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.io.*;
import  java.util.*;
import static java.lang.System.in;

public class Main{
    static int n,k;
    //static ArrayList<Integer>[] graph;
    public static void main(String[] args)throws IOException{
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt(); k = sc.nextInt();
        int[] a = new int[n+1];
        a[0] = Integer.MIN_VALUE/2;
        for(int i=1;i<=n;i++) a[i]=sc.nextInt();
        Arrays.sort(a);
        // dp[i][j]: first i items, split into j groups, the a[i] being in the j-th group
        // optimal result
        int[][] dp = new int[n+1][k+1];
        for(int i=1;i<=k;i++) dp[i][i] = i;
        for(int i=2;i<=n;i++){
            for(int j=1;j<=Math.min(i,k);j++){
                int idx = lowerBound(a,a[i]-5);
                if(idx-1<=j-1) dp[i][j] = i; // all students can be used
                else dp[i][j] = i-idx+1+dp[idx-1][j-1];
                dp[i][j] = Math.max(dp[i][j],dp[i-1][j]);
            }
        }
        int ans = 0;
        for(int i=1;i<=n;i++) ans = Math.max(ans,dp[i][k]);
        System.out.println(ans);
    }
    // returns the smallest index where a[index]>=target, for sorted array
    static int lowerBound(int[] a, int  target){
        if(a[0]>=target) return 0;
        if(a[n-1]<target) return n;
        int hi = n-1, lo = 0, mid;
        while(hi-lo>1){
            mid = (hi+lo)/2;
            if(a[mid]>=target) hi = mid;
            else lo = mid;
        }
        return hi;
    }
}