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, sums[1010], f[1010][1 << 8], cnt[8], ans = -1;
vector<int> v[8];
void update(int& x, int y) {
  if (y > x) x = y;
}
bool judge(int x) {
  memset(f, -1, sizeof f);
  memset(cnt, 0, sizeof(int) * 8);
  f[0][0] = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j != 1 << 8; ++j)
      if (~f[i][j]) {
        for (int k = 0; k != 8; ++k)
          if ((~j) & 1 << k) {
            int pos = cnt[k] + x - 1;
            if (pos < v[k].size()) update(f[v[k][pos]][j | 1 << k], f[i][j]);
            if (++pos < v[k].size())
              update(f[v[k][pos]][j | 1 << k], f[i][j] + 1);
          }
      }
    if (i) ++cnt[sums[i]];
  }
  int t = -1;
  for (int i = 1; i <= n; ++i) update(t, f[i][(1 << 8) - 1]);
  if (~t) {
    update(ans, 8 * x + t);
    return true;
  }
  return false;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &sums[i]);
    v[--sums[i]].push_back(i);
  }
  bool flag = false;
  for (int i = 0; i != 8; ++i)
    if (!v[i].size()) {
      flag = true;
      break;
    }
  if (flag) {
    int ans = 0;
    for (int i = 0; i != 8; ++i)
      if (v[i].size()) ++ans;
    printf("%d\n", ans);
    return 0;
  }
  int l = 0, r = n;
  while (l <= r) {
    int mid = l + r >> 1;
    if (judge(mid))
      l = mid + 1;
    else
      r = mid - 1;
  }
  cout << ans << endl;
  return 0;
}
