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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n, k, f[5010][5010], a[5010], s[5010], ans = 0;
int main() {
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  sort(a + 1, a + n + 1);
  int t = 1, tt = 2;
  while (t <= n) {
    while (tt <= n && a[tt] - a[t] <= 5) ++tt;
    s[t] += (tt - t);
    ++t;
  }
  for (int i = 1; i <= n; ++i)
    for (int j = 0; j <= min(i, k); ++j) {
      f[i + 1][j] = max(f[i][j], f[i + 1][j]);
      f[i + s[i]][j + 1] = max(f[i + s[i]][j + 1], f[i][j] + s[i]);
    }
  for (int i = 0; i <= k; ++i) ans = max(ans, f[n + 1][i]);
  cout << ans << endl;
  return 0;
}