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:
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt(),k=sc.nextInt();
		int[] a=new int[n+1];
		for(int i=0;i<n;i++)a[i]=sc.nextInt();
		a[n]=Integer.MAX_VALUE;
		Arrays.sort(a);
		int l=0;
		int[] val=new int[n];
		for(int i=0;i<=n;){
			if(a[i]-a[l]>5){
				// System.out.println(i+" "+l+" "+a[i]+" "+a[l]);
				val[l]=i-l;
				l++;
				continue;
			}
			i++;
		}
		
		// System.out.println(Arrays.toString(val));
		int[][] dp=new int[n][k];
		for(int i=0;i<n;i++){dp[i][k-1]=val[i];}
		int[] max=new int[n];
		max[n-1]=dp[n-1][k-1];
		for(int i=n-2;i>=0;i--)
			max[i]=Math.max(max[i+1],dp[i][k-1]);
		for(int j=k-2;j>=0;j--){
			for(int i=0;i<n;i++){
				dp[i][j]=val[i]+((i+val[i]<n)?max[i+val[i]]:0);
			}
			max[n-1]=dp[n-1][j];
			for(int i=n-2;i>=0;i--)
				max[i]=Math.max(max[i+1],dp[i][j]);
		}
		int ans=-1;
		for(int i=0;i<n;i++){
			ans=Math.max(ans,dp[i][0]);
		}
		System.out.println(ans);
	}
}