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)

r, c = gets.split.map(&:to_i)

maze = []
queue = []
(0..r-1).each do |rr|
  line = gets.chomp
  line.each_char.each_with_index { |c, cc|
    queue << [rr, cc] if c == '#'
  }
  maze << line.split('').map{ |e| e=='#'? 0 : nil }
end

cnt = nil
until queue.empty?
  qx, qy = queue.shift
  cnt = maze[qx][qy].to_i + 1

  if qx + 1 < r && maze[qx+1][qy].nil?
    maze[qx+1][qy] = cnt
    queue << [qx+1, qy]
  end

  if qx > 0 && maze[qx-1][qy].nil?
    maze[qx-1][qy] = cnt
    queue << [qx-1, qy]
  end

  if qy + 1 < c && maze[qx][qy+1].nil?
    maze[qx][qy+1] = cnt
    queue << [qx, qy+1]
  end

  if qy > 0 && maze[qx][qy-1].nil?
    maze[qx][qy-1] = cnt
    queue << [qx, qy-1]
  end
end

p cnt - 1