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(input())
dxdy = [(-1,0), (0,-1), (0,1), (1,0)]
seen = [[False]*w for _ in range(h)]
ans = 0
for i in range(h):
    for j in range(w):
        if seen[i][j]:
            continue
        q = deque([(j, i)])
        cnt = [0, 0]
        cnt[int(s[i][j]=='#')] += 1
        seen[i][j] = True
        while q:
            x, y = q.popleft()
            for dx, dy in dxdy:
                if not (0<=x+dx<w and 0<=y+dy<h):
                    continue
                if seen[y+dy][x+dx] or s[y][x]==s[y+dy][x+dx]:
                    continue
                cnt[int(s[y+dy][x+dx]=='#')] += 1
                seen[y+dy][x+dx] = True
                q.append((x+dx, y+dy))
        ans += cnt[0]*cnt[1]
print(ans)