You are given an integer $$$n$$$. Find any permutation $$$p$$$ of length $$$n$$$$$$^{\text{∗}}$$$ such that:

For all $$$2 \le i \le n$$$, $$$\max(p_{i - 1}, p_i) \bmod i$$$ $$$^{\text{†}}$$$ $$$= i - 1$$$ is satisfied.

If it is impossible to find such a permutation $$$p$$$, output $$$-1$$$.

$$$^{\text{∗}}$$$A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

$$$^{\text{†}}$$$$$$x \bmod y$$$ denotes the remainder from dividing $$$x$$$ by $$$y$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 99$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 100$$$).

Output

For each test case:

If such a permutation $$$p$$$ doesn't exist, output a single integer $$$-1$$$.
Otherwise, output $$$n$$$ integers $$$p_1, p_2, \ldots, p_n$$$ — the permutation $$$p$$$ you've found. If there are multiple answers, output any of them.

Note

In the first test case, it is impossible to find such a permutation $$$p$$$, so you should output $$$-1$$$.

In the fourth test case, $$$p = [1, 5, 2, 3, 4]$$$ satisfies the condition:

For $$$i = 2$$$, $$$\max(p_1, p_2) = 5$$$ and $$$5 \bmod 2 = 1$$$.
For $$$i = 3$$$, $$$\max(p_2, p_3) = 5$$$ and $$$5 \bmod 3 = 2$$$.
For $$$i = 4$$$, $$$\max(p_3, p_4) = 3$$$ and $$$3 \bmod 4 = 3$$$.
For $$$i = 5$$$, $$$\max(p_4, p_5) = 4$$$ and $$$4 \bmod 5 = 4$$$.

Max and Mod

Examples