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 MAX = 1001;
const long long MOD = (int)1e9 + 7;
const int INF = 1e9;
const long long LLINF = 0x3f3f3f3f3f3f3f3f;
const long double EPS = 1e-7;
int n, qt, t;
int prox[MAX][9][MAX];
int tab[MAX][MAX], tempo[MAX][MAX];
vector<int> v;
int dp(int i, int mask) {
  if (mask >= (1 << 8) - 1) return 0;
  if (i >= n) return -INF;
  if (tempo[i][mask] == t) return tab[i][mask];
  tempo[i][mask] = t;
  int res = -INF, val = v[i];
  if (((1 << val) & mask) == 0) {
    int p = prox[i][v[i]][qt];
    int p2 = prox[i][v[i]][qt + 1];
    if (p != -1) res = max(res, qt + dp(p + 1, mask | (1 << val)));
    if (p2 != -1) res = max(res, qt + 1 + dp(p2 + 1, mask | (1 << val)));
  }
  res = max(res, dp(i + 1, mask));
  return tab[i][mask] = res;
}
int32_t main() {
  memset(tab, -1, sizeof(tab));
  memset(prox, -1, sizeof(prox));
  cin >> n;
  v.assign(n, 0);
  vector<int> tmp(8, 0);
  int res = 0;
  for (int i = 0; i < (int)n; i++) {
    cin >> v[i];
    v[i]--;
    if (tmp[v[i]] == 0) {
      res++;
    }
    tmp[v[i]]++;
  }
  for (int val = 0; val <= 7; val++) {
    for (int i = 0; i < n; i++) {
      int qt = 0;
      prox[i][val][0] = i - 1;
      for (int j = i; j < n; j++) {
        if (v[j] == val) {
          qt++;
          prox[i][val][qt] = j;
        }
      }
    }
  }
  int menor = INF;
  for (int i = 0; i < (int)8; i++) {
    menor = min(menor, tmp[i]);
  }
  int l = 1, r = menor;
  t = 1;
  while (l <= r) {
    int mid = (l + r) / 2;
    qt = mid;
    int ret = dp(0, 0);
    if (ret >= 0) {
      l = mid + 1;
      res = max(res, ret);
    } else {
      r = mid - 1;
    }
    t++;
  }
  cout << res << '\n';
  return 0;
}
