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>
const int N = 1010, M = 256;
int n, a[N], dp[N][M], pos[N][M][8];
void getData() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &a[i]);
    a[i]--;
  }
}
void prepare() {
  for (int i = 0; i < 8; ++i) {
    for (int j = n; j >= 1; --j) {
      for (int k = 1; k < M; ++k) {
        if (i == a[j]) {
          if (k == 1)
            pos[j][k][i] = j;
          else if (j == n)
            pos[j][k][i] = -1;
          else
            pos[j][k][i] = pos[j + 1][k - 1][i];
        } else {
          if (j == n)
            pos[j][k][i] = -1;
          else
            pos[j][k][i] = pos[j + 1][k][i];
        }
      }
    }
  }
}
void checkMax(int &a, int b) {
  if (a == -1 || a < b) a = b;
}
int check(int x) {
  memset(dp, -1, sizeof(dp));
  dp[0][0] = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < M; ++j) {
      if (dp[i][j] == -1) continue;
      checkMax(dp[i + 1][j], dp[i][j]);
      for (int k = 0; k < 8; ++k) {
        if (((j >> k) & 1) != 0) continue;
        if (pos[i + 1][x][k] != -1)
          checkMax(dp[pos[i + 1][x][k]][j | (1 << k)], dp[i][j] + x);
        if (pos[i + 1][x - 1][k] != -1)
          checkMax(dp[pos[i + 1][x - 1][k]][j | (1 << k)], dp[i][j] + x - 1);
      }
    }
  }
  return dp[n][M - 1];
}
void solve() {
  int lo, hi, mid, ans = 0, mask = 0;
  for (int i = 1; i <= n; ++i) mask |= (1 << a[i]);
  for (int i = 0; i < 8; ++i)
    if ((mask >> i) & 1) ans++;
  lo = 2;
  hi = 125;
  while (lo <= hi) {
    mid = (lo + hi) >> 1;
    int temp = check(mid);
    ;
    if (temp == -1)
      hi = mid - 1;
    else {
      ans = std::max(ans, temp);
      lo = mid + 1;
    }
  }
  printf("%d\n", ans);
}
int main() {
  getData();
  prepare();
  solve();
  return 0;
}
