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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
  val sc = if (args.size > 1) java.util.Scanner(java.io.File(args[1])) else java.util.Scanner(System.`in`)
  solve(sc)
}

fun solve(sc: java.util.Scanner) {
  val N = sc.nextInt()
  val a = IntArray(N) { sc.nextInt() }
  val r = mutableMapOf<Int, Int>()
  a.forEach {
    r[it] = (r[it] ?: 0) + 1
    r[it - 1] = (r[it - 1] ?: 0) + 1
    r[it + 1] = (r[it + 1] ?: 0) + 1
  }
  println(r.maxBy { it.value }?.value)
}