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: Runtime Error)

H,W=gets.chomp.split.map(&:to_i)
s = []
s << ["+"] * (W+2)
H.times { s << ["+"] + gets.chomp.split("") + ["+"]}
s << ["+"] * (W+2)

v = Array.new(H+2).map{Array.new(W+2, 0)  }

def solve_b(s,i,j,v,cnt)
  return if v[i][j] > 0
  v[i][j] = cnt
  solve_w(s,i-1,j,v,cnt) if s[i-1][j] == '.'
  solve_w(s,i+1,j,v,cnt) if s[i+1][j] == '.'
  solve_w(s,i,j-1,v,cnt) if s[i][j-1] == '.'
  solve_w(s,i,j+1,v,cnt) if s[i][j+1] == '.'
end

def solve_w(s,i,j,v,cnt)
  return if v[i][j] > 0
  v[i][j] = cnt
  solve_b(s,i-1,j,v,cnt) if s[i-1][j] == '#'
  solve_b(s,i+1,j,v,cnt) if s[i+1][j] == '#'
  solve_b(s,i,j-1,v,cnt) if s[i][j-1] == '#'
  solve_b(s,i,j+1,v,cnt) if s[i][j+1] == '#'
end

cnt = 1
1.upto(H) do |i|
  1.upto(W) do |j|
    if s[i][j] == '#' && v[i][j] == 0
      solve_b(s,i,j,v,cnt)
      cnt += 1
    end
  end
end

h = {}
1.upto(H) do |i|
  1.upto(W) do |j|
    if v[i][j] > 0
      if h.has_key?(v[i][j])
      
      else
        h[v[i][j]] = Hash.new(0)
      end
      h[v[i][j]][s[i][j]] += 1
    end
  end
end

ans = 0
h.each do |k,vv| 
  ans += vv['#'] * vv['.']
end
puts ans