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)

FIELD=[]
H.times do
  FIELD << gets.chomp
end

def check(x,y,color)
  return [0,0] if x < 0 || W <= x
  return [0,0] if y < 0 || H <= y

  if color == FIELD[y][x]
    m,n = color == '#' ? [1,0] : [0,1]

    FIELD[y][x] = 'x'

    rev_color = color == '#' ? '.' : '#'
    a,b = check(x-1,y,rev_color)
    c,d = check(x+1,y,rev_color)
    e,f = check(x,y-1,rev_color)
    g,h = check(x,y+1,rev_color)
    [m+a+c+e+g,n+b+d+f+h]
  else
    [0,0]
  end

end

ret = []
H.times do |y|
  W.times do |x|
    if FIELD[y][x] == '#'
      ret << check(x,y,'#')
    end
  end
end

ret_n = 0
ret.each do |a,b|
  ret_n += a*b
end
p ret_n