Problem: You are a coach at your local university. There are n students under your supervision, the programming skill of the i-th student is a_i.

You have to create a team for a new programming competition. As you know, the more students some team has the more probable its victory is! So you have to create a team with the maximum number of students. But you also know that a team should be balanced. It means that the programming skill of each pair of students in a created team should differ by no more than 5.

Your task is to report the maximum possible number of students in a balanced team.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of students.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is a programming skill of the i-th student.

Output

Print one integer — the maximum possible number of students in a balanced team.

Examples

Input


6
1 10 17 12 15 2


Output


3


Input


10
1337 1337 1337 1337 1337 1337 1337 1337 1337 1337


Output


10


Input


6
1 1000 10000 10 100 1000000000


Output


1

Note

In the first example you can create a team with skills [12, 17, 15].

In the second example you can take all students in a team because their programming skills are equal.

In the third example you can create a team consisting of a single student (and you cannot create a team consisting of at least two students).

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class E_K_Balanced {
	
	static int dp [][];
	static int arr[];
	
	public static void main(String[] args) throws IOException {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		dp = new int [n + 1][ k + 1];
		arr = new int [n];
		for(int i = 0 ; i < n; i++)
			arr[i] = in.nextInt();
		Arrays.sort(arr);
		
		int [] count = new int[n];
		for(int i = 0; i < n; i++)
		{
			while(i + count[i] < n && arr[i + count[i]] - arr[i] <= 5)
				count[i]++;
		}
		
		for (int i = 0; i < n; ++i) {
			for (int j = 0; j <= k; ++j) {
				dp[i + 1][j] = Math.max(dp[i + 1][j], dp[i][j]);
				if (j + 1 <= k) {
					dp[i + count[i]][j + 1] = Math.max(dp[i + count[i]][j + 1], dp[i][j] + count[i]);
				}
			}
			//display(dp);
			//System.out.println(i + 1 + " number student\n");
		}
		
		System.out.println(dp[n][k]);
		in.close();
	}
	
	
	static void display(int arr [][])
	{
		for(int i = 0; i< arr.length; ++i)
		{
			System.out.println(i + ": " + Arrays.toString(arr[i]));
		}
	}
	
	
	
	
}