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)

require 'set'; require 'prime'
INF=Float::INFINITY
h,w = gets.chomp.split.map(&:to_i)
grid=[]
h.times do
  grid.push gets.chomp.split(//).map(&:to_sym)
end

kuro = Set.new()
h.times do |i|
  w.times do |j|
    if grid[i][j] == :'#'
      kuro.add [i,j]
    end
  end
end

ans = 0
finished_kuro = Set.new()
dy = [0, 1, 0, -1]; dx = [1, 0, -1, 0]
kuro.each do |y,x|
  q = [[y,x, :'#']]
  next if finished_kuro.include?([y,x]) # 通過済み
  black = Set.new([[y,x]])
  white = Set.new()

  until q.empty?
    y,x,iro = q.shift
    4.times do |i|
      ny = y + dy[i]; nx = x + dx[i]
      if (0 <= ny && ny < h) && (0 <= nx && nx < w) && grid[ny][nx] != iro && !white.include?([ny,nx]) && !black.include?([ny,nx])
        if grid[ny][nx] == :'.'
          white.add [ny,nx]
        else
          black.add [ny,nx]
        end
        q.push [ny, nx, grid[ny][nx]]
      end
    end
  end

  ans += black.size * white.size
  finished_kuro.merge black
end

puts ans