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, a[1005];
vector<int> v[10];
int Map[1005];
int dp[1001][257];
int Set(int n, int pos) { return n | (1 << pos); }
bool Check(int n, int pos) { return (bool)(n & (1 << pos)); }
int solve(int i, int mask, int take) {
  if (i > n) {
    if (take == 0)
      return 0;
    else if (mask == 255)
      return 0;
    else
      return INT_MIN;
  }
  if (dp[i][mask] != -1) return dp[i][mask];
  dp[i][mask] = solve(i + 1, mask, take);
  int d = a[i];
  if (Check(mask, d)) return dp[i][mask];
  int pos = Map[i];
  if (take > 0 && v[d].size() > pos + take - 1) {
    dp[i][mask] = max(dp[i][mask], take + solve(v[d][pos + take - 1] + 1,
                                                Set(mask, d), take));
  }
  if (v[d].size() > pos + take) {
    dp[i][mask] =
        max(dp[i][mask],
            take + 1 + solve(v[d][pos + take] + 1, Set(mask, d), take));
  }
  return dp[i][mask];
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    a[i]--;
    v[a[i]].push_back(i);
  }
  for (int i = 0; i < 8; i++) {
    for (int j = 0; j < v[i].size(); j++) {
      Map[v[i][j]] = j;
    }
  }
  int mx = 0;
  for (int i = 0; i <= (n / 8); i++) {
    memset(dp, -1, sizeof dp);
    mx = max(mx, solve(1, 0, i));
  }
  printf("%d\n", mx);
}
