Problem: 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 n/2 elements of a are even (divisible by 2); 
  * the second 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 (∑_{i=1}^{n/2} a_i = ∑_{i=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 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 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 ⋅ 10^5 (∑ n ≤ 2 ⋅ 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, ..., a_n (1 ≤ a_i ≤ 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

Solution (in PYTHON3):

Solution:
import io, os
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

tokens = []
tokens_next = 0


def next_str():
    global tokens, tokens_next
    while tokens_next >= len(tokens):
        tokens = input().split()
        tokens_next = 0
    tokens_next += 1
    return tokens[tokens_next - 1]


def nextInt():
    return int(next_str())


t = nextInt()
for _ in range(t):
    n = nextInt()

    if n % 4 != 0:
        print('NO')
        continue

    a = []
    i = 0
    while len(a) < n // 2:
        i += 2
        a.append(i)

    b = []
    for i in range(len(a)):
        if i < n // 4:
            b.append(a[i] - 1)
        else:
            b.append(a[i] + 1)

    print('YES')
    print(' '.join(map(str, a + b)))