Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3 3
.#.
..#
#..

Sample Output 1

10

Some of the pairs satisfying the condition are ((1, 2), (3, 3)) and ((3, 1), (3, 2)), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

Sample Input 2

2 4
....
....

Sample Output 2

0

Sample Input 3

4 3
###
###
...
###

Sample Output 3

6

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

H, W = gets.split.map(&:to_i)
*S = *$<, 'x'*W
A = *0...H*W
Spread = lambda{|(i,j)|
	a = A[i*W+j]
	neighbor = "#."[S[i][j].ord&1]
	[[i-1,j],[i,j-1],[i+1,j],[i,j+1]].select{|i,j|
		S[i][j] == neighbor and A[i*W+j] != a
	}.each{|i,j|
		A[i*W+j] = a
	}.each(&Spread)
}
(H*W).times{|a|
	Spread[a.divmod(W)] if A[a] == a
}
B = []
A.each_with_index{|id, iWj|
	(B[id] ||= [0,0])[S[iWj/W][iWj%W].ord&1] += 1
}
p B.compact.inject(0){|a,(o,e)| a + o*e }