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**6)
input=sys.stdin.readline


def DFS(add,next,cnt):
    x,y=add
    for i,j in [[1,0],[-1,0],[0,1],[0,-1]]:
        X,Y=x+i,y+j
        if 0<=X<h and 0<=Y<w:
            if S[X][Y]==next and color[X][Y]=="white":
                color[X][Y]=str(cnt)
                DFS([X,Y],"." if next=="#" else "#",cnt)


h,w=map(int,input().split())
S=[list(input()) for _ in range(h)]
cnt=0

color=[["white" for _ in range(w)] for _ in range(h)]
for i in range(h):
    for j in range(w):
        if S[i][j]=="#" and color[i][j]=="white":
            cnt +=1
            DFS([i,j],".",cnt)

dictionary={str(i+1):[0,0] for i in range(cnt)}
for i in range(h):
    for j in range(w):
        if color[i][j]!="white":
            if S[i][j]==".":dictionary[color[i][j]][0] +=1
            else:dictionary[color[i][j]][1] +=1

ans=0
for v,m in dictionary.values():
    ans +=v*m
print(ans)