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: Time Limit Exceeded)

h, w = gets.split.map(&:to_i)
list = h.times.map{ gets.chomp.split('') }
s = list.flatten.map.with_index{ |c, i| i if c == '#' }.compact
move = [[-1, 0], [0, 1], [1, 0], [0, -1]]
ans = 0

s.each do |i|
  x = i % w
  y = i / w
  q = [[x, y, 0]]
  visited = h.times.map{ [false] * w }
  visited[y][x] = true
  until q.empty?
    x, y, color = q.shift
    move.each do |mx, my|
      nx = x + mx
      ny = y + my
     if 0 <= nx && nx < w && 0 <= ny && ny < h
        if !visited[ny][nx]
          visited[ny][nx] = true
          if color == 0 && list[ny][nx] == '.' || color == 1 && list[ny][nx] == '#'
            q << [nx, ny, 1 - color]
            if color == 0
              ans += 1
            end
          end
        end
      end
    end
  end
end
puts ans