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>
using namespace std;
int n;
int a[5005];
int f1[8];
int f2[100005];
int dp[5005][5005];
int ans;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  for (int i = 0; i <= n; ++i) {
    for (int j = 0; j < 7; ++j) f1[j] = 0;
    for (int j = 0; j <= n; ++j) f2[a[j]] = 0;
    for (int j = 1; j <= n; ++j) {
      if (j == i) continue;
      if (j < i) {
        f1[a[j] % 7] = max(f1[a[j] % 7], dp[i][j]);
        f2[a[j]] = max(f2[a[j]], dp[i][j]);
        continue;
      }
      dp[j][i] = max(dp[j][i], f1[a[j] % 7] + 1);
      dp[j][i] = max(dp[j][i], f2[a[j] - 1] + 1);
      dp[j][i] = max(dp[j][i], f2[a[j] + 1] + 1);
      dp[j][i] = max(dp[j][i], dp[i][0] + 1);
      ans = max(ans, dp[j][i]);
      f1[a[j] % 7] = max(f1[a[j] % 7], dp[j][i]);
      f2[a[j]] = max(f2[a[j]], dp[j][i]);
    }
  }
  cout << ans;
}