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;
int s[1005];
int nxt[1005][8], jmp[1005][1005];
bool comb(int lower, int* perm, int curr, int left) {
  if (left == 0) {
    int pos = -1;
    for (int i = 0; i < 8; i++) {
      int cnt = lower + ((curr & (1 << i)) != 0);
      if (cnt > 0) {
        pos = nxt[pos + 1][perm[i]];
        if (pos == -1) {
          return false;
        }
        pos = jmp[pos][cnt - 1];
        if (pos == -1) {
          return false;
        }
      }
    }
    return true;
  } else {
    for (int nb = (curr & -curr) >> 1; nb >= 1 << (left - 1); nb >>= 1) {
      if (comb(lower, perm, curr | nb, left - 1)) {
        return true;
      }
    }
    return false;
  }
}
bool can(int length) {
  int lower = length / 8, gcnt = length % 8;
  int perm[8] = {0, 1, 2, 3, 4, 5, 6, 7};
  do {
    if (comb(lower, perm, 1 << 8, gcnt)) {
      return true;
    }
  } while (next_permutation(perm, perm + 8));
  return false;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> s[i];
    s[i]--;
  }
  for (int i = 0; i < 8; i++) {
    nxt[n][i] = -1;
  }
  for (int i = n - 1; i >= 0; i--) {
    for (int j = 0; j < 8; j++) {
      nxt[i][j] = nxt[i + 1][j];
    }
    nxt[i][s[i]] = i;
  }
  for (int i = 0; i < n; i++) {
    jmp[i][0] = i;
    for (int j = 1; j < n; j++) {
      jmp[i][j] = jmp[i][j - 1] == -1 ? -1 : nxt[jmp[i][j - 1] + 1][s[i]];
    }
  }
  int l = 1, r = n;
  while (l < r) {
    int mid = (l + r + 1) / 2;
    if (can(mid)) {
      l = mid;
    } else {
      r = mid - 1;
    }
  }
  cout << l << '\n';
}
