A11263 | Dating

This story is happening in a town named BubbleLand. There are $n$ houses in BubbleLand. In each of these $n$ houses lives a boy or a girl. People there really love numbers and everyone has their favorite number $f$ . That means that the boy or girl that lives in the $i$ -th house has favorite number equal to $f_{i}$ .

The houses are numerated with numbers $1$ to $n$ .

The houses are connected with $n-1$ bidirectional roads and you can travel from any house to any other house in the town. There is exactly one path between every pair of houses.

A new dating had agency opened their offices in this mysterious town and the citizens were very excited. They immediately sent $q$ questions to the agency and each question was of the following format:

- $a\ b$ — asking how many ways are there to choose a couple (boy and girl) that have the same favorite number and live in one of the houses on the unique path from house $a$ to house $b$ .

Help the dating agency to answer the questions and grow their business.

The first line contains an integer $n$ ( $1<=n<=10^{5}$ ), the number of houses in the town.

The second line contains $n$ integers, where the $i$ -th number is $1$ if a boy lives in the $i$ -th house or $0$ if a girl lives in $i$ -th house.

The third line contains $n$ integers, where the $i$ -th number represents the favorite number $f_{i}$ ( $1<=f_{i}<=10^{9}$ ) of the girl or boy that lives in the $i$ -th house.

The next $n-1$ lines contain information about the roads and the $i$ -th line contains two integers $a_{i}$ and $b_{i}$ ( $1<=a_{i},b_{i}<=n$ ) which means that there exists road between those two houses. It is guaranteed that it's possible to reach any house from any other.

The following line contains an integer $q$ ( $1<=q<=10^{5}$ ), the number of queries.

Each of the following $q$ lines represents a question and consists of two integers $a$ and $b$ ( $1<=a,b<=n$ ).

For each of the $q$ questions output a single number, the answer to the citizens question.