Balanced Array

题意翻译

### 题意简述 给定 $n$（$n$ 是偶数），要求构造一个长度为 $n$ 的数列 $\{a_n\}$，使其满足以下条件： - 前 $\dfrac{n}{2}$ 个数为偶数，后 $\dfrac{n}{2}$ 个数为奇数。 - 前 $\dfrac{n}{2}$ 个数的和等于后 $\dfrac{n}{2}$ 个数的和。 - $a_i\ne a_j(1\le i,j\le n)$。 感谢 @[CSP_Sept](/user/224931) 提供的翻译。

题目描述

You are given a positive integer $ n $ , it is guaranteed that $ n $ is even (i.e. divisible by $ 2 $ ). You want to construct the array $ a $ of length $ n $ such that: - The first $ \frac{n}{2} $ elements of $ a $ are even (divisible by $ 2 $ ); - the second $ \frac{n}{2} $ elements of $ a $ are odd (not divisible by $ 2 $ ); - all elements of $ a $ are distinct and positive; - the sum of the first half equals to the sum of the second half ( $ \sum\limits_{i=1}^{\frac{n}{2}} a_i = \sum\limits_{i=\frac{n}{2} + 1}^{n} a_i $ ). If there are multiple answers, you can print any. It is not guaranteed that the answer exists. You have to answer $ t $ independent test cases.

输入输出格式

输入格式

The first line of the input contains one integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Then $ t $ test cases follow. The only line of the test case contains one integer $ n $ ( $ 2 \le n \le 2 \cdot 10^5 $ ) — the length of the array. It is guaranteed that that $ n $ is even (i.e. divisible by $ 2 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ ( $ \sum n \le 2 \cdot 10^5 $ ).

输出格式

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a1,a2,…,an (1≤ai≤10^9) satisfying conditions from the problem statement on the second line.

输入输出样例

输入样例 #1

5
2
4
6
8
10

输出样例 #1

NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO