Problem #4902 - ECNU Online Judge

单点时限: 5.0 sec

内存限制: 512 MB

Given three permutations of length $n$:

Find three subsequences:

The following conditions are satisfied:

Three subsequences with equal length;
$i_1 < i_2 < \cdots < i_m$，$j_1 < j_2 < \cdots < j_m$，$k_1 < k_2 < \cdots < k_m$;
For any $t \in [1, m]$ that satisfies $a_{i_t} = b_{j_t} \times c_{k_t}$ holds or $b_{j_t} = a_{i_t} \times c_{k_t}$ holds or $c_{k_t} = a_{i_t} \times b_{j_t}$.

Find the length of the longest subsequence that can be selected to satisfy the condition.

The first line of an integer $n$ represents the length of the arrangement.

The next three rows of $n$ integers each represent the permutations $A, B$ and $C$ respectively.

One integer in a row represents the length of the longest subsequence.

Input

6
1 2 3 4 5 6
3 4 2 1 6 5
2 4 3 5 6 1

Output

$1 \le n \le 20000$, $1 \le a_i, b_i, c_i \le n$.

Note that for any $1\le i,j\le n,i\ne j$, $\ a_i\ne a_j, b_i\ne b_j , c_i\ne c_j$ holds.

Sample explanation:

A legal subsequence is taken as

1 2 5
4 6 5
4 3 1

8 人解决，22 人已尝试。

8 份提交通过，共有 76 份提交。

7.8 EMB 奖励。

创建: 2 年，1 月前.

修改: 2 年，1 月前.

最后提交: 1 年，9 月前.

来源: N/A

4902. Permutation