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;
inline int in() {
  int32_t x;
  scanf("%d", &x);
  return x;
}
inline long long lin() {
  long long x;
  scanf("%lld", &x);
  return x;
}
const int maxn = 2e5 + 10;
const int mod = 1e9 + 7;
const int SZ = (1 << 8);
int dp[SZ], n;
vector<int> pos[10];
inline bool can(int cnt) {
  int extraCnt = cnt % 8;
  for (int extmask = 0; extmask < SZ; extmask++) {
    if (__builtin_popcount(extmask) != extraCnt) continue;
    dp[0] = 0;
    for (int mask = 1; mask < SZ; mask++) {
      dp[mask] = n + 5;
      for (int lst = 0; lst < 8; lst++) {
        if (mask >> lst & 1) {
          int premask = mask ^ (1 << lst);
          int start = dp[premask];
          int low = (int)(lower_bound(pos[lst].begin(), pos[lst].end(), start) -
                          pos[lst].begin());
          int need = cnt / 8 + bool(extmask >> lst & 1);
          if (!need)
            dp[mask] = min(dp[mask], dp[premask]);
          else if (low + need <= pos[lst].size()) {
            dp[mask] = min(dp[mask], pos[lst][low + need - 1] + 1);
          }
        }
      }
      if (mask == SZ - 1 && dp[mask] <= n) {
        return true;
      }
    }
  }
  return 0;
}
int32_t main() {
  n = in();
  for (int i = 0; i < n; i++) pos[in() - 1].push_back(i);
  int low = 0, hi = n + 1;
  while (low + 1 < hi) {
    int mid = (low + hi) >> 1;
    if (can(mid))
      low = mid;
    else
      hi = mid;
  }
  cout << low << endl;
}
