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 p[1001][1001], res, n, a[1001];
int f[1001][1 << 8];
bool dd[9];
bool check(int x) {
  for (int mask = 0; mask <= (1 << 8) - 1; mask++)
    for (int i = 0; i <= n; i++) f[i][mask] = -(n + 1);
  f[0][0] = 0;
  for (int mask = 0; mask <= (1 << 8) - 1; mask++)
    for (int i = 1; i <= n; i++) {
      f[i][mask] = f[i - 1][mask];
      if ((mask & (1 << (a[i] - 1))) != 0) {
        int s = mask ^ (1 << (a[i] - 1));
        int j = p[i][x];
        if (j) f[i][mask] = max(f[i][mask], f[j - 1][s] + x);
        j = p[i][x + 1];
        if (j) f[i][mask] = max(f[i][mask], f[j - 1][s] + x + 1);
      }
    }
  res = max(res, f[n][(1 << 8) - 1]);
  if (f[n][(1 << 8) - 1] > 0) return true;
  return false;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i], dd[a[i]] = true;
  res = 8;
  for (int i = 1; i <= 8; i++)
    if (!dd[i]) res--;
  for (int i = 1; i <= n; i++) {
    p[i][1] = i;
    int t = 0;
    for (int j = i - 1; j >= 1; j--)
      if (a[j] == a[i]) {
        t = j;
        break;
      }
    if (!t) continue;
    for (int j = 2; j <= i; j++) p[i][j] = p[t][j - 1];
  }
  int l = 1;
  int r = n;
  int mid;
  while (l <= r) {
    mid = (l + r) / 2;
    if (check(mid))
      l = mid + 1;
    else
      r = mid - 1;
  }
  cout << res;
}
