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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

use v5.18; # strict say state
use warnings;
use List::Util qw(reduce first max min sum0);

chomp (my ($h, $w) = split / /, <STDIN>);
my ($x, $y);
$x = "0"x($w+2);
$y = "0"x($w+2);
for my $i (0..$h-1) {
  chomp (my $in = <STDIN>);
  $x .= "0" . $in . "0";
  $y .= "0" . ("1"x$w) . "0";
}
$x .= "0"x($w+2);
$y .= "0"x($w+2);
$x =~ s/\./0/g;
$x =~ s/#/1/g;

my $ans = 0;

while ($x ne $y) {
  $x = bitcalc($x, $y, $w+2);
  $ans++;
}
say $ans;
sub bitcalc2 {
  my ($x, $y) = @_;
  for my $i (0..length($x)-1) {
    if (substr($x, $i, 1) eq "1" && substr($y, $i, 1) eq "1") {
      substr($x, $i, 1) = "1";
    } else {
      substr($x, $i, 1) = "0";
    }
  }
  return $x;
}
sub bitcalc {
  my ($s, $v, $w) = @_;
  my $n = length($s);
  my $t1 = "0" . substr($s, 0, $n-1);
  my $t2 = substr($s, 1, $n-1) . "0";
  my $t3 = "0"x$w . substr($s, 0, $n-$w);
  my $t4 = substr($s, $w, $n-$w) . "0"x$w;
  my $u = bitor($s, $t1, $t2, $t3, $t4);
  return $u;
  sub bitor {
    my ($s, $t1, $t2, $t3, $t4) = @_;
    for my $i (0..length($s)-1) {
      if (substr($v, $i, 1) eq "1" && (substr($s, $i, 1) eq "1" || substr($t1, $i, 1) eq "1" || substr($t2, $i, 1) eq "1" || substr($t3, $i, 1) eq "1" || substr($t4, $i, 1) eq "1")) {
        substr($s, $i, 1) = "1"
      } else {
        substr($s, $i, 1) = "0"
      }
    }
    return $s;
  }
}