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 collections
H, W = map(int, input().split())
S = [list(input()) for i in range(H)]

remaining = set()
for i in range(H):
    for j in range(W):
        remaining.add((i, j))

q = collections.deque()
ans = 0
while(remaining):
    i, j = remaining.pop()
    q.append((i, j))
    black = 0
    white = 0
    while(q):
        y, x = q.popleft()
        if S[y][x] == "#":
            black += 1
        else:
            white += 1

        if (y-1, x) in remaining and S[y][x] != S[y-1][x]:
            remaining.remove((y-1, x))
            q.append((y-1, x))
        if (y, x-1) in remaining and S[y][x] != S[y][x-1]:
            remaining.remove((y, x-1))
            q.append((y, x-1))
        if (y+1, x) in remaining and S[y][x] != S[y+1][x]:
            remaining.remove((y+1, x))
            q.append((y+1, x))
        if (y, x+1) in remaining and S[y][x] != S[y][x+1]:
            remaining.remove((y, x+1))
            q.append((y, x+1))
    ans += black * white
print(ans)