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**7)

h,w=map(int,input().split())
s=[input() for _ in range(h)]
flag = [[0]*w for _ in range(h)]

def dfs(th,tw):
    global flag,h,w,s
    flag[th][tw] = True
    tblack = 0
    twhite = 0
    if s[th][tw] == "#":
        tblack += 1
    else:
        twhite += 1 
    for x,y in ([0,1],[0,-1],[1,0],[-1,0]):
        nth = th + x
        ntw = tw + y
        if nth >= 0 and nth < h and ntw >= 0 and ntw < w:
            if not flag[nth][ntw] and s[th][tw] != s[nth][ntw]:
                ttb,ttw = dfs(nth,ntw)
                tblack += ttb
                twhite += ttw
    return [tblack,twhite]
                
def main():
    global flag,h,w,s
    res = 0
    for i in range(h):
        for j in range(w):
            if not flag[i][j]:
                black,white = dfs(i,j)
                res += black * white 

    return res
print(main())