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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner reader= new Scanner(System.in);
        int num=reader.nextInt();
        int[] A= new int[100001];
        for(int i=0; i<num; i++){
            int x= reader.nextInt();
            if (x==0){
                A[0]++;
                A[1]++;
            }
            else
            {if(x==9999){
                A[9999]++;
                A[9998]++;
            }
            else{
                A[x]++;
                A[x+1]++;
                A[x-1]++;
            }}}
            int max=A[0];
            for (int j=1; j<100001; j++){
                if (A[j]>max)
                    max=A[j];
            }
            System.out.println(max);
        }

    }