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:
H, W = map(int, input().split())
C = [input() for i in range(H)]

import sys
sys.setrecursionlimit(500000)

itta = [[0] * W for i in range(H)]

def search(x, y, z):
    if y >= H or x >= W or x < 0 or y <  0:
        return
    elif C[y][x] == z:
        return
    elif itta[y][x] == 1:
        return
    elif C[y][x] == z:
        return
    else:
        itta[y][x] = 1
        
        if C[y][x] == '.':
            bw_count[0] += 1
        else:
            bw_count[1] += 1
        
        prez = C[y][x]
        
    search(x+1, y, prez)
    search(x-1, y, prez)
    search(x, y+1, prez)
    search(x, y-1, prez) 

ans = 0

for y in range(H):
    for x in range(W):
        if itta[y][x] ==1:
            pass
        else:
            bw_count = [0, 0]
            search(x, y, '-')
            
            ans += bw_count[0] * bw_count[1]  

print(ans)