0 <= j < W:
                continue
            if S[i][j] == "x":
                continue
            dist = i + j - h - w
            if dist % 2 == 0 and shw != S[i][j]:
                continue
            if dist % 2 == 1 and shw == S[i][j]:
                continue
            if S[i][j] == "#":
                bl += 1
            else:
                wh += 1
            S[i][j] = "x"
            q.append((i-1, j))
            q.append((i+1, j))
            q.append((i, j-1))
            q.append((i, j+1))
        ans += bl * wh

print(ans)