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;
const int ALL_SET = (1 << 8) - 1;
int dp[1005][(1 << 8)];
int arr[1004];
int solve(int ind, int mask, int c) {
  if (ind == n) {
    if (mask == ALL_SET || c == 1)
      return 0;
    else
      return -1e6;
  }
  if (dp[ind][mask] != -1) return dp[ind][mask];
  int ans = solve(ind + 1, mask, c);
  int x = (1 << (arr[ind] - 1));
  if ((x & mask) == 0) {
    int c2 = 0;
    for (int i = ind; i < n && c2 <= c; i++) {
      if (arr[i] == arr[ind]) {
        c2++;
        if (c2 == c - 1) {
          int mask1 = (mask | x);
          ans = max(ans, c2 + solve(i + 1, mask1, c));
        }
        if (c2 == c) {
          int mask1 = (mask | x);
          ans = max(ans, c + solve(i + 1, mask1, c));
        }
      }
    }
  }
  return dp[ind][mask] = ans;
}
int bin_search() {
  int l = 1, h = n / 8 + 2, mid;
  while (l < h) {
    mid = l + (h - l + 1) / 2;
    memset(dp, -1, sizeof(dp));
    int ans = solve(0, 0, mid);
    if (ans > 0)
      l = mid;
    else
      h = mid - 1;
  }
  memset(dp, -1, sizeof(dp));
  int ans = solve(0, 0, l);
  return ans;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d", &arr[i]);
  printf("%d\n", bin_search());
  return 0;
}
