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 nMax = 1004;
const int maxVal = 9;
const int maxConf = 1 << 8;
int a[nMax], n;
int freq[maxVal];
int Next[maxVal][nMax][nMax];
int dp[nMax][maxConf];
int Solve(const int maxLength) {
  int ans = 0;
  for (int i = 0; i <= n; ++i)
    for (int j = 0; j < maxConf; ++j) dp[i][j] = -(1 << 29);
  dp[0][0] = 0;
  for (int i = 0; i <= n; ++i) {
    for (int val = 1; val <= 8; ++val) {
      for (int length = maxLength - 1; length <= maxLength; ++length) {
        int pos = Next[val][i + 1][length];
        if (pos != 0) {
          for (int j = 0; j < maxConf; ++j) {
            if (((1 << (val - 1)) & j) != 0) continue;
            dp[pos][j | (1 << (val - 1))] =
                max(dp[pos][j | (1 << (val - 1))], dp[i][j] + length);
          }
        }
      }
    }
    ans = max(ans, dp[i][maxConf - 1]);
  }
  return ans;
}
int main() {
  int sol = 0;
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    if (freq[a[i]] == 0) sol++;
    freq[a[i]] = 1;
  }
  for (int val = 1; val <= 8; ++val) {
    for (int i = 1; i <= n; ++i) {
      int steps = 0;
      for (int j = i; j <= n; ++j) {
        if (a[j] == val) {
          steps++;
          Next[val][i][steps] = j;
        }
      }
    }
  }
  for (int i = 2; i <= n; ++i) {
    sol = max(sol, Solve(i));
  }
  cout << sol;
  return 0;
}
