Score : $2000$ points

Problem Statement

You are given a rooted tree with $N$ vertices. The vertices are numbered $0, 1, ..., N-1$. The root is Vertex $0$, and the parent of Vertex $i$ $(i = 1, 2, ..., N-1)$ is Vertex $p_i$.

Initially, an integer $a_i$ is written in Vertex $i$. Here, $(a_0, a_1, ..., a_{N-1})$ is a permutation of $(0, 1, ..., N-1)$.

You can execute the following operation at most $25$ $000$ times. Do it so that the value written in Vertex $i$ becomes $i$.

• Choose a vertex and call it $v$. Consider the path connecting Vertex $0$ and $v$.
• Rotate the values written on the path. That is, For each edge $(i, p_i)$ along the path, replace the value written in Vertex $p_i$ with the value written in Vertex $i$ (just before this operation), and replace the value of $v$ with the value written in Vertex $0$ (just before this operation).
• You may choose Vertex $0$, in which case the operation does nothing.

Constraints

• $2 \leq N \leq 2000$
• $0 \leq p_i \leq i-1$
• $(a_0, a_1, ..., a_{N-1})$ is a permutation of $(0, 1, ..., N-1)$.

Input

Input is given from Standard Input in the following format:

$N$

$p_1$ $p_2$ ... $p_{N-1}$

$a_0$ $a_1$ ... $a_{N-1}$

Output

In the first line, print the number of operations, $Q$. In the second through $(Q+1)$-th lines, print the chosen vertices in order.

5
0 1 2 3
2 4 0 1 3

2
3
4

• After the first operation, the values written in Vertex $0, 1, .., 4$ are $4, 0, 1, 2, 3$.

5
0 1 2 2
4 3 1 2 0

3
4
3
1

• After the first operation, the values written in Vertex $0, 1, .., 4$ are $3, 1, 0, 2, 4$.
• After the second operation, the values written in Vertex $0, 1, .., 4$ are $1, 0, 2, 3, 4$.