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)

H, W = gets.split.map(&:to_i)
a = Array.new(W).map{Array.new(H)}
for i in 0..(H-1)
  a[i] = gets.chomp.split("")
end
blkN = whtN = 0
blk_i = []
blk_j = []
wht_i = []
wht_j = []
for i in 0..(H-1)
  for j in 0..(W-1)
    if a[i][j] == "."
      whtN += 1
      wht_i.push(i)
      wht_j.push(j)
    elsif a[i][j] == "#"
      blkN += 1
      blk_i.push(i)
      blk_j.push(j)
    end
  end
end
max = 0
for i in 0..(whtN - 1)
  mind = 10000
  for j in 0..(blkN - 1)
    d = (wht_i[i] - blk_i[j]).abs + (wht_j[i] - blk_j[j]).abs
    mind = d if mind > d
  end
  max = mind if max < mind
end
puts max