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 = [input() for _ in range(H)]
visited = [[False]*W for _ in range(H)]
ans = 0
for i in range(H):
    for j in range(W):
        stk = deque([(i,j)]) # stack
        visited[i][j] = True
        black,white = 0,0
        while stk: # なくなるまで
            y,x = stk.popleft()
            # print("now: ",y,x)
            from_ = s[y][x]
            if from_==".": white += 1
            else:          black += 1
            for dy,dx in ([1,0],[0,1],[-1,0],[0,-1]): 
                if not (0<=y+dy<H and 0<=x+dx<W):
                    continue
                to_   = s[y+dy][x+dx]
                if ((from_=="." and to_ == "#")
                 or (from_=="#" and to_ == ".") ):
                    if visited[y+dy][x+dx]: continue
                    stk.append([y+dy,x+dx])
                    visited[y+dy][x+dx] = True
        # print("black:{}, white:{}".format(black,white))
        ans += black*white
print(ans)