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:
tests = int(input())
values = [0] * tests

for i in range(tests):
    values[i] = int(input())

for i in range(tests):

    if (values[i]//2)%2 == 1:
        print('NO')
        continue
    list_1 = [0] * (values[i]//2)
    list_2 = [0] * (values[i]//2)
    zap1 = 4
    zap2 = 1
    sum1 = 0
    sum2 = 0
    for k in range(len(list_1)):
        list_1[k] = zap1
        sum1+=zap1
        zap1+=2
    for k in range(len(list_2) - 1):
        list_2[k] = zap2
        sum2+=zap2
        zap2+=2
        
    list_2[len(list_2) - 1] = sum1 - sum2
    print('YES')
    print(*list_1, *list_2)