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 K = 8, MN = 1005, MM = (1 << 8), INF = 1000 * 1000 * 1000 + 5;
int t[MN];
int dp[MN][MM];
int skok[MN][MN][K];
int ile[K + 3];
int res, n;
void czysc() {
  for (int i = 0; i <= n; ++i)
    for (int j = 0; j < MM; ++j) dp[i][j] = 0;
}
int licz(int currL) {
  czysc();
  for (int i = 0; i <= n; ++i) {
    for (int j = 0; j < MM; ++j) {
      if (!j || dp[i][j]) {
        for (int l = 0; l < K; ++l) {
          if (!(j & (1 << l))) {
            if (skok[i][currL][l] != INF)
              dp[skok[i][currL][l]][(j | (1 << l))] =
                  max(dp[skok[i][currL][l]][(j | (1 << l))], dp[i][j] + currL);
            if (skok[i][currL + 1][l] != INF)
              dp[skok[i][currL + 1][l]][(j | (1 << l))] =
                  max(dp[skok[i][currL + 1][l]][(j | (1 << l))],
                      dp[i][j] + currL + 1);
          }
        }
      }
    }
  }
  int cbest = 0;
  for (int i = 1; i <= n; ++i) cbest = max(cbest, dp[i][MM - 1]);
  res = max(res, cbest);
  return cbest;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", &t[i]);
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= n; ++j)
      for (int l = 0; l < K; ++l) skok[i][j][l] = INF;
    for (int j = 1; j <= K; ++j) {
      ile[j] = 0;
      skok[i][0][j - 1] = i;
    }
    for (int j = i; j <= n; ++j) skok[i][++ile[t[j]]][t[j] - 1] = j;
  }
  int zd = 0, zg = n;
  while (zd < zg) {
    int mid = (zd + zg) >> 1;
    if (licz(mid))
      zd = mid;
    else
      zg = mid;
    if (zd + 1 == zg) {
      licz(zd);
      licz(zg);
      break;
    }
  }
  printf("%d", res);
}
