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:
def balanced_array():
    cases = int(input())
    for i in range(cases):
        num = int(input())
        lista_pari = []
        lista_dispari = []
        for i in range(1, num-1):
            if i % 2 == 0:
                lista_pari.append(i)
            else:
                lista_dispari.append(i)
        if len(lista_pari) == 0:
            lista_pari.append(2)
        else:
            lista_pari.append(lista_pari[len(lista_pari)-1] + 2)
        pari = 0
        dispari = 0
        for i in lista_pari:
            pari += i
        for i in lista_dispari:
            dispari += i
        if (pari - dispari) % 2 == 1:
            numero = pari - dispari
            risultato = ""
            print("YES")
            for i in lista_pari:
                risultato += str(i) + " "
            for i in lista_dispari:
                risultato += str(i) + " "
            print(risultato + str(numero))
                
        else:
            print("NO")
balanced_array()