Farmer John is building PLUSworld, a giant barn complex with $n$ barns numbered from $1$ to $n$. For each $1 \le i \le n$, there is currently a one-way walkway from barn $i$ to barn $a_i$.

Before opening PLUSworld, Farmer John wants to reconfigure the roads so that, for every $1 \le i \le n$, the road from barn $i$ points to barn $b_i$. The target roads have the special property that each road points to its own barn or to a higher-numbered barn $(i \le b_i)$.

To do this, he sends Bessie to one barn of his choice. Let $p$ be the barn where Bessie is currently located. Bessie may perform the following operations any number of times:

• Operation $1$: Increase the destination of the road from the current barn by $1$. More formally, set $a_p := a_p + 1$. This operation may only be performed if $a_p \lt n$.
• Operation $2$: Follow the road from the current barn. More formally, set $p := a_p$.

Operation $1$ changes the array $a$, but Bessie stays at the same barn. Operation $2$ changes Bessie's current barn, but does not change the array.

Your goal is to make the array $a$ equal to the array $b$.

Determine whether this is possible. If it is possible, output any valid starting barn and any sequence of operations that makes $a=b$.

It can be shown that if a solution exists, then there exists one using at most $2n^2$ operations.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1\le n\le 1000$).

The second line contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\le a_i\le n$).

The third line contains $n$ integers $b_1,b_2,\ldots,b_n$ ($\color{red}{i\le b_i}\le n$).

It is guaranteed that the sum of $n^2$ over all test cases does not exceed $1000^2$.

Output

For each test case, if it is impossible to make $a$ equal to $b$, output a single integer $-1$.

Otherwise, output two lines.

On the first line, output two integers $o$ and $p$ — the number of operations you will perform and the initial index you choose ($0 \leq o \leq 2n^2$, $1 \leq p \leq n$).

On the second line, output $o$ integers $c_1,c_2,\ldots,c_o$ ($1\le c_i\le 2$), where $c_i$ is the type of the $i$-th operation.

If $c_i=1$, you perform operation $1$ and set $a_p:=a_p+1$. This operation may only be used if $a_p \lt n$ at that moment.

If $c_i=2$, you perform operation $2$ and set $p:=a_p$.

After performing all $o$ operations, the array $a$ must be equal to $b$.

If there are multiple valid answers, you may output any of them.

Note

For the first test case, Bessie starts at barn $1$. She increases $a_1$ from $1$ to $2$, follows the road to barn $2$, and increases $a_2$ from $2$ to $3$. The resulting array is $[2,3,3]$, which is equal to $b$.

For the second test case, $a_1=2 \gt b_1=1$. Since road destinations can only be increased, it is impossible to make $a_1$ equal to $b_1$, so the answer is $-1$.

For the third test case, Bessie starts at barn $1$. She changes $a_1$ from $1$ to $2$ and follows the road to barn $2$. She then changes $a_2$ from $1$ to $3$ and moves to barn $3$, changes $a_3$ from $1$ to $4$ and moves to barn $4$, and finally changes $a_4$ from $4$ to $5$. The resulting array is $[2,3,4,5,5]$, which is equal to $b$.