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)

h,w=gets.chomp.split(" ").map { |e| e.to_i }
s=[]
h.times do |i|
  s[i] = gets.chomp.split("")
end

$dp = Array.new(h).map { Array.new(w,0)}

def judge(i, j, h, w)
  if 0 <= i && i <= h-1 && 0 <= j && j<= w-1
    return true
  else
    return false
  end
end

def bfs(s, i, j, h, w)
  queue = [[i,j]]
  $dp[i][j] = 1
  ary = [[1, 0],[-1, 0],[0, 1],[0, -1]]
  white = 0
  black = 1

  until queue.empty?
    temp = queue.pop
    x = temp[0]
    y = temp[1]

    for a in ary do
      if judge(x+a[0], y+a[1], h, w)
        if $dp[x+a[0]][y+a[1]] == 0 && s[x][y] != s[x+a[0]][y+a[1]]
          queue.push([x+a[0],y+a[1]])
          $dp[x+a[0]][y+a[1]] = 1
          if s[x+a[0]][y+a[1]] == "#"
            black += 1
          else
            white += 1
          end
        end
      end
    end
  end
  print black, white
  return black*white
end

ans = 0

for i in 0..h-1 do
  for j in 0..w-1 do
    print $dp
    puts
    if $dp[i][j] == 0 && s[i][j] == "#"
      ans += bfs(s, i, j, h, w)
    end
  end
end

puts ans