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 K = 8;
const int N = 1005;
const int M = 256;
const int INF = 1e9;
int a[N];
int num[N][K];
int dp[N][M];
inline int get_num(int l, int r, int h) {
  if (l >= 0)
    return num[r - 1][h] - num[l - 1][h];
  else
    return num[r - 1][h];
}
inline int func(int i, int t, int h, int digit_num, int nxt) {
  int tmp;
  int min_num = dp[t][nxt] / (digit_num - 1);
  if (get_num(i, t, h) < min_num)
    tmp = (get_num(i, t, h) + 1) * digit_num - 1;
  else
    tmp = min(get_num(i, t, h), min_num + 1) + dp[t][nxt];
  return tmp;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(nullptr);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    a[i]--;
    for (int j = 0; j < K; j++) num[i][j] = i == 0 ? 0 : num[i - 1][j];
    num[i][a[i]]++;
  }
  for (int j = 0; j < M; j++) dp[n][j] = 0;
  for (int i = n - 1; i >= 0; i--) {
    for (int j = 0; j < M; j++) {
      if (j == 0) {
        dp[i][j] = 0;
        continue;
      }
      int digit_num = 0;
      for (int h = 0; h < K; h++) digit_num += ((j >> h) & 1);
      if (digit_num == 1) {
        for (int h = 0; h < K; h++) {
          if ((j >> h) & 1) {
            dp[i][j] = get_num(i, n, h);
            break;
          }
        }
        continue;
      }
      dp[i][j] = 0;
      for (int h = 0; h < K; h++) {
        if ((j >> h) & 1) {
          int nxt = (j ^ (1 << h));
          int l = i, r = n;
          while (r - l > 0) {
            int m = (l + r) / 2;
            int min_num = dp[m][nxt] / (digit_num - 1);
            if (get_num(i, m, h) < min_num)
              l = m + 1;
            else
              r = m;
          }
          for (int t = max(0, l - 1); t <= l; t++)
            dp[i][j] = max(func(i, t, h, digit_num, nxt), dp[i][j]);
          l = i, r = n;
          while (r - l > 0) {
            int m = (l + r) / 2;
            int min_num = dp[m][nxt] / (digit_num - 1);
            if (get_num(i, m, h) < min_num + 1)
              l = m + 1;
            else
              r = m;
          }
          for (int t = max(0, l - 1); t <= l; t++)
            dp[i][j] = max(func(i, t, h, digit_num, nxt), dp[i][j]);
        }
      }
    }
  }
  cout << dp[0][M - 1] << "\n";
  return 0;
}
