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 liczba_kart;
int kolejne_karty[1000 + 1];
void wczytaj() {
  cin >> liczba_kart;
  for (int i = 0; i < liczba_kart; ++i) {
    cin >> kolejne_karty[i];
  }
}
map<int, int> dp[(1 << 8) + 1][500 + 1];
int indexy_wartosci[9][1000 + 1][500 + 1];
void oblicz_indexy_wartosci() {
  for (int i = 1; i <= 8; ++i) {
    for (int j = 0; j < liczba_kart; ++j) {
      for (int k = 0; k <= 500; ++k) {
        if (k == 0) {
          indexy_wartosci[i][j][k] = j - 1;
        } else {
          indexy_wartosci[i][j][k] = liczba_kart + 2;
        }
      }
    }
  }
  for (int i = 1; i <= 8; ++i) {
    for (int j = 0; j < liczba_kart; ++j) {
      int licznik = 0;
      for (int k = j; k < liczba_kart; ++k) {
        if (kolejne_karty[k] == i) licznik++;
        indexy_wartosci[i][j][licznik] = min(indexy_wartosci[i][j][licznik], k);
      }
    }
  }
}
void inicjalizuj() {
  for (int i = 0; i < (1 << 8); ++i) {
    for (int j = 0; j <= liczba_kart; ++j) {
      for (int k = 0; k <= liczba_kart + 1; ++k) {
        dp[i][j][k] = -1;
      }
    }
  }
}
void wypisz() { cout << indexy_wartosci[2][0][1] << endl; }
int DFS_wyn(int maska, int index, int min_dlugosc) {
  if (maska == (1 << 8) - 1) {
    if (index <= liczba_kart) return 0;
    return -100000000;
  }
  if (index == liczba_kart) {
    if (min_dlugosc == 0) return 0;
    return -100000000;
  }
  if (index > liczba_kart) return -100000000;
  if (dp[maska][min_dlugosc].find(index) != dp[maska][min_dlugosc].end())
    return dp[maska][min_dlugosc][index];
  int max_wyn = -100000000;
  for (int i = 0; i < 8; ++i) {
    if (!((1 << i) & maska)) {
      int kolejny_index_1 = indexy_wartosci[i + 1][index][min_dlugosc] + 1;
      max_wyn =
          max(max_wyn, DFS_wyn(maska | (1 << i), kolejny_index_1, min_dlugosc) +
                           min_dlugosc);
      int kolejny_index_2 = indexy_wartosci[i + 1][index][min_dlugosc + 1] + 1;
      max_wyn =
          max(max_wyn, DFS_wyn(maska | (1 << i), kolejny_index_2, min_dlugosc) +
                           min_dlugosc + 1);
    }
  }
  dp[maska][min_dlugosc][index] = max_wyn;
  return dp[maska][min_dlugosc][index];
}
int main() {
  ios_base::sync_with_stdio(false);
  wczytaj();
  oblicz_indexy_wartosci();
  int max_wyn = 0;
  for (int i = 0; i <= min(liczba_kart / 8 + 10, liczba_kart - 1); ++i) {
    max_wyn = max(max_wyn, DFS_wyn(0, 0, i));
  }
  cout << max_wyn << endl;
  return 0;
}
