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)

require 'set'

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

def search(i, j, y, x)
  return if $grid[y][x] == '#'
  return if $set.include?([[i,j], [y,x]])

  $set.add([[i,j], [y,x]])
  $set.add([[y,x], [i,j]])

  search(i, j, y-1, x-1) if y > 0    && x > 0    && ($grid[y-1][x] == '#' || $grid[y][x-1] == '#')
  search(i, j, y+1, x-1) if y < $h-1 && x > 0    && ($grid[y+1][x] == '#' || $grid[y][x-1] == '#')
  search(i, j, y-1, x+1) if y > 0    && x < $w-1 && ($grid[y-1][x] == '#' || $grid[y][x+1] == '#')
  search(i, j, y+1, x+1) if y < $h-1 && x < $w-1 && ($grid[y+1][x] == '#' || $grid[y][x+1] == '#')
end


$set = Set.new
$h.times do |i|
  $w.times do |j|
    if $grid[i][j] == '#'
      search(i,j, i-1, j) if i > 0
      search(i,j, i+1, j) if i < $h-1
      search(i,j, i, j-1) if j > 0
      search(i,j, i, j+1) if j < $w-1
    end
  end
end

#p $set
#puts $set.count
puts $set.count / 2