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 INF = 1e9;
int n;
int A[1010];
int cnt[1010][10];
int ID[1010][10];
int memo[1010][260][2];
int mid;
int solve(int i, int mask, int ok) {
  if (mask == (1LL << (8)) - 1) {
    return 0;
  }
  if (i > n) return -INF;
  int &Cur = memo[i][mask][ok];
  if (Cur != -1) return memo[i][mask][ok];
  Cur = -INF;
  for (int j = 0; j < 8; j++) {
    if ((((mask) >> (j)) & 1)) continue;
    if (ID[cnt[i - 1][j] + mid][j]) {
      int id = ID[cnt[i - 1][j] + mid][j];
      Cur = max(Cur, solve(id + 1, ((mask) | (1LL << (j))), ok) + mid);
    }
    if (ok) {
      if (ID[cnt[i - 1][j] + mid - 1][j]) {
        int id = ID[cnt[i - 1][j] + mid - 1][j];
        Cur = max(Cur, solve(id + 1, ((mask) | (1LL << (j))), ok) + mid - 1);
      }
    } else {
      if (ID[cnt[i - 1][j] + mid + 1][j]) {
        int id = ID[cnt[i - 1][j] + mid + 1][j];
        Cur = max(Cur, solve(id + 1, ((mask) | (1LL << (j))), ok) + mid + 1);
      }
    }
  }
  return Cur;
}
bool Check() {
  memset(memo, -1, sizeof memo);
  if (solve(1, 0, 0) >= 0 || solve(1, 0, 1) >= 0)
    return true;
  else
    return false;
}
inline void Init(void) {
  int Cur = 0;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> A[i];
    Cur |= (1LL << (A[i] - 1));
    for (int j = 0; j < 8; j++) {
      cnt[i][j] += cnt[i - 1][j] + (A[i] == (j + 1));
    }
  }
  for (int i = n; i >= 1; i--) {
    for (int j = 0; j < 8; j++) {
      ID[cnt[i][j]][j] = i;
    }
  }
  int Ans = 0;
  int l = 1, r = n;
  while (r >= l) {
    mid = (l + r) / 2;
    if (Check()) {
      Ans = mid;
      l = mid + 1;
    } else {
      r = mid - 1;
    }
  }
  mid = Ans;
  memset(memo, -1, sizeof memo);
  cout << max((int)__builtin_popcountll(Cur),
              max(solve(1, 0, 1), solve(1, 0, 0)))
       << '\n';
  return;
}
inline void Process(void) { return; }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  Init();
  Process();
}
