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: Wrong Answer)

<?php
fscanf(STDIN, '%d%d', $H, $W);
for($y = 0; $y < $H; $y++){
    $map[$y] = str_split(fgets(STDIN));
    for($x = 0; $x < $W; $x++){
        if($map[$y][$x] == '#'){
            $list[$y][$x] = 1;
        }
    }
}
$count = 0;
$HM = $H - 1;
$WM = $W - 1;
while($list){
    $count++;
    $nextList = [];
    foreach($list as $y => $xs)foreach($xs as $x => $_){
        if($x && $map[$y][$x-1] == '.')$nextList[$y][$x-1] = $map[$y][$x-1] = 1;
        if($y && $map[$y-1][$x] == '.')$nextList[$y-1][$x] = $map[$y-1][$x] = 1;
        if($x < $WM && $map[$y][$x+1] == '.')$nextList[$y][$x+1] = $map[$y][$x+1] = 1;
        if($y < $HM && $map[$y+1][$x] == '.')$nextList[$y+1][$x] = $map[$y+1][$x] = 1;
    }
    $list = $nextList;
}
echo $count;