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 long long MOD = 1e9 + 7;
int n, a[1010], dp[260][1010], lb = 0, ub = 1e9, mid, ans = 0;
vector<int> poss[10];
bool check() {
  for (int i = 0; i < 258; i++)
    for (int j = 0; j < 1005; j++) dp[i][j] = -1;
  dp[0][0] = 0;
  for (int i = 0; i < 256; i++) {
    for (int j = 0; j < n; j++) {
      if (dp[i][j] == -1) continue;
      for (int k = 0; k < 8; k++) {
        if (((i >> k) & 1) == 1) continue;
        int pos =
            lower_bound(poss[k].begin(), poss[k].end(), j) - poss[k].begin();
        if (pos + mid - 1 >= (int)(poss[k].size())) continue;
        if (mid == 0)
          dp[i | (1 << k)][j] = max(dp[i | (1 << k)][j], dp[i][j]);
        else
          dp[i | (1 << k)][poss[k][pos + mid - 1] + 1] =
              max(dp[i | (1 << k)][poss[k][pos + mid - 1] + 1], dp[i][j] + mid);
        if (pos + mid >= poss[k].size()) continue;
        dp[i | (1 << k)][poss[k][pos + mid] + 1] =
            max(dp[i | (1 << k)][poss[k][pos + mid] + 1], dp[i][j] + mid + 1);
      }
    }
  }
  bool ret = false;
  for (int i = 1; i <= n; i++) {
    if (dp[255][i] != -1) {
      ret = true;
      ans = max(ans, dp[255][i]);
    }
  }
  return ret;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    poss[a[i] - 1].push_back(i);
  }
  for (int i = 0; i < 8; i++) ub = min(ub, int(poss[i].size()));
  while (lb < ub) {
    mid = (lb + ub + 1) / 2;
    if (check())
      lb = mid;
    else
      ub = mid - 1;
  }
  mid = lb;
  check();
  cout << ans << endl;
  return 0;
}
