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)

DBG = true
$h,$w = gets.split.map{|x| x.to_i}
$s = []
for i in 0...$h
  $s <<  gets.chomp
end

def label(col, x, y, lab)
  return [0,0] if $s[x][y] != (col==0 ? '#' : '.') || $marked[x][y]>0
  $marked[x][y] = lab
  difs = [ [-1,0], [1,0], [0,-1], [0,1] ]
  mysums = [0,0]
  for d in difs
    xx = x + d[0]
    yy = y + d[1]
    if 0 <= xx && xx < $h && 0 <= yy && yy < $w
      sums = label(1-col, xx, yy, lab)
      mysums[0] += sums[0]
      mysums[1] += sums[1]
    end
  end
  mysums[col] += 1
  return mysums
end


# # # # main # # # #
$sums = [ [0,0] ]
$marked = Array.new($h)
$marked.map!{Array.new($w)}
for i in 0...$h
  for j in 0...$w
    $marked[i][j] = 0
  end
end

lab = 1
for i in 0...$h
  for j in 0...$w
    if $s[i][j] == '#' && $marked[i][j] == 0
      $sums << label(0, i, j, lab)
      lab += 1
    end
  end
end

psum = 0
for p in $sums
  psum += p[0] * p[1]
end
print psum