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 = 1010;
int N;
int A[MAXN], nocc[8][MAXN], fst[8][MAXN];
int dp[MAXN][MAXN];
int go(int mxocc) {
  memset(dp, -2, sizeof(dp));
  memset(dp[0], 0, sizeof(dp[0]));
  for (int msk = 1; msk < 256; msk++) {
    for (int j = 1; j <= N; j++) {
      dp[msk][j] = dp[msk][j - 1];
      for (int i = 0; i < 8; i++) {
        if (!(msk & (1 << i))) {
          continue;
        }
        int pocc = nocc[i][j];
        if (A[j] != i) {
          continue;
        }
        for (int c : {mxocc, mxocc - 1}) {
          if (pocc >= c) {
            int pj = fst[i][pocc - c + 1];
            assert(pj);
            dp[msk][j] = max(dp[msk][j], dp[msk ^ (1 << i)][pj - 1] + c);
          }
        }
      }
    }
  }
  return dp[255][N];
}
int main() {
  scanf("%d", &N);
  for (int i = 1; i <= N; i++) {
    scanf("%d", &A[i]);
    A[i]--;
    for (int j = 0; j < 8; j++) {
      nocc[j][i] = nocc[j][i - 1] + (A[i] == j);
      int &ref = fst[j][nocc[j][i]];
      if (ref == 0) {
        ref = i;
      }
    }
  }
  int ans = 0;
  for (int i = 0; i < 8; i++) {
    ans += bool(nocc[i][N]);
  }
  int lo = 1, hi = N + 1;
  while (hi - lo > 1) {
    int mid = (lo + hi) / 2;
    (go(mid) < 0 ? hi : lo) = mid;
  }
  if (lo > 1) {
    ans = max(ans, go(lo));
  }
  printf("%d\n", ans);
}
