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;
vector<int> arr;
vector<int> col[8];
const int N = 1100;
int memo[N][300][126];
int id[N];
int n;
int getnext(int idx, int len) {
  int justnxt = id[idx];
  int sz = col[arr[idx] - 1].size();
  if (justnxt + len - 1 < sz) return col[arr[idx] - 1][justnxt + len - 1];
  return -1;
}
int DP(int idx, int mask, int cut) {
  if (__builtin_popcount(mask) == 8) return 0;
  if (n == idx) return -1e9;
  int &ret = memo[idx][mask][cut];
  if (ret != -1) return ret;
  if (mask & (1 << (arr[idx] - 1))) {
    ret = DP(idx + 1, mask, cut);
    return ret;
  }
  ret = DP(idx + 1, mask, cut);
  int idx2 = getnext(idx, cut);
  if (idx2 != -1)
    ret = max(ret, cut + DP(idx2, mask | (1 << (arr[idx] - 1)), cut));
  idx2 = getnext(idx, cut + 1);
  if (idx2 != -1)
    ret = max(ret, cut + 1 + DP(idx2, mask | (1 << (arr[idx] - 1)), cut));
  return ret;
}
int main() {
  int c;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> c;
    arr.push_back(c);
    c--;
    col[c].push_back(i);
    id[i] = col[c].size() - 1;
  }
  int ans = 0;
  for (int i = 0; i < 8; i++)
    if (col[i].size()) ans++;
  memset(memo, -1, sizeof(memo));
  for (int len = 1; len <= 125; len++) ans = max(ans, DP(0, 0, len));
  cout << ans;
  return 0;
}
