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 (1.3.71) (judge verdict: Accepted)

import java.util.*

fun main(args: Array<String>) {
  val sc = Scanner(System.`in`)
  val n = sc.nextInt()
  val a = (1..n).map { sc.nextInt() }

  val map = mutableMapOf<Int, Int>()
  for (ai in a) {
    val tmp = map.getOrElse(ai) { 0 }
    map.put(ai, tmp + 1)
  }

  val min = a.min()!!
  val max = a.max()!!

  var sumMax = 0
  // var index = min
  for (i in min..max) {
    var sum = map.getOrElse(i) { 0 }
    sum += map.getOrElse(i+1) { 0 }
    sum += map.getOrElse(i+2) { 0 }

    if (sum >= sumMax) {
      sumMax = sum
      // index = i
    }
  }

  println(sumMax)

}