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, i, j;
int v[1005];
int p[10][1005];
int cnt[10];
int id[1005];
int l, r, mid, ans;
int f[1005][256];
bool check(int u) {
  int ret = 0;
  memset(f, 0xC0, sizeof(f));
  f[0][0] = 0;
  for (i = 1; i <= n; i++)
    for (j = 0; j < 256; j++) {
      if (j & (1 << v[i] - 1)) {
        if (p[v[i]][id[i] - u + 1] > 0)
          if (f[p[v[i]][id[i] - u + 1] - 1][j ^ (1 << v[i] - 1)] + u > f[i][j])
            f[i][j] = f[p[v[i]][id[i] - u + 1] - 1][j ^ (1 << v[i] - 1)] + u;
        if (p[v[i]][id[i] - u] > 0)
          if (f[p[v[i]][id[i] - u] - 1][j ^ (1 << v[i] - 1)] + u + 1 > f[i][j])
            f[i][j] = f[p[v[i]][id[i] - u] - 1][j ^ (1 << v[i] - 1)] + u + 1;
        if (u != 0)
          if (j == 255 && f[i][j] > ret) ret = f[i][j];
        if (u == 0)
          if (f[i][j] > ret) ret = f[i][j];
      }
      if (f[i - 1][j] > f[i][j]) f[i][j] = f[i - 1][j];
    }
  if (ret > ans) ans = ret;
  return ret > 0;
}
int main() {
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    scanf("%d", &v[i]);
    cnt[v[i]]++;
    id[i] = cnt[v[i]];
    p[v[i]][id[i]] = i;
  }
  l = 0;
  r = n;
  while (l <= r) {
    mid = (l + r) >> 1;
    if (check(mid))
      l = mid + 1;
    else
      r = mid - 1;
  }
  printf("%d\n", ans);
  return 0;
}
