CF429A.Xor-tree

Iahub is very proud of his recent discovery, propagating trees. Right now, he invented a new tree, called xor-tree. After this new revolutionary discovery, he invented a game for kids which uses xor-trees.

The game is played on a tree having n nodes, numbered from 1 to n. Each node i has an initial value init__i, which is either 0 or 1. The root of the tree is node 1.

One can perform several (possibly, zero) operations on the tree during the game. The only available type of operation is to pick a node x. Right after someone has picked node x, the value of node x flips, the values of sons of x remain the same, the values of sons of sons of x flips, the values of sons of sons of sons of x remain the same and so on.

The goal of the game is to get each node i to have value goal__i, which can also be only 0 or 1. You need to reach the goal of the game by using minimum number of operations.

伊阿胡布为他最近发现的“传播树”感到非常自豪。目前，他发明了一种新树，称为“异或树（xor-tree）”。在这一革命性新发现之后，他又为孩子们设计了一款使用异或树的游戏。

该游戏在一个含有 $ n $ 个节点的树上进行，节点编号为 $ 1 $ 到 $ n $。每个节点 $ i $ 具有一个初始值 $ \text{init}_i $，其值仅为 $ 0 $ 或 $ 1 $。树的根节点为节点 $ 1 $。

游戏过程中，玩家可对树执行若干次（可能为零次）操作。唯一允许的操作是选择一个节点 $ x $。一旦选中节点 $ x $，则：节点 $ x $ 的值发生翻转；$ x $ 的子节点的值保持不变；$ x $ 的孙节点（即子节点的子节点）的值发生翻转；$ x $ 的曾孙节点（即子节点的子节点的子节点）的值保持不变；依此类推。

游戏的目标是使每个节点 $ i $ 的最终值恰好等于目标值 $ \text{goal}_i $，其中每个 $ \text{goal}_i $ 同样仅为 $ 0 $ 或 $ 1 $。你需要以最少的操作次数达成该目标。

The first line contains an integer n (1 ≤ n ≤ 105). Each of the next n - 1 lines contains two integers u__i and v__i (1 ≤ u__i, v__i ≤ n; u__i ≠ v__i) meaning there is an edge between nodes u__i and v__i.

The next line contains n integer numbers, the i-th of them corresponds to init__i (init__i is either 0 or 1). The following line also contains n integer numbers, the i-th number corresponds to goal__i (goal__i is either 0 or 1).

第一行包含一个整数 $n$（$1 \leq n \leq 10^5$）。接下来的 $n-1$ 行每行包含两个整数 $u_i$ 和 $v_i$（$1 \leq u_i, v_i \leq n$；$u_i \neq v_i$），表示节点 $u_i$ 与 $v_i$ 之间存在一条边。

下一行包含 $n$ 个整数，其中第 $i$ 个数对应 $init_i$（$init_i$ 为 $0$ 或 $1$）。再下一行也包含 $n$ 个整数，其中第 $i$ 个数对应 $goal_i$（$goal_i$ 为 $0$ 或 $1$）。

In the first line output an integer number cnt, representing the minimal number of operations you perform. Each of the next cnt lines should contain an integer x__i, representing that you pick a node x__i.

第一行输出一个整数 cnt，表示你执行的最少操作次数。接下来的 cnt 行中，每行输出一个整数 x__i，表示你选择节点 x__i。