B. Permutation We Stand
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a positive integer $$$n$$$.

Your task is to find a permutation $$$p$$$ of size $$$n$$$ that satisfies the following conditions:

  • For every $$$i$$$ ($$$1 \le i \le n - 2$$$), $$$\gcd(p_i, p_{i+1}) = 1$$$.
  • $$$\gcd(p_{n - 1}, p_n) \neq 1$$$.

Here $$$\operatorname{gcd}$$$ denotes the greatest common divisor.

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 $$$[1,2,2]$$$ and $$$[1,3,4]$$$ are not permutations.

Output any valid permutation that satisfies these conditions. If a valid permutation does not exist, output $$$-1$$$ instead.

Input

The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le $$$ $$$10 ^ 3$$$). The description of the test cases follows.

A single line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^{5}$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10 ^ 5$$$.

Output

For each test case, output any valid permutation. If multiple solutions exist, output any one of them. If no valid permutations exist, output $$$-1$$$ instead.

Example
Input
2
2
6
Output
-1
4 1 2 5 6 3