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 memo[1010][1 << 8], n;
vector<int> a[10];
int b[1010];
int id[1010];
int fx = 0;
int solve(int in, int mask) {
  if (in == n + 1) {
    if (fx == 0)
      return 0;
    else if (fx != 0 && mask == 255)
      return 0;
    else
      return -1e9 - 1;
  }
  if (memo[in][mask] != -1) return memo[in][mask];
  int cur = solve(in + 1, mask);
  if ((mask & (1 << (b[in] - 1))) == 0) {
    int index = id[in];
    if (index + fx - 1 < a[b[in]].size())
      cur = max(
          cur,
          solve(a[b[in]][index + fx - 1] + 1, mask | (1 << (b[in] - 1))) + fx);
    if (index + fx < a[b[in]].size())
      cur =
          max(cur, solve(a[b[in]][index + fx] + 1, mask | (1 << (b[in] - 1))) +
                       fx + 1);
  }
  return memo[in][mask] = cur;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> b[i];
    a[b[i]].push_back(i);
    id[i] = a[b[i]].size() - 1;
  }
  int ans = 0;
  for (int i = 0; i <= n / 8; i++) {
    fx = i;
    memset(memo, -1, sizeof(memo));
    ans = max(ans, solve(1, 0));
  }
  cout << ans;
}
