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


def bfs(S):  # 幅優先探索  # キュー
    que = deque([S])
    b, w = 0, 0
    while len(que) > 0:
        p, q = que.popleft()
        b += int(s[p][q] == '#')
        w += int(s[p][q] == '.')
        for i, j in near[p][q]:  # 移動先の候補
            if (i, j) in frag:  # 処理済みか否か
                continue
            que.append((i, j)), frag.add((i, j))
    return b * w


h, w = map(int, input().split())
s = [input() for _ in range(h)]

near = [[set() for j in range(w)] for i in range(h)]
for i, si in enumerate(s):
    for j, sij in enumerate(si):
        for p, q in [(i - 1, j), (i, j - 1), (i + 1, j), (i, j + 1)]:
            if 0 <= p < h and 0 <= q < w and s[p][q] != sij:
                near[i][j].add((p, q))

ans, frag = 0,set()
for i in range(h):
    for j in range(w):
        if (i, j) not in frag:
            frag.add((i, j))
            ans += bfs((i, j))
print(ans)