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 m[100005];
int dp[5005][5005];
int tm[5005];
int tm2[5005], tmp[5005];
int s[100005];
int var[5005][5005];
int arr[100005];
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> arr[i];
  }
  int ans = 1;
  for (int j = 0; j <= n; j++) {
    for (int i = 0; i <= n; i++) {
      if (i == j)
        dp[j][j] = 0;
      else if (i < j) {
        dp[i][j] = dp[j][i];
        if (i != 0) {
          m[arr[i]] = max(m[arr[i]], dp[i][j]);
          s[arr[i] % 7] = max(s[arr[i] % 7], dp[i][j]);
        }
      } else {
        dp[i][j] = max(m[arr[i] - 1], m[arr[i] + 1]);
        dp[i][j] = max(dp[i][j], s[arr[i] % 7]);
        dp[i][j]++;
        dp[i][j] = max(dp[i][j], 1 + dp[0][j]);
        s[arr[i] % 7] = max(s[arr[i] % 7], dp[i][j]);
        m[arr[i]] = max(m[arr[i]], dp[i][j]);
      }
      if (dp[i][j] > ans) ans = dp[i][j];
    }
    for (int i = 1; i <= n; i++) m[arr[i]] = 0;
    for (int i = 0; i < 7; i++) s[i] = 0;
  }
  cout << ans;
}