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: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		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();
		}
		sc.close();
		if(n==1) {
			System.out.println(1);
			System.exit(0);
		}
		Arrays.sort(a);
		int max = 0;
		for(int i=0; i<n; i++) {
			int count = 0;
			int tmp = a[i];
			while(a[i]==tmp){
				i++;
				count++;
				if(i==n) break;
			}
			int k = i;
			while(k<n && a[k]-tmp<=2) {
				count++;
				k++;
				if(k==n) break;
			}
			max = max>count?max:count;
		}
		System.out.println(max);
	}

}