Communication Network Between Vertices

Yeonguk made a fortune in the stock market, used the money to found a country, and installed communication towers that handle the country's communications.

As everyone knows, Yeonguk's country is a tree made of $N$ regions connected by $N-1$ roads. Each region is numbered from $1$ to $N$. Region $1$ is where Yeonguk lives, and it is both the capital and the root of the tree. Each region has one communication tower, and the towers of two regions that are ancestors and descendants in the tree can exchange information.

However, Daniel from an enemy country saw this and began firing communication jamming waves. Because of the jamming waves, only some pairs of towers can now communicate. Each tower is assigned one frequency, and only towers whose frequencies are divisors or multiples of each other can communicate.

We must count the number of distinct pairs of communication towers in Yeonguk's country that can communicate. Indirect communication through another tower is not allowed.

The first line gives the number of regions $N$ that make up Yeonguk's country.

The second line gives the frequency $A[i]$ of the communication tower in region $i$ for each $i$ from $1$ to $N$.

The third line gives the number $P[i]$ of the region containing the parent node of region $i$, in order for $i=2, \cdots, N$.

Print the number of distinct pairs of communication towers that can communicate.

• $1 \leq N \leq 100\,000$
• $1 \leq A[i] \leq 100\,000$ ($1 \leq i \leq N$)
• $1 \leq P[i] < i$ ($2 \leq i \leq N$)
• All input values are integers.