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: Runtime Error)

fun main(args: Array<String>) {
    val (h, w) = readLine()!!.split(" ").map(String::toInt)
    var bSet = mutableSetOf<Pair<Int, Int>>()
    val map = Array(h) { IntArray(w + 1) { 0 } }
    (1..h).forEach { hi ->
        readLine()!!.forEachIndexed { wi, c ->
            if (c == '#') {
                map[hi][wi + 1] = 1
                bSet.add(Pair(hi, wi + 1))
            }
        }
    }

    val dir = mutableListOf(Pair(1, 0), Pair(0, 1), Pair(-1, 0), Pair(0, -1))//上下左右
    var times = 0 // 操作実行回数
    var wNum = h * w - bSet.size
    while (wNum > 0) {//白マスがなくなるまで
        times++
        val tSet = mutableSetOf<Pair<Int, Int>>()
        for (b in bSet) {
            for (d in dir) {
                val th = b.first + d.first
                val tw = b.second + d.second
                if (th in 1..h && tw in 1..w && map[th][tw] == 0) {
                    tSet.add(Pair(th, tw))
                    map[th][tw] = 1
                    wNum--
                }
            }
        }
        bSet = tSet
    }
    println(times)
}