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.*;
import java.awt.Point;

public class CF_1133E {
    static final String name = "CF_1133E";
    static final boolean test = new File(name + ".in").exists();

    public static void main(String args[]) throws Exception {
        BufferedScanner in = new BufferedScanner(test ? new FileInputStream(name + ".in") : System.in);
        BufferedPrinter out = new BufferedPrinter(test ? new FileOutputStream(name + ".out") : System.out);

        int n = in.nextInt(), k = in.nextInt();
        int[] a = in.nextN(n);

        Arrays.sort(a);

        int ret = 0;
        int[][] dp = new int[n + 1][k + 1];
        for (int i = 0; i < n; i++) {
            int j = i + 1;
            while (j < n && a[i] + 5 >= a[j]) j++;

            for (int l = 0; l < k; l++) {
                dp[j][l + 1] = Math.max(dp[j][l + 1], dp[i][l] + j - i);
                dp[i+1][l] = Math.max(dp[i+1][l], dp[i][l]);
            }

            ret = Math.max(ret, Arrays.stream(dp[i]).max().getAsInt());
        }
        ret = Math.max(ret, Arrays.stream(dp[n]).max().getAsInt());

        out.println(ret);

        out.close();
        in.close();
    }

    /**
     * My template below. FastIO and utility functions.
     * Minimized with https://codebeautify.org/javaviewer.
     */

    // @formatter:off
    static<T>ArrayList<ArrayList<T>>get2D(int n){ArrayList<ArrayList<T>>ret=new ArrayList<>();for(int i=0;i<n;i++)ret.add(new ArrayList<>());return ret;}
    static void force(boolean condition){if(!condition)throw new IllegalStateException();}
    static void debug(Object obj){if(obj instanceof long[][]){for(long[]a:(long[][])obj)System.out.println(Arrays.toString(a));}
    else if(obj instanceof int[][]){for(int[]a:(int[][])obj)System.out.println(Arrays.toString(a));}
    else if(obj instanceof char[][]){for(char[]a:(char[][])obj)System.out.println(Arrays.toString(a));}
    else if(obj instanceof boolean[][]){for(boolean[]a:(boolean[][])obj)System.out.println(Arrays.toString(a));}
    else if(obj instanceof long[]){System.out.println(Arrays.toString((long[])obj));}
    else if(obj instanceof int[]){System.out.println(Arrays.toString((int[])obj));}
    else if(obj instanceof char[]){System.out.println(Arrays.toString((char[])obj));}
    else if(obj instanceof boolean[]){System.out.println(Arrays.toString((boolean[])obj));}
    else{System.out.println(obj);}}
    static class BufferedPrinter{PrintWriter out;BufferedPrinter(OutputStream out){this(new OutputStreamWriter(out));}
    BufferedPrinter(Writer out){this.out=new PrintWriter(new BufferedWriter(out));}
    void print(Object...os){for(int i=0;i<os.length;i++){if(i!=0)out.print(' ');out.print(os[i]);}}
    void println(Object...os){print(os);out.println();}
    void close(){out.close();}
    void flush(){out.flush();}}
    static class BufferedScanner{private final InputStream in;private final byte[]buf=new byte[1<<13];int pos,count;BufferedScanner(InputStream in)throws IOException{this.in=in;}
    long nextLong()throws IOException{return Long.parseLong(next());}
    int[]nextN(int n)throws IOException{int[]ret=new int[n];for(int i=0;i<n;i++)ret[i]=this.nextInt();return ret;}
    long[]nextNL(int n)throws IOException{long[]ret=new long[n];for(int i=0;i<n;i++)ret[i]=this.nextLong();return ret;}
    private int read(){if(count==-1)err();try{if(pos>=count){pos=0;count=in.read(buf);if(count<=0)return-1;}}catch(IOException e){err();}
    return buf[pos++];}
    private static boolean isSpace(int c){return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;}
    private int readSkipSpace(){int ret;do{ret=read();}while(isSpace(ret));return ret;}
    int nextInt(){int sign=1;int c=readSkipSpace();if(c=='-'){sign=-1;c=read();}
    int ret=0;do{if(c<'0'||c>'9')err();ret=ret*10+c-'0';c=read();}while(!isSpace(c));return sign*ret;}
    String next(){StringBuilder sb=new StringBuilder();int c=readSkipSpace();do{sb.append((char)c);c=read();}while(!isSpace(c));return sb.toString();}
    private void err(){throw new InputMismatchException();}
    void close()throws IOException{in.close();}}
    // @formatter:on
}
