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 (@s, @que);
for my $i (1..$h) {
  chomp (my $in = <STDIN>);
  my @b = split //, $in;
  for my $j (1..$w) {
    if ($b[$j-1] eq '.') {
      $s[$i][$j] = -1;
    } else {
      $s[$i][$j] = 0;
      push @que, $i;
      push @que, $j;
    }
  }
}
my $ans = 0;
while (@que) {
  my ($i, $j);
  $i = shift @que;
  $j = shift @que;
  $ans = $s[$i][$j];
  if ($s[$i+1][$j] == -1) {
    $s[$i+1][$j] = $ans + 1;
    push @que, $i+1;
    push @que, $j;
  }
  if ($s[$i-1][$j] == -1) {
    $s[$i-1][$j] = $ans + 1;
    push @que, $i-1;
    push @que, $j;
  }
  if ($s[$i][$j+1] == -1) {
    $s[$i][$j+1] = $ans + 1;
    push @que, $i;
    push @que, $j+1;
  }
  if ($s[$i][$j-1] == -1) {
    $s[$i][$j-1] = $ans + 1;
    push @que, $i;
    push @que, $j-1;
  }
}
say $ans;