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: Wrong Answer)

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

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

$map = [];
$graph = [];
$q = [];
for ($i=0; $i < $h; $i++) { 
	$input = trim(fgets(STDIN));
	$tmp = [];
	$nexts = [];
	for ($j=0; $j < $w; $j++) { 
		$tmp[$j+1] = $input[$j];
		$next = [];
		if ($input[$j] === '#') {
			$q[] = [$i+1, $j+1];
		}
		if ($i !== 0 && $map[$i][$j+1] === '.') {
			$next[] = [$i, $j+1];
		}
		if ($i !== $h-1) {
			$next[] = [$i+2, $j+1];
		}
		if ($j !== 0 && $tmp[$j] === '.') {
			$next[] = [$i+1, $j];
		}
		if ($j !== $w-1 && $tmp[$j] === '.') {
			$next[] = [$i+1, $j+2];
		}
		$nexts[$j+1] = $next;
	}
	$map[$i+1] = $tmp;
	$graph[$i+1] = $nexts;
}
$cnt = 0;

while (count($q) > 0) {
	++$cnt;
	$newq = [];
	foreach ($q as $tmp) {
		$cand = $graph[$tmp[0]][$tmp[1]];
		foreach ($cand as $v) {
			if ($v !== $tmp && $map[$v[0]][$v[1]] === '.') {
				$map[$v[0]][$v[1]] = '#';
				$newq[] = $v;
			}
		}
	}
	// dumpMap($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;
// }

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