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)

h, w = gets.split.map(&:to_i)
grid = []
h.times do
  grid << gets.chomp.chars
end
memo = Array.new(h) { Array.new(w) }
h.times do |r|
  w.times do |c|
    next if memo[r][c] || grid[r][c] == "."
    visited_blacks = [[r, c]]
    visited_white_count = 0
    memo[r][c] = 0
    queue = [[r, c, true]]
    until queue.empty?
      current_r, current_c, approaching_white = queue.shift
      approaching = approaching_white ? "." : "#"

      if current_r > 0 && grid[current_r - 1][current_c] == approaching && !memo[current_r - 1][current_c]
        queue << [current_r - 1, current_c, !approaching_white]
        memo[current_r - 1][current_c] = 0
        if approaching_white
          visited_white_count += 1
        else
          visited_blacks << [current_r - 1, current_c]
        end
      end

      if current_r < h - 1 && grid[current_r + 1][current_c] == approaching && !memo[current_r + 1][current_c]
        queue << [current_r + 1, current_c, !approaching_white]
        memo[current_r + 1][current_c] = 0
        if approaching_white
          visited_white_count += 1
        else
          visited_blacks << [current_r + 1, current_c]
        end
      end

      if current_c > 0 && grid[current_r][current_c - 1] == approaching && !memo[current_r][current_c - 1]
        queue << [current_r, current_c - 1, !approaching_white]
        memo[current_r][current_c - 1] = 0
        if approaching_white
          visited_white_count += 1
        else
          visited_blacks << [current_r, current_c - 1]
        end
      end

      if current_c < w - 1 && grid[current_r][current_c + 1] == approaching && !memo[current_r][current_c + 1]
        queue << [current_r, current_c + 1, !approaching_white]
        memo[current_r][current_c + 1] = 0
        if approaching_white
          visited_white_count += 1
        else
          visited_blacks << [current_r, current_c + 1]
        end
      end
    end
    visited_blacks.each do |visited_r, visited_c|
      memo[visited_r][visited_c] = visited_white_count
    end
  end
end

puts memo.flatten.compact.inject(:+) || 0