201331: [AtCoder]ARC133 B - Dividing Subsequence

Problem Statement

Given are permutations $P=(P_1,P_2,\cdots,P_N)$ and $Q=(Q_1,Q_2,\cdots,Q_N)$ of $(1,2,\cdots,N)$.

Snuke is going to extract (not necessarily contiguous) subsequences from $P$ and $Q$. Here, the subsequences must satisfy the conditions below.

• The length of the subsequence extracted from $P$ and that extracted from $Q$ are the same. Below, let $k$ be this length.
• Let $a=(a_1,a_2,\cdots,a_k)$ and $b=(b_1,b_2,\cdots,b_k)$ be the subsequences extracted from $P$ and $Q$, respectively. Then, for each $1 \leq i \leq k$, $b_i$ is a multiple of $a_i$.

Find the maximum possible length of each subsequence extracted by Snuke.

Constraints

• $1 \leq N \leq 200000$
• $P$ is a permutation of $(1,2,\cdots,N)$.
• $Q$ is a permutation of $(1,2,\cdots,N)$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$
$P_1$ $P_2$ $\cdots$ $P_N$
$Q_1$ $Q_2$ $\cdots$ $Q_N$

Output

Print the answer.

Sample Input 1

4
3 1 4 2
4 2 1 3

Sample Output 1

2

If we extract the subsequence $(1,2)$ from $P$ and $(4,2)$ from $Q$, they satisfy the conditions. It is impossible to extract subsequences of length $3$ or greater to satisfy the conditions, so the answer is $2$.

Sample Input 2

5
1 2 3 4 5
5 4 3 2 1

Sample Output 2

3

Sample Input 3

10
4 3 1 10 9 2 8 6 5 7
9 6 5 4 2 3 8 10 1 7

Sample Output 3

6