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)

import scala.collection.mutable
import java.io.{BufferedReader, InputStreamReader}

object Main extends App {
  val in = new BufferedReader(new InputStreamReader(System.in))
  val set = mutable.HashSet[Int]()
  val n = in.readLine.toInt
  val a = in.readLine.split(" ").map(_.toInt)

  a.foreach(e => {
    // set += e -1
    set += e
    // set += e +1
  })

  val x = set.toArray

  val ans = {
    var max = -1
    for {
      i <- x
    } {
      var cnt = 0
      a.foreach(e => {
        if(i-1 <= e && e <= i+1) cnt += 1
      })

      if(cnt > max) max = cnt
    }
    max
  }

  println(ans)
}