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;
char _;
const int maxN = 1000 + 5;
const int mod = 1000 * 1000 * 1000 + 7;
const int base = 701;
const int SQ = 500;
const int maxL = 20;
vector<int> a[10];
int dp[1 << 8];
int n;
bool check(int x) {
  dp[0] = 0;
  for (int mask = 1; mask < (1 << 8); mask++) {
    dp[mask] = mod;
    for (int i = 0; i < 8; i++)
      if (mask >> i & 1) {
        int st = dp[mask ^ (1 << i)];
        int ps = lower_bound(a[i].begin(), a[i].end(), st) - a[i].begin();
        if (ps + x - 1 >= a[i].size()) continue;
        dp[mask] = min(dp[mask], a[i][ps + x - 1]);
      }
  }
  return (dp[(1 << 8) - 1] <= n);
}
int go[maxN][1 << 8];
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    x--;
    a[x].push_back(i + 1);
  }
  int lo = 0, hi = 1000;
  while (hi - lo > 1) {
    int mid = (hi + lo) >> 1;
    if (check(mid))
      lo = mid;
    else
      hi = mid;
  }
  for (int i = 0; i < maxN; i++)
    for (int j = 0; j < (1 << 8); j++) go[i][j] = -mod;
  go[0][0] = 0;
  for (int i = 1; i <= n; i++) {
    go[i][0] = 0;
    for (int mask = 1; mask < (1 << 8); mask++) {
      go[i][mask] = go[i - 1][mask];
      for (int j = 0; j < 8; j++)
        if (mask >> j & 1) {
          if (lo == 0) go[i][mask] = max(go[i][mask], go[i][mask ^ (1 << j)]);
          int ps = upper_bound(a[j].begin(), a[j].end(), i) - a[j].begin();
          if (ps < lo) continue;
          if (ps - lo < a[j].size())
            go[i][mask] =
                max(go[i][mask], go[a[j][ps - lo] - 1][mask ^ (1 << j)] + lo);
          if (ps > lo && ps - lo - 1 < a[j].size())
            go[i][mask] =
                max(go[i][mask],
                    go[a[j][ps - lo - 1] - 1][mask ^ (1 << j)] + lo + 1);
        }
    }
  }
  cout << go[n][(1 << 8) - 1] << endl;
  return 0;
}
