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;
int main() {
  int n;
  cin >> n;
  int a[n];
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    a[i]--;
  }
  int len = (n + 7) / 8 + 1;
  int ind[n][len];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < len; j++) {
      ind[i][j] = -1;
    }
  }
  int last[n][8];
  for (int i = 0; i < 8; i++) {
    last[0][i] = -1;
  }
  for (int i = 0; i < n; i++) {
    ind[i][0] = ind[i][1] = i;
    if (i) {
      for (int j = 0; j < 8; j++) {
        last[i][j] = last[i - 1][j];
      }
      if (last[i][a[i]] != -1) {
        for (int j = 2; j < len; j++) {
          ind[i][j] = ind[last[i][a[i]]][j - 1];
        }
      }
    }
    last[i][a[i]] = i;
  }
  int ans = -1;
  for (int i = 1; i < len; i++) {
    int dp[n][(1 << 8)];
    for (int j = 0; j < n; j++) {
      dp[j][0] = 0;
      for (int mask = 1; mask < (1 << 8); mask++) {
        if (i - 1) {
          dp[j][mask] = -n;
        } else {
          dp[j][mask] = 0;
        }
      }
    }
    for (int j = 0; j < n; j++) {
      for (int mask = 0; mask < (1 << 8); mask++) {
        if (mask & (1 << a[j])) continue;
        for (int k = 0; k < 8; k++) {
          if (((mask & (1 << k)) || (mask == 0)) && ind[j][i - 1] != -1) {
            if (last[ind[j][i - 1]][k] != -1) {
              dp[j][(mask | (1 << a[j]))] =
                  max(dp[j][(mask | (1 << a[j]))],
                      dp[last[ind[j][i - 1]][k]][mask] + i - 1);
            } else if (i == 1) {
              dp[j][(mask | (1 << a[j]))] =
                  max(dp[j][(mask | (1 << a[j]))], i - 1);
            }
          }
        }
      }
      for (int mask = 0; mask < (1 << 8); mask++) {
        if (mask & (1 << a[j])) continue;
        for (int k = 0; k < 8; k++) {
          if (((mask & (1 << k)) || (mask == 0)) && ind[j][i] != -1) {
            if (last[ind[j][i]][k] != -1) {
              dp[j][(mask | (1 << a[j]))] =
                  max(dp[j][(mask | (1 << a[j]))],
                      dp[last[ind[j][i]][k]][mask] + i);
            } else if (i == 1) {
              dp[j][(mask | (1 << a[j]))] = max(dp[j][(mask | (1 << a[j]))], i);
            }
          }
        }
      }
    }
    for (int j = 0; j < n; j++) {
      ans = max(ans, dp[j][(1 << 8) - 1]);
    }
  }
  cout << ans;
  return 0;
}
