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 INF = 1e9;
const int N = 8;
int n;
int total = (1 << N);
vector<vector<int> > dp;
vector<vector<int> > position(N);
vector<vector<int> > precalc;
int calcDP(int pos, int mask, int len) {
  if (pos == n) {
    return !mask ? 0 : -INF;
  }
  if (dp[pos][mask] != -1) {
    return dp[pos][mask];
  }
  dp[pos][mask] = !mask ? 0 : -INF;
  if (pos == n) {
    return dp[pos][mask];
  }
  for (int i = 0; i < N; i++) {
    if (mask & (1 << i)) {
      int idx = precalc[i][pos];
      if (idx + len < position[i].size()) {
        dp[pos][mask] =
            max(dp[pos][mask],
                1 + calcDP(position[i][idx + len] + 1, mask ^ (1 << i), len));
      }
      if (len) {
        if (idx + len - 1 < position[i].size()) {
          dp[pos][mask] =
              max(dp[pos][mask],
                  calcDP(position[i][idx + len - 1] + 1, mask ^ (1 << i), len));
        }
      } else {
        dp[pos][mask] = max(dp[pos][mask], calcDP(pos, mask ^ (1 << i), len));
      }
    }
  }
  return dp[pos][mask];
}
void solve() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    int item;
    cin >> item;
    item--;
    position[item].push_back(i);
  }
  precalc.resize(N, vector<int>(n));
  for (int i = 0; i < N; i++) {
    int ptr = 0;
    for (int j = 0; j < position[i].size(); j++) {
      while (ptr <= position[i][j]) {
        precalc[i][ptr] = j;
        ptr++;
      }
    }
    while (ptr < n) {
      precalc[i][ptr] = position[i].size();
      ptr++;
    }
  }
  int lf = -1;
  int rg = n / N + 1;
  while (rg - lf > 1) {
    int middle = (lf + rg) / 2;
    dp.clear();
    dp.resize(n, vector<int>(total, -1));
    if (calcDP(0, total - 1, middle) >= 0) {
      lf = middle;
    } else {
      rg = middle;
    }
  }
  dp.clear();
  dp.resize(n, vector<int>(total, -1));
  cout << lf * N + calcDP(0, total - 1, lf) << endl;
}
int main() {
  srand(time(NULL));
  solve();
  return 0;
}
