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 = 1010;
int n;
int dp[1011][260][10], a[N];
vector<int> v[10];
int rem = 0;
int ans = 0;
int getNxt(int cc, int cur, int step) {
  if (step == 0) return cc;
  ;
  if (lower_bound(v[cur].begin(), v[cur].end(), cc) == v[cur].end()) return -1;
  int curIdx = lower_bound(v[cur].begin(), v[cur].end(), cc) - v[cur].begin();
  if (curIdx + step - 1 >= v[cur].size()) return -1;
  return v[cur][curIdx + step - 1] + 1;
}
int calc(int idx, int msk, int cur) {
  if (idx == n) {
    int cnt = 0;
    int tmp = msk;
    while (tmp) {
      cnt += (tmp & 1);
      tmp /= 2;
    }
    return (cnt == 8) ? 0 : -1e9;
  }
  int &ret = dp[idx][msk][cur];
  if (ret != -1) return ret;
  ret = -1e9;
  for (int it = 0; it < 2; it++) {
    int newIdx = getNxt(idx, cur, rem - it);
    if (cur == 9) newIdx = 0;
    if (newIdx == -1) continue;
    int op = rem - it;
    ret = max(ret, op + calc(n, msk, cur));
    for (int nx = 7; nx >= 0; --nx) {
      if (!(msk & (1 << nx))) {
        ret =
            max(ret, (cur == 9 ? 0 : op) + calc(newIdx, (msk | (1 << nx)), nx));
      }
    }
  }
  return ret;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", &a[i]);
    a[i]--;
    v[a[i]].push_back(i);
  }
  int lo = 1, hi = 126;
  for (rem = 1; rem <= 125; rem++) {
    memset(dp, -1, sizeof dp);
    ans = max(ans, calc(0, 0, 9));
  }
  printf("%d\n", ans);
  return 0;
}
