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 = [];
$white = [];
for ($i=0; $i < $h; $i++) { 
	$input = trim(fgets(STDIN));
	$tmp = [];
	for ($j=0; $j < $w; $j++) { 
		$tmp[$j+1] = $input[$j];
		if ($input[$j] === '.') {
			$white[] = [$i+1, $j+1];
		}
	}
	$map[$i+1] = $tmp;
}
$max = 0;

foreach ($white as $s) {
	$max = max($max, searchBlack($s[0], $s[1], 1));
}
echo $max;


function searchBlack($i, $j, $d){
	global $map;
	$cand = [
		[$i-$d, $j],
		[$i+$d, $j],
		[$i, $j-$d],
		[$i, $j+$d],
	];
	for ($a=1; $a < $d; $a++) { 
		$b=$d-$a;
		$cand[] = [
			$i-$a,
			$j-$b
		];
		$cand[] = [
			$i+$a,
			$j-$b
		];
		$cand[] = [
			$i-$a,
			$j+$b
		];
		$cand[] = [
			$i+$a,
			$j+$b
		];
	}
	// var_dump($cand);
	// fgets(STDIN);
	foreach ($cand as $c) {
		// if ($v === $i && $h === $j) {
		// 	continue;
		// }
		// fgets(STDIN);
		// echo 'd: ' . $d . ' ' . implode(',', $c) . PHP_EOL;
		if (isset($map[$c[0]][$c[1]]) && $map[$c[0]][$c[1]] === '#') {
			return $d;
		}
	}
	return searchBlack($i,$j,$d+1);
}