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 a[1010], nxt[1010][10][1010];
int cnt[10], n, dp[260][10], num;
inline bool check(int len) {
  num = 0;
  if (len * 8 > n) return false;
  for (int i = 0; i < 256; i++)
    for (int j = 0; j <= 8; j++) dp[i][j] = 0x3f3f3f3f;
  dp[0][0] = 1;
  for (int mask = 0; mask < 256; ++mask) {
    for (int num = 0; num <= 8; ++num) {
      if (dp[mask][num] > n) continue;
      for (int i = 1; i <= 8; ++i) {
        if (mask & (1 << (i - 1))) continue;
        dp[mask | (1 << (i - 1))][num] =
            min(dp[mask | (1 << (i - 1))][num], nxt[dp[mask][num]][i][len] + 1);
        dp[mask | (1 << (i - 1))][num + 1] =
            min(dp[mask | (1 << (i - 1))][num + 1],
                nxt[dp[mask][num]][i][len + 1] + 1);
      }
    }
  }
  for (int i = 8; i >= 0; --i)
    if (dp[255][i] <= n + 1) {
      num = i;
      return true;
    }
  return false;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= 8; j++)
      for (int k = 1; k <= n; k++) nxt[i][j][k] = 0x3f3f3f3f;
  for (int i = 1; i <= n; ++i) {
    memset(cnt, 0, sizeof(cnt));
    for (int j = i; j <= n; ++j) {
      cnt[a[j]]++;
      nxt[i][a[j]][cnt[a[j]]] = j;
    }
  }
  int L = 0, R = n, ans = 0;
  while (L <= R) {
    int mid = ((L + R) >> 1);
    if (check(mid)) {
      ans = mid * 8 + num;
      L = mid + 1;
    } else
      R = mid - 1;
  }
  printf("%d\n", ans);
}
