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;
int n;
int nxt[maxn][maxn];
int a[maxn];
bool dp[maxn][1 << 8][8];
bool can(int k) {
  for (int i = 0; i < maxn; i++) {
    for (int j = 0; j < (1 << 8); j++) {
      for (int t = 0; t < 8; t++) {
        dp[i][j][t] = false;
      }
    }
  }
  dp[1][0][0] = true;
  for (int i = 1; i <= n; i++) {
    for (int m = 0; m < (1 << 8); m++) {
      for (int t = 0; t < 8; t++) {
        if (!dp[i][m][t]) continue;
        dp[i + 1][m][t] = true;
        if (m & (1 << a[i])) continue;
        if (nxt[i][k / 8] != -1) dp[nxt[i][k / 8]][m | (1 << a[i])][t] = true;
        if (t < 7 && nxt[i][k / 8 + 1] != -1)
          dp[nxt[i][k / 8 + 1]][m | (1 << a[i])][t + 1] = true;
      }
    }
  }
  return dp[n][(1 << 8) - 1][k % 8];
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", a + i);
    a[i]--;
  }
  for (int i = n; i >= 1; i--) {
    nxt[i][1] = i;
    nxt[i][2] = -1;
    for (int j = n; j > i; j--) {
      if (a[j] == a[i]) nxt[i][2] = j;
    }
  }
  for (int i = n; i >= 1; i--) {
    for (int j = 3; j <= n; j++) {
      if (nxt[i][2] == -1) {
        nxt[i][j] = -1;
      } else {
        nxt[i][j] = nxt[nxt[i][2]][j - 1];
      }
    }
  }
  int ans = 0;
  for (int x = 0; x < 8; x++) {
    for (int i = 1; i <= n; i++) {
      if (a[i] == x) {
        ans++;
        break;
      }
    }
  }
  int low = 8, high = n;
  while (low <= high) {
    int mid = (low + high) / 2;
    if (can(mid)) {
      ans = mid;
      low = mid + 1;
    } else {
      high = mid - 1;
    }
  }
  printf("%d", ans);
}
