CF1779F.Xorcerer's Stones

Misha had been banned from playing chess for good since he was accused of cheating with an engine. Therefore, he retired and decided to become a xorcerer.

One day, while taking a walk in a park, Misha came across a rooted tree with nodes numbered from $1$ to $n$. The root of the tree is node $1$.

For each $1\le i\le n$, node $i$ contains $a_i$ stones in it. Misha has recently learned a new spell in his xorcery class and wants to test it out. A spell consists of:

• Choose some node $i$ ($1 \leq i \leq n$).
• Calculate the bitwise XOR $x$ of all $a_j$ such that node $j$ is in the subtree of $i$ ($i$ belongs to its own subtree).
• Set $a_j$ equal to $x$ for all nodes $j$ in the subtree of $i$.

Misha can perform at most $2n$ spells and he wants to remove all stones from the tree. More formally, he wants $a_i=0$ to hold for each $1\leq i \leq n$. Can you help him perform the spells?

A tree with $n$ nodes is a connected acyclic graph which contains $n-1$ edges. The subtree of node $i$ is the set of all nodes $j$ such that $i$ lies on the simple path from $1$ (the root) to $j$. We consider $i$ to be contained in its own subtree.

米沙因被指控使用引擎作弊而被永久禁止下国际象棋。因此，他选择退役，并决定成为一名异或法师（xorcerer）。

一天，米沙在公园散步时，遇到了一棵以节点 $1$ 为根的有根树，树上共有 $n$ 个节点，编号从 $1$ 到 $n$。

对每个 $1 \le i \le n$，节点 $i$ 中含有 $a_i$ 颗石子。米沙最近在异或魔法课上学会了一个新咒语，想借此一试身手。该咒语的操作步骤如下：

• 任选一个节点 $i$（$1 \leq i \leq n$）；
• 计算所有满足“节点 $j$ 属于节点 $i$ 的子树”条件的 $a_j$ 的按位异或（bitwise XOR）值 $x$（注意：节点 $i$ 自身属于其子树）；
• 将节点 $i$ 的子树中所有节点 $j$ 对应的 $a_j$ 值全部设为 $x$。

米沙最多可施放 $2n$ 次该咒语，目标是清空整棵树上的所有石子——即令所有 $1 \leq i \leq n$ 均满足 $a_i = 0$。你能帮他设计出施法方案吗？

含 $n$ 个节点的树是一个包含 $n-1$ 条边的连通无环图。节点 $i$ 的子树定义为所有满足“从根节点 $1$ 到节点 $j$ 的简单路径经过节点 $i$”的节点 $j$ 所构成的集合。我们约定：节点 $i$ 自身属于其子树。

The first line contains a single integer $n$ ($2 \leq n \leq 2\cdot 10^5$) — the size of the tree

The second line contains an array of integers $a_1,a_2,\ldots, a_n$ ($0 \leq a_i \leq 31$), describing the number of stones in each node initially.

The third line contains an array of integers $p_2,p_3,\ldots, p_n$ ($1 \leq p_i \leq i-1$), where $p_i$ means that there is an edge connecting $p_i$ and $i$.

第一行包含一个整数 $n$（$2 \leq n \leq 2\cdot 10^5$）——树的大小。

第二行包含一个整数数组 $a_1,a_2,\ldots, a_n$（$0 \leq a_i \leq 31$），表示每个节点初始时的石子数量。

第三行包含一个整数数组 $p_2,p_3,\ldots, p_n$（$1 \leq p_i \leq i-1$），其中 $p_i$ 表示存在一条连接节点 $p_i$ 与节点 $i$ 的边。

If there is not a valid sequence of spells, output $-1$.

Otherwise, output a single integer $q$ ($0 \leq q \leq 2n$) in the first line — the number of performed spells.

In the second line output a sequence of integers $v_1,v_2,\ldots,v_q$ ($1 \leq v_i \leq n$) — the $i$-th spell will be performed on the subtree of node $v_i$. Please note that order matters.

If multiple solutions exist, output any. You don't have to minimize the number of operations.

如果不存在合法的法术序列，则输出 $-1$。

否则，在第一行输出一个整数 $q$（$0 \leq q \leq 2n$）——表示执行的法术数量。

在第二行输出一个整数序列 $v_1,v_2,\ldots,v_q$（$1 \leq v_i \leq n$）——第 $i$ 个法术将施加于节点 $v_i$ 的子树上。请注意，顺序至关重要。

若存在多个解，输出任意一个即可。你无需最小化操作次数。

Please refer to the following pictures for an explanation of the third test. Only the first $4$ spells are shown since the last $2$ do nothing. The first picture represents the tree initially with the number of stones for each node written above it in green. Changes applied by the current spell are highlighted in red.

请参考以下图片以了解第三个测试用例的说明。仅展示了前 $4$ 个法术，因为最后 $2$ 个法术不产生任何效果。第一张图片表示初始树结构，每个节点上方以绿色数字标出其石子数量。当前法术所引起的变化以红色高亮显示。