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;
long long P = 1e9 + 7;
long long P1 = 998244353;
const int sqr = 500;
const int arrn = 1e6 + 5;
const int arrn2 = 6e3 + 5;
void solve() {
  int n;
  cin >> n;
  vector<int> in(n);
  for (int i = 0; i < n; i++) cin >> in[i];
  for (int i = 0; i < n; i++) in[i]--;
  in.push_back(8);
  vector<vector<int>> dp(n + 1, vector<int>(1 << 8, 0));
  for (int i = n - 1; i >= 0; i--) {
    for (int bit = 0; bit < (1 << 8); bit++) {
      dp[i][bit] = dp[i + 1][bit];
      if (bit & (1 << in[i])) {
        int neg = (bit ^ (1 << in[i]));
        int cnt = __builtin_popcount(neg);
        int icnt = 1;
        for (int j = i + 1; j < n + 1; j++) {
          if (in[j] == in[i]) icnt++;
          int xs;
          if (cnt > 0)
            xs = dp[j][neg] / cnt;
          else
            xs = n;
          if (icnt >= xs)
            dp[i][bit] = max(dp[i][bit], dp[j][neg] + min(xs + 1, icnt));
          else
            dp[i][bit] = max(dp[i][bit], (icnt + 1) * cnt + icnt);
        }
      }
    }
  }
  int ans = 0;
  for (int i = 0; i < n; i++) {
    ans = max(ans, dp[i][(1 << 8) - 1]);
  }
  cout << ans;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  int T = 1;
  while (T--) {
    solve();
  }
  return 0;
}
