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(500*500)

h,w=list(map(int,input().split()))
s=[[1 if c=='#' else 0 for c in input()] for _ in range(h)]
g=[[] for _ in range(h*w)]

for i in range(w):
    for j in range(h):
        for di in [-1,0,1]:
            for dj in [-1,0,1]:
                if abs(di)+abs(dj)!=1:
                    continue
                if 0<=i+di<w and 0<=j+dj<h:
                    if s[j][i]!=s[j+dj][i+di]:
                        g[j*w+i].append(i+di+(j+dj)*w)

visit=[0]*(h*w)
black=[0]*(h*w)
white=[0]*(h*w)

def rec(j,i,rj,ri):
    if s[j][i]:
        black[rj*w+ri]+=1
    else:
        white[rj*w+ri]+=1
    
    for n in g[j*w+i]:
        if visit[n]:
            continue

        visit[n]=1

        rec(n//w,n%w,rj,ri)

ans=0

for i in range(w):
    for j in range(h):
        if visit[w*j+i]:
            continue
        visit[w*j+i]=1

        rec(j,i,j,i)
        
        ans+=black[w*j+i]*white[w*j+i]

print(ans)