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 PYTHON3):

Solution:
import io
import os
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline


def main():
    n, k = map(int, input().split())
    a = sorted(list(map(int, input().split())))

    maxFromI = [0] * n  # max students in the team starting from student i with skill a[i]
    end = -1
    for i in range(n):
        while end+1 < n and a[end+1] <= a[i] + 5:
            end += 1
        maxFromI[i] = end - i + 1

    dp = [[0] * (k+1) for _ in range(n+1)]
    for i in range(n):
        for j in range(k+1):
            dp[i+1][j] = max(dp[i+1][j], dp[i][j])  # skip the student
            if j+1 <= k:
                dp[i+maxFromI[i]][j+1] = max(dp[i+maxFromI[i]][j+1], dp[i][j] + maxFromI[i])

    print(dp[n][k])


if __name__ == '__main__':
    main()