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;
const int inf = 0x3f3f3f3f;
const double eps = 1e-8;
int n;
int arr[1001];
vector<int> num[10];
int memo[256][1001];
int done;
int dfs(int mask, int pos, int mn) {
  if (mask == done) return 0;
  if (pos >= n) return 0;
  if (memo[mask][pos] != -1) return memo[mask][pos];
  int res = -inf;
  for (int i = 0; i < 8; ++i) {
    if (!((1 << i) & mask)) {
      int new_mask = mask | (1 << i);
      if (num[i + 1].size()) {
        int st = lower_bound(num[i + 1].begin(), num[i + 1].end(), pos) -
                 num[i + 1].begin();
        if (mn && st + mn - 1 >= num[i + 1].size()) {
        } else {
          if (mn) {
            res = max(res, mn + dfs(new_mask, num[i + 1][st + mn - 1] + 1, mn));
          } else {
            res = max(res, dfs(new_mask, pos, mn));
          }
          if (st + mn < num[i + 1].size()) {
            res = max(res, mn + 1 + dfs(new_mask, num[i + 1][st + mn] + 1, mn));
          }
        }
      } else {
        res = max(res, dfs(new_mask, pos, mn));
      }
    }
  }
  return memo[mask][pos] = res;
}
int main() {
  done = (1 << 8) - 1;
  while (cin >> n) {
    for (int i = 0; i < n; ++i) {
      cin >> arr[i];
      num[arr[i]].push_back(i);
    }
    int mn = 1000;
    for (int i = 1; i < 9; ++i) {
      mn = min(mn, (int)num[i].size());
    }
    int len = 0;
    for (int j = mn; j >= 0; --j) {
      memset(memo, -1, sizeof(memo));
      len = max(len, dfs(0, 0, j));
    }
    cout << len << "\n";
    for (int i = 1; i < 9; ++i) {
      num[i].clear();
    }
  }
  return 0;
}
