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: Time Limit Exceeded)

io = STDIN
H,W=io.gets.split.map(&:to_i)
S=H.times.map{" #{io.gets.chomp} "}
S.unshift " "*(H+2)
S << " "*(H+2)
HASH={}
def reverse(ch)
  (ch=="#") ? "." : "#"
end
def search(i,j,orgi,orgj,bw,hist)
  if bw=="."  && !HASH[[orgi,orgj,i,j]]
    HASH[[orgi,orgj,i,j]]=true
  end
  [[0,1],[1,0],[0,-1],[-1,0]].each do |x,y|
    if S[i+x][j+y]==reverse(bw) && !hist.include?([i+x,j+y])
        search(i+x,j+y,orgi,orgj,reverse(bw),hist+[[i+x,j+y]])
    else
    end
  end
end
(1..H).each do |i|
  (1..W).each do |j|
    search(i,j,i,j,"#",[[i,j]]) if S[i][j]=="#"
  end
end
puts HASH.size