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.Arrays;
import java.util.Scanner;
 
public class P1133E {
	private static Scanner in;

    private static int n;
    private static int k;
    private static int[] a;

    private static int[][] dp;

	public static void main(String[] args) {
		in = new Scanner(System.in);
		n = in.nextInt();
        k = in.nextInt();
        a = new int[n];

        for(int i=0; i<n; i++) {
            a[i] = in.nextInt();
        }

        dp = new int[n][k+1];

        for(int i=0; i<n; i++) {
            Arrays.fill(dp[i], -1);
        }

        Arrays.sort(a);
        
        System.out.println(solve(0, k));
		
	}

    private static int solve(int i, int kLeft) {
        if (kLeft==0) return 0;
        if (i==n) return 0;

        if (dp[i][kLeft]!=-1) return dp[i][kLeft];

        int j = search(i);

        int ans = Math.max(j-i+1+solve(j+1, kLeft-1), solve(i+1, kLeft));

        return dp[i][kLeft] = ans;
    }

    private static int search(int i) {
        int low = 0;
        int high = n-1;
        int mid = 0;
        while(low<high) {
            mid = low+(high-low+1)/2;

            if (a[mid]-a[i]<=5) {
                low = mid;
            } else {
                high = mid-1;
            }
        }

        if (a[low]-a[i]<=5) {
            return low;
        } else {
            return -1;
        }
    }
 
}