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(10**6)

around = [(0,1),(1,0),(0,-1),(-1,0)]

H,W = map(int,input().split())
grid = [list(input()) for _ in range(H)]

checked = [[0]*W for _ in range(H)]

def dfs(i,j):
    checked[i][j] = 1
    for di,dj in around:
        ni = i + di; nj = j + dj
        if not(0 <= ni <= H-1 and 0 <= nj <= W-1):
            continue
        if checked[ni][nj]:
            continue
        p = grid[i][j]
        np = grid[ni][nj]
        if (p,np) == (".","#"):
            global b
            b += 1
            dfs(ni,nj)
        if (p,np) == ("#","."):
            global w
            w += 1
            dfs(ni,nj)

ans = 0
for i in range(H):
    for j in range(W):
        b = 0; w = 1
        if not checked[i][j] and grid[i][j] == ".":
            dfs(i,j)
        ans += b*w
print(ans)