CF1327D.Infinite Path

You are given a colored permutation $p_1, p_2, \dots, p_n$. The $i$-th element of the permutation has color $c_i$.

Let's define an infinite path as infinite sequence $i, p[i], p[p[i]], p[p[p[i]]] \dots$ where all elements have same color ($c[i] = c[p[i]] = c[p[p[i]]] = \dots$).

We can also define a multiplication of permutations $a$ and $b$ as permutation $c = a \times b$ where $c[i] = b[a[i]]$. Moreover, we can define a power $k$ of permutation $p$ as $p^k=\underbrace{p \times p \times \dots \times p}_{k \text{ times}}$.

Find the minimum $k \gt 0$ such that $p^k$ has at least one infinite path (i.e. there is a position $i$ in $p^k$ such that the sequence starting from $i$ is an infinite path).

It can be proved that the answer always exists.

给你一个带颜色的排列 $p_1, p_2, \dots, p_n$，其中第 $i$ 个元素的颜色为 $c_i$。

我们定义一条无限路径为无限序列 $i, p[i], p[p[i]], p[p[p[i]]], \dots$，要求该序列中所有元素颜色相同（即 $c[i] = c[p[i]] = c[p[p[i]]] = \dots$）。

我们还可以定义两个排列 $a$ 和 $b$ 的乘法为排列 $c = a \times b$，其中 $c[i] = b[a[i]]$。此外，可将排列 $p$ 的 $k$ 次幂定义为 $p^k = \underbrace{p \times p \times \dots \times p}_{k \text{ 次}}$。

请找出最小的正整数 $k > 0$，使得 $p^k$ 中至少存在一条无限路径（即在 $p^k$ 中存在某个位置 $i$，使得从 $i$ 开始的序列构成一条无限路径）。

可以证明，答案一定存在。

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

Next $3T$ lines contain test cases — one per three lines. The first line contains single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the size of the permutation.

The second line contains $n$ integers $p_1, p_2, \dots, p_n$ ($1 \le p_i \le n$, $p_i \neq p_j$ for $i \neq j$) — the permutation $p$.

The third line contains $n$ integers $c_1, c_2, \dots, c_n$ ($1 \le c_i \le n$) — the colors of elements of the permutation.

It is guaranteed that the total sum of $n$ doesn't 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。

接下来的 $3T$ 行包含测试用例，每个测试用例占三行。第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$）—— 排列的长度。

第二行包含 $n$ 个整数 $p_1, p_2, \dots, p_n$（$1 \le p_i \le n$，且当 $i \neq j$ 时 $p_i \neq p_j$）—— 排列 $p$。

第三行包含 $n$ 个整数 $c_1, c_2, \dots, c_n$（$1 \le c_i \le n$）—— 排列中各元素的颜色。

保证所有测试用例的 $n$ 之和不超过 $2 \cdot 10^5$。

Print $T$ integers — one per test case. For each test case print minimum $k \gt 0$ such that $p^k$ has at least one infinite path.

输出 $T$ 个整数——每个测试用例输出一个整数。对于每个测试用例，输出满足条件的最小正整数 $k > 0$，使得 $p^k$ 至少存在一条无限路径。

In the first test case, $p^1 = p = [1, 3, 4, 2]$ and the sequence starting from $1$: $1, p[1] = 1, \dots$ is an infinite path.

In the second test case, $p^5 = [1, 2, 3, 4, 5]$ and it obviously contains several infinite paths.

In the third test case, $p^2 = [3, 6, 1, 8, 7, 2, 5, 4]$ and the sequence starting from $4$: $4, p^2[4]=8, p^2[8]=4, \dots$ is an infinite path since $c_4 = c_8 = 4$.

在第一个测试用例中，$p^1 = p = [1, 3, 4, 2]$，且从 $1$ 开始的序列：$1, p[1] = 1, \dots$ 是一条无限路径。

在第二个测试用例中，$p^5 = [1, 2, 3, 4, 5]$，显然包含多条无限路径。

在第三个测试用例中，$p^2 = [3, 6, 1, 8, 7, 2, 5, 4]$，且从 $4$ 开始的序列：$4, p^2[4]=8, p^2[8]=4, \dots$ 是一条无限路径，因为 $c_4 = c_8 = 4$。