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 PYTHON):

Solution:
#!/usr/bin/env python2
import os
from bisect import bisect_right
from io import BytesIO

range = xrange
input = BytesIO(os.read(0, os.fstat(0).st_size)).readline


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

    next_end = [0] * n

    i, j = 0, 0
    while j < n:
        if a[i] + 5 >= a[j]:
            j += 1
        else:
            i += 1

        next_end[i] = j

    dp = [[0] * (k + 1) for _ in range(n + 1)]

    for i in range(n - 1, -1, -1):
        dpi = dp[i]
        dpip1 = dp[i + 1]
        x = next_end[i]
        dpx = dp[x]
        for j in range(1, k + 1):
            dpi[j] = max(1 + dpip1[j - 1], dpip1[j], x - i + dpx[j - 1])

    os.write(1, str(dp[0][k]))


if __name__ == '__main__':
    main()