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 sys
sys.setrecursionlimit(100000)

dxdy = {(-1, 0), (1, 0), (0, -1), (0, 1)}

h,w = map(int,input().split())
s = [str(input()) for i in range(h)]

ch = [[0] * w for i in range(h)]

ans = 0

for i in range(h):
    for j in range(w):
        if ch[i][j] == 0:
            black,white = 0,0
            q = [(i,j)]
            while q:
                y,x = q.pop()
                if ch[y][x] == 0:
                    if s[y][x] == "#":black += 1
                    else:white += 1
                    ch[y][x] = 1
                    for dx,dy in dxdy:
                        if 0 <= x + dx < w and 0 <= y + dy < h and ch[y+dy][x+dx] == 0 and s[y+dy][x+dx] != s[y][x]:
                            q.append((y+dy,x+dx))
            ans += black * white

print(ans)