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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

object Main extends App {
  val start = System.nanoTime
  //println(System.currentTimeMillis - start)
  val in = scala.io.Source.stdin.getLines.toSeq
  val ls = in.tail
  //println(ls)
  //val q = scala.collection.mutable.Queue[(Int,Int)]()
  var q = scala.collection.mutable.LinkedHashSet[(Int,Int)]()
  val ls0indices = ls(0).indices
  //println(System.currentTimeMillis - start)
  val tt = ls.indices.map{ y =>
    (Int.MaxValue +:
     ls0indices.map{ x =>
      if(ls(y)(x) == '#'){
        q.add((x-1+1, y+1))
        q.add((x-1+1, y+1))       
        q.add((x+1, y+1+1))        
        q.add((x+1, y+1+1))        
        0
      }else{
        Int.MaxValue - 1
      }
    } :+ Int.MaxValue).toArray
  }
  val ww = tt(0).map(e => Int.MaxValue)
  val t = (ww +: tt :+ ww).toArray
  //t.map(e => println(e.mkString(",")))
  var max = 0
  //private def func(n:Int):Int
  //println(System.currentTimeMillis - start)
  while(q.nonEmpty){
    val elapsed = System.nanoTime - start
    if(elapsed > 100000000L){ println(max); sys.exit()}
    val (x,y) = q.head
    q = q.tail
    if(t(y)(x) == Int.MaxValue-1){
      val inc = 1 + Math.min(
        Math.min(t(y-1)(x), t(y)(x-1)),
        Math.min(t(y+1)(x), t(y)(x+1)))
      //println(x,y,t(y)(x))
      t(y)(x) = inc
      max = Math.max(max, inc)
      if(t(y-1)(x) == Int.MaxValue-1) q.add((x,y-1))
      if(t(y+1)(x) == Int.MaxValue-1) q.add((x,y+1))
      if(t(y)(x-1) == Int.MaxValue-1) q.add((x-1,y))
      if(t(y)(x+1) == Int.MaxValue-1) q.add((x+1,y))
    }
  }
  //println(System.currentTimeMillis - start)
  println(max)
}