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 n, a[1005], in[1005], f[1005][300];
vector<int> pos[10];
int check(int x) {
  for (int i = 0; i <= n; ++i)
    for (int j = 1; j < 256; ++j) f[i][j] = -1e9;
  f[0][0] = 0;
  if (!x)
    for (int i = 1; i < 256; ++i) f[0][i] = 0;
  for (int i = 1; i <= n; ++i) {
    for (int j = 0; j < 256; ++j) {
      f[i][j] = max(f[i][j], f[i - 1][j]);
      for (int k = 0; k < 8; ++k) {
        if ((j >> k & 1) && a[i] == k) {
          if (x && in[i] >= x - 1) {
            int tmp = pos[k][in[i] - x + 1];
            f[i][j] = max(f[i][j], f[tmp - 1][j ^ (1 << k)] + x);
          }
          if (in[i] >= x) {
            int tmp = pos[k][in[i] - x];
            f[i][j] = max(f[i][j], f[tmp - 1][j ^ (1 << k)] + x + 1);
          }
        }
      }
    }
  }
  return f[n][255];
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    a[i]--;
    in[i] = pos[a[i]].size();
    pos[a[i]].push_back(i);
  }
  int l = 0, r = n;
  while (l < r) {
    int mid = (l + r + 1) / 2;
    if (check(mid) >= 0)
      l = mid;
    else
      r = mid - 1;
  }
  cout << check(l);
}
