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 map = mutable.HashMap[Int,Int]()

  val n = in.readLine.toInt
  in.readLine.split(" ").map(_.toInt)
    .foreach(e => {
      if(!map.contains(e)) map += e -> 1
      else map(e) +=1
    })

  val x = map.keySet

  val ans = {
    var max = -1
    for {
      i <- x
    } {
      var cnt = 0
      map.foreach(e => {
        if(i-1 <= e._1 && e._1 <= i+1) cnt += e._2
      })

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

  println(ans)
}