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)

def nxt(i,j,h,w)
  ret = []
  ret << [i-1,j] if i > 0
  ret << [i+1,j] if i < h-1
  ret << [i,j-1] if j > 0
  ret << [i,j+1] if j < w-1
  return ret
end

h,w = gets.split.map(&:to_i)
s = []
h.times do 
  s << gets.chomp
end
table=Array.new(h){Array.new(w,true)}
id = 1
ans = 0
h.times do |i|
  w.times do |j|
    if table[i][j]
      table[i][j] = false
      search = [[i,j]]
      cnt = [0,0]
      cnt[s[i][j]=="#" ? 0 : 1] += 1
      while tmp = search.shift
        a,b = tmp
        color = s[a][b] == "#" ? "." : "#"
        nxt(a,b,h,w).each do |x,y|
          if table[x][y] && s[x][y] == color
            table[x][y] = false
            search << [x,y]
            cnt[s[x][y]=="#" ? 0 : 1] += 1
          end
        end
      end
      ans += cnt[0]*cnt[1]
      #p cnt
    end
  end
end
p ans