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 cnt[9], pos[9][300];
int nextpos[9][2000];
int maxcnt;
int dp[1 << 8][2000];
int main() {
  memset(pos, 0xff, sizeof(pos));
  int n;
  int a[3000];
  bool presented[9];
  memset(presented, 0x00, sizeof(presented));
  int ans = -1;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    pos[a[i]][++cnt[a[i]]] = i;
    presented[a[i]] = true;
  }
  for (int i = 1; i <= 8; i++) {
    pos[i][0] = 0, pos[i][cnt[i] + 1] = n + 1;
    nextpos[i][0] = 1;
  }
  for (int i = 1; i <= 8; i++)
    for (int j = 0; j <= cnt[i]; j++)
      for (int k = pos[i][j] + 1; k <= pos[i][j + 1]; k++)
        nextpos[i][k] = j + 1;
  for (int i = 1; i <= 8; i++) {
    maxcnt = max(maxcnt, cnt[i]);
  }
  for (int contlen = 1; contlen * 8 <= n && contlen <= maxcnt; contlen++) {
    memset(dp, 0xFF, sizeof(dp));
    dp[0][0] = 0;
    for (int p = 0; p <= n; p++) {
      for (int state = 0; state < (1 << 8) - 1; state++) {
        if (dp[state][p] != -1) {
          for (int pro = 1; pro <= 8; pro++) {
            if (!(state & (1 << (pro - 1)))) {
              if (nextpos[pro][p] + contlen - 1 <= cnt[pro])
                dp[state | (1 << (pro - 1))]
                  [pos[pro][nextpos[pro][p] + contlen - 1]] =
                      max(dp[state][p] + contlen,
                          dp[state | (1 << (pro - 1))]
                            [pos[pro][nextpos[pro][p] + contlen - 1]]);
              if (nextpos[pro][p] + contlen <= cnt[pro])
                dp[state | (1 << (pro - 1))]
                  [pos[pro][nextpos[pro][p] + contlen]] =
                      max(dp[state | (1 << (pro - 1))]
                            [pos[pro][nextpos[pro][p] + contlen]],
                          dp[state][p] + contlen + 1);
            }
          }
        }
      }
      ans = max(ans, dp[(1 << 8) - 1][p]);
    }
  }
  if (ans == -1) {
    ans = 0;
    for (int i = 1; i <= 8; i++)
      if (presented[i]) ans++;
  }
  cout << ans;
  return 0;
}
