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 = 1010;
int a[maxn];
int n;
int cnt[maxn][10];
int f[maxn][1 << 8][2];
struct Segment {
  int l, r;
  Segment() {}
  Segment(int l, int r) : l(l), r(r) {}
} SM[maxn][1 << 8][2];
int Count(int j, int i) { return cnt[i][a[i]] - cnt[j - 1][a[i]]; }
bool fre[10];
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &a[i]);
    a[i]--;
    for (int j = 0; j < 8; ++j) cnt[i][j] = cnt[i - 1][j];
    cnt[i][a[i]]++;
  }
  memset(f, -1, sizeof f);
  for (int i = 1; i <= n; ++i) {
    f[i][1 << a[i]][0] = cnt[i][a[i]];
    SM[i][1 << a[i]][0].l = cnt[i][a[i]];
    SM[i][1 << a[i]][0].r = cnt[i][a[i]];
  }
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= i; ++j) {
      int C = Count(j, i);
      for (int mask = 0; mask < 1 << 8; ++mask)
        if ((mask >> a[i] & 1) == 0)
          for (int diff = 0; diff <= 1; ++diff)
            if (f[j - 1][mask][diff] != -1 &&
                abs(C - SM[j - 1][mask][diff].l) <= 1 &&
                abs(C - SM[j - 1][mask][diff].r) <= 1) {
              int NewDiff = max(diff, max(abs(C - SM[j - 1][mask][diff].l),
                                          abs(C - SM[j - 1][mask][diff].r)));
              if (f[j - 1][mask][diff] + C >
                  f[i][mask | (1 << a[i])][NewDiff]) {
                f[i][mask | (1 << a[i])][NewDiff] = f[j - 1][mask][diff] + C;
                SM[i][mask | (1 << a[i])][NewDiff].l =
                    min(SM[j - 1][mask][diff].l, C);
                SM[i][mask | (1 << a[i])][NewDiff].r =
                    max(SM[j - 1][mask][diff].r, C);
              }
            }
    }
  }
  int ans = 0;
  for (int i = 1; i <= n; ++i)
    for (int diff = 0; diff <= 1; ++diff)
      ans = max(ans, f[i][(1 << 8) - 1][diff]);
  int ASD = 0;
  for (int i = 1; i <= n; ++i)
    if (!fre[a[i]]) ++ASD, fre[a[i]] = 1;
  printf("%d", max(ans, ASD));
  return 0;
}
