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, ans = 0;
int a[1000 + 10], pre[9][1000 + 10], kr[9][1000 + 10], cnt[10];
int f[1000 + 10][1 << 8];
int g[9] = {0, 1, 2, 4, 8, 16, 32, 64, 128};
int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
  return x * f;
}
int find(int t, int p) {
  int l = 1, r = n, tmp;
  while (l <= r) {
    int mid = l + r >> 1;
    pre[t][mid] > p || pre[t][mid] == 0 ? r = mid - 1
                                        : (l = mid + 1, tmp = mid);
  }
  return tmp;
}
bool check(int st) {
  memset(f, -1, sizeof(f));
  int tmp = -1;
  for (int i = 1; i <= n; i++) {
    f[i][0] = 0;
    for (int j = 0; j < (1 << 8); j++) {
      if (j != (1 << 8) - 1) {
        for (int k = 1; k <= 8; k++)
          if (!(j & g[k]) && f[i][j] != -1) {
            int p = pre[k][i - (a[i] == k)];
            if (st == 0) tmp = max(tmp, f[i][j]);
            if (kr[k][p + st] != 0)
              f[kr[k][p + st]][j | g[k]] =
                  max(f[kr[k][p + st]][j | g[k]], f[i][j] + st);
            if (kr[k][p + st + 1] != 0)
              f[kr[k][p + st + 1]][j | g[k]] =
                  max(f[kr[k][p + st + 1]][j | g[k]], f[i][j] + st + 1);
          }
      } else if (f[i][j] != -1)
        tmp = max(tmp, f[i][j]);
    }
  }
  if (tmp != -1) {
    ans = max(ans, tmp);
    return true;
  } else
    return false;
}
int main() {
  n = read();
  for (int i = 1; i <= n; i++) {
    a[i] = read();
    for (int j = 1; j <= 8; j++) pre[j][i] = pre[j][i - 1] + (a[i] == j);
    kr[a[i]][++cnt[a[i]]] = i;
  }
  int l = 0, r = n;
  while (l <= r) {
    int mid = l + r >> 1;
    check(mid) ? l = mid + 1 : r = mid - 1;
  }
  printf("%d", ans);
  return 0;
}
