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;
int main() {
  ios_base::sync_with_stdio(false);
  int n, a[1005], c[9][1005] = {0};
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) c[a[i]][i]++;
  for (int i = 1; i <= 8; i++) {
    for (int j = 1; j <= n; j++) c[i][j] += c[i][j - 1];
  }
  int lo = 1, hi = n, mid, ans;
  while (lo <= hi) {
    mid = (lo + hi) / 2;
    int b[8];
    for (int i = 0; i <= 7; i++) b[i] = i + 1;
    int f = 0;
    do {
      int x = mid / 8, y = mid - 8 * x;
      for (int msk = 0; msk <= (1 << 8) - 1; msk++) {
        if (__builtin_popcount(msk) == y) {
          int lst = 0, f1 = 1;
          for (int i = 0; i <= 7; i++) {
            int cnt;
            if (msk & (1 << i))
              cnt = x + 1;
            else
              cnt = x;
            if (c[b[i]][n] - c[b[i]][lst] < cnt) {
              f1 = 0;
              break;
            }
            int l1 = lst + 1, h1 = n, m1, kk;
            while (l1 <= h1) {
              m1 = (l1 + h1) / 2;
              if (c[b[i]][m1] - c[b[i]][lst] >= cnt)
                h1 = m1 - 1, kk = m1;
              else
                l1 = m1 + 1;
            }
            lst = kk;
          }
          f |= f1;
          if (f) break;
        }
      }
      if (f) break;
    } while (next_permutation(b, b + 8));
    if (f) {
      ans = mid, lo = mid + 1;
    } else {
      hi = mid - 1;
    }
  }
  cout << ans;
  return 0;
}
