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 maxn = 1009;
const int maxv = 10;
const int maxf = 128;
const int maxb = 258;
int n;
int dp[maxn][maxf][maxb];
int v[maxn], sfreq[maxn][maxv];
int can(int val, int sl, int want) {
  int l = sl, r = n;
  int ans = 9999;
  while (l <= r) {
    int h = (l + r) / 2;
    int here = sfreq[h][val] - sfreq[sl - 1][val];
    if (here == want) ans = min(ans, h);
    if (here < want)
      l = h + 1;
    else
      r = h - 1;
  }
  return ans == 9999 ? -1 : ans;
}
int calc(int pos, int freq, int mask) {
  if (mask == 255) return 0;
  if (pos == n + 1) {
    if (freq == 1) return 0;
    return -9999;
  }
  int& ref = dp[pos][freq][mask];
  if (ref != -1) return ref;
  ref = calc(pos + 1, freq, mask);
  if ((mask & (1 << v[pos])) == 0) {
    int minpf1 = can(v[pos], pos, freq - 1);
    if (minpf1 != -1)
      ref = max(ref, (freq - 1) + calc(minpf1 + 1, freq, mask | (1 << v[pos])));
    int minpf = can(v[pos], pos, freq);
    if (minpf != -1)
      ref = max(ref, freq + calc(minpf + 1, freq, mask | (1 << v[pos])));
  }
  return ref;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> v[i];
    --v[i];
    ++sfreq[i][v[i]];
  }
  for (int i = 1; i <= n; ++i) {
    for (int j = 0; j < maxv; ++j) sfreq[i][j] += sfreq[i - 1][j];
  }
  memset(dp, 0xff, sizeof(dp));
  int ans = 0;
  for (int i = 0; i < maxf; ++i) ans = max(ans, calc(1, i, 0));
  cout << ans << endl;
}
