Contest: Task: Related: TaskB

Score : $300$ points

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.

- $1 \leq H,W \leq 1000$
- $A_{ij}$ is
`#`

or`.`

. - The given grid has at least one black square.

Input is given from Standard Input in the following format:

$H$ $W$ $A_{11}$$A_{12}$$...$$A_{1W}$ $:$ $A_{H1}$$A_{H2}$$...$$A_{HW}$

Print the number of operations that will be performed.

3 3 ... .#. ...

2

After one operation, all but the corners of the grid will be black. After one more operation, all the squares will be black.

6 6 ..#..# ...... #..#.. ...... .#.... ....#.

3