A13378. Special Permutation

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.

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 $n$ ( $2 \le n \le 1000$ ).

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.