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)

def dfs(i, j):
    visited[i][j] = True
    res_b = 0
    res_w = 0
    if N[i][j]:
        res_b += 1
    else:
        res_w += 1
    for di, dj in d:
        if i + di < 0 or i + di >= H or j + dj < 0 or j + dj >= W:
            continue
        if N[i][j] == N[i+di][j+dj]:
            continue
        if visited[i+di][j+dj]:
            continue
        tmp_b, tmp_w = dfs(i + di, j + dj)
        res_b += tmp_b
        res_w += tmp_w
    return res_b, res_w

H, W = map(int, input().split())
N = [[False] * W for _ in range(H)]
for i in range(H):
    s = input()
    for j in range(W):
        N[i][j] = (s[j] == "#")

d = [(-1, 0), (1, 0), (0, -1), (0, 1)]
visited = [[False] * W for _ in range(H)]
ans = 0
for i in range(H):
    for j in range(W):
        if not N[i][j]:
            continue
        if visited[i][j]:
            continue
        b, w = dfs(i, j)
        ans += (b * w)

print(ans)