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 = 1e5 + 5;
const int oo = 1e9;
vector<int> v[1005];
int a[1005];
int n;
int len;
int memo[1005][550];
int vis[1005][550];
int t = 0;
int f(int i, int mask) {
  if (i == n) {
    if (len == 1) return 0;
    return mask == 510 ? 0 : -oo;
  }
  int &ret = memo[i][mask];
  if (vis[i][mask] == t) return ret;
  int cur = a[i];
  if (mask & (1 << cur)) {
    vis[i][mask] = t;
    return ret = f(i + 1, mask);
  }
  int c1 = f(i + 1, mask);
  int c2 = -oo;
  int c3 = -oo;
  int sz = v[i].size();
  if (len == 1) return max(c1, len + f(i + 1, mask | (1 << cur)));
  if (sz >= len - 1) {
    c2 = len + f(v[i][len - 2] + 1, mask | (1 << cur));
  }
  if (len != 2 && sz >= len - 2) {
    c3 = len - 1 + f(v[i][len - 3] + 1, mask | (1 << cur));
  } else if (len == 2) {
    c3 = len - 1 + f(i + 1, mask | (1 << cur));
  }
  vis[i][mask] = t;
  return ret = max(c1, max(c2, c3));
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      if (a[j] == a[i]) {
        v[i].push_back(j);
      }
    }
  }
  int maxx = 1;
  for (len = 152; len >= 1; len--) {
    t++;
    memset(memo, -1, sizeof(memo));
    maxx = max(maxx, f(0, 0));
  }
  cout << maxx << endl;
  return 0;
}
