Special Permutation

题意翻译

给定 $t$ 组数据，每组数据包含一个整数 $n$。 对于每个整数 $n$，你需要输出一个长度为 $n$ 的全排列 $p$，输出要求对于所有满足 $i \in [1,n)$ 的 $i$，有 $|p_i-p_{i+1}| \in [2,4]$，如果不存在，输出 $-1$，对于每一组数据，输出占一行。 如果有多组解，请输出其中任意一个。

题目描述

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.

输入输出格式

输入格式

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 $ ).

输出格式

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.

输入输出样例

输入样例 #1

6
10
2
4
6
7
13

输出样例 #1

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