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 ** 7)

dct = {"#": 0, ".": 1, "-": 2}


def f(c):
    return dct[c]


h, w = map(int, input().split())
s = [[2] * (w + 2)]
for _ in range(h):
    s.append([2] + list(map(f, input())) + [2])
s.append([2] * (w + 2))

d = [(-1, 0), (1, 0), (0, -1), (0, 1)]


def dfs(col, hh, ww):
    if s[hh][ww] != col:
        return

    cnt[col] += 1
    s[hh][ww] = 2

    for dh, dw in d:
        nh = hh + dh
        nw = ww + dw
        dfs(1-col, nh, nw)


ans = 0
for hi in range(1, h + 1):
    for wi in range(1, w + 1):
        cnt = [0, 0]
        if s[hi][wi] != 2:
            dfs(s[hi][wi], hi, wi)
        ans += cnt[0] * cnt[1]

print(ans)