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:
from collections import deque

dr = [0, 0, 1, -1]
dc = [1, -1, 0, 0]

H, W = map(int, input().split())
a = [[None for _ in range(W)] for _ in range(H)]  # black == True
reached = [[False for _ in range(W)] for _ in range(H)]
for r in range(H):
    s = input()
    for c in range(W):
        a[r][c] = (s[c] == '#')

ans = 0
for r in range(H):
    for c in range(W):
        if reached[r][c]: continue
        reached[r][c] = True

        b = 0
        w = 0

        dq = deque()
        dq.append((r, c))

        while dq:
            rr, cc = dq.popleft()
            if a[rr][cc]:
                b += 1
            else:
                w += 1
            for di in range(4):
                nr = rr + dr[di]
                if not (0 <= nr < H): continue

                nc = cc + dc[di]
                if not (0 <= nc < W): continue

                if a[rr][cc] == a[nr][nc]: continue

                if reached[nr][nc]: continue
                reached[nr][nc] = True

                dq.append((nr, nc))
        ans += b * w

print(ans)