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;
const int N = 1000 + 5;
const int S = 1 << 8;
int n;
int a[N];
int nxt[N][8];
int ptr[N][8];
int lst[8];
int f[N][S + 1];
int ans;
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    a[i]--;
  }
  for (int i = 0; i < 8; ++i) {
    lst[i] = -1;
    nxt[n][i] = -1;
  }
  for (int i = n - 1; i >= 0; --i) {
    lst[a[i]] = i + 1;
    for (int j = 0; j < 8; ++j) {
      nxt[i][j] = lst[j];
      ptr[i][j] = i;
    }
  }
  ans = 1;
  for (int min_len = 0; min_len * 8 <= n; ++min_len) {
    memset(f, -1, sizeof f);
    f[0][0] = 0;
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < S; ++j) {
        if (f[i][j] < 0) continue;
        for (int k = 0; k < 8; ++k) {
          if (j >> k & 1) {
          } else {
            int p = ptr[i][k];
            if (p != -1) {
              f[p][j + (1 << k)] = max(f[p][j + (1 << k)], f[i][j] + min_len);
              p = nxt[p][k];
              if (p != -1) {
                f[p][j + (1 << k)] =
                    max(f[p][j + (1 << k)], f[i][j] + min_len + 1);
              }
            }
          }
        }
      }
    }
    for (int i = 0; i <= n; ++i) {
      ans = max(ans, f[i][S - 1]);
    }
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < 8; ++j) {
        if (ptr[i][j] != -1) ptr[i][j] = nxt[ptr[i][j]][j];
      }
    }
  }
  cout << ans << endl;
  return 0;
}
