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 = 1004, INF = 1e9 + 10, ALL = (1 << 8) - 1;
int n;
int num[N], f[N][1 << 8], nxt[N][N], cnt1[1 << 8];
inline int Ri() {
  register int r = 0, c = getchar();
  while (c < '0' || '9' < c) c = getchar();
  while ('0' <= c && c <= '9') r = (r << 1) + (r << 3) + c - '0', c = getchar();
  return r;
}
int main() {
  n = Ri();
  for (int i = 1; i <= ALL; i++) cnt1[i] = cnt1[i ^ ((i) & (-(i)))] + 1;
  for (int i = 1; i <= n; i++) num[i] = Ri() - 1;
  for (int i = 1; i <= n; i++)
    for (int j = i, cnt = 0; j <= n; j++)
      if (num[j] == num[i]) nxt[i][++cnt] = j;
  f[0][0] = INF;
  for (int i = 0; i < n; i++)
    for (int S = 0; S <= ALL; S++) {
      f[i + 1][S] = max(f[i + 1][S], f[i][S]);
      if (S >> num[i + 1] & 1 || !f[i][S]) continue;
      int T = S | (1 << num[i + 1]);
      int per = cnt1[S] ? f[i + 1][S] / cnt1[S] : INF;
      for (int j = 1; nxt[i + 1][j]; j++)
        if (j < per)
          f[nxt[i + 1][j]][T] = max(f[nxt[i + 1][j]][T], cnt1[S] * (j + 1) + j);
        else
          f[nxt[i + 1][j]][T] =
              max(f[nxt[i + 1][j]][T], f[i][S] + min(j, per + 1));
    }
  int ans = 0;
  for (int S = 0; S < ALL; S++)
    if (f[n][S]) ans = max(ans, cnt1[S]);
  ans = max(ans, f[n][ALL]);
  printf("%d\n", ans);
  return 0;
}
