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>
int getbit(long long x, int y) { return (x >> y) & 1; }
long long getoff(long long x, int y) { return x ^ ((1ll) << y); }
using namespace std;
int n, res, a[1010], b[1010][9], c[1010][9], f[1010][256];
void dp(int kc) {
  for (int i = 0; i <= n; ++i)
    for (int mask = 1; mask < 256; ++mask) f[i][mask] = -1e9;
  for (int i = 1; i <= n; ++i)
    for (int mask = 1; mask < (1 << 8); ++mask) {
      for (int j = 1; j <= 8; ++j)
        if (getbit(mask, j - 1) == 1) {
          int k;
          int ts = b[i][j];
          if (ts < kc) continue;
          k = c[ts - kc][j];
          f[i][mask] = max(f[i][mask], f[k][getoff(mask, j - 1)] + kc);
          if (ts < kc + 1) continue;
          k = c[ts - kc - 1][j];
          f[i][mask] = max(f[i][mask], f[k][getoff(mask, j - 1)] + kc + 1);
        }
      f[i][mask] = max(f[i][mask], f[i - 1][mask]);
    }
  res = max(res, f[n][255]);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    for (int j = 1; j <= 8; ++j) b[i][j] = b[i - 1][j];
    b[i][a[i]]++;
    for (int j = 1; j <= 8; ++j) c[b[i][j]][j] = i;
  }
  for (int kc = 0; kc <= n / 8; ++kc) dp(kc);
  cout << res;
  return 0;
}
