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>
const long long INF = (long long)1e18 + 123;
const int inf = (int)2e9 + 123;
const int mod = 1e9 + 7;
using namespace std;
int a[100011];
int n;
vector<int> v[8];
int dp[1011][512];
int cur[8];
int check(int length) {
  for (int i = 0; i <= n; i++) {
    for (int mask = 0; mask < (1 << 8); mask++) dp[i][mask] = -inf;
  }
  memset(cur, 0, sizeof(cur));
  dp[0][0] = 0;
  for (int i = 0; i < n; i++) {
    for (int mask = 0; mask < (1 << 8); mask++) {
      if (dp[i][mask] < 0) continue;
      for (int j = 0; j < 8; j++) {
        if (mask & (1 << j)) continue;
        int pos = max(0, cur[j] + length - 1);
        if (pos >= v[j].size()) continue;
        dp[v[j][pos] + 1][mask | (1 << j)] =
            max(dp[i][mask], dp[v[j][pos] + 1][mask | (1 << j)]);
        pos++;
        if (pos >= v[j].size()) continue;
        dp[v[j][pos] + 1][mask | (1 << j)] =
            max(dp[i][mask] + 1, dp[v[j][pos] + 1][mask | (1 << j)]);
      }
    }
    cur[a[i]]++;
  }
  int mx = -inf;
  for (int i = 0; i <= n; i++) {
    mx = max(mx, dp[i][(1 << 8) - 1]);
  }
  return mx;
}
bool is[8];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    a[i]--;
    v[a[i]].push_back(i);
    if (!is[a[i]]) cnt++;
    is[a[i]] = 1;
  }
  int l = 0, r = n, ans = cnt;
  while (l <= r) {
    int mid = (l + r) / 2;
    int x = check(mid);
    if (x >= 0) {
      ans = max(ans, mid * (8 - x) + x * (mid + 1));
      l = mid + 1;
    } else
      r = mid - 1;
  }
  cout << ans;
  return 0;
}
