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(200000)
h, w = map(int, input().split())
s = []
for i in range(h):
    s.append(input())

ans = 0

dx = [0, 0, 1, -1]
dy = [1, -1, 0, 0]

was = [[0 for i in range(w)] for j in range(h)]

def dfs(x, y):
    global cc
    global was
    was[x][y] = 1
    if s[x][y] == '#':
        cc[1] += 1
    else:
        cc[0] += 1
    for i in range(4):
        nx = x + dx[i]
        ny = y + dy[i]
        if nx >= 0 and ny >= 0 and nx < h and ny < w and s[nx][ny] != s[x][y] and not was[nx][ny]:
            dfs(nx, ny)

for i in range(h):
    for j in range(w):
        if not was[i][j]:
            cc = [0] * 2
            dfs(i, j)
            ans += cc[1] * cc[0]
print(ans)