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 maxn = 1050;
int dp[maxn][9], nxt[maxn][9][maxn], a[maxn], n, cnt[9];
inline int ask(int k) { return (1 << (k - 1)); }
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= 8; ++j) cnt[j] = 0;
    for (int j = 1; j <= 8; ++j)
      for (int k = 1; k <= n; ++k) nxt[i][j][k] = 1e9;
    for (int j = i; j <= n; ++j) nxt[i][a[j]][++cnt[a[j]]] = j;
  }
  int ans = 0;
  for (int num = 0; num * 8 <= n; ++num) {
    for (int i = 0; i < 256; ++i)
      for (int k = 0; k <= 8; ++k) dp[i][k] = 1e9;
    dp[0][0] = 1;
    for (int i = 0; i < 256; ++i)
      for (int j = 0; j <= 8; ++j)
        for (int k = 1; k <= 8; ++k) {
          if (dp[i][j] > n || ask(k) & i) continue;
          dp[i ^ ask(k)][j] = min(dp[i ^ ask(k)][j], nxt[dp[i][j]][k][num] + 1);
          dp[i ^ ask(k)][j + 1] =
              min(dp[i ^ ask(k)][j + 1], nxt[dp[i][j]][k][num + 1] + 1);
        }
    for (int i = 0; i <= 8; ++i)
      if (dp[255][i] <= n + 1) ans = max(ans, 8 * num + i);
  }
  cout << ans << endl;
  return 0;
}
