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.*;
import java.io.*;

public class KBalancedTeams {
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int N = scanner.nextInt();
        int K = scanner.nextInt();
        Integer[] skills = new Integer[N+1];
        skills[0] = 0;
        for(int i = 1; i <= N; i++) skills[i] = scanner.nextInt();
        // need a 2d dp
        Arrays.sort(skills);
        int p1 = 1;
        int p2 = 1;
        int[][] dp = new int[N+1][K+1];
        for(int i = 1; i <= N; i++) {
            Arrays.fill(dp[i], -1);
            dp[i][0] = 0;
        }
        while(p2 <= N) {
            if (skills[p2] - skills[p1] <= 5) {
                for(int j = K; j > 0; j--) {
                    if (dp[p1-1][j-1] >= 0) {
                        dp[p2][j] = Math.max(Math.max(dp[p2][j], dp[p1-1][j-1] + p2-p1+1), dp[p2-1][j]);
                    }
                }
                p2++;
            }
            else {
                p1++;
            }
        }
        int ans = 0;
        for(int i= 0; i <= K; i++) {
            ans = Math.max(ans, dp[N][i]);
        }
        out.println(ans);
        out.flush();
    }
    
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        
        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }
        
        public FastScanner() {
            this(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 readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        
        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextInt();
            }
            return a;
        }
    }
}