Problem:
Score : 300 points

Problem Statement

You are given a grid of squares with H horizontal rows and W vertical columns, where each square is painted white or black.
HW characters from A_{11} to A_{HW} represent the colors of the squares.
A_{ij} is # if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is . if that square is white.

We will repeatedly perform the following operation until all the squares are black:

Every white square that shares a side with a black square, becomes black.

Find the number of operations that will be performed.
The initial grid has at least one black square.

Constraints

1 \leq H,W \leq 1000

A_{ij} is # or ..

The given grid has at least one black square.

Input

Input is given from Standard Input in the following format:

H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}

Output

Print the number of operations that will be performed.

Sample Input 1

3 3
...
.#.
...

Sample Output 1

2

After one operation, all but the corners of the grid will be black. After one more operation, all the squares will be black.

Sample Input 2

6 6
..#..#
......
#..#..
......
.#....
....#.

Sample Output 2

3

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

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc *bufio.Scanner

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

const INF = 1000000000

type node struct {
	depth int
	adj   []*node
}

func main() {
	sc = bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	h, w := nextInt(), nextInt()

	root := node{depth: -1}
	board := make([][]*node, h)
	for i := range board {
		sc.Scan()
		s := sc.Text()
		line := make([]*node, w)
		for j, r := range s {
			line[j] = &node{depth: INF}
			if r == '#' {
				root.adj = append(root.adj, line[j])
			}
		}
		board[i] = line
	}

	for i, line := range board {
		for j := range line {
			if i > 0 {
				board[i][j].adj = append(board[i][j].adj, board[i-1][j])
			}
			if i < h-1 {
				board[i][j].adj = append(board[i][j].adj, board[i+1][j])
			}
			if j > 0 {
				board[i][j].adj = append(board[i][j].adj, board[i][j-1])
			}
			if j < w-1 {
				board[i][j].adj = append(board[i][j].adj, board[i][j+1])
			}
		}
	}

	queue := []*node{&root}
	for len(queue) > 0 {
		grid := queue[0]
		queue = queue[1:]
		for _, other := range grid.adj {
			if other.depth > grid.depth+1 {
				other.depth = grid.depth + 1
				queue = append(queue, other)
			}
		}
	}

	ans := 0
	for _, line := range board {
		for _, grid := range line {
			if ans < grid.depth {
				ans = grid.depth
			}
		}
	}
	fmt.Println(ans)
}