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;
double dp[1 << 18];
int main() {
  int n;
  cin >> n;
  int a[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) {
    --a[i];
  }
  int ans = 0;
  for (int mx = 1; mx <= n / 8 + 1; mx++) {
    int dp[n + 1][1 << 8];
    for (int i = 0; i <= n; i++) {
      for (int j = 0; j < 1 << 8; j++) {
        if (i == 0) {
          if (mx == 1)
            dp[i][j] = 0;
          else {
            if (j == 0)
              dp[i][j] = 0;
            else
              dp[i][j] = -1000000000;
          }
        } else
          dp[i][j] = -1000000000;
      }
    }
    vector<int> pos[8];
    for (int i = 1; i <= n; i++) {
      int curr = a[i - 1];
      pos[curr].push_back(i);
      for (int msk = 0; msk < 1 << 8; msk++) {
        for (int j = 0; j < 8; j++)
          dp[i][msk] = max(dp[i][msk], dp[i - 1][msk]);
        if (msk & (1 << curr)) {
          if (pos[curr].size() >= mx) {
            dp[i][msk] = max(
                dp[i][msk],
                dp[pos[curr][pos[curr].size() - mx] - 1][msk ^ (1 << curr)] +
                    mx);
          }
          if (pos[curr].size() >= mx - 1) {
            if (mx > 1)
              dp[i][msk] =
                  max(dp[i][msk], dp[pos[curr][pos[curr].size() - (mx - 1)] - 1]
                                    [msk ^ (1 << curr)] +
                                      mx - 1);
          }
        }
        if (msk == 255) ans = max(ans, dp[i][msk]);
      }
    }
  }
  cout << ans << endl;
}
