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: Accepted)

str1 = gets.split
H,W = str1[0].to_i, str1[1].to_i

a,b = "0","0"
(0...W).each do
  a << "0"
  b << "1"
end
a << "0"
b << "0"
X,Y = "",""
X << a
Y << a

(0...H).each do
  X << "0"
  X << gets.chomp
  Y << b
  X << "0"
end

X.gsub!('#', '1')
X.gsub!('.', '0')

X << a
Y << a

X1 = X.to_i(2)
Y1 = Y.to_i(2)

i = 0
while X1 != Y1
  X1 = ( X1 | X1 << 1 | X1 << (W+2) | X1 >> 1 | X1 >> (W+2) ) & Y1
  i += 1
end
puts i