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.Arrays;
import java.util.Scanner;
public class Main {

	public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
       int n = sc.nextInt();
       int []a = new int [n];
       
       for(int i = 0; i< n ;i++) {
    	   a[i] = sc.nextInt() - 1;
       }
       Arrays.sort(a);
       
       int maxnum = a[n-1];
       int max = 0;
       
       for(int i = a[0] ; i <= maxnum; i++) {
    	   int tmp = 0;
    	   for(int j = 0; j < n ; j++) {
    		   if((a[j] - i) <= 2 && (a[j] - i) >= 0) {
    			   tmp++;
    		   }
    	   }
    	   max = Math.max(max, tmp);
    	  }
       System.out.println(max);
	}

}