G. Special Permutation
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

A permutation of length $n$ is an array $p=[p_1,p_2,\dots,p_n]$, which contains every integer from $1$ to $n$ (inclusive) and, moreover, each number appears exactly once. For example, $p=[3,1,4,2,5]$ is a permutation of length $5$.

For a given number $n$ ($n \ge 2$), find a permutation $p$ in which absolute difference (that is, the absolute value of difference) of any two neighboring (adjacent) elements is between $2$ and $4$, inclusive. Formally, find such permutation $p$ that $2 \le |p_i - p_{i+1}| \le 4$ for each $i$ ($1 \le i < n$).

Print any such permutation for the given integer $n$ or determine that it does not exist.

Input

The first line contains an integer $t$ ($1 \le t \le 100$) — the number of test cases in the input. Then $t$ test cases follow.

Each test case is described by a single line containing an integer $n$ ($2 \le n \le 1000$).

Output

Print $t$ lines. Print a permutation that meets the given requirements. If there are several such permutations, then print any of them. If no such permutation exists, print -1.

Example
Input
6
10
2
4
6
7
13

Output
9 6 10 8 4 7 3 1 5 2
-1
3 1 4 2
5 3 6 2 4 1
5 1 3 6 2 4 7
13 9 7 11 8 4 1 3 5 2 6 10 12