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 Go (1.6) (judge verdict: Time Limit Exceeded)

// Package main provides
//
// File:  c.go
// Author: ymiyamoto
//
// Created on Sat Jan 12 21:05:35 2019
//
package main

import "fmt"

const (
	WHITE = '.'
	BLACK = '#'
)

func dfs(visited [][]bool, board []string, x, y int, color rune) int {
	visited[x][y] = true

	ret := 0
	if rune(board[x][y]) == color {
		if color == WHITE {
			ret++
		}
		for _, d := range [][]int{{-1, 0}, {1, 0}, {0, -1}, {0, 1}} {
			dx := x + d[0]
			dy := y + d[1]

			nextColor := WHITE
			if color == nextColor {
				nextColor = BLACK
			}

			if 0 <= dx && dx < len(board) && 0 <= dy && dy < len(board[0]) && visited[dx][dy] == false {
				ret += dfs(visited, board, dx, dy, nextColor)
			}
		}
	}

	return ret
}

func routes(board []string, x, y int, color rune) int {
	visited := make([][]bool, len(board))
	for i := range visited {
		visited[i] = make([]bool, len(board[0]))
	}

	return dfs(visited, board, x, y, color)
}

type pair struct {
	x, y int
}

func main() {
	var H, W int
	fmt.Scan(&H, &W)
	board := make([]string, H)
	for i := range board {
		fmt.Scan(&board[i])
	}

	blacks := make([]pair, 0)
	for i := 0; i < H; i++ {
		for j := 0; j < W; j++ {
			if board[i][j] == BLACK {
				blacks = append(blacks, pair{x: i, y: j})
			}
		}
	}

	ans := 0
	for _, b := range blacks {
		ans += routes(board, b.x, b.y, BLACK)
	}

	fmt.Println(ans)
}