Codeforces Round 636 (Div. 3) |
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Finished |

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constructive algorithms

math

*800

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B. Balanced Array

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

Input

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 $$$2 \cdot 10^5$$$ ($$$\sum n \le 2 \cdot 10^5$$$).

Output

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 $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) satisfying conditions from the problem statement on the second line.

Example

Input

5 2 4 6 8 10

Output

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

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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