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:
# -*- coding: utf-8 -*-
from collections import deque
H, W = list(map(int, input().split()))
Sn = [input() for _ in range(H)]

def func(h,w): # 黒のみ
    move = [(0,-1),(-1,0),(0,1),(1,0)]
    w_cnt = 0
    b_cnt = 0
    que = deque()
    que.append((h,w))
    while len(que) > 0:
        xh,xw = que.popleft()
        if visited[xh][xw] == 0:
            visited[xh][xw] = 1
            if Sn[xh][xw] == "#":
                b_cnt += 1
            else:
                w_cnt += 1
        else:
            continue
            
        for mh, mw in move:
            if 0 <= xh + mh < H and 0 <= xw + mw < W:
                if Sn[xh][xw] != Sn[xh + mh][xw + mw] and visited[xh + mh][xw + mw] == 0:
                    que.append((xh + mh, xw + mw))

    return b_cnt, w_cnt

cnt = 0
visited = [[0 for _ in range(W)] for _ in range(H)]

for i in range(H):
    for j in range(W):
        if Sn[i][j] == "#" and visited[i][j]==0:
            b_cnt, w_cnt = func(i, j)
            cnt += b_cnt*w_cnt
            
print(cnt)