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.*
import java.math.*
import java.lang.Math.*


private val readString: ()->String = {readLine()!!}
private val readInt: ()->Int = { readLine()!!.toInt() }
private val readLong: ()->Long = { readLine()!!.toLong() }
private val readListInt: ()->List<Int> = { readLine()!!.split(' ').map(String::toInt) }
private val readListLong: ()->List<Long> = { readLine()!!.split(' ').map(String::toLong) }
private val errPrintln: (String)->Unit = { msg -> System.err.println(msg) }
//private val MOD = 1e9.toLong()+7
//private val INF = Int.MAX_VALUE/2
//private val LINF = Long.MAX_VALUE/2


class GridBfs(val G: List<String>, val Start:Char = '#',
              val ToPaint:Char = '.') {

    var H:Int = 0
    var W:Int = 0
    private val starts = ArrayList<Pair<Int, Int>>()
    init {
        H = G.size
        W = G[0].length
        for (i in 0 until H) {
            for (j in 0 until W) {
                if (G[i][j] == Start) {
                    starts.add(Pair(i,j))
                }
            }
        }
    }

    private val dx = intArrayOf(0,1,0,-1)
    private val dy = intArrayOf(1,0,-1,-0)
    private val INF = Int.MAX_VALUE/2

    fun fill(): Int {
        //val que = LinkedList<Pair<Int, Int>>()
        val que = ArrayDeque<Pair<Int, Int>>()
        val step = Array(H){Array<Int>(W){INF}}

        for (pr in starts) {
            que.addLast(pr)
            step[pr.first][pr.second] = 0
        }

        while (que.isNotEmpty()) {
            //val (x, y) = que.removeFirst()
            val (x, y) = que.poll()


            /*for (i in dx.indices) {
                val nx = x + dx[i]; val ny = y + dy[i]
                if (nx<0 || H<=nx || ny<0 || W<=ny) {
                    continue
                }

                val st = step[x][y]
                if (step[nx][ny] > st + 1) {
                    step[nx][ny] = st + 1
                    que.addLast(Pair(nx, ny))
                    painted++
                    res = max(res, st+1)
                }
            }*/

            val st = step[x][y]

            var nx = x; var ny = y + 1
            if (ny<W && step[nx][ny] > st + 1) {
                step[nx][ny] = st + 1
                que.add(Pair(nx, ny))
            }

            nx = x + 1; ny = y
            if (nx<H && step[nx][ny] > st + 1) {
                step[nx][ny] = st + 1
                que.add(Pair(nx, ny))
            }

            nx = x; ny = y - 1
            if (0<=ny && step[nx][ny] > st + 1) {
                step[nx][ny] = st + 1
                que.add(Pair(nx, ny))
            }

            nx = x - 1; ny = y
            if (0<=nx && step[nx][ny] > st + 1) {
                step[nx][ny] = st + 1
                que.add(Pair(nx, ny))
            }
        }

        var res = 0
        for (i in 0 until H) {
            for (j in 0 until W) {
                res = max(res, step[i][j])
            }
        }

        return res
    }
}


fun main(args: Array<String>) {
    val (H, W) = readListInt()
    val A = Array<String>(H){""}
    for (i in 0 until H) {
        A[i] = readString()
    }
    assert(A[0].length == W)

    val bfs = GridBfs(A.toList())
    val ans = bfs.fill()

    println(ans)
}