Problem:
Score : 300 points

Problem Statement

You are given an integer sequence of length N, a_1,a_2,...,a_N.

For each 1≤i≤N, you have three choices: add 1 to a_i, subtract 1 from a_i or do nothing.

After these operations, you select an integer X and count the number of i such that a_i=X.

Maximize this count by making optimal choices.

Constraints

1≤N≤10^5

0≤a_i<10^5 (1≤i≤N)

a_i is an integer.

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N

Output

Print the maximum possible number of i such that a_i=X.

Sample Input 1

7
3 1 4 1 5 9 2

Sample Output 1

4

For example, turn the sequence into 2,2,3,2,6,9,2 and select X=2 to obtain 4, the maximum possible count.

Sample Input 2

10
0 1 2 3 4 5 6 7 8 9

Sample Output 2

3

Sample Input 3

1
99999

Sample Output 3

1

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

object Main extends App {
  val n: Int = io.StdIn.readLine().toInt
  val arr: Array[String] = io.StdIn.readLine().split(' ')
  val arrInt: Array[Int] = arr.map(str => str.toInt)
  val arrUniq: Array[Int] = arrInt.distinct
  // val (minV, maxV) = (arrUniq.min, arrUniq.max)
  val lst: Array[List[Int]] = for (x <- arrInt ) yield List(x - 1, x, x + 1)
  val lstUniq: Array[Int] = lst.flatten.distinct
  // map if contain x 1 else 0
  val map = scala.collection.mutable.Map[Int,Int]()
  for (x <- lstUniq) {
     map.put(x, lst.map(x1 => if(x1.contains(x)) 1 else 0).sum)
  }
  println(map.maxBy(_._2)._2)
}