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 maxN = 1e3 + 10;
int N, len, ans;
int A[maxN], B[10], P[50000][10], F[10][130], C[10];
vector<int> L;
bool found(int k, int x) {
  int cnt = 0, j = 1;
  for (int i = 1; i <= N && j <= 8; i++) {
    if (A[i] == P[k][j]) cnt++;
    if (cnt == x) j++, cnt = 0;
  }
  return j > 8;
}
bool check(int x) {
  bool flag = 0;
  if (L.empty()) {
    for (int i = 1; i <= 40320; i++)
      if (found(i, x)) L.push_back(i), flag = 1;
  } else {
    vector<int> R;
    for (int i = 0; i < L.size(); i++)
      if (found(L[i], x)) R.push_back(L[i]), flag = 1;
    if (flag) L = R;
  }
  return flag;
}
int solve(int x) {
  memset(F, 0, sizeof(F));
  int sum = 0;
  for (int i = 1; i <= N; i++) {
    int vt;
    for (int j = 1; j <= 8; j++)
      if (P[x][j] == A[i]) vt = j;
    for (int k = len + 1; k >= 1; k--) {
      if (k > 1)
        F[vt][k] = F[vt][k - 1] + 1;
      else
        F[vt][k] = max(F[vt - 1][len], F[vt - 1][len + 1]) + 1;
    }
  }
  return max(F[8][len], F[8][len + 1]);
}
int main() {
  cin >> N;
  for (int i = 1; i <= N; i++) cin >> A[i];
  for (int j = 1; j <= 8; j++) B[j] = j;
  for (int i = 1; i <= 40320; i++) {
    for (int j = 1; j <= 8; j++) P[i][j] = B[j];
    next_permutation(B + 1, B + 9);
  }
  int l = 1, r = N / 8;
  while (l <= r) {
    int mid = (l + r) / 2;
    if (check(mid))
      len = mid, l = mid + 1;
    else
      r = mid - 1;
  }
  if (L.empty()) {
    for (int i = 1; i <= N; i++) C[A[i]]++;
    for (int i = 1; i <= 8; i++) ans += (C[i] > 0);
    cout << ans;
  } else {
    for (int i = 0; i < L.size(); i++) {
      int per = L[i];
      ans = max(ans, solve(per));
    }
    cout << ans;
  }
}
