Vladik was bored on his way home and decided to play the following game. He took n cards and put them in a row in front of himself. Every card has a positive integer number not exceeding 8 written on it. He decided to find the longest subsequence of cards which satisfies the following conditions:

  * the number of occurrences of each number from 1 to 8 in the subsequence doesn't differ by more then 1 from the number of occurrences of any other number. Formally, if there are ck cards with number k on them in the subsequence, than for all pairs of integers <image> the condition |ci - cj| ≤ 1 must hold. 
  * if there is at least one card with number x on it in the subsequence, then all cards with number x in this subsequence must form a continuous segment in it (but not necessarily a continuous segment in the original sequence). For example, the subsequence [1, 1, 2, 2] satisfies this condition while the subsequence [1, 2, 2, 1] doesn't. Note that [1, 1, 2, 2] doesn't satisfy the first condition. 



Please help Vladik to find the length of the longest subsequence that satisfies both conditions.

Input

The first line contains single integer n (1 ≤ n ≤ 1000) — the number of cards in Vladik's sequence.

The second line contains the sequence of n positive integers not exceeding 8 — the description of Vladik's sequence.

Output

Print single integer — the length of the longest subsequence of Vladik's sequence that satisfies both conditions.

Examples

Input

3
1 1 1


Output

1

Input

8
8 7 6 5 4 3 2 1


Output

8

Input

24
1 8 1 2 8 2 3 8 3 4 8 4 5 8 5 6 8 6 7 8 7 8 8 8


Output

17

Note

In the first sample all the numbers written on the cards are equal, so you can't take more than one card, otherwise you'll violate the first condition.
#include <bits/stdc++.h>
using namespace std;
int main(void) {
  srand(time(0));
  cout << fixed << setprecision(7);
  cerr << fixed << setprecision(7);
  static int s[1 << 20];
  static int D[11][1 << 10][1 << 10];
  int n;
  cin >> n;
  for (int i = 1; i <= n; ++i) cin >> s[i];
  for (int w = 1; w < 9; ++w) {
    for (int k = 0; k <= n; ++k) D[w][k][n + 1] = n + 1;
    for (int i = 1; i <= n + 1; ++i) D[w][0][i] = i - 1;
    for (int i = n; i; --i) {
      if (s[i] == w)
        D[w][1][i] = i;
      else
        D[w][1][i] = D[w][1][i + 1];
    }
    for (int k = 2; k <= n; ++k)
      for (int i = n; i; --i) {
        if (s[i] == w)
          D[w][k][i] = D[w][k - 1][i + 1];
        else
          D[w][k][i] = D[w][k][i + 1];
      }
  }
  auto f = [&](int mask, int len) {
    static int p[1 << 20];
    for (int i = 1; i <= 8; ++i) p[i] = i;
    do {
      int cur = 0;
      for (int i = 1; i <= 8 && cur <= n; ++i)
        cur = D[p[i]][len + ((mask >> (p[i] - 1)) & 1)][cur + 1];
      if (cur <= n) return 1;
    } while (next_permutation(p + 1, p + 9));
    return 0;
  };
  int ans = 0;
  for (int k = 1 << 10; k; k /= 2)
    if (ans + k <= n) {
      for (int mask = 0; mask < (1 << 8); ++mask)
        if ((ans + k - __builtin_popcount(mask)) % 8 == 0) {
          if (f(mask, (ans + k - __builtin_popcount(mask)) / 8)) {
            ans += k;
            break;
          }
        }
    }
  cout << ans << '\n';
  cerr << "Time elapsed :" << clock() * 1000.0 / CLOCKS_PER_SEC << " ms"
       << '\n';
  return 0;
}
