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, ara[1001];
bool flag[10];
int dp[1001][(1 << 8)];
int call(int id, int mask, int val, bool temp) {
  if (id >= n) return 0;
  if (mask == (1 << 8) - 1) {
    return 0;
  }
  if (dp[id][mask] != -1) return dp[id][mask];
  int res = 0;
  for (int i = 0; i < 8; i++) {
    if ((mask & (1 << i)) == 0) {
      int p = i + 1;
      int cnt = 0;
      for (int j = id; j < n; j++) {
        if (ara[j] == p) {
          cnt++;
        }
        if (cnt == val) {
          res = max(res, val + call(j + 1, (mask | (1 << i)), val, temp));
        } else if (cnt == val + 1 && temp) {
          res = max(res, 1 + val + call(j + 1, (mask | (1 << i)), val, temp));
        } else if (cnt > val + 1) {
          break;
        }
      }
    }
  }
  return dp[id][mask] = res;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &ara[i]);
    flag[ara[i]] = 1;
  }
  int low = 0, high = n;
  int ans = 0;
  int cnt = 0;
  for (int i = 1; i < 9; i++) {
    if (flag[i]) cnt++;
  }
  if (cnt == 1) {
    cout << "1" << endl;
    return 0;
  }
  bool flag = 0;
  int aa = 500;
  if (cnt < 8) aa = 1, flag = 1;
  for (int i = 1; i <= aa; i++) {
    memset(dp, -1, sizeof(dp));
    int x;
    if (flag)
      x = call(0, 0, i, 0);
    else
      x = call(0, 0, i, 1);
    if (x < ans) {
      break;
    } else {
      ans = x;
    }
  }
  cout << ans << endl;
  return 0;
}
