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.*;
public class Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            int n=input.nextInt();
            int k=input.nextInt();
            int a[]=new int[n];
            for(int i=0;i<n;i++)
            {
                a[i]=input.nextInt();
            }
            mergeSort(a,0,n-1);
            long dp[][]=new long[n][n+1];
            for(int i=0;i<n;i++)
            {
                if(i==0)
                {
                    dp[0][1]=1;
                }
                else
                {
                    long sum=0;
                    int index=0;
                    for(int j=i;j>0;j--)
                    {
                        long dif=a[j]-a[j-1];
                        if(sum+dif>5)
                        {
                            index=j;
                            break;
                        }
                        else
                        {
                            sum+=dif;
                        }
                    }
                    for(int j=1;j<=(i+1);j++)
                    {
                        if(j==1)
                        {
                            dp[i][j]=Math.max(dp[i-1][j],i-index+1);
                        }
                        else if(j==(i+1))
                        {
                            dp[i][j]=(i+1);
                        }
                        else
                        {
                            int in=index-1;
                            if(in<j-1)
                            {
                                in=j-2;
                            }
                            dp[i][j]=Math.max(dp[i-1][j],dp[in][j-1]+(i-in));
                        }
                    }
                }
            }
            out.println(dp[n-1][k]);
        }
        out.close();
    }
    public static void mergeSort(int a[],int p,int r)
    {
        if(p<r)
        {
            int q=(p+r)/2;
            mergeSort(a,p,q);
            mergeSort(a,q+1,r);
            merge(a,p,q,r);
        }
    }
    public static void merge(int a[],int p,int q,int r)
    {
        int n1=q-p+2;
        int L[]=new int[n1];
        int n2=r-q+1;
        int R[]=new int[n2];
        for(int i=p;i<=q;i++)
        {
            L[i-p]=a[i];
        }
        L[n1-1]=Integer.MAX_VALUE;
        for(int i=q+1;i<=r;i++)
        {
            R[i-q-1]=a[i];
        }
        R[n2-1]=Integer.MAX_VALUE;
        int x=0,y=0;
        for(int i=p;i<=r;i++)
        {
            if(L[x]<=R[y])
            {
                a[i]=L[x];
                x++;
            }
            else
            {
                a[i]=R[y];
                y++;
            }
        }
    }
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
        public FastReader()
        {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt()
        {
            return Integer.parseInt(next());
        }
        long nextLong()
        {
            return Long.parseLong(next());
        }
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}