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:
'''
n = четное
первые n/2 четные
вторые n/2 нечетные
все элементы разные и положительные
сумма первых и вторых частей равна
'''
t = int(input())
lstx = []
for i in range(t):
    n = int(input())
    k = 0
    lstp = []
    for i in range(1,n+1):
        if i % 2 == 0:
            lstp.append(i)

    for i in range(n):
        if i % 2 == 1:
            lstp.append(i)

    lstp[len(lstp)-1] += n // 2
    if lstp[len(lstp)-1] % 2 == 0:
        lstx.append('NO')
    else:
        lstx.append(['YES',lstp])

for i in range(len(lstx)):
    if lstx[i] == 'NO':
        print(lstx[i])
    if lstx[i][0] == 'YES':
        print('YES')
        for i in lstx[i][1]:
            print(i, end = ' ')
        print()

'''
2 no
4 yes, 2 4 1 5
6 no
8 yes, 2 4 8 1 3 5 11
10 no
'''