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:
is_even = list()
is_odd = list()

for i in range(1,305001,1):
    if(i%2==0):
        is_even.append(i)
    else:
        is_odd.append(i)
# print(len(is_even))

# print(len(is_odd))


# print(is_odd)

# print(is_even)

k = int(input())


for i in range(k):

    s = int(input())

    su = s//2

    if(su%2 == 0):
        # print(su)
        print('YES')
        su_even = is_even[0:su]
        su_odd = is_odd[0:su-1]
        
        pu = su//2

        sup = su - 1 + pu

        # print(sup)

        su2 = is_odd[sup]

        # print(su2)
        # print(su_odd)

        su_odd.append(su2)

        # print(su_odd)
        # print('sa',sum(su_even))

        # print('sap',sum(su_odd))

        ulti = su_even+su_odd
        print(*ulti)
        
    else:
        print('NO')