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 dp[10][310];
int nex[1010][10][1010];
int ai[1010];
int up;
void init(void) {
  memset(dp, -1, sizeof(dp));
  int i, j;
  int cnt[10];
  for (i = 1; i <= n; i++) {
    memset(cnt, 0, sizeof(cnt));
    for (j = 1; j <= 8; j++)
      for (int k = 1; k <= n; k++) nex[i][j][k] = 1e9;
    for (j = i; j <= n; j++) {
      cnt[ai[j]]++;
      nex[i][ai[j]][cnt[ai[j]]] = j;
    }
  }
}
int main() {
  int i, j, k;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> ai[i];
  }
  init();
  up = (1 << 8) - 1;
  int ans = 0;
  for (int num = 0; num * 8 <= n; num++) {
    for (int i = 0; i < 256; i++)
      for (int k = 0; k <= 8; k++) dp[k][i] = 1e9;
    dp[0][0] = 1;
    for (i = 0; i <= up; i++) {
      for (j = 0; j <= 8; j++) {
        for (k = 1; k <= 8; k++) {
          if (i & (1 << (k - 1))) continue;
          if (dp[j][i] > n) continue;
          dp[j][i ^ (1 << (k - 1))] =
              min(dp[j][i ^ (1 << (k - 1))], nex[dp[j][i]][k][num] + 1);
          dp[j + 1][i ^ (1 << (k - 1))] =
              min(dp[j + 1][i ^ (1 << (k - 1))], nex[dp[j][i]][k][num + 1] + 1);
        }
      }
    }
    for (i = 0; i <= 8; i++)
      if (dp[i][up] <= n + 1) {
        ans = max(ans, num * 8 + i);
      }
  }
  cout << ans;
  return 0;
}
