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 5.18.2;

my $H;
my $W;
my $loop=1;
my $count=0;
my @given;
my @pattern;

($H,$W)=split(/ /,<>);
push(@given,split(//,<>)) for(1..$H);
@given=grep $_ ne "\n", @given;

while($loop){
	$loop=0;
	@pattern=@given;

	for(0..$W*$H-1){
		if($given[$_]eq"#"){
			$pattern[$_+1]="#" if $_%$W!=$W-1;
			$pattern[$_-1]="#" if $_%$W!=0;
			$pattern[$_+$W]="#" if $_/$W!=0;
			$pattern[$_-$W]="#" if $_/$W!=$H-1;
		}

		for my $i(0..$W*$H-1){
			if ($pattern[$i] ne "#"){
				$loop=1;
				last;
			}
		}
	}

	@given=@pattern;
	$count++ if $loop;
}

say $count;