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 = [list(input()) for _ in range(h)]
dx = (0, 0, 1, -1)
dy = (1, -1, 0, 0)
seen = [[False] * w for _ in range(h)]

numb = 0
numw = 0


def dfs(x, y):
    global numb, numw
    seen[x][y] = True
    if s[x][y] == '#':
        numb += 1
    else:
        numw += 1
    for di in range(4):
        nx = x + dx[di]
        ny = y + dy[di]
        if (nx < 0 or nx >= h or ny < 0 or ny >= w):
            continue
        if s[x][y] == s[nx][ny]:
            continue
        if seen[nx][ny]:
            continue
        dfs(nx, ny)


ans = 0
for x in range(h):
    for y in range(w):
        if seen[x][y]:
            continue
        if s[x][y] == '.':
            continue
        numb = 0
        numw = 0
        dfs(x, y)
        ans += numb * numw
print(ans)