Description

Input

The first line contains an integer $t$ $(1\le t\le 3 \cdot 10^5)$ — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $n$ $(2\le n\le 3 \cdot 10^5)$.

The second line of each test case contains $n-1$ integers $a_2, \ldots, a_n$ $(1 \le a_i < i)$, $a_i$ being the parent of the vertex $i$ in Soroush's tree.

The third line of each test case contains $n-1$ integers $b_2, \ldots, b_n$ $(1 \le b_i < i)$, $b_i$ being the parent of the vertex $i$ in Keshi's tree.

It is guaranteed that the given graphs are trees.

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $3 \cdot 10^5$.

Output

For each test case print a single integer — the size of the maximum clique in the memorial graph.

4
4
1 2 3
1 2 3
5
1 2 3 4
1 1 1 1
6
1 1 1 1 2
1 2 1 2 2
7
1 1 3 4 4 5
1 2 1 4 2 5

1
4
1
3

Note

In the first and third test cases, you can pick any vertex.

In the second test case, one of the maximum cliques is $\{2, 3, 4, 5\}$.

In the fourth test case, one of the maximum cliques is $\{3, 4, 6\}$.