D. Fairplay
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are playing an online game, you have a team of $$$N$$$ players, and you decided to challenge your friend's team that also consists of $$$N$$$ players, let's call them team $$$A$$$ and team $$$B$$$ respectively. Each player has a specific strength, more specifically the $$$i_{th}$$$ player in team $$$A$$$ has strength equal to $$$i$$$ for each $$$i$$$ between $$$1$$$ and $$$N$$$, and the $$$j_{th}$$$ player from team $$$B$$$ has strength equal to $$$j+1$$$ for each $$$j$$$ between $$$1$$$ and $$$N$$$.

The total strength of a team is the product of strengths of all players in the team. To make the game fair, you can swap the $$$i_{th}$$$ player from team $$$A$$$ with the $$$i_{th}$$$ player from team $$$B$$$ for any $$$i$$$ between $$$1$$$ and $$$N$$$, in other words, you can only swap players that have the same index in both teams. You can repeat the previous operation any number of times.

A game is fair when both of the teams have a equal strengths. Can you make the game fair?

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$T$$$ ($$$1 \le T \le 10^5$$$). Description of the test cases follows.

Each of the following $$$T$$$ lines, contains a single integer $$$N$$$ ($$$1\le{N}\le{10}^5$$$).

Output

For each test case, if you can make the game fair then print in one line an integer $$$M$$$,the total number of operations needed, on the next line print $$$M$$$ ($$$ 1 \le M \le N$$$) distinct integers, the indices where you want to apply the swap operation. If you can't make the game fair, then print in one line the value $$$-1$$$.

Note that you don't have to minimize the total number of operations. If there exists more than one answer print any of them.

Example
Input
2
8
4
Output
3
1 4 5
-1
Note

In the first test case, the initial strengths are:

team $$$A$$$: $$$1, 2, 3, 4, 5, 6, 7, 8$$$ with total team strength equal to $$$40\,320$$$.

team $$$B$$$: $$$2, 3, 4, 5, 6, 7, 8, 9$$$ with total team strength equal to $$$362\,880$$$.

After swapping the players in indices $$$1, 4$$$ and $$$5$$$, the strengths become like this:

team $$$A$$$: $$$2, 2 ,3, 5, 6, 6, 7, 8$$$ with total team strength equal to $$$120\,960$$$.

team $$$B$$$: $$$1, 3, 4, 4, 5, 7, 8, 9$$$ with total team strength equal to $$$120\,960$$$.

So the strengths are now equal and the game is fair.

In the second test case, you can't make the strengths equal no matter how you perform the swaps.