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)

import scala.collection.mutable
import scala.io.StdIn._
object Main extends App {


  val Array(h, w) = readLine.trim.split(' ').map(_.toInt)
  val state = Array.fill(h){readLine.trim.toCharArray.map(_ == '#')}
  val memo = Array.fill(h){Array.fill(w){-1}}
  val queue = mutable.Queue[Point]()
  for (p ← (0 until h).flatMap{y ⇒ (0 until w).filter{x ⇒ state(y)(x)}.map{x ⇒ Point(x, y)}}) {
    queue.enqueue(p)
    memo(p.y)(p.x) = 0
  }
  while(queue.nonEmpty) {
    val current = queue.dequeue()
    for (next ← current.neighbors if (0 until h).contains(next.y) && (0 until w).contains(next.x) && !state(next.y)(next.x)) if (!state(next.y)(next.x)) {
      memo(next.y)(next.x) = memo(current.y)(current.x) + 1
      state(next.y)(next.x) = true
      queue.enqueue(next)
    }
  }
  println(memo.map{_.max}.max)

  case class Point(x: Int, y: Int){
    def neighbors = List(Point(x + 1, y), Point(x - 1, y), Point(x, y + 1), Point(x, y - 1))
  }
}