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: Time Limit Exceeded)

import java.util.*;
import java.lang.*;
 
 //O(100000000)
public class Main {
    public static void main(String[] args) {

        Scanner sc  = new Scanner(System.in);
        long N = Long.parseLong(sc.next());

        long[] a  = new long[(int)N];
        long[] b  = new long[(int)N];
        long[] c  = new long[(int)N];
        for(int i=0;i<N;i++){
            a[i] = Long.parseLong(sc.next());
            b[i] = a[i] + 1;
            c[i] = a[i] - 1;
        }
        
        int max=0;
        int now=0;
        
        for(int i=0;i<1000000;i++){
            now = 0;
            for(int j=0;j<N;j++){
                
                if(a[j] == i)  now++;
                if(b[j] == i)  now++;
                if(c[j] == i)  now++;
                
            }
            
            max = Math.max( max, now);
        }
        
     
        System.out.print( max);
        System.out.println();
    }

}