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)

h, w = gets.strip.split.map(&:to_i)

aa = Array.new(h) { [0]*w }
dist = Array.new(h) { [-1]*w }
q = []

counter=0
h.times do |i|
  gets.chomp.each_char.with_index do |c,j|
    next if c == '.'
    aa[i][j] = 1
    q << [i, j]
    dist[i][j]=0
    counter+=1
  end
end

result = 0
until counter == h*w
  cy, cx = q.shift

  nc = dist[cy][cx]+1

  x=cx
  if (y = cy+1) < h && dist[y][x] == -1
    result = nc if nc > result
    dist[y][x]=nc
    q.push([y, x])
  end

  if (y = cy-1) >= 0 && dist[y][x] == -1
    result = nc if nc > result
    dist[y][x] = nc
    q.push([y, x])
  end

  y=cy
  if (x = cx-1) >= 0 && dist[y][x] == -1
    result = nc if nc > result
    dist[y][x] = nc
    q.push([y, x])
  end

  if (x = cx+1) < w && dist[y][x] == -1
    result = nc if nc > result
    dist[y][x] = nc
    q.push([y, x])
  end
end

p result