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:
h,w=map(int,input().split())
s=[]
for _ in range(h):
	s.append(input())
num=[[-1]*w for _ in range(h)]
stack=[]
def dfs():
	while stack:
		r=stack.pop()
		for x in ((1,0),(-1,0),(0,1),(0,-1)):
			a,b,c,d=r[0],r[1],x[0],x[1]
			if 0<=a+c<h and 0<=b+d<w:
				if s[a+c][b+d]!=s[a][b] and num[a+c][b+d]==-1:
					num[a+c][b+d]=num[a][b]
					stack.append((a+c,b+d))
color=0
for i in range(h):
	for j in range(w):
		if num[i][j]==-1:
			stack.append((i,j))
			num[i][j]=color
			dfs()
			color+=1
color_num=[[0,0]for _ in range(color)]
for i in range(h):
	for j in range(w):
		if s[i][j]==".":
			color_num[num[i][j]][0]+=1
		else:
			color_num[num[i][j]][1]+=1
ans=0
for x in color_num:
	ans+=x[0]*x[1]
print(ans)