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
//error_reporting(0);
//$N = trim(fgets(STDIN));
list($H,$W) =  explode(" ",trim(fgets(STDIN)));
//$m[] = explode(" ",trim(fgets(STDIN)));
for($i=0;$i<$H;$i++) {
  $m = trim(fgets(STDIN));
  for($k=0;$k<$W;$k++) {
    if ($m[$k]=='#'){
       $e[]=[$k,$i];
       $d[$k][$i]=0;
    }
  }
}

$dx = [0,0,-1,1];
$dy = [-1,1,0,0];

$ans  = 0;
for($i=0;$i<count($e);$i++) {
  $x = $e[$i][0];
  $y = $e[$i][1];
  $ans = max($ans,$d[$x][$y]);
  for($t=0;$t<4;$t++) {
    $gx = $x + $dx[$t];
    $gy = $y + $dy[$t];
    if (0 <= $gx && $gx < $W && 0 <= $gy && $gy < $H) {
      if (!isset($d[$gx][$gy])) {
        $d[$gx][$gy]=$d[$x][$y]+1;
        $e[]=[$gx,$gy];
      }
    }
  }
}
printf("%d\n",$ans);