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;
inline int getint() {
  static char c;
  while ((c = getchar()) < '0' || c > '9')
    ;
  int res = c - '0';
  while ((c = getchar()) >= '0' && c <= '9') res = res * 10 + c - '0';
  return res;
}
const int MaxN = 3005;
const int MaxM = 100005;
const int G = 4;
const int MaxNV = MaxN * 2 + 2;
const int MaxNE = MaxN * (3 + G * 2);
const int QN = 32767;
const int INF = 0x3f3f3f3f;
int n;
int a[MaxN];
struct halfEdge {
  int v, w, c;
  halfEdge *next;
};
halfEdge adj_pool[MaxNE * 2], *adj_tail = adj_pool;
halfEdge *adj[MaxNV];
inline void addEdge(const int &u, const int &v, const int &w, const int &c) {
  adj_tail->v = v, adj_tail->w = w, adj_tail->c = c;
  adj_tail->next = adj[u], adj[u] = adj_tail++;
  adj_tail->v = u, adj_tail->w = 0, adj_tail->c = -c;
  adj_tail->next = adj[v], adj[v] = adj_tail++;
}
inline halfEdge *oppo(const halfEdge *e) {
  return adj_pool + ((e - adj_pool) ^ 1);
}
int vS, vT;
halfEdge *dfs_cur[MaxNV];
int dist[MaxNV];
bool book[MaxNV];
int q_l, q_r;
int q[QN + 1];
bool vis[MaxNV];
int outcome = 0;
inline bool calc_dist() {
  for (int i = vS; i <= vT; ++i)
    dfs_cur[i] = adj[i], dist[i] = INF, vis[i] = true;
  dist[vS] = 0;
  q_l = 0, q_r = 0;
  q[++q_r] = vS;
  while (q_l != q_r) {
    int u = q[++q_l &= QN];
    book[u] = false;
    for (halfEdge *e = adj[u]; e; e = e->next) {
      int l = dist[u] + e->c;
      if (l < dist[e->v] && e->w) {
        dist[e->v] = l;
        if (!book[e->v]) {
          book[e->v] = true;
          q[++q_r &= QN] = e->v;
        }
      }
    }
  }
  return dist[vT] < INF;
}
int dfs(int u, int flow) {
  if (u == vT || !flow) {
    outcome -= flow * dist[u];
    return flow;
  }
  vis[u] = false;
  int res = 0;
  for (halfEdge *&e = dfs_cur[u]; e; e = e->next) {
    if (!e->w || !vis[e->v]) continue;
    if (dist[e->v] != dist[u] + e->c) continue;
    int delta = dfs(e->v, min(e->w, flow - res));
    if (delta > 0) {
      e->w -= delta, oppo(e)->w += delta;
      if ((res += delta) == flow) break;
    }
  }
  return res;
}
template <class T>
inline void link_previous(int x, T validator) {
  int now = 0;
  for (int i = x - 1; i; --i)
    if (validator(a[i], a[x])) {
      addEdge(i + n, x, 1, 0);
      if (++now == G) break;
    }
}
inline bool validator1(int a, int b) { return abs(a - b) == 1; }
inline bool validator2(int a, int b) { return a % 7 == b % 7; }
int main() {
  n = getint();
  for (int i = 1; i <= n; ++i) a[i] = getint();
  vS = 0, vT = n + n + 1;
  for (int i = 1; i <= n; ++i) {
    int u = i, v = i + n;
    addEdge(vS, u, 1, 0);
    addEdge(v, vT, 1, 0);
    addEdge(u, v, 1, -1);
    link_previous(i, validator1);
    link_previous(i, validator2);
  }
  addEdge(vT, vT + 1, 4, 0), ++vT;
  while (calc_dist())
    while (dfs(vS, INF))
      ;
  cout << outcome << endl;
  return 0;
}