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, ans;
int a[1005], v[10];
int pre[1005][1005];
int f[1005][1005];
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    a[i]--;
    if (!v[a[i]]) v[a[i]] = 1, ans++;
  }
  for (int i = 1; i <= n; i++) {
    int num = 0;
    for (int j = i; j; j--)
      if (a[j] == a[i]) {
        num++;
        pre[i][num] = j;
      }
  }
  for (int len = 1; len <= n / 8; len++) {
    memset(f, -1, sizeof(f));
    for (int i = 1; i <= n; i++) {
      for (int j = 0; j < (1 << 8); j++) f[i][j] = f[i - 1][j];
      f[i][0] = 0;
      for (int j = 0; j < (1 << 8); j++) {
        if (j & (1 << a[i])) {
          if (pre[i][len] && f[pre[i][len]][j - (1 << a[i])] != -1)
            f[i][j] = max(f[i][j], f[pre[i][len]][j - (1 << a[i])] + len);
          if (pre[i][len + 1] && f[pre[i][len + 1]][j - (1 << a[i])] != -1)
            f[i][j] =
                max(f[i][j], f[pre[i][len + 1]][j - (1 << a[i])] + len + 1);
        }
        if (j == (1 << 8) - 1) ans = max(ans, f[i][j]);
      }
    }
  }
  printf("%d\n", ans);
  return 0;
}
