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 Main {
    static int n, k, max = Integer.MAX_VALUE / 2;
    static Integer[] arr;
    static int[] next;
    static int[][] dp;
	public static void main (String[] args) throws IOException {
	    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	    String[] line = br.readLine().split(" ");
	    n = p(line[0]);
	    k = p(line[1]);
	    arr = new Integer[n];
	    next = new int[n];
	    dp = new int[n + 1][k + 1];
	    line = br.readLine().split(" ");
	    for(int i = 0; i < n; ++i){
	        arr[i] = p(line[i]);
	        Arrays.fill(dp[i], -1);
	    }
	    Arrays.fill(dp[n], -1);
	    Arrays.sort(arr);
	    
	    next = new int[n];
	    int r = 0;
	    for(int l = 0; l < n; ++l){
	        while(r + 1 < n && arr[r + 1] - arr[l] <= 5) ++r;
	        
	        next[l] = r;
	    }
	    
	    int out = go(0, 0);
	    System.out.println(out);
	}
	static int go(int idx, int formed){
	    if(dp[idx][formed] != -1) return dp[idx][formed];
	    
	    if(idx == n){
	        if(formed == 0) return dp[idx][formed] = -max;
	        return dp[idx][formed] = 0;
	    }
	    if(formed == k) return dp[idx][formed] = 0;
	    
	    int take = 0;
	    if(formed < k){
	        int nextI = next[idx] + 1;
	        take = nextI - idx + go(nextI, formed + 1);
	    }
	    int dont = go(idx + 1, formed);
	    
	    int out = Math.max(take, dont);
	    return dp[idx][formed] = out;
	}
	static int p(String in){
	    return Integer.parseInt(in);
	}
}