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)

//TLE?
fun main(args: Array<String>) {
    val (h, w) = readLine()!!.split(" ").map(String::toInt)
    val total = h * w
    val whiteList = mutableListOf<Pair<Int, Int>>()
    val blackList = mutableListOf<Pair<Int, Int>>()
    (1..h).forEach { hi ->
        readLine()!!.toCharArray().forEachIndexed { wi, c ->
            if (c == '.') {
                whiteList.add(Pair(hi, wi + 1))
            } else if (c == '#') {
                blackList.add(Pair(hi, wi + 1))
            }
        }
    }

    var max = 0
    for (white in whiteList) {
        var min = Integer.MAX_VALUE
        for (black in blackList) {
            val dist = calcDist(white, black)
            min = Math.min(dist, min)
        }
        max = Math.max(max, min)
    }
    println(max)
}

fun calcDist(one: Pair<Int, Int>, two: Pair<Int, Int>) = Math.abs(one.first - two.first) + Math.abs(one.second - two.second)