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:
import sys
sys.setrecursionlimit(10**6)

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

is_used = [[False] * w for _ in range(h)]

di = [+1, 0, -1, 0]
dj = [0, +1, 0, -1]


def dfs(i, j):
    if s[i][j] == '#':
        cnt_w, cnt_b = 0, 1
    else:
        cnt_w, cnt_b = 1, 0

    for k in range(4):
        ni = i + di[k]
        nj = j + dj[k]
        if ni < 0 or ni >= h or nj < 0 or nj >= w:
            continue
        if is_used[ni][nj]:
            continue
        if s[i][j] == s[ni][nj]:
            continue

        is_used[ni][nj] = True
        cw, cb = dfs(ni, nj)
        cnt_w += cw
        cnt_b += cb
    return (cnt_w, cnt_b)


ans = 0
for i in range(h):
    for j in range(w):
        if not is_used[i][j]:
            is_used[i][j] = True
            cnt_w, cnt_b = dfs(i, j)
            ans += cnt_w * cnt_b

print(ans)