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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
$input = explode(' ', trim(fgets(STDIN)));

$h = (int)$input[0];
$w = (int)$input[1];

$map = [];
$q = new SimpleQueue();
for ($i=0; $i < $h; $i++) { 
	$input = trim(fgets(STDIN));
	$tmp = [];
	for ($j=0; $j < $w; $j++) { 
		if ($input[$j] === '#') {
			$q->enq([$i, $j]);
			$tmp[] = 0;
		}else{
			$tmp[] = -1;
		}
	}
	$map[] = $tmp;
}
$max = 0;

while (!$q->isEmpty()) {
	$tmp = $q->deq();
	$dist = $map[$tmp[0]][$tmp[1]] + 1;
	$cand = getSur($tmp);
	$found = false;

	if ($tmp[0] > 0 && $map[$tmp[0]-1][$tmp[1]] === -1) {
		$found = true;
		$map[$tmp[0]-1][$tmp[1]] = $dist;
		$q->enq([$tmp[0]-1, $tmp[1]]);
	}
	if ($tmp[0] < $h-1 && $map[$tmp[0]+1][$tmp[1]] === -1) {
		$found = true;
		$map[$tmp[0]+1][$tmp[1]] = $dist;
		$q->enq([$tmp[0]+1, $tmp[1]]);
	}
	if ($tmp[1] > 0 && $map[$tmp[0]][$tmp[1]-1] === -1) {
		$found = true;
		$map[$tmp[0]][$tmp[1]-1] = $dist;
		$q->enq([$tmp[0], $tmp[1]-1]);
	}
	if ($tmp[0] < $w-1 && $map[$tmp[0]][$tmp[1]+1] === -1) {
		$found = true;
		$map[$tmp[0]][$tmp[1]+1] = $dist;
		$q->enq([$tmp[0], $tmp[1]+1]);
	}
	if ($found) {
		$max = max($max, $dist);
	}
	// dumpMap($map);
	// echo $q->getCount() . PHP_EOL;
}
echo $max;


// function dumpMap($map){
// 	foreach ($map as $row) {
// 		echo implode(' ', $row) . PHP_EOL;
// 	}
// 	// echo PHP_EOL;
// }

function getSur($xy){
	return [
		[$xy[0]-1, $xy[1]],
		[$xy[0]+1, $xy[1]],
		[$xy[0], $xy[1]-1],
		[$xy[0], $xy[1]+1],
	];
}

/**
 * 
 */
class SimpleQueue
{
	private $data = [];
	private $idx = 0;

	public function enq($d){
		$this->data[] = $d;
	}
	public function deq(){
		$d = $this->data[$this->idx];
		$this->idx += 1;
		return $d;
	}
	public function isEmpty(){
		return count($this->data) === $this->idx;
	}
}