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.HashSet;
import java.util.Scanner;

public class Main{


	public static void main(String[] args) {
		HashSet<Integer> chosedBefore = new HashSet<Integer>();
		Scanner scan = new Scanner(System.in);

		int n = scan.nextInt();
		scan.nextLine();

		int[] array = new int[n];
		for (int i = 0; i < n; i++) {
			array[i] = scan.nextInt();
		}
		int ans = 0;
		for (int i = 0; i < n; i++) {
			int chosen = array[i];
			if (!chosedBefore.contains(chosen)) {
				chosedBefore.add(chosen);
				int result = 0;
				for (int j = 0; j < n; j++) {
					if (array[j] - chosen == 1 || array[j] - chosen == 0
							|| array[j] - chosen == -1) {
						result++;
					}
				}
				ans = Math.max(ans, result);
			}

		}
		System.out.println(ans);

	}

}