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 $$$1$$$ 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.
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 $$$1000^2$$$.
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.
931 2 32 3 322 21 251 1 1 4 52 3 4 5 531 1 11 2 331 1 13 2 331 1 31 2 341 1 1 43 3 4 441 4 3 41 4 3 451 3 4 5 42 3 4 5 5
5 11 2 1 2 2-112 11 2 1 1 2 1 1 1 2 1 2 2-1-12 21 212 11 1 2 1 2 1 1 2 1 1 2 20 17 11 2 2 2 2 1 2
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 $$$b$$$.