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 deque
H,W=map(int,input().split())
S=["*"*(W+2) for _ in range(H+2)]
for i in range(1,H+1):
    S[i]="*"+input()+"*"

K=0
T=[[0]*(W+2) for _ in range(H+2)]
Neighborhood=[(0,1),(0,-1),(1,0),(-1,0)]
p=0

for y in range(1,H+1):
    for x in range(1,W+1):
        if T[y][x]==0:
            p+=1

            if S[y][x]=="#":
                Black,White=1,0
            elif S[y][x]==".":
                Black,White=0,1

            Q=deque([(x,y)])
            T[y][x]=p

            while Q:
                (u,v)=Q.popleft()
                for (a,b) in Neighborhood:
                    if S[v][u]=="#" and S[v+b][u+a]=="." and T[v+b][u+a]==0:
                        Q.append((u+a,v+b))
                        White+=1
                        T[v+b][u+a]=p
                    elif S[v][u]=="." and S[v+b][u+a]=="#" and T[v+b][u+a]==0:
                        Q.append((u+a,v+b))
                        Black+=1
                        T[v+b][u+a]=p

            K+=Black*White
print(K)