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)

#n = gets.chomp.to_i
h,w = gets.chomp.split().map(&:to_i)

grid = Array.new(h){Array.new(w, 0)}
q = []
h.times do |i|
  line = gets.chomp.split(//)
  w.times do |j|
    if line[j] == '#'
      grid[i][j] = 1
      q.push [i,j, 0]
    end
  end
end
#p grid

ans = 0
count = 0
until q.empty?
  y,x,cost = q.shift
  if 0 < y && grid[y-1][x] != 1
    grid[y-1][x] = 1
    q.push [y-1, x, cost+1]
    ans = cost+1 if ans < cost+1
  end
  if y < h-1 && grid[y+1][x] != 1
    grid[y+1][x] = 1
    q.push [y+1, x, cost+1]
    ans = cost+1 if ans < cost+1
  end
  if 0 < x && grid[y][x-1] != 1
    grid[y][x-1] = 1
    q.push [y, x-1, cost+1]
    ans = cost+1 if ans < cost+1
  end
  if x < w-1 && grid[y][x+1] != 1
    grid[y][x+1] = 1
    q.push [y, x+1, cost+1]
    ans = cost+1 if ans < cost+1
  end
end

puts ans