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 maxn = 1e3 + 10;
const int INF = 0x3f3f3f3f;
int n, a[maxn];
vector<int> vec[8];
unordered_map<int, int> M;
int freq;
int dp[maxn][1 << 8];
int func(int i, int mask) {
  if (dp[i][mask] == -1) {
    if (i > n) {
      if (!freq) return dp[i][mask] = 0;
      if (mask) return dp[i][mask] = -INF;
      return dp[i][mask] = 0;
    }
    dp[i][mask] = func(i + 1, mask);
    if ((1 << a[i]) & mask) {
      int x = M[i];
      int y = x + freq - 1;
      if (y >= x && y < vec[a[i]].size())
        dp[i][mask] =
            max(dp[i][mask], freq + func(vec[a[i]][y] + 1, mask - (1 << a[i])));
      y = x + freq;
      if (y >= x && y < vec[a[i]].size())
        dp[i][mask] = max(
            dp[i][mask], freq + 1 + func(vec[a[i]][y] + 1, mask - (1 << a[i])));
    }
  }
  return dp[i][mask];
}
int solve() {
  int ans = 0;
  for (int f = 0; f <= n; ++f) {
    memset(dp, -1, sizeof(dp));
    freq = f;
    int len = func(1, (1 << 8) - 1);
    if (len == -INF) break;
    ans = max(ans, len);
  }
  return ans;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &a[i]);
    --a[i];
    vec[a[i]].push_back(i);
    M[i] = vec[a[i]].size() - 1;
  }
  printf("%d\n", solve());
  return 0;
}
