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:
número_de_casos_t = int (input())
for a in range (1, número_de_casos_t+1):
    b = int (input ())
    if (b//2)%2 != 0:
        print ("NO")
    else : 
        lista = list (range(b))
        for i in range (b) :
            if 0 <=  i  < (b//2) :
                valor = 2*i + 2
            else: 
                valor = 2 * (i - (b//2))+1
                if valor == b-1 :
                    valor = (b-1) + b//2 
            lista [i] = str (valor) 
        print ("YES")
        s = " ".join(lista)
        print (s)
       # lista_para_imprimir = ""
        #for index, x  in enumerate(lista) :
         #   if index != b-1:
         #       lista_para_imprimir = lista_para_imprimir + str (x) + " "
          #  else : 
           #     lista_para_imprimir = lista_para_imprimir + str (x)
 #       print (lista_para_imprimir)