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 N = 1010;
struct state {
  bool qt[8];
  state() { memset(qt, 0, sizeof qt); }
};
int dp[N][2][2][2][2][2][2][2][2];
int v[N], pre[N];
vector<int> pos[8];
int n, k;
int go(int i, state cur) {
  if (i == n) {
    if (k == 0) return 0;
    bool ok = true;
    for (int j = 0; j < 8; j++) ok = ok && cur.qt[j];
    if (ok)
      return 0;
    else
      return -0x3f3f3f3f;
  }
  if (dp[i][cur.qt[0]][cur.qt[1]][cur.qt[2]][cur.qt[3]][cur.qt[4]][cur.qt[5]]
        [cur.qt[6]][cur.qt[7]] != -1) {
    return dp[i][cur.qt[0]][cur.qt[1]][cur.qt[2]][cur.qt[3]][cur.qt[4]]
             [cur.qt[5]][cur.qt[6]][cur.qt[7]];
  }
  if (cur.qt[v[i]])
    return dp[i][cur.qt[0]][cur.qt[1]][cur.qt[2]][cur.qt[3]][cur.qt[4]]
             [cur.qt[5]][cur.qt[6]][cur.qt[7]] = go(i + 1, cur);
  int ans = go(i + 1, cur);
  int left = pos[v[i]].size() - pre[i];
  if (left >= k && k > 0) {
    state nxt = cur;
    nxt.qt[v[i]] = true;
    ans = max(ans, k + go(pos[v[i]][pre[i] + k - 1] + 1, nxt));
  }
  if (left >= k + 1) {
    state nxt = cur;
    nxt.qt[v[i]] = true;
    ans = max(ans, k + 1 + go(pos[v[i]][pre[i] + k] + 1, nxt));
  }
  return dp[i][cur.qt[0]][cur.qt[1]][cur.qt[2]][cur.qt[3]][cur.qt[4]][cur.qt[5]]
           [cur.qt[6]][cur.qt[7]] = ans;
}
int main() {
  scanf("%d", &n);
  int s[8];
  memset(s, 0, sizeof s);
  for (int i = 0; i < n; i++) {
    scanf("%d", v + i);
    v[i]--;
    pos[v[i]].push_back(i);
    pre[i] = s[v[i]];
    s[v[i]]++;
  }
  int ans = 0;
  for (k = 0; 8 * k <= n; k++) {
    memset(dp, -1, sizeof dp);
    state init;
    ans = max(ans, go(0, init));
  }
  printf("%d\n", ans);
  return 0;
}
