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 mod = 1e9 + 7;
const int N = 5e5 + 10;
int n, arr[1001], sum[10];
vector<int> indx[10];
int dp[1001][270], dp2[1001][270];
int ans;
int ok(int pos, int mask, int mid) {
  if (mask == (1 << 8) - 1) return 1;
  if (pos >= n) return 0;
  int &ret = dp[pos][mask];
  if (ret != -1) return ret;
  ret = 0;
  for (int i = 1; i <= 8; i++) {
    if (mask & (1 << (i - 1))) continue;
    int x = lower_bound(indx[i].begin(), indx[i].end(), pos) - indx[i].begin();
    if (x + mid < indx[i].size()) {
      ret = ret | ok(indx[i][x + mid] + 1, mask | (1 << (i - 1)), mid);
    }
    if (x + mid - 1 < indx[i].size()) {
      ret = ret | ok(indx[i][x + mid - 1] + 1, mask | (1 << (i - 1)), mid);
    }
  }
  return ret;
}
int giveres(int pos, int mask, int mid) {
  if (mask == (1 << 8) - 1) return 0;
  if (pos >= n) return -1e9;
  int &ret = dp2[pos][mask];
  if (ret != -1) return ret;
  ret = 0;
  for (int i = 1; i <= 8; i++) {
    if (mask & (1 << (i - 1))) continue;
    int x = lower_bound(indx[i].begin(), indx[i].end(), pos) - indx[i].begin();
    if (x + mid < indx[i].size()) {
      if (ok(indx[i][x + mid] + 1, mask | (1 << (i - 1)), mid)) {
        ret =
            max(ret, giveres(indx[i][x + mid] + 1, mask | (1 << (i - 1)), mid) +
                         mid + 1);
      }
    }
    if (x + mid - 1 < indx[i].size()) {
      if (ok(indx[i][x + mid - 1] + 1, mask | (1 << (i - 1)), mid)) {
        ret = max(ret, mid + giveres(indx[i][x + mid - 1] + 1,
                                     mask | (1 << (i - 1)), mid));
      }
    }
  }
  return ret;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    sum[arr[i]]++;
    indx[arr[i]].push_back(i);
  }
  int low = 1, high = n, mid;
  while (low < high) {
    mid = (low + high + 1) / 2;
    memset(dp, -1, sizeof(dp));
    if (ok(0, 0, mid)) {
      low = mid;
    } else
      high = mid - 1;
  }
  memset(dp, -1, sizeof(dp));
  if (ok(0, 0, low)) {
    memset(dp2, -1, sizeof(dp2));
    cout << giveres(0, 0, low) << "\n";
  } else {
    for (int i = 1; i <= 8; i++) {
      if (indx[i].size() > 0) ans++;
    }
    cout << ans << "\n";
  }
  return 0;
}
