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 n;
int a[1005];
int nex[1005][10][150];
int dp[1 << 10][10];
int main() {
  while (~scanf("%d", &n)) {
    for (int i = 1; i <= n; i++) {
      scanf("%d", &a[i]);
    }
    for (int i = 0; i <= 1000; i++) {
      for (int j = 0; j < 10; j++) {
        for (int k = 0; k < 150; k++) {
          nex[i][j][k] = 1e9;
        }
      }
    }
    for (int i = 0; i < (1 << 10); i++) {
      for (int j = 0; j < 10; j++) {
        dp[i][j] = 1e9;
      }
    }
    for (int i = 0; i <= n; i++) {
      for (int j = 1; j <= 8; j++) {
        int cnt = 0;
        nex[i][j][0] = i;
        for (int k = i + 1; k <= n; k++) {
          if (a[k] == j) {
            cnt++;
            nex[i][j][cnt] = k;
          }
        }
      }
    }
    int len = (1 << 8);
    int ans = 0;
    dp[0][0] = 0;
    for (int num = 0; num * 8 <= n; num++) {
      for (int i = 0; i < len; i++)
        for (int j = 0; j <= 8; j++) dp[i][j] = 1e9;
      dp[0][0] = 0;
      for (int i = 0; i < len; i++) {
        for (int j = 0; j <= 8; j++) {
          if (dp[i][j] == 1e9) continue;
          for (int k = 1; k <= 8; k++) {
            int id = (1 << (k - 1));
            if ((i & id) == 0) {
              dp[i | id][j] = min(dp[i | id][j], nex[dp[i][j]][k][num]);
              dp[i | id][j + 1] =
                  min(dp[i | id][j + 1], nex[dp[i][j]][k][num + 1]);
            }
          }
        }
      }
      for (int i = 0; i <= 8; i++) {
        if (dp[len - 1][i] <= n) ans = max(ans, 8 * num + i);
      }
    }
    printf("%d\n", ans);
  }
}
