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 = 1024;
const int CNT = 10;
const int MASK = 1 << 9;
const int INF = (1e9) + 7;
int n, a[N];
int cnt;
int nxt[CNT][N][N];
int occ;
bool used[N][MASK];
int state[N][MASK];
int ans;
int recurse(int pos, int mask) {
  if (mask == (1 << 8) - 1) return 0;
  if (pos > n) return -INF;
  if (used[pos][mask]) return state[pos][mask];
  int ans = -INF;
  if (mask & (1 << (a[pos] - 1)))
    ans = recurse(pos + 1, mask);
  else {
    ans = max(ans, recurse(pos + 1, mask));
    if (nxt[a[pos]][pos][occ])
      ans = max(ans, occ + recurse(nxt[a[pos]][pos][occ] + 1,
                                   mask | (1 << (a[pos] - 1))));
    if (nxt[a[pos]][pos][occ + 1])
      ans = max(ans, occ + 1 +
                         recurse(nxt[a[pos]][pos][occ + 1] + 1,
                                 mask | (1 << (a[pos] - 1))));
  }
  used[pos][mask] = true;
  state[pos][mask] = ans;
  return ans;
}
int main() {
  int i, j, z, cnt;
  set<int> s;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  for (z = 1; z <= 8; z++) {
    for (i = 1; i <= n; i++) {
      cnt = 0;
      for (j = i; j <= n; j++) {
        if (a[j] == z) ++cnt, nxt[z][i][cnt] = j;
      }
    }
  }
  for (i = 1; i <= n; i++) s.insert(a[i]);
  ans = (int)(s.size());
  for (occ = 1; (occ - 2) * 8 <= n; ++occ) {
    memset(used, 0, sizeof(used));
    ans = max(ans, recurse(1, 0));
  }
  printf("%d\n", ans);
  return 0;
}
