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.Scanner;

/**
 *
 * @author lenovo
 */
public class Main {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] a = new int[N];
        int[] b = new int[3*N];
        for (int i=0;i<N;i++){
            a[i] = sc.nextInt();
        }
        for(int i=0;i<3*N;i++){
            if (i<N){
                b[i] = a[i];
            }else if(i<2*N){
                b[i] = a[i-N]+1;
            }else{
                b[i] = a[i-2*N]-1;
            }
        }
        int t_cnt =0;
        int[] cntB = new int[3*N];
        
        for(int i=0;i<3*N;i++){
            int tmp = b[i];
            for(int k=i;k<3*N;k++){
                if (b[k]==tmp){
                    t_cnt++;
                }
            }
            cntB[i] = t_cnt;
            t_cnt = 0;
        }
        int max=0;
        for(int i=0;i<3*N;i++){
            if(cntB[i]>max){
                max = cntB[i];
            }
        }
        System.out.println(max);
    }
    
}