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 defaultdict

def find(tab, a):
    if tab[a] == -1: return a
    tab[a] = find(tab, tab[a])
    return tab[a]

def union(tab, a, b):
    pa, pb = (find(tab, a), find(tab, b))
    if pa!=pb:
        tab[pb] = pa

H,W=map(int,input().split())
S=[input() for _ in range(H)]
N=H*W
tab = [-1]*N

for y in range(H):
    for x in range(W):
        for dx,dy in [(-1,0),(1,0),(0,1),(0,-1)]:
            xx=x+dx
            yy=y+dy
            if xx < 0 or xx>=W or yy<0 or yy>=H:
                continue
            src = W*y+x
            dst = W*yy+xx
            if S[y][x]!=S[yy][xx]:
                union(tab, src, dst)
dic = defaultdict(lambda: {"#":0,".":0})
for i in range(N):
    p = find(tab, i)
    t = S[i//W][i%W]
    dic[p][t]+=1

ans = 0
for d in dic.values():
    ans += (d["#"]*d["."])
print(ans)