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 MAX = 1e3 + 1;
int n, arr[MAX], cnt[MAX][8], adp[MAX][257], ans;
int main() {
  ios::sync_with_stdio(0);
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> arr[i], --arr[i];
    for (int j = 0; j < 8; ++j) cnt[i][j] = cnt[i - 1][j];
    ++cnt[i][arr[i]];
  }
  arr[0] = -1;
  int l = -1, r = 125;
  while (l < r - 1) {
    int len = (l + r) >> 1;
    for (int i = 0; i <= n; ++i)
      for (int k = 0; k < 256; ++k) adp[i][k] = -1e6;
    adp[0][0] = 0;
    int now = 0;
    for (int i = 1; i <= n; ++i) {
      for (int j = 0; j < i; ++j)
        if (arr[i] != arr[j] && cnt[i][arr[i]] - cnt[j][arr[i]] >= len)
          for (int k = 0; k < 256; ++k)
            if (!(k & (1 << arr[i])))
              adp[i][k | (1 << arr[i])] = max(
                  adp[i][k | (1 << arr[i])],
                  adp[j][k] + min(cnt[i][arr[i]] - cnt[j][arr[i]], len + 1));
      if (len == 0)
        for (int k = 0; k < 256; ++k) now = max(now, adp[i][k]);
      else
        now = max(now, adp[i][255]);
    }
    ans = max(ans, now);
    if (now <= 0)
      r = len;
    else
      l = len;
  }
  cout << ans << endl;
  return 0;
}
