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: Accepted)

#!/usr/bin/ruby
D=[[-1,0],[0,-1],[1,0],[0,1]]
def fill(_x,_y,_c)
	r=[0,0]
	q=[[_x,_y,_c]]
	while !q.empty?
		x,y,c=q.shift
		r[c]+=1
		D.each{|dx,dy|
			nx=x+dx
			ny=y+dy
			if 0<=nx&&nx<$n&&0<=ny&&ny<$m&&$T[ny][nx]&&$T[ny][nx]==c^1
				$T[ny][nx]=nil
				q.push([nx,ny,c^1])
			end
		}
	end
	r[0]*r[1]
end
$m,$n=gets.split.map(&:to_i)
$T=$m.times.map{gets.chomp.chars.map{|c|c=='#' ? 1 : 0}}
r=0
$m.times{|i|
	$n.times{|j|
		if $T[i][j]
			c=$T[i][j]
			$T[i][j]=nil
			r+=fill(j,i,c)
		end
	}
}
p r