CF852I.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.

这个故事发生在一座名为 BubbleLand 的小镇。BubbleLand 有 $n$ 座房屋，每座房屋中住着一名男孩或一名女孩。当地居民非常热爱数字，每个人都有一个自己最钟爱的数字 $f$。也就是说，住在第 $i$ 座房屋中的男孩或女孩，其最钟爱的数字为 $f_i$。

房屋编号为 $1$ 到 $n$。

这些房屋由 $n-1$ 条双向道路连接，使得从任意一座房屋出发均可到达小镇内的任意其他房屋。任意两座房屋之间恰好存在唯一一条路径。

一家新的婚恋机构在这座神秘小镇开设了办事处，镇民们对此感到异常兴奋。他们立即向该机构提出了 $q$ 个问题，每个问题的格式如下：

• $a\ b$ —— 询问：在从房屋 $a$ 到房屋 $b$ 的唯一路径所经过的所有房屋中，有多少种方式可以选出一对情侣（即一名男孩和一名女孩），使得他们拥有相同的最钟爱数字？

请帮助这家婚恋机构回答这些问题，以助其发展壮大。

The first line contains an integer n (1 ≤ n ≤ 105), 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 ≤ 109) 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 ≤ 105), 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).

第一行包含一个整数 $n$（$1 \leq n \leq 10^5$），表示镇上的房屋数量。

第二行包含 $n$ 个整数，其中第 $i$ 个数为 $1$ 表示第 $i$ 栋房屋住着一名男孩，为 $0$ 表示住着一名女孩。

第三行包含 $n$ 个整数，其中第 $i$ 个数表示住在第 $i$ 栋房屋中的男孩或女孩的最喜欢数字 $f_i$（$1 \leq f_i \leq 10^9$）。

接下来的 $n-1$ 行描述道路信息，其中第 $i$ 行包含两个整数 $a_i$ 和 $b_i$（$1 \leq a_i, b_i \leq n$），表示这两栋房屋之间存在一条道路。保证任意两栋房屋之间均可相互到达。

下一行包含一个整数 $q$（$1 \leq q \leq 10^5$），表示查询的数量。

接下来的 $q$ 行每行代表一个查询，包含两个整数 $a$ 和 $b$（$1 \leq a, b \leq n$）。

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

对于每个问题，输出一个数字，即该市民问题的答案。

In the first question from house 1 to house 3, the potential couples are (1, 3) and (6, 3).

In the second question from house 7 to house 5, the potential couples are (7, 6), (4, 2) and (4, 5).

第一个问题中，从房屋 1 到房屋 3，潜在的配对为 $(1,\,3)$ 和 $(6,\,3)$。

第二个问题中，从房屋 7 到房屋 5，潜在的配对为 $(7,\,6)$、$(4,\,2)$ 和 $(4,\,5)$。