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.split.map(&:to_i)
s = h.times.map{gets.chomp.chars.map{|c|c==?#}}

#p s

def saiki(h,w,s,i,j,used)
  return 0 if used[i][j]
  used[i][j] = true
  res = 0
  res += saiki(h,w,s,i-1,j,used) if 0<i   && s[i][j]!=s[i-1][j]
  res += saiki(h,w,s,i+1,j,used) if i<h-1 && s[i][j]!=s[i+1][j]
  res += saiki(h,w,s,i,j-1,used) if 0<j   && s[i][j]!=s[i][j-1]
  res += saiki(h,w,s,i,j+1,used) if j<w-1 && s[i][j]!=s[i][j+1]
  res += (s[i][j] ? 0:1)
  return res
end

memo = h.times.map{Array.new(w, -1)}

ans = 0
h.times{|i|
  w.times{|j|
    used = h.times.map{Array.new(w, false)}
    ans += saiki(h,w,s,i,j,used) if s[i][j]
  }
}

p ans