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 = 1000, C = 8;
int arr[N], n, mid;
int dp[N][1 << C];
bool visit[N][1 << C];
int solve(int startIdx, int canNotPickMask) {
  if (canNotPickMask == (1 << C) - 1) return 0;
  if (startIdx >= n) return -N;
  int &ans = dp[startIdx][canNotPickMask];
  if (visit[startIdx][canNotPickMask]) return ans;
  visit[startIdx][canNotPickMask] = true;
  ans = solve(startIdx + 1, canNotPickMask);
  if (((canNotPickMask >> arr[startIdx]) & 1) == 0) {
    int nextIndex = startIdx, remainNum = mid;
    while (remainNum > 0 && nextIndex < n) {
      if (arr[nextIndex] == arr[startIdx]) remainNum--;
      nextIndex++;
    }
    if (remainNum == 0) {
      ans = max(ans,
                mid + solve(nextIndex, canNotPickMask | (1 << arr[startIdx])));
      remainNum = 1;
      while (remainNum > 0 && nextIndex < n) {
        if (arr[nextIndex] == arr[startIdx]) remainNum--;
        nextIndex++;
      }
      if (remainNum == 0)
        ans = max(
            ans,
            mid + 1 + solve(nextIndex, canNotPickMask | (1 << arr[startIdx])));
    }
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  set<int> s;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    arr[i]--;
    s.insert(arr[i]);
  }
  int low = 1, high = n / C, ans = s.size(), temp;
  while (low <= high) {
    mid = (low + high) / 2;
    memset(visit, false, sizeof visit);
    temp = solve(0, 0);
    if (temp <= 0)
      high = mid - 1;
    else {
      ans = max(ans, temp);
      low = mid + 1;
    }
  }
  cout << ans << endl;
  return 0;
}
