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

H, W = map(int, input().split())
S = []
for i in range(H):
    s = input()
    temp = []
    for j in range(W):
        temp.append(s[j])
    S.append(temp)

ret = 0
for i in range(H):
    for j in range(W):
        if S[i][j] != '?':
            q = deque()
            q.appendleft((i, j))
            white = 0
            black = 0
            while q:
                h, w= q.pop()
                color = S[h][w]
                if color == '?':
                    continue
                elif color == '#':
                    black += 1
                else:
                    white += 1
                S[h][w] = '?'
                cand = [(h+1, w), (h-1, w), (h, w+1), (h, w-1)]
                for hc, wc in cand:
                    if 0 <= hc < H and 0 <= wc < W and (S[hc][wc] not in [color, '?']):
                        q.appendleft((hc, wc))

            ret += black * white

print(ret)