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>
const int maxn = 5010;
const int mxan = 1e5 + 10;
const int INF = 1e9 + 7;
using namespace std;
inline int read() {
  char ls;
  int x = 0, sng = 1;
  for (; ls < '0' || ls > '9'; ls = getchar())
    if (ls == '-') sng = -1;
  for (; ls >= '0' && ls <= '9'; ls = getchar()) x = x * 10 + ls - '0';
  return x * sng;
}
int n;
int a[maxn], f[maxn][maxn], ans = -1;
int maxnum[mxan], maxmod[7];
void init() {
  memset(maxnum, 0, sizeof(maxnum));
  memset(maxmod, 0, sizeof(maxmod));
}
int main() {
  n = read();
  for (int i = 1; i <= n; i++) a[i] = read();
  for (int y = 0; y <= n; y++) {
    init();
    for (int x = 1; x <= n; x++) {
      if (x == y) continue;
      if (y > x) {
        maxnum[a[x]] = max(maxnum[a[x]], f[x][y]);
        maxmod[a[x] % 7] = max(maxmod[a[x] % 7], f[x][y]);
        continue;
      }
      f[x][y] = max(f[x][y], maxmod[a[x] % 7] + 1);
      f[x][y] = max(f[x][y], maxnum[a[x] - 1] + 1);
      f[x][y] = max(f[x][y], maxnum[a[x] + 1] + 1);
      f[x][y] = max(f[x][y], f[0][y] + 1);
      f[y][x] = f[x][y];
      maxmod[a[x] % 7] = max(maxmod[a[x] % 7], f[x][y]);
      maxnum[a[x]] = max(maxnum[a[x]], f[x][y]);
      ans = max(ans, f[x][y]);
    }
  }
  cout << ans;
}