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: Wrong Answer)

import io.StdIn._
object Main extends App {
    val n = readInt
    val as = readLine.split(" ").map(_.toInt)
    
    val number = as.distinct
    val counts = number.map(n => as.count(_ == n))

    val length = number.length
    def rec(index: Int, acc: List[Int]): List[Int] = {
        if(length-1 < index) return acc
        else if(index == length-1) {
            val target = counts(index)
            val prev = counts(index-1)
            rec(index+1, acc:+(target+prev))
        }
        else if(0 < index && index < length-1) {
            val target = counts(index)
            val prev = counts(index-1)
            val next = counts(index+1)
            rec(index+1, acc:+(target+prev+next))
        }
        else {
            val target = counts(index)
            val next = counts(index+1)
            rec(index+1, acc:+(target+next))
        }
    }

    if(length == 1) println(1) else println(rec(0, Nil).max)

}