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];
$q = new SimpleQueue();

$map = [];
$black = [];
for ($i=0; $i < $h; $i++) { 
	$input = trim(fgets(STDIN));
	$tmp = [];
	for ($j=0; $j < $w; $j++) { 
		$tmp[$j+1] = $input[$j];
		if ($input[$j] === '#') {
			$black[] = [$i+1, $j+1];
		}
	}
	$map[$i+1] = $tmp;
}
$cnt = 0;
foreach ($black as $b) {
	$cand = getSur($map, $b);
	foreach ($cand as $c) {
		if (isset($map[$c[0]][$c[1]]) && $map[$c[0]][$c[1]] !== '#') {
			$map[$c[0]][$c[1]] = '?';
			$q->enq($c);
		}
	}
}
while (!$q->isEmpty()) {
	++$cnt;
	$newq = new SimpleQueue();
	while (!$q->isEmpty()) {
		$tmp = $q->deq();
		if ($map[$tmp[0]][$tmp[1]] !== '#') {
			$map[$tmp[0]][$tmp[1]] = '#';
			$cand = getSur($map, $tmp);
			foreach ($cand as $v) {
				if (isset($map[$v[0]][$v[1]]) && $map[$v[0]][$v[1]] === '.') {
					$map[$v[0]][$v[1]] = '?';
					$newq->enq($v);
				}
			}
		}
	}
	// dumpMap($map);
	// echo $q->getCount() . PHP_EOL;
	$q = $newq;
}
echo $cnt;


function dumpMap($map){
	foreach ($map as $row) {
		echo implode(' ', $row) . PHP_EOL;
	}
	// echo PHP_EOL;
}
/**
 * 
 */
class SimpleQueue
{
	private $data = [];
	private $idx = 0;

	public function enq($d){
		$this->data[] = $d;
	}

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

	public function isEmpty(){
		return count($this->data) === $this->idx;
	}

	public function getCount(){
		return count($this->data) - $this->idx;
	}

}

function getSur($map, $xy){
	$y = $xy[0];
	$x = $xy[1];
	$cand = [
		[$y-1, $x],
		[$y+1, $x],
		[$y, $x-1],
		[$y, $x+1],
	];
	return $cand;
}