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;
int n, in[1005];
short int save[1001][256][125][2];
bool vis[1005][256][126][3];
vector<int> vc[10];
short int rec(int pos, int mask, int len, int f) {
  if (mask == (1 << 8) - 1) return 0;
  short int &ret = save[pos][mask][len][f];
  if (vis[pos][mask][len][f]) return ret;
  vis[pos][mask][len][f] = 1;
  ret = -1000;
  short int i, j, fu;
  if (mask == 0) {
    for (i = 1; i <= 8; i++) {
      for (j = 0; j < vc[i].size(); j++) {
        fu = j + 1 + rec(vc[i][j], 1 << (i - 1), j + 1, 0);
        if (fu > ret) ret = fu;
        fu = j + 1 + rec(vc[i][j], 1 << (i - 1), j + 1, 1);
        if (fu > ret) ret = fu;
        fu = j + 1 + rec(vc[i][j], 1 << (i - 1), j + 1, 2);
        if (fu > ret) ret = fu;
      }
    }
  } else {
    for (i = 1; i <= 8; i++) {
      if (mask & (1 << (i - 1))) continue;
      int p = upper_bound(vc[i].begin(), vc[i].end(), pos) - vc[i].begin();
      int sz = vc[i].size();
      if (f == 0) {
        if (sz - p >= len) {
          fu = len + rec(vc[i][p + len - 1], mask | (1 << (i - 1)), len, f);
          if (fu > ret) ret = fu;
        }
      } else if (f == 1) {
        if (sz - p == 0 && len == 1) {
          fu = rec(pos, mask | (1 << (i - 1)), len, f);
          if (fu > ret) ret = fu;
        }
        if (sz - p >= len) {
          fu = len + rec(vc[i][p + len - 1], mask | (1 << (i - 1)), len, f);
          if (fu > ret) ret = fu;
        }
        if (sz - p >= len - 1 && len > 1) {
          fu = len - 1 + rec(vc[i][p + len - 2], mask | (1 << (i - 1)), len, f);
          if (fu > ret) ret = fu;
        }
      } else {
        if (sz - p >= len) {
          fu = len + rec(vc[i][p + len - 1], mask | (1 << (i - 1)), len, f);
          if (fu > ret) ret = fu;
        }
        if (sz - p >= len + 1) {
          fu = len + 1 + rec(vc[i][p + len], mask | (1 << (i - 1)), len, f);
          if (fu > ret) ret = fu;
        }
      }
    }
  }
  return ret;
}
int main() {
  int i;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> in[i];
    vc[in[i]].push_back(i);
  }
  cout << rec(1, 0, 0, 0) << endl;
}
