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: Runtime Error)

import io.StdIn._
object Main extends App {
    val n = readInt
    val as = readLine.split(" ").map(_.toInt)
    
    val sorted = as.sorted

    def rec(index: Int, acc: List[Int]): List[Int] = {
        if(n-1 < index) {
            return acc
        } else {
            val target = sorted(index)
            val count_target = sorted.count(_ == target)
            if(index == 0) {
                val next = if(index+count_target+1 <= n) sorted(index+count_target) else 0
                val count_next = sorted.count(_ == next)
                rec(index+count_target, acc:+(count_target+count_next))
            } else if(index == n-1) {
                val prev = sorted(index-1)
                val count_prev = sorted.count(_ == prev)
                rec(index+count_target, acc:+(count_target+count_prev))
            } else {
                val next = sorted(index+count_target)
                val count_next = sorted.count(_ == next)
                val prev = sorted(index-1)
                val count_prev = sorted.count(_ == prev)
                rec(index+count_target, acc:+(count_target+count_prev+count_next))
            }
        }
    }

    val counts = rec(0, Nil)

    println(counts.max)

}