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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)


import java.io.IOException;
import java.util.Scanner;

public class Main
{
	public static void main(String[] Arguments) throws IOException 
	{
		Scanner sc = new Scanner(System.in);
		int[] freq = new int[(int)1e5 + 5];
		int N = sc.nextInt();
		for (int i = 0; i < N; i++)
		{
			int number = sc.nextInt(); number++;
			freq[number]++;
			freq[number - 1]++;
			freq[number + 1]++;
		}
		int best = 0;
		for (int i = 0; i < freq.length; i++)
		{
			best = Math.max(freq[i], best);
		}
		System.out.println(best);
	}
}