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 = 1000 + 10;
const int INF = 0x3f3f3f3f;
int n, a[N], pre[N][N], pos[N][10];
int dp[N][1 << 8];
void Init() {
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= 8; ++j) pos[i][j] = pos[i - 1][j];
    pos[i][a[i]] = i;
  }
  for (int i = 1; i <= n; ++i) {
    pre[i][0] = i + 1;
    pre[i][1] = i;
    pre[i][2] = pos[i - 1][a[i]];
  }
  for (int i = 1; i <= n; ++i)
    for (int j = 3; j <= i; ++j) pre[i][j] = pre[pre[i][j - 1]][2];
}
int Count(int len) {
  for (int x = 0; x < 1 << 8; ++x) dp[0][x] = -INF;
  dp[0][0] = 0;
  for (int i = 1; i <= n; ++i)
    for (int x = 0; x < 1 << 8; ++x) {
      dp[i][x] = dp[i - 1][x];
      for (int k = 1; k <= 8; ++k)
        if (x >> (k - 1) & 1) {
          for (int t = len; t <= len + 1; ++t) {
            if (t == 0)
              dp[i][x] = max(dp[i][x], dp[i][x - (1 << (k - 1))]);
            else {
              int r = pos[i][k];
              int l = pre[r][t];
              if (l > 0)
                dp[i][x] =
                    max(dp[i][x], dp[l - 1][x - (1 << (k - 1))] + (t > len));
            }
          }
        }
    }
  return dp[n][(1 << 8) - 1];
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
  int l = 0, r = n / 8, f = 0;
  Init();
  while (l <= r) {
    int m = (l + r) >> 1;
    if (Count(m) >= 0) {
      f = m;
      l = m + 1;
    } else
      r = m - 1;
  }
  printf("%d", f * 8 + Count(f));
  return 0;
}
