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 (2.13.1) (judge verdict: Accepted)

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val N = sc.nextInt()
  val hashMap = scala.collection.mutable.HashMap.empty[Int, Int]
  (1 to N).foreach { _ =>
    val a = sc.nextInt()
    hashMap.update(a, hashMap.getOrElse(a, 0) + 1)
  }
  val max = hashMap.foldLeft(0) { case (acc, (a, count)) =>
    acc.max(hashMap.getOrElse(a - 1, 0) + count + hashMap.getOrElse(a + 1, 0))
  }
  println(max)
}