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: Wrong Answer)

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;
$x = oct('b0'.$x);
$y = oct('b0'.$y);

my $ans = 0;
while ($x != $y) {
  $x = bitcalc($x, $y, $w+2);
  $ans++;
}
say $ans;
sub bitcalc {
  my ($s, $v, $w) = @_;
  my $t1 = $s >> 1;
  my $t2 = $s << 1;
  my $t3 = $s >> $w;
  my $t4 = $s << $w;
  my $u = $s | $t1 | $t2 | $t3 | $t4;
  $u &= $v;
  return $u;
}