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>
#pragma comment(linker, "/STACK:102400000,102400000")
using namespace std;
const int lowbit(int x) { return x & -x; }
const double eps = 1e-8;
const int INF = 0x3F3F3F3F;
const int mod = 1e9 + 7;
const int N = 1e3 + 10;
const int MM = (1 << 8);
vector<int> v[8];
int dp[N][MM];
int a[N];
int ans = 0, n, inf;
int dfs(int i, int mark, int sum) {
  if (dp[i][mark] != inf) return dp[i][mark];
  if (i > n) {
    if (mark == MM - 1) return 0;
    return inf;
  }
  int ret = inf;
  if (((mark >> a[i]) & 1) == 0) {
    int pos = lower_bound(v[a[i]].begin(), v[a[i]].end(), i) - v[a[i]].begin();
    if (pos + sum - 1 < v[a[i]].size()) {
      ret = max(sum + dfs(v[a[i]][pos + sum - 1] + 1, mark | (1 << a[i]), sum),
                ret);
    }
    if (pos + sum < v[a[i]].size()) {
      ret = max(sum + 1 + dfs(v[a[i]][pos + sum] + 1, mark | (1 << a[i]), sum),
                ret);
    }
  }
  ret = max(ret, dfs(i + 1, mark, sum));
  return dp[i][mark] = ret;
}
bool check(int x) {
  memset(dp, -INF, sizeof(dp));
  inf = dp[0][0];
  int tmp = dfs(1, 0, x);
  ans = max(ans, tmp);
  if (tmp > 0) return true;
  return false;
}
int main() {
  cin >> n;
  int mark = 0;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    a[i]--;
    if (!((mark >> a[i]) & 1)) ans++, mark |= (1 << a[i]);
    v[a[i]].push_back(i);
  }
  int l = 1, r = n / 8;
  while (l <= r) {
    int mid = (l + r) >> 1;
    if (check(mid))
      l = mid + 1;
    else
      r = mid - 1;
  }
  cout << ans << endl;
}
