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 Sumof(tab):
    sm = 0
    for item in tab:
        sm += item
    return sm


def main():
    t = int(input())
    for turn in range(t):
        n = int(input())
        if (n // 2) % 2 != 0:
            print("NO")
            pass
        else:
            print('YES')
            tab = []
            tab1 = []
            tab2 = []
            d = 2
            e = 1
            for x in range(0, n//2):
                tab1.append(d)
                d += 2
            m = Sumof(tab1)
            #print(m)
            for x in range(0, n//2):
                if x == (n//2)-1:
                    if m%2 != 0:
                        #print(m)
                        tab2.append(m)
                        break
                    else:
                        pass
                else:
                    tab2.append(e)
                    m -= e
                    e += 2

            tab = tab1 + tab2

            for i in tab:
                print(i, end=" ")


    return 0


if __name__ == '__main__':
    main()