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.chomp.split(" ").map(&:to_i)
@color = []
@h.times do
  row = gets.chomp.split("").map{|x| x == "#"}
  @color << row
end

@di = [-1, 0, 1, 0]
@dj = [0, 1, 0, -1]

def isin(i, j)
  i >= 0 && i < @h && j >= 0 && j < @w
end

def check(i, j, d)
  ni = i + @di[d]
  nj = j + @dj[d]
  return false if !isin(ni, nj)
  return false if @color[i][j] == @color[ni][nj]
  true
end

used = Array.new(@h){Array.new(@w, false)}

ans = 0
b = 0
w = 0
@h.times do |i|
  @w.times do |j|
    next if used[i][j]
    b = 0
    w = 0
    que = []
    used[i][j] = true
    que << [i, j]
    while !que.empty?
      ci, cj = que.pop
      if @color[ci][cj]
        b += 1
      else
        w += 1
      end
      4.times do |d|
        next if !check(ci, cj, d)
        ni = ci + @di[d]
        nj = cj + @dj[d]
        next if used[ni][nj]
        used[ni][nj] = true
        que << [ni, nj]
      end
    end
    ans += b * w
  end
end

puts ans