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, arr[1500], pos[1500];
vector<int> vec[10];
int dp[1100][1 << 8], num;
int solve(int idx, int mask) {
  if (idx == n) return mask == (1 << 8) - 1 ? 0 : -100000;
  int& ret = dp[idx][mask];
  if (ret != -1) return ret;
  ret = solve(idx + 1, mask);
  if ((mask & (1 << (arr[idx] - 1))) == 0) {
    int x = pos[idx];
    if (x + num - 1 < vec[arr[idx]].size())
      ret = max(ret, num + solve(vec[arr[idx]][x + num - 1] + 1,
                                 mask | (1 << (arr[idx] - 1))));
    if (x + num < vec[arr[idx]].size())
      ret = max(ret, num + 1 +
                         solve(vec[arr[idx]][x + num] + 1,
                               mask | (1 << (arr[idx] - 1))));
  }
  return ret;
}
int ok(int mid) {
  memset(dp, -1, sizeof dp);
  num = mid;
  int ans = solve(0, 0);
  return ans;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    arr[i] = x;
    pos[i] = vec[x].size();
    vec[x].push_back(i);
  }
  int sum = 0;
  for (int i = 1; i <= 8; i++) sum += vec[i].size() > 0;
  for (int i = 1; i <= 8; i++)
    if (vec[i].size() == 0) {
      cout << sum << endl;
      return 0;
    }
  int l = 1, r = 128;
  while (l < r) {
    int mid = (l + r + 1) / 2;
    if (ok(mid) >= mid * 8)
      l = mid;
    else
      r = mid - 1;
  }
  cout << ok(l) << endl;
  return 0;
}
