CF1872F.Selling a Menagerie

You are the owner of a menagerie consisting of $n$ animals numbered from $1$ to $n$. However, maintaining the menagerie is quite expensive, so you have decided to sell it!

It is known that each animal is afraid of exactly one other animal. More precisely, animal $i$ is afraid of animal $a_i$ ($a_i \neq i$). Also, the cost of each animal is known, for animal $i$ it is equal to $c_i$.

You will sell all your animals in some fixed order. Formally, you will need to choose some permutation$^\dagger$ $p_1, p_2, \ldots, p_n$, and sell animal $p_1$ first, then animal $p_2$, and so on, selling animal $p_n$ last.

When you sell animal $i$, there are two possible outcomes:

• If animal $a_i$ was sold before animal $i$, you receive $c_i$ money for selling animal $i$.
• If animal $a_i$ was not sold before animal $i$, you receive $2 \cdot c_i$ money for selling animal $i$. (Surprisingly, animals that are currently afraid are more valuable).

Your task is to choose the order of selling the animals in order to maximize the total profit.

For example, if $a = [3, 4, 4, 1, 3]$, $c = [3, 4, 5, 6, 7]$, and the permutation you choose is $[4, 2, 5, 1, 3]$, then:

• The first animal to be sold is animal $4$. Animal $a_4 = 1$ was not sold before, so you receive $2 \cdot c_4 = 12$ money for selling it.
• The second animal to be sold is animal $2$. Animal $a_2 = 4$ was sold before, so you receive $c_2 = 4$ money for selling it.
• The third animal to be sold is animal $5$. Animal $a_5 = 3$ was not sold before, so you receive $2 \cdot c_5 = 14$ money for selling it.
• The fourth animal to be sold is animal $1$. Animal $a_1 = 3$ was not sold before, so you receive $2 \cdot c_1 = 6$ money for selling it.
• The fifth animal to be sold is animal $3$. Animal $a_3 = 4$ was sold before, so you receive $c_3 = 5$ money for selling it.

Your total profit, with this choice of permutation, is $12 + 4 + 14 + 6 + 5 = 41$. Note that $41$ is not the maximum possible profit in this example.

$^\dagger$ A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in any order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array) and $[1,3,4]$ is also not a permutation ($n=3$, but $4$ is present in the array).

你是一家动物园的主人，园中饲养着编号为 $1$ 到 $n$ 的 $n$ 只动物。然而，维持动物园开销巨大，因此你决定将其全部出售！

已知每只动物恰好害怕另一只动物。更准确地说，动物 $i$ 害怕动物 $a_i$（其中 $a_i \neq i$）。此外，每只动物的售价也已知：动物 $i$ 的售价为 $c_i$。

你将以某种固定顺序出售所有动物。形式上，你需要选择某个排列$^\dagger$ $p_1, p_2, \ldots, p_n$，首先出售动物 $p_1$，然后出售动物 $p_2$，依此类推，最后出售动物 $p_n$。

当你出售动物 $i$ 时，会出现以下两种情形之一：

• 若动物 $a_i$ 在动物 $i$ 之前已被售出，则你从出售动物 $i$ 中获得 $c_i$ 的收入；
• 若动物 $a_i$ 在动物 $i$ 之前尚未被售出，则你从出售动物 $i$ 中获得 $2 \cdot c_i$ 的收入。（令人惊讶的是，当前仍处于恐惧状态的动物反而更具价值。）

你的任务是选择动物的出售顺序，以使总收益最大化。

例如，若 $a = [3, 4, 4, 1, 3]$，$c = [3, 4, 5, 6, 7]$，且你选择的排列为 $[4, 2, 5, 1, 3]$，则：

• 第一只被出售的动物是动物 $4$。由于动物 $a_4 = 1$ 尚未被售出，你获得 $2 \cdot c_4 = 12$ 的收入；
• 第二只被出售的动物是动物 $2$。由于动物 $a_2 = 4$ 已被售出，你获得 $c_2 = 4$ 的收入；
• 第三只被出售的动物是动物 $5$。由于动物 $a_5 = 3$ 尚未被售出，你获得 $2 \cdot c_5 = 14$ 的收入；
• 第四只被出售的动物是动物 $1$。由于动物 $a_1 = 3$ 尚未被售出，你获得 $2 \cdot c_1 = 6$ 的收入；
• 第五只被出售的动物是动物 $3$。由于动物 $a_3 = 4$ 已被售出，你获得 $c_3 = 5$ 的收入。

按此排列所得的总收益为 $12 + 4 + 14 + 6 + 5 = 41$。注意，在本例中，$41$ 并非可能的最大收益。

$^\dagger$ 长度为 $n$ 的排列是指由 $1$ 到 $n$ 中互不相同的 $n$ 个整数以任意顺序组成的数组。例如，$[2,3,1,5,4]$ 是一个排列，但 $[1,2,2]$ 不是排列（数字 $2$ 出现了两次），$[1,3,4]$ 也不是排列（此时 $n=3$，但数组中出现了 $4$）。

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

Then follow the descriptions of the test cases.

The first line of each test case description contains an integer $n$ ($2 \le n \le 10^5$) — the number of animals.

The second line of the test case description contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le n$, $a_i \neq i$) — $a_i$ means the index of the animal that animal $i$ is afraid of.

The third line of the test case description contains $n$ integers $c_1, c_2, \dots, c_n$ ($1 \le c_i \le 10^9$) — the costs of the animals.

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

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

接下来是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$2 \le n \le 10^5$）—— 表示动物的数量。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \le a_i \le n$，且 $a_i \neq i$）—— 其中 $a_i$ 表示第 $i$ 只动物所害怕的动物的编号。

每个测试用例的第三行包含 $n$ 个整数 $c_1, c_2, \dots, c_n$（$1 \le c_i \le 10^9$）—— 表示各只动物的成本。

保证所有测试用例的 $n$ 值之和不超过 $10^5$。

Output $t$ lines, each containing the answer to the corresponding test case. The answer should be $n$ integers — the permutation $p_1, p_2, \ldots, p_n$, indicating in which order to sell the animals in order to maximize the profit. If there are multiple possible answers, you can output any of them.

输出 $t$ 行，每行包含对应测试用例的答案。答案应为 $n$ 个整数——排列 $p_1, p_2, \ldots, p_n$，表示为使利润最大化而出售动物的顺序。若存在多个可能的答案，输出任意一个即可。