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;
template <typename T>
inline T read1() {
  T t = 0;
  char k = getchar();
  bool flag = 0;
  while ('0' > k || k > '9') {
    if (k == '-') flag = 1;
    k = getchar();
  }
  while ('0' <= k && k <= '9')
    t = (t << 3) + (t << 1) + (k ^ 48), k = getchar();
  return flag ? -t : t;
}
int s;
vector<int> w[8];
int dp[1001][257];
int judge(int n) {
  for (int i = 0; i <= s; ++i)
    for (int j = 1; j < 256; ++j) dp[i][j] = -1e9;
  for (int i = 1; i <= s; ++i)
    for (int j = 1; j < 256; ++j)
      for (int k = 0; k < 8; ++k)
        if (j >> k & 1) {
          vector<int>::iterator it = upper_bound(w[k].begin(), w[k].end(), i);
          if (it - w[k].begin() < n) continue;
          it -= n;
          dp[i][j] = max(dp[i][j], dp[*it - 1][j ^ (1 << k)] + n);
          if (it != w[k].begin())
            dp[i][j] = max(dp[i][j], dp[*--it - 1][j ^ (1 << k)] + n + 1);
        }
  return dp[s][255];
}
int main() {
  s = read1<long long>();
  for (int i = 1; i <= s; ++i) w[read1<long long>() - 1].push_back(i);
  for (int i = 0; i < 8; ++i)
    if (!w[i].size()) {
      int t = 0;
      for (int j = 0; j < 8; ++j) t += !!w[j].size();
      return printf("%d", t), 0;
    }
  int l = 0, r = s, ans = 1, mid;
  while (l <= r)
    judge(mid = l + r >> 1) > 0                              ? l = mid + 1,
                                  ans = max(ans, dp[s][255]) : r = mid - 1;
  printf("%d", ans);
  return 0;
}
