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 {
  def main(args: Array[String]): Unit = {
    val s = new Main()
    s.solve()
    s.out.flush()
  }
}

class Main {
  import java.io._
  import java.util.StringTokenizer
  import java.util.Arrays.sort

  import scala.collection.mutable
  import math.{abs, max, min}
  import mutable.ArrayBuffer
  import scala.reflect.ClassTag

  val MOD = 1000000007
  val out = new PrintWriter(System.out)

  def solve(): Unit = {
    val H, W = ni()
    val g = nm_c(H, W)

    case class P(h: Int, w: Int)
    val q = new Queue[P](W * H)
    REP(H) { h =>
      REP(W) { w =>
        if (g(h)(w) == '#') {
          q += P(h, w)
        }
      }
    }

    val D = Array(
      P(-1, 0), P(1, 0), P(0, -1), P(0, 1)
    )
    val V = Array.ofDim[Int](H, W)

    while(q.nonEmpty) {
      val p = q.dequeue()
      REP(4) { i =>
        val hh = D(i).h + p.h
        val ww = D(i).w + p.w
        if (0 <= hh && hh < H && 0 <= ww && ww < W && g(hh)(ww) == '.') {
          g(hh)(ww) = '#'
          V(hh)(ww) = V(p.h)(p.w) + 1
          q += P(hh, ww)
        }
      }
    }

    val ans = V.map(_.max).max
    out.println(ans)
  }

  class Queue[A: ClassTag](n: Int) {
    private val as = Array.ofDim[A](n)
    var p = 0
    var cur = 0

    def +=(a: A): Unit = {
      as(p) = a
      p += 1
    }

    def dequeue(): A = {
      val a = as(cur)
      cur += 1
      a
    }

    def head: A = as(cur)

    def apply(i: Int): A = as(cur + i)

    def length: Int = p - cur
    def isEmpty: Boolean = length == 0
    def nonEmpty: Boolean = !isEmpty

    def mkString(delimiter: String = ""): String = as.slice(cur, cur + length).mkString(delimiter)
  }

  private val oj = System.getenv("ATCODER_DEBUG") == null

  def DEBUG(f: => Unit): Unit = {
    if (!oj){ f }
  }

  def debug(as: Array[Boolean]): Unit = DEBUG {
    debug(as.map(x => if(x) "1" else "0").mkString)
  }

  def debug(as: Array[Int]): Unit = DEBUG {
    debug(as.mkString(" "))
  }

  def debug(as: Array[Long]): Unit = DEBUG {
    debug(as.mkString(" "))
  }

  def debugDim(m: Array[Array[Long]]): Unit = DEBUG {
    REP(m.length) { i =>
      debug(m(i))
    }
  }

  def debugDimFlip(m: Array[Array[Long]]): Unit = DEBUG {
    REP(m(0).length) { j =>
      REP(m.length) { i =>
        System.err.print(m(i)(j))
        System.err.print(" ")
      }
      System.err.println()
    }
  }

  def debug(s: => String): Unit = DEBUG {
    System.err.println(s)
  }

  def debugL(num: => Long): Unit = DEBUG {
    System.err.println(num)
  }

  class InputReader(val stream: InputStream) {
    private val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private var tokenizer: StringTokenizer = _

    def next(): String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = next().toInt
    def nextLong(): Long = next().toLong
    def nextChar(): Char = next().charAt(0)
  }
  val sc = new InputReader(System.in)
  def ni(): Int = sc.nextInt()
  def nl(): Long = sc.nextLong()
  def nc(): Char = sc.nextChar()
  def ns(): String = sc.next()
  def ns(n: Int): Array[Char] = ns().toCharArray
  def na(n: Int, offset: Int = 0): Array[Int] = map(n)(_ => ni() + offset)
  def na2(n: Int, offset: Int = 0): (Array[Int], Array[Int]) = {
    val A1, A2 = Array.ofDim[Int](n)
    REP(n) { i =>
      A1(i) = ni() + offset
      A2(i) = ni() + offset
    }
    (A1, A2)
  }
  def nm(n: Int, m: Int): Array[Array[Int]] = {
    val A = Array.ofDim[Int](n, m)
    REP(n) { i =>
      REP(m) { j =>
        A(i)(j) = ni()
      }
    }
    A
  }
  def nal(n: Int): Array[Long] = map(n)(_ => nl())
  def nm_c(n: Int, m: Int): Array[Array[Char]] = map(n) (_ => ns(m))
  def REP(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = offset
    val N = n + offset
    while(i < N) { f(i); i += 1 }
  }
  def REP_r(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = n - 1 + offset
    while(i >= offset) { f(i); i -= 1 }
  }
  def TO(from: Int, to: Int)(f: Int => Unit): Unit = {
    REP(to - from + 1, from) { i =>
      f(i)
    }
  }

  def map[@specialized A: ClassTag](n: Int, offset: Int = 0)(f: Int => A): Array[A] = {
    val res = Array.ofDim[A](n)
    REP(n)(i => res(i) = f(i + offset))
    res
  }


  def sumL(as: Array[Int]): Long = {
    var s = 0L
    REP(as.length)(i => s += as(i))
    s
  }

  def cumSum(as: Array[Int]): Array[Long] = {
    val cum = Array.ofDim[Long](as.length + 1)
    REP(as.length) { i =>
      cum(i + 1) = cum(i) + as(i)
    }
    cum
  }
}