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)

input = STDIN.read.split("\n")
f = input.shift.split(" ")
H = f[0].to_i
W = f[1].to_i

TABLE = input.map{|l| l.split("")}
CHECKED_BLACK = Array.new(H).map{Array.new(W)}

def check(i, j, checked = {}, prev = nil, passed_white = 0, passed_black = 0)
    if checked[i][j] == true
        return
    end
    if i == H && j == W
        return
    end

    c = TABLE[i][j]
    checked[i][j] = true

    if c == '#' && (prev == nil || prev == '.')
        $black = $black + 1
        CHECKED_BLACK[i][j] = true
        check(i - 1, j, checked, '#') if i > 0
        check(i + 1, j, checked, '#') if i < (H - 1)
        check(i, j - 1, checked, '#') if j > 0
        check(i, j + 1, checked, '#') if j < (W - 1)
    end
    if c == '.' && prev == '#'
        $count = $count + 1
        check(i - 1, j, checked,'.') if i > 0
        check(i + 1, j, checked,'.') if i < (H - 1)
        check(i, j - 1, checked, '.') if j > 0
        check(i, j + 1, checked, '.') if j < (W - 1)
    end
end

cnt = 0
for i in 0..(H - 1)
    for j in 0..(W - 1)
        c = TABLE[i][j]
        if c ==  '#' && CHECKED_BLACK[i][j] == nil
            CHECKED_BLACK[i][j] = true
            $count = 0
            $black = 0
            che = Array.new(H).map{Array.new(W)}
            check(i, j, che)
            cnt = cnt + ($count * $black)
        end
    end
end
puts cnt