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, m, x, y, z, p, q, r;
int percards[10][2000];
vector<int> vec[10];
int ara[2000];
pair<int, int> dp[1002][260];
int cur;
pair<int, int> nxt[1002][260];
int vis[1002][260];
pair<int, int> possible(int pos, int mask) {
  if (pos > n) {
    if (mask == 255)
      return {1, 0};
    else
      return {0, 0};
  }
  if (vis[pos][mask]) return dp[pos][mask];
  vis[pos][mask] = 1;
  pair<int, int> re = {0, -1};
  int frnxt1 = -1, frnxt2 = -1;
  for (int j = 0; j >= -1; j--) {
    for (int i = 0; i < 8; i++) {
      if (mask & (1 << i)) continue;
      int tillnow = percards[i][pos - 1];
      int xxx = -1;
      int to = tillnow + cur + j;
      if (to >= vec[i].size()) continue;
      int topos = vec[i][to];
      topos = max(topos, pos);
      if (to == 0) topos = pos - 1;
      auto xx = possible(topos + 1, mask | (1 << i));
      xx.second += cur + j;
      if (xx.first && xx.second > re.second) {
        nxt[pos][mask] = {i, cur + j};
        re.first = 1;
        re.second = xx.second;
      }
    }
  }
  auto tmp = possible(pos + 1, mask);
  if (tmp.first && tmp.second > re.second) {
    re.first = 1;
    re.second = tmp.second;
    nxt[pos][mask] = {-1, -1};
  }
  return dp[pos][mask] = re;
}
int main() {
  for (int i = 0; i < 8; i++) vec[i].push_back(0);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &ara[i]);
    percards[ara[i] - 1][i]++;
    vec[ara[i] - 1].push_back(i);
    for (int j = 0; j < 8; j++) percards[j][i] += percards[j][i - 1];
  }
  int low = 1, high = n;
  cur = 2;
  int an = -1, ans = -1;
  while (low <= high) {
    int mid = (low + high) / 2;
    cur = mid;
    memset(vis, 0, sizeof(vis));
    auto val = possible(1, 0);
    if (val.first) {
      an = mid;
      low = mid + 1;
      ans = val.second;
    } else
      high = mid - 1;
  }
  cout << ans << endl;
  return 0;
}
