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 form k teams for yet another new programming competition. As you know, the more students are involved in competition the more probable the victory of your university is! So you have to form no more than k (and at least one) non-empty teams so that the total number of students in them is maximized. But you also know that each team should be balanced. It means that the programming skill of each pair of students in each team should differ by no more than 5. Teams are independent from one another (it means that the difference between programming skills of two students from two different teams does not matter).

It is possible that some students not be included in any team at all.

Your task is to report the maximum possible total number of students in no more than k (and at least one) non-empty balanced teams.

If you are Python programmer, consider using PyPy instead of Python when you submit your code.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 5000) — the number of students and the maximum number of teams, correspondingly.

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 total number of students in no more than k (and at least one) non-empty balanced teams.

Examples

Input


5 2
1 2 15 15 15


Output


5


Input


6 1
36 4 1 25 9 16


Output


2


Input


4 4
1 10 100 1000


Output


4
import java.io.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;
 
public  class realfast implements Runnable {
    private static final int INF = (int) 1e9;
 
    public  void solve() throws IOException 
    {
  
      int n = readInt();
      int k = readInt();
      int arr[]= new int[n];
      for(int i =0;i<n;i++)
       arr[i]= readInt();
       Arrays.sort(arr);
       int end[]= new int [n];
       int j=0;
       for(int i=0;i<n;i++)
       {
           while(j<n&&arr[j]<=arr[i]+5)
           {
               j++;
               
           }
           end[i]=j;
       }
    int dp[][]= new int[n][k+1];
    for(int i=0;i<n;i++)
     for( j=0;j<=k;j++)
      dp[i][j]=-1;
    
    int value1 = val(arr,0,k,dp,end);
    out.println(value1);

        
    }
    public int val(int arr[], int i ,int k , int dp[][], int end[])
    {
        if(k==0)
        return 0;

        if(i>=arr.length)
         return 0;

        if(dp[i][k]!=-1)
         return dp[i][k];
        
        int val1 = val(arr,i+1,k,dp,end);
        
        int val2 = end[i]-i+ val(arr,end[i],k-1,dp,end);
        val1=Math.max(val1,val2);
        dp[i][k]=val1;
        return dp[i][k];
    }

    
    ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) {
        new Thread(null, new realfast(), "", 128 * (1L << 20)).start();
    }
 
    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private PrintWriter out;
 
    @Override
    public void run() {
        try {
            if (ONLINE_JUDGE || !new File("input.txt").exists()) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                reader = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }
            solve();
        } catch (IOException e) {
            throw new RuntimeException(e);
        } finally {
            try {
                reader.close();
            } catch (IOException e) {
                // nothing
            }
            out.close();
        }
    }
 
    private String readString() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
 
    @SuppressWarnings("unused")
    private int readInt() throws IOException {
        return Integer.parseInt(readString());
    }
 
    @SuppressWarnings("unused")
    private long readLong() throws IOException {
        return Long.parseLong(readString());
    }
 
    @SuppressWarnings("unused")
    private double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }
}
class edge implements Comparable<edge>{
    int u ;
    int v ;
    int val;
    edge(int u1, int v1 , int val1)
    {
       this.u=u1;
       this.v=v1;
       this.val=val1;
    }
    public int compareTo(edge e)
    {
        return this.val-e.val;
    }
}