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[1010], each, cut, mp[10][1010], sum[10][1010];
bool dfs(int pos, int zy, int cnt, int res) {
  if (pos >= n + 1) return false;
  if (res == 0) return true;
  for (int i = 1; i <= 8; i++) {
    if (zy & (1 << (i - 1))) continue;
    int p = sum[i][pos];
    int s = p + each;
    if (cnt != 0)
      if (dfs(mp[i][s + 1], zy | (1 << (i - 1)), cnt - 1, res - each - 1))
        return true;
    if (dfs(mp[i][s], zy | (1 << (i - 1)), cnt, res - each)) return true;
  }
  return false;
}
int main() {
  scanf("%d", &n);
  memset(mp, 0x3f, sizeof(mp));
  for (int i = 1; i <= n; i++) {
    int x;
    scanf("%d", &x);
    a[x]++;
    mp[x][a[x]] = i;
    for (int j = 1; j <= 8; j++) sum[j][i] = sum[j][i - 1];
    sum[x][i]++;
  }
  int l = 9999, r = n, mid;
  for (int i = 1; i <= 8; i++) l = min(l, a[i]);
  l = 1;
  while (l < r) {
    mid = (l + r + 1) / 2;
    each = mid / 8;
    cut = mid % 8;
    if (dfs(0, 0, cut, mid))
      l = mid;
    else
      r = mid - 1;
  }
  printf("%d", l);
  return 0;
}
