Problem: Author note: I think some of you might remember the problem "Two Melodies" from Eductational Codeforces Round 22. Now it's time to make it a bit more difficult!

Alice is a composer, and recently she had recorded two tracks that became very popular. Now she has got a lot of fans who are waiting for new tracks. 

This time Alice wants to form four melodies for her tracks.

Alice has a sheet with n notes written on it. She wants to take four such non-empty non-intersecting subsequences that all of them form a melody and sum of their lengths is maximal.

Subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

Subsequence forms a melody when each two adjacent notes either differ by 1 or are congruent modulo 7.

You should write a program which will calculate maximum sum of lengths of such four non-empty non-intersecting subsequences that all of them form a melody.

Input

The first line contains one integer number n (4 ≤ n ≤ 3000).

The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105) — notes written on a sheet.

Output

Print maximum sum of lengths of such four non-empty non-intersecting subsequences that all of them form a melody.

Examples

Input

5
1 3 5 7 9


Output

4


Input

5
1 3 5 7 2


Output

5

Note

In the first example it is possible to compose 4 melodies by choosing any 4 notes (and each melody will consist of only one note).

In the second example it is possible to compose one melody with 2 notes — {1, 2}. Remaining notes are used in other three melodies (one note per each melody).

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
long long mod = 1000000007;
using namespace std;
int ar[5009], modmx[9], valmx[100009];
int dp[5009][5009];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> ar[i];
  for (int j = 0; j <= n; j++) {
    memset(modmx, 0, sizeof(modmx));
    memset(valmx, 0, sizeof(valmx));
    for (int i = 0; i <= n; i++) {
      if (i > j) {
        dp[i][j] = dp[0][j];
        dp[i][j] = max(dp[i][j], modmx[ar[i] % 7]);
        dp[i][j] = max(dp[i][j], valmx[ar[i] + 1]);
        dp[i][j] = max(dp[i][j], valmx[ar[i] - 1]);
        dp[i][j]++;
        dp[j][i] = dp[i][j];
      }
      modmx[ar[i] % 7] = max(modmx[ar[i] % 7], dp[i][j]);
      valmx[ar[i]] = max(valmx[ar[i]], dp[i][j]);
    }
  }
  int ans = 0;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) ans = max(ans, dp[i][j]);
  cout << ans << "\n";
  return 0;
}