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;
long long int power[22];
long long int dp[1002][258];
long long int arr[1005][152][8];
signed main() {
  power[0] = 1;
  long long int inf = 1000000000;
  for (long long int i = 1; i <= 20; i++) {
    power[i] = power[i - 1] * 2;
  }
  long long int n;
  cin >> n;
  vector<long long int> v;
  v.push_back(0);
  set<long long int> s;
  for (long long int i = 1; i <= n; i++) {
    long long int z;
    cin >> z;
    s.insert(z);
    v.push_back(z);
  }
  for (long long int i = 0; i <= 1004; i++) {
    for (long long int j = 0; j <= 150; j++) {
      for (long long int k = 0; k <= 7; k++) {
        if (j == 0) {
          arr[i][j][k] = i;
          continue;
        }
        arr[i][j][k] = inf;
      }
    }
  }
  for (long long int i = n - 1; i >= 0; i--) {
    for (long long int j = 1; j <= 150; j++) {
      for (long long int k = 0; k <= 7; k++) {
        if (k == v[i + 1] - 1) {
          arr[i][j][k] = min(arr[i + 1][j - 1][k], arr[i][j][k]);
        } else {
          arr[i][j][k] = min(arr[i][j][k], arr[i + 1][j][k]);
        }
      }
    }
  }
  long long int ans = s.size();
  for (long long int k = 1; k <= n / 8; k++) {
    for (long long int i = 0; i <= n + 1; i++) {
      for (long long int j = 0; j <= 257; j++) {
        dp[i][j] = 0;
      }
    }
    for (long long int i = 0; i <= n - 1; i++) {
      for (long long int j = 0; j <= 255; j++) {
        if ((dp[i][j]) || (j == 0)) {
          for (long long int l = 0; l <= 7; l++) {
            if ((power[l] & j) == 0) {
              if (arr[i][k][l] <= n) {
                dp[arr[i][k][l]][power[l] | j] =
                    max(dp[i][j] + k, dp[arr[i][k][l]][power[l] | j]);
              }
              if (arr[i][k + 1][l] <= n) {
                dp[arr[i][k + 1][l]][power[l] | j] =
                    max(dp[i][j] + k + 1, dp[arr[i][k + 1][l]][power[l] | j]);
              }
            }
          }
        }
        dp[i + 1][j] = max(dp[i][j], dp[i + 1][j]);
      }
    }
    ans = max(ans, dp[n][255]);
  }
  cout << ans;
}
