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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

io = STDIN
h,w=io.gets.split.map(&:to_i)
$board=[]
$board << [" "]*(w+2)
h.times do
  $board << ([" "]+io.gets.chomp.split(//)+[" "])
end
$board << [" "]*(w+2)
require 'pp'
stack=[]
(1..h).each do |i|
  (1..w).each do |j|
    if $board[i][j]=="#"
      stack << [i,j]
      $board[i][j]=0
    end
  end
end
cur=0
while (res=stack.shift;i,j=res)
  cur=$board[i][j]
  [[1,0],[0,-1],[-1,0],[0,1]].each do |x,y|
    if $board[i+x][j+y]=="."
      $board[i+x][j+y]=cur+1
      stack << [i+x,j+y]
    end
  end
end
p cur