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 n, a[1010], cnt[1010], id[1010], pos[1010][1010], f[1010][256][1010 / 8];
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    int x;
    scanf("%d", &x);
    a[i] = --x;
    pos[x][++cnt[x]] = i;
    id[i] = cnt[x];
  }
  for (int j = 1; j < 256; j++) {
    for (int k = 1; k <= n / 8; k++) f[0][j][k] = -1000000000;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < 256; j++) {
      for (int k = 0; k <= n / 8; k++) {
        f[i][j][k] = f[i - 1][j][k];
        int x = a[i];
        if (!(j & (1 << x))) continue;
        if (k && id[i] >= k) {
          int I = pos[x][id[i] - k + 1] - 1;
          f[i][j][k] = max(f[i][j][k], f[I][j ^ (1 << x)][k] + k);
        }
        if (id[i] >= k + 1) {
          int I = pos[x][id[i] - k] - 1;
          f[i][j][k] = max(f[i][j][k], f[I][j ^ (1 << x)][k] + k + 1);
        }
      }
    }
  }
  int ans = 0;
  for (int k = 0; k <= n / 8; k++) ans = max(ans, f[n][255][k]);
  printf("%d\n", ans);
  return 0;
}
