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
import sys
input = sys.stdin.readline

def C(i, j):
    p = [1, 0]
    q = deque([(i, j, ".")])
    while q:
        x, y, c = q.popleft()
        for u, v in d:
            dx, dy = x + u, y + v
            if 0 <= dx < h and 0 <= dy < w and s[dx][dy] != c and use[dx][dy]:
                use[dx][dy] = False
                p[s[dx][dy] == "#"] += 1
                q.append((dx, dy, s[dx][dy]))
    return p[0]*p[1]


h, w = map(int, input().split())
s = [input() for i in range(h)]
use = [[1] * w for i in range(h)]
d = [(0, 1), (1, 0), (0, -1), (-1, 0)]
ans = 0
for i in range(h):
    for j in range(w):
        if use[i][j] and s[i][j] == ".":
            use[i][j] = False
            ans += C(i, j)
print(ans)