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, a[1001], dp[1011][1 << 8];
int cnt[8][1011];
int check(int len) {
  for (int i = 0; i <= n; i++) {
    for (int j = 0; j < (1 << 8); j++) {
      dp[i][j] = -100000000;
    }
  }
  dp[0][0] = 0;
  for (int i = 0; i < n; i++) {
    int x = a[i + 1];
    int l = i + 1, r = n, ind1 = n + 1, ind2 = n + 1;
    while (l <= r) {
      int mid = (l + r) >> 1;
      if (cnt[x][mid] - cnt[x][i] >= len - 1) {
        ind1 = mid;
        r = mid - 1;
      } else
        l = mid + 1;
    }
    assert(ind1 > 0);
    l = i + 1, r = n;
    while (l <= r) {
      int mid = (l + r) >> 1;
      if (cnt[x][mid] - cnt[x][i] >= len) {
        ind2 = mid;
        r = mid - 1;
      } else
        l = mid + 1;
    }
    assert(ind2 > 0);
    for (int j = 0; j < 1 << 8; j++) dp[i + 1][j] = max(dp[i + 1][j], dp[i][j]);
    for (int j = 0; j < (1 << 8); j++) {
      if (j >> x & 1) continue;
      dp[ind1][j ^ (1 << x)] = max(dp[ind1][j ^ (1 << x)], dp[i][j] + len - 1);
      dp[ind2][j ^ (1 << x)] = max(dp[ind2][j ^ (1 << x)], dp[i][j] + len);
    }
  }
  return dp[n][255];
}
int main() {
  cin.tie(0);
  cout.tie(0);
  ios_base::sync_with_stdio(false);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    a[i]--;
    for (int j = 0; j < 8; j++) cnt[j][i] = cnt[j][i - 1];
    cnt[a[i]][i]++;
  }
  int z = 0;
  for (int i = 0; i < 8; i++) z += cnt[i][n] == 0;
  if (z) {
    cout << 8 - z << '\n';
    return 0;
  }
  int ans = 0;
  int l = 1, r = 125;
  while (l <= r) {
    int mid = (l + r) >> 1;
    int t = check(mid);
    if (t > 0) {
      ans = t;
      l = mid + 1;
    } else
      r = mid - 1;
  }
  cout << ans << '\n';
}
