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: Runtime Error)

require 'matrix'

h, w = gets.split.map(&:to_i)
cm = Matrix.zero(h + 2, w + 2)
que = []
1.upto(h) do |i|
  s = gets.chomp
  1.upto(w) do |j|
    if s[j - 1] == '.'
      cm[i, j] = -1
    else
      que.push(i)
      que.push(j)
    end
  end
end
ans = 0
while que.size > 0
  y = que.shift
  x = que.shift
  ans = cm[y, x] + 1
  if cm[y + 1, x] == -1
    cm[y + 1, x] = ans
    que.push(y + 1)
    que.push(x)
  end
  if cm[y - 1, x] == -1
    cm[y - 1, x] = ans
    que.push(y - 1)
    que.push(x)
  end
  if cm[y, x + 1] == -1
    cm[y, x + 1] = ans
    que.push(y)
    que.push(x + 1)
  end
  if cm[y, x - 1] == -1
    cm[y, x - 1] = ans
    que.push(y)
    que.push(x - 1)
  end
end
puts ans - 1