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 tr4 {
    static ArrayList<Integer>[]ed;
    static int n,k;
    static int []a,b;
    static int [][]memo;
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		 n=sc.nextInt();
		 k=sc.nextInt();
		 a=new int [n];
		 for(int i=0;i<n;i++)
			 a[i]=sc.nextInt();
		 b=new int [n];
		 Arrays.sort(a);
		 for(int i=0;i<n;i++) {
			 int lo=i;
			 int hi=n-1;
			 b[i]=i;
			 while(lo<=hi) {
				 int mid=(lo+hi)/2;
				 if(a[mid]-a[i]<=5) {
					 b[i]=mid;
					 lo=mid+1;
				 }
				 else
					 hi=mid-1;
			 }
		 }
		// System.out.println(Arrays.toString(b));
		// System.out.println(Arrays.toString(a));
		 memo=new int [n][k+1];
		 for(int []a:memo)
			 Arrays.fill(a, -1);
		 out.println(dp(0,k));
		// for(int []a:memo)
			// System.out.println(Arrays.toString(a));
		out.flush();
	}
    static int dp(int idx,int op) { 
    	if(idx==n || op==0)
    	  return 0;
    	if(memo[idx][op]!=-1)
    	     return memo[idx][op];
    	int take=b[idx]-idx+1+dp(b[idx]+1,op-1);
    	int leave=dp(idx+1,op);
    	return memo[idx][op]=Math.max(take,leave);
    }
 
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}