CF2244F.Anya Loves Trees!

Anya considers a rooted tree with the root at vertex $1$. The leaves of the tree contain integers from $1$ to $k$, where $k$ is the number of leaves. Each leaf contains exactly one number. For every vertex, its children are ordered from left to right in increasing order of their indices.

Anya noticed that if we list the leaves from left to right, their values form a sequence. She wants this sequence to become strictly increasing.

To achieve this, Anya can perform the following operation: choose any vertex and cyclically shift its children to the left$^{\text{∗}}$. For example, if a vertex has children in the order $[1, 2, 3]$, after the shift the order becomes $[2, 3, 1]$. This operation can be applied to any vertices any number of times.

A visual example of a cyclic shift of the children of vertex $1$:

An example of a cyclic shift of children.

Help Yura determine whether Anya can make the sequence of integers in the leaves strictly increasing from left to right using such operations.

$^{\text{∗}}$A cyclic left shift is an operation where all elements are shifted left by $1$, and the first element becomes the last.

安雅考虑一棵以顶点 $1$ 为根的有根树。树的叶子节点中存放着从 $1$ 到 $k$ 的整数，其中 $k$ 是叶子节点的总数。每个叶子节点恰好包含一个数字。对于任意一个顶点，其子节点按索引从小到大的顺序从左到右排列。

安雅注意到，如果从左到右依次列出所有叶子节点，它们的数值会构成一个序列。她希望该序列严格递增。

为实现这一目标，安雅可以执行如下操作：任选一个顶点，并将其子节点向左循环移位$^{\text{∗}}$。例如，若某顶点的子节点顺序为 $[1, 2, 3]$，则移位后变为 $[2, 3, 1]$。该操作可对任意顶点执行任意多次。

对顶点 $1$ 的子节点进行循环移位的图示示例：

子节点循环移位示例。

请帮助尤拉判断：安雅能否通过上述操作，使得从左到右的叶子节点所含整数序列严格递增？

$^{\text{∗}}$循环左移是指将所有元素向左移动一位，原第一个元素移至末尾的操作。

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of vertices.

The next line contains $n - 1$ integers $p_2, p_3, \dots, p_n$ ($1 \le p_i \le n$), where $p_i$ is the parent of vertex $i$. The children of each vertex are ordered from left to right in increasing order of their indices.

The third line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le n$). If vertex $i$ is not a leaf, then $a_i = 0$. If vertex $i$ is a leaf, then $a_i \gt 0$ and represents the number written in that vertex. It is guaranteed that all positive values $a_i$ form a permutation.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$）—— 顶点的数量。

下一行包含 $n - 1$ 个整数 $p_2, p_3, \dots, p_n$（$1 \le p_i \le n$），其中 $p_i$ 表示顶点 $i$ 的父节点。每个顶点的子节点按其索引从小到大的顺序从左到右排列。

第三行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$0 \le a_i \le n$）。若顶点 $i$ 不是叶子节点，则 $a_i = 0$；若顶点 $i$ 是叶子节点，则 $a_i \gt 0$，且表示写在该顶点上的数字。保证所有正数 $a_i$ 构成一个排列。

保证所有测试用例的 $n$ 之和不超过 $2 \cdot 10^5$。

For each test case, output 'YES" if it is possible to reorder the integers in the leaves to be strictly increasing, and 'NO" otherwise.

You may output each letter in any case (lowercase or uppercase). For example, the strings 'yEs", 'yes", 'Yes", and 'YES" will be accepted.

对于每个测试用例，如果可以重新排列叶子节点中的整数，使其严格递增，则输出 YES；否则输出 NO。

你可以以任意大小写形式输出每个字母（小写或大写）。例如，字符串 yEs、yes、Yes 和 YES 均可被接受。

null