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 = h.times.map do
  gets.chomp.chars
end

max_cell = h*w
cell = 0
queue = []

(0...h).each do |y| 
  (0...w).each do |x|
    if a[y][x] == "#"
      cell += 1
      queue << [x-1, y] if x > 0
      queue << [x+1, y] if x < w-1
      queue << [x, y-1] if y > 0
      queue << [x, y+1] if y < h-1
    end
  end
end

n = 0

while true
  break if cell >= max_cell
  new_queue = []
  queue.each do |x,y|
    if a[y][x] == "."
      a[y][x] = "#"
      cell += 1
      new_queue << [x-1, y] if x > 0
      new_queue << [x+1, y] if x < w-1
      new_queue << [x, y-1] if y > 0
      new_queue << [x, y+1] if y < h-1
    end
  end
  queue = new_queue
  n += 1
end

puts n