Score : $500$ points

Problem Statement

You are given sequences of positive integers of length $N$: $A=(A_1,A_2,\dots,A_N)$ and $B=(B_1,B_2,\dots,B_N)$.

You can repeat the following operation any number of times (possibly zero).

• Choose an integer $i$ such that $1 \le i \le N$ and replace $A_i$ with $A_{i+1}$.

Here, regard $A_{N+1}$ as $A_1$.

Determine whether it is possible to make $A$ equal $B$.

You have $T$ test cases to solve.

Constraints

• $1 \le T \le 5000$
• $1 \le N \le 5000$
• $1 \le A_i,B_i \le N$
• For each input file, the sum of $N$ over all test cases does not exceed $5000$.

Input

The input is given from Standard Input in the following format:

$T$

$\mathrm{case}_1$

$\mathrm{case}_2$

$\vdots$

$\mathrm{case}_T$

Each test case is in the following format:

$N$

$A_1$ $A_2$ $\dots$ $A_N$

$B_1$ $B_2$ $\dots$ $B_N$

Output

Print $T$ lines. The $i$-th line should contain Yes if it is possible to make $A$ equal $B$ in the $i$-th test case, and No otherwise.

3
2
1 2
2 2
4
2 3 1 1
2 1 1 2
2
1 1
2 2

Yes
Yes
No

In the first test case, you can make $A$ equal $B$ as follows.

• Choose $i=1$ to replace $A_1$ with $A_2$, making $A=(2,2)$.

In the second test case, you can make $A$ equal $B$ as follows.

• Choose $i=4$ to replace $A_4$ with $A_1$, making $A=(2,3,1,2)$.
• Choose $i=2$ to replace $A_2$ with $A_3$, making $A=(2,1,1,2)$.

In the third test case, there is no way to make $A$ equal $B$.