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: Wrong Answer)

require 'set'

$h, $w = gets.chomp.split.map(&:to_i)
$grid = []
$h.times do
  $grid.push gets.chomp
end

def search(cluster, y, x)
  if y > 0 && $grid[y-1][x] == '#' && !cluster[0].include?([y-1,x])
    if x > 0 && $grid[y-1][x-1] == '.'
      cluster[0].add([y-1, x])
      cluster[1].add([y-1, x-1])
    end
    if x < $w-1 && $grid[y-1][x+1] == '.'
      cluster[0].add([y-1, x])
      cluster[1].add([y-1, x+1])
    end
  end

  if y < $h-1 && $grid[y+1][x] == '#' && !cluster[0].include?([y+1,x])
    if x > 0 && $grid[y+1][x-1] == '.'
      cluster[0].add([y+1, x])
      cluster[1].add([y+1, x-1])
    end
    if x < $w-1 && $grid[y+1][x+1] == '.'
      cluster[0].add([y+1, x])
      cluster[1].add([y+1, x+1])
    end
  end

  if x > 0 && $grid[y][x-1] == '#' && !cluster[0].include?([y,x-1])
    if y > 0 && $grid[y-1][x-1] == '.'
      cluster[0].add([y, x-1])
      cluster[1].add([y-1, x-1])
    end
    if y < $h-1 && $grid[y+1][x-1] == '.'
      cluster[0].add([y, x-1])
      cluster[1].add([y+1, x-1])
    end
  end

  if x < $w-1 && $grid[y][x+1] == '#' && !cluster[0].include?([y,x+1])
    if y > 0 && $grid[y-1][x+1] == '.'
      cluster[0].add([y, x+1])
      cluster[1].add([y-1, x+1])
    end
    if y < $h-1 && $grid[y+1][x+1] == '.'
      cluster[0].add([y, x+1])
      cluster[1].add([y+1, x+1])
    end
  end
end

def make_cluster(i,j)
  cluster = [Set.new, Set.new]
  cluster[0].add([i,j])
  if i > 0 && $grid[i-1][j] == '.'
    cluster[1].add [i-1,j]
    search(cluster, i-1, j)
  end
  if i < $h-1 && $grid[i+1][j] == '.'
    cluster[1].add [i+1,j]
    search(cluster, i+1, j)
  end
  if j > 0 && $grid[i][j-1] == '.'
    cluster[1].add [i,j-1]
    search(cluster, i, j-1)
  end
  if j < $w-1 && $grid[i][j+1] == '.'
    cluster[1].add [i,j+1]
    search(cluster, i, j+1)
  end
  cluster
end

$clusters = []
$h.times do |i|
  $w.times do |j|
    if $grid[i][j] == '#'
      if $clusters.all?{|cluster| not cluster[0].include?([i,j])}
        $clusters.push make_cluster(i,j)
      end
    end
  end
end

ans = 0
$clusters.each do |c|
  ans += c[0].count * c[1].count
end

puts ans