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 PYTHON):

Solution:
from collections import deque

H,W=map(int, raw_input().split() )
S=[ raw_input() for i in range(H) ] 


D=[ (1,0), (-1,0), (0,1), (0,-1) ] 


V=[ [ 0 for i in range(W) ] for j in range(H) ]


def dfs(x,y,current):
	bc=0	#black count
	wc=0	#white count
	q = deque([]) 
	V[x][y]=1
	q.append( (x,y,current) )

	while q:
		x,y,current=q.popleft()

		if current == "#":	  bc+=1
		else:  wc+=1

		for dx,dy in D:
			if 0<=x+dx<H and 0<=y+dy<W:
				next=S[x+dx][y+dy] 
				if V[x+dx][y+dy]==0 and current !=next:
						V[x+dx][y+dy]=1
						q.append( (x+dx, y+dy,next) )

	return bc*wc




ans=0
for x in range(H):
	for y in range(W):
		if S[x][y]=="#" and V[x][y]==0:
			ans+=dfs(x,y, "#")

print ans