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 MAX_N = 7 + 1000;
int ans = 0;
int dig[MAX_N];
int tag[10], tab[10];
int pos[10][MAX_N], num[10];
int sum[MAX_N][10];
bool pass(int mask, int mid) {
  int now = 0;
  for (int i = 0; i < 8; i++) tag[i + 1] = (mask >> i) & 1;
  for (int i = 1; i <= 8; i++) {
    int d = tab[i];
    int ned = mid + tag[i];
    if (!ned) continue;
    if (sum[now][d] + ned > num[d]) return false;
    now = pos[d][sum[now][d] + ned];
  }
  return true;
}
void work(int mask) {
  int ret = -1;
  for (int l = 0, r = 130, mid = (l + r) >> 1; l <= r; mid = (l + r) >> 1) {
    if (pass(mask, mid))
      l = (ret = mid) + 1;
    else
      r = mid - 1;
  }
  if (~ret) ans = max(ans, ret * 8 + __builtin_popcount(mask));
}
int main() {
  for (int i = 1; i <= 8; i++) tab[i] = i;
  memset(num, 0, sizeof(num));
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &dig[i]);
    pos[dig[i]][++num[dig[i]]] = i;
    for (int j = 1; j <= 8; j++) sum[i][j] = sum[i - 1][j];
    sum[i][dig[i]]++;
  }
  for (;;) {
    for (int i = 0, lim = (1 << 8); i < lim; i++) work(i);
    if (!next_permutation(tab + 1, tab + 1 + 8)) break;
  }
  printf("%d", ans);
}
