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: Wrong Answer)

class Position(val h: Int, val w: Int)

fun main(args : Array<String>) {
    val (H, W) = readLine()!!.split(" ").map { it.toInt() }
    val blacks = mutableListOf<Position>()
    val whites = mutableListOf<Position>()
    (0..(H-1)).forEach { h ->
        readLine()!!.forEachIndexed { w, c ->
            if (c == '#') {
                blacks.add(Position(h, w))
            } else {
                whites.add(Position(h, w))
            }
        }
    }

    val targets = if (blacks.size >= whites.size) {
        blacks
    } else {
        whites
    }

    // O(HWlog(NW))
    var maxDistance = 0
    (0..(H-1)).forEach {h ->
        (0..(W-1)).forEach { w ->
            val closest = targets.map { abs(it.h - h) + abs(it.w - w) }.min()!!
            val distance = closest
            if (distance > maxDistance) {
                maxDistance = distance
            }
        }
    }

    println(maxDistance)
}

fun abs(num: Int) : Int {
    if (num < 0) {
        return num * -1
    }
    return num
}