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 = 1012345678;
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    --a[i];
  }
  int ans = 0;
  for (int i = 0; i < 8; ++i) {
    if (find(a.begin(), a.end(), i) != a.end()) {
      ++ans;
    }
  }
  for (int i = 1; i <= n / 8; ++i) {
    vector<int> p1(n, n + 1), p2(n, n + 1);
    for (int j = 0; j < n; ++j) {
      int ptr = j, cnt = 0;
      while (ptr != n && cnt < i) {
        cnt += (a[ptr] == a[j]);
        ++ptr;
      }
      if (cnt == i) p1[j] = ptr;
      while (ptr != n && cnt < i + 1) {
        cnt += (a[ptr] == a[j]);
        ++ptr;
      }
      if (cnt == i + 1) p2[j] = ptr;
    }
    vector<vector<int> > dp(n + 1, vector<int>(1 << 8, -inf));
    dp[0][0] = 0;
    for (int j = 0; j < n; ++j) {
      for (int k = 0; k < 1 << 8; ++k) {
        dp[j + 1][k] = max(dp[j + 1][k], dp[j][k]);
        if (((k >> a[j]) & 1) || p1[j] == n + 1) continue;
        dp[p1[j]][k + (1 << a[j])] =
            max(dp[p1[j]][k + (1 << a[j])], dp[j][k] + i);
        if (p2[j] != n + 1) {
          dp[p2[j]][k + (1 << a[j])] =
              max(dp[p2[j]][k + (1 << a[j])], dp[j][k] + i + 1);
        }
      }
    }
    ans = max(ans, dp[n][(1 << 8) - 1]);
  }
  cout << ans << endl;
  return 0;
}
