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;
template <typename T>
bool chmax(T& a, const T& b) {
  return a < b ? (a = b, true) : false;
}
template <typename T>
bool chmin(T& a, const T& b) {
  return b < a ? (a = b, true) : false;
}
int N;
int dp[1001][1 << 8];
const int INF = 1e9;
int f(int m, vector<int>& A) {
  fill(dp[0], dp[N + 1], -INF);
  dp[0][0] = 0;
  for (int i = (int)0; i < (int)N; i++)
    for (int mask = (int)0; mask < (int)1 << 8; mask++)
      if (dp[i][mask] != -INF) {
        chmax(dp[i + 1][mask], dp[i][mask]);
        for (int j = (int)0; j < (int)8; j++)
          if ((mask >> j & 1) == 0) {
            int cnt = 0, nmask = mask | (1 << j);
            for (int k = i; k <= N; k++) {
              if (cnt == m) {
                chmax(dp[k][nmask], dp[i][mask]);
              } else if (cnt == m + 1) {
                chmax(dp[k][nmask], dp[i][mask] + 1);
                break;
              }
              if (k < N) {
                cnt += A[k] == j + 1;
              }
            }
          }
      }
  return dp[N][(1 << 8) - 1];
}
int main() {
  scanf("%d", &N);
  vector<int> A(N);
  for (int i = (int)0; i < (int)N; i++) {
    scanf("%d", &A[i]);
  }
  int lo = 0, hi = N / 8 + 1, mid;
  while (hi - lo > 1) {
    mid = (lo + hi) / 2;
    if (f(mid, A) != -INF) {
      lo = mid;
    } else {
      hi = mid;
    }
  }
  printf("%d\n", f(lo, A) + lo * 8);
  return 0;
}
