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.chomp.split(" ").map(&:to_i)

arr = [Array.new(w+2, -1)]
tmp_keys = []
count = 0
result = 0
(1..h).each do |h_i|
  tmp_arr = [-1]
  a = gets.chomp.split("")
  (1..w).each do |w_i|
    if a[w_i - 1] == "#" then
      tmp_arr << 1
      tmp_keys << [h_i, w_i]
      count += 1
    else
      tmp_arr << 0
    end
  end
  tmp_arr << -1
  arr << tmp_arr
end
arr << Array.new(w+2, -1)

keys = [tmp_keys]
total = h * w
while count < total do
  result += 1
  keys[result] = []
  keys[result-1].each do |(h_i, w_i)|
    if arr[h_i - 1][w_i] == 0 then
      keys[result] << [h_i - 1, w_i]
      arr[h_i - 1][w_i] = 1
    end
    if arr[h_i + 1][w_i] == 0 then
      keys[result] << [h_i + 1, w_i]
      arr[h_i + 1][w_i] = 1
    end
    if arr[h_i][w_i - 1] == 0 then
      keys[result] << [h_i, w_i - 1]
      arr[h_i][w_i - 1] = 1
    end
    if arr[h_i][w_i + 1] == 0 then
      keys[result] << [h_i, w_i + 1]
      arr[h_i][w_i + 1] = 1
    end
  end
  count += keys[result].size
end

puts result