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:
from collections import defaultdict

def solve(n, k, nums):
    nums.sort()

    new_nums = [0]
    for i in range(1, n):
        x = min(nums[i] - nums[i-1], 6)
        new_nums.append(new_nums[-1] + x)

    cand_count = new_nums[-1] + 1
    candidates = [0] * cand_count

    for n in new_nums:
        for i in range(n-5, n+1):
            if 0 <= i < cand_count:
                candidates[i] += 1

    prev = [None] * cand_count
    max_val = 0
    for i in range(cand_count):
        max_val = max(max_val, candidates[i])
        prev[i] = max_val
        
    for ki in range(1, k):
        new = [None] * cand_count
        new[0:6] = prev[0:6]
        for i in range(6, cand_count):
            new[i] = max(new[i-1], prev[i-6]+candidates[i])
        prev = new
        
    print(prev[-1])


def solve_from_stdin():
    n, k = map(int, input().split())
    nums = list(map(int, input().split()))
    solve(n, k, nums)

def test():
    n, k = 1000, 500
    nums = list(range(n))
    solve(n, k, nums)

solve_from_stdin()