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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

import java.util.*

fun main(arr:Array<String>) {
    val (h,w) = readLine()!!.split(" ").map { it.toInt() }
    val map = (1..h).map { readLine()!! }
    val step = (1..h).map { (1..w).map { h*w+1 }.toMutableList() }
    val queue = LinkedList<Pos>()
    for(i in map.indices) {
        for(j in map[i].indices) {
            if(map[i][j] == '#') {
                queue.push(Pos(i,j))
                step[i][j] = 0
            }
        }
    }
    while (queue.isNotEmpty()) {
        val cur = queue.pop()
        val nextStep = step[cur.r][cur.c] + 1
        for(i in (cur.r-1..cur.r + 1)) {
            if(i <  0) {
                continue
            }
            if(i >= h) {
                break
            }
            for(j in (cur.c-1..cur.c+1)) {
                if(j < 0) {
                    continue
                }
                if(j >= w) {
                    break
                }
                if(i == cur.r && j == cur.c) {
                    continue
                }
                if(i != cur.r && j != cur.c) {
                    continue
                }
                if(step[i][j] > nextStep) {
                    step[i][j] = nextStep
                    queue.push(Pos(i,j))
                }
            }
        }
    }
    val ans = step.map { it.max()?:0 }.max()!!
    println(ans)
}

class Pos(val r:Int, val c:Int)