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)

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

$dp = Array.new(a).map { Array.new(b,0)}

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

def dfs(s, i, j, hsh)
ary = [[1,0],[-1,0],[0,1],[0,-1]]

for a in ary do
  if judge(i+a[0], j+a[1])
    if $dp[i+a[0]][j+a[1]] == 0 && s[i][j] != s[i+a[0]][j+a[1]]
      $dp[i+a[0]][j+a[1]] = 1

      if s[i+a[0]][j+a[1]] == "#"
        hsh["x"] += 1
      else
        hsh["y"] += 1
      end

      dfs(s, i+a[0], j+a[1], hsh)
    end
  end
end

  return hsh
end

ans = 0

for i in 0..$h-1 do
  for j in 0..$w-1 do

    if $dp[i][j] == 0
      $dp[i][j] = 1
      if s[i][j] == "#"
        temp = dfs(s, i, j, {"x" => 1, "y" => 0})
      else
        temp = dfs(s, i, j, {"x" => 0, "y" => 1})
      end
      ans += temp["x"] * temp["y"]
    end
  end
end

puts ans