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: Accepted)

"AGC 033 A - Darker and Darker"
# 入力
H, W = gets.split.map(&:to_i)
c = []
H.times do |i|
  #.charsで1文字ずつ別の配列に入れる
  #.mapで '#'をtrue、それ以外をfalseに置き換える
  c[i] = gets.chomp.chars.map{ |x| x == '#'}
end

# main
# '#'のある位置をqに入れていく
q = []
H.times do |i|
  W.times do |j|
    if c[i][j]
      q.push([i, j])
    end
  end
end

res = 0
# 移動方向
# dx = [1, 0, -1, 0]
# dy = [0, 1, 0, -1]
y, x = 0, 0
# 移動先
# ny, nx = 0, 0
# 移動先を保存するキュー
nq = []
loop do
  # キューが空でない間   
  until q.empty?
    # キューから1個取り出す
    y, x = q.shift

    if x+1<W && !c[y][x+1]
      nq.push([y, x+1])
      c[y][x+1] = true
    end

    if y+1<H && !c[y+1][x]
      nq.push([y+1, x])
      c[y+1][x] = true
    end

    if 0<=x-1 && !c[y][x-1]
      nq.push([y, x-1])
      c[y][x-1] = true
    end

    if 0<=y-1 && !c[y-1][x]
      nq.push([y-1, x])
      c[y-1][x] = true
    end

    

    # 各方向についてループ
    # 4.times do |i|
    #   ny = y + dy[i]
    #   nx = x + dx[i]
    #   # 移動先がcの範囲内で壁ではなく、かつ白色ならば
    #   if (0<=nx) && (nx<W) && (0<=ny) && (ny<H) && (!c[ny][nx])
    #     # 移動先に追加する
    #     nq.push([ny, nx])
    #     # 移動先を白から黒にする
    #     c[ny][nx] = true
    #   end
    # end
  end
  if nq.empty?
    # nqが空ってことは行ける先がないのでreturn
    break
  else
    # nqが空でないなら、resを1増やしてqとnqを交換して上に戻る
    res += 1
    q, nq = nq, q
  end
end

puts res