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.chomp.split.map(&:to_i)
s,cou = [],0
h.times do
  s << gets.chomp.split("").map(&:to_s)
end
for aa in 0...w;for bb in 0...h
  if s[aa][bb] == "#"
    begin
    if s[aa+1][bb] == "."
      cou += 1
    end
    rescue;end
    begin
    if s[aa-1][bb] == "." && (aa-1) >= 0
      cou += 1
    end
    rescue;end
    begin
    if s[aa][bb+1] == "."
      cou += 1
    end
    rescue;end
    begin
    if s[aa][bb-1] == "."&&(bb-1) >= 0
      cou += 1
    end
    rescue;end
    begin
    if s[aa-1][bb-1] == "#";if s[aa-1][bb] == "." || s[aa][bb-1] == "."
      cou += 1 if (aa-1) >= 0 && (bb-1) >= 0
    end;end
    rescue;end
    begin
    if s[aa-1][bb+1] == "#";if s[aa-1][bb] == "." || s[aa][bb+1] == "."
      cou += 1 if (aa-1) >= 0 && (bb-1) >= 0
    end;end
    rescue;end
    begin
    if s[aa+1][bb-1] == "#";if s[aa+1][bb] == "." || s[aa][bb-1] == "."
      cou += 1 if (aa-1) >= 0 && (bb-1) >= 0
    end;end
    rescue;end
    begin
    if s[aa+1][bb+1] == "#";if s[aa+1][bb] == "." || s[aa][bb+1] == "."
      cou += 1 if (aa-1) >= 0 && (bb-1) >= 0
    end;end
    rescue;end
   end
end;end
puts cou