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 M[1003][1 << 8], n;
int V[1003], PX[8][1003], L[8];
int bs(int val, int card) {
  int lo = 0, hi = L[card], mid;
  while (hi - lo > 1) {
    mid = (lo + hi) >> 1;
    if (PX[card][mid] > val)
      hi = mid;
    else
      lo = mid;
  }
  return lo;
}
int dp(int cnt, int px, int mask) {
  int &dx = M[px][mask];
  if (dx != -1) return dx;
  if (px == n) {
    if (mask == 0 || cnt == 1) return 0;
    return -(1 << 30);
  }
  dx = dp(cnt, px + 1, mask);
  int c = V[px];
  if (((1 << c) & mask) > 0) {
    int ipx = bs(px, c);
    if (ipx + cnt <= L[c]) {
      dx = max(dx, cnt + dp(cnt, PX[c][ipx + cnt - 1] + 1, mask ^ (1 << c)));
    }
    if (cnt > 1 && ipx + cnt - 1 <= L[c]) {
      dx =
          max(dx, cnt - 1 + dp(cnt, PX[c][ipx + cnt - 2] + 1, mask ^ (1 << c)));
    }
  }
  return dx;
}
int main(int nargs, char **args) {
  cin >> n;
  for (int i = 0, x; i < n; i++) {
    cin >> x;
    x--;
    V[i] = x;
    PX[x][L[x]++] = i;
  }
  int lo = 1, hi = n / 8 + 2, mid;
  while (hi - lo > 1) {
    mid = (hi + lo) / 2;
    memset(M, -1, sizeof M);
    if (dp(mid, 0, 255) <= 0) {
      hi = mid;
    } else {
      lo = mid;
    }
  }
  memset(M, -1, sizeof M);
  cout << dp(lo, 0, 255) << endl;
  return 0;
}
