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 + 7;
const int M = 100000 + 2;
const int inf = 1e9 + 7;
const long long linf = 1ll * inf * inf + 7;
const double pi = acos(-1);
const double eps = 1e-8;
const bool multipleTest = 0;
int n;
int a[N];
int dp[N][126][270];
int pre[N][10];
int last[10];
void solve() {
  memset(dp, -inf, sizeof(dp));
  for (int mask = (0); mask < (1 << 8); mask++) dp[0][0][mask] = 0;
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    int u;
    scanf("%d", &u);
    --u;
    a[i] = u;
    for (int j = 0; j < 8; ++j) pre[i][j] = last[j];
    last[u] = i;
  }
  for (int i = 1; i <= n; ++i) {
    for (int mask = (0); mask < (1 << 8); mask++) {
      if (!(mask & (1 << a[i]))) {
        for (int len = (0); len < (126); len++)
          dp[i][len][mask] = dp[i - 1][len][mask];
      } else {
        for (int len = (0); len < (126); len++)
          dp[i][len][mask] = dp[i - 1][len][mask];
        int other = mask ^ (1 << a[i]);
        for (int len = 1, cur = i; len <= 125 && cur > 0;
             ++len, cur = pre[cur][a[i]]) {
          dp[i][len][mask] =
              max(dp[i][len][mask], dp[cur - 1][len][other] + len);
          dp[i][len - 1][mask] =
              max(dp[i][len - 1][mask], dp[cur - 1][len - 1][other] + len);
        }
      }
      int curMask = 1 << a[i];
      for (int len = 1, cur = i; len <= 125 && cur > 0;
           ++len, cur = pre[cur][a[i]]) {
        dp[i][len][curMask] = max(dp[i][len][curMask], len);
        dp[i][len - 1][curMask] = max(dp[i][len - 1][curMask], len);
      }
    }
  }
  int ans = 0;
  for (int len = (0); len < (126); len++) {
    ans = max(ans, dp[n][len][(1 << 8) - 1]);
  }
  cout << ans << '\n';
}
void createTest() {
  freopen("in.txt", "w", stdout);
  int n = 500000;
  cout << n << "\n";
  for (int i = 1; i < n; ++i) {
    int u = i;
    char c = (rand() % 22) + 'a';
    printf("%d %c\n", u, c);
  }
}
int main() {
  if (fopen("bishops.in", "r")) {
    freopen("bishops.in", "r", stdin);
  }
  int Test = 1;
  if (multipleTest) {
    cin >> Test;
  }
  for (int i = 0; i < Test; ++i) {
    solve();
  }
}
