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:
t = int(input())
list1 = []
list2 = []
list3 = []
list4 = []
list5 = []
sum3 = 0
sum4 = 0
for test_case in range(t):
    n = int(input())
    if (n/2) % 2 == 1:
        list1.append("NO")
    elif n == 2:
        list1.append("NO")
    else:
        list1.append("YES")
        for number1 in range(2, n + 1, 2):
            list2.append(number1)
        list3 = list2[int(-n/2):]
        for number3 in list3:
            sum3 += number3
        list1.extend(list3)
        for number2 in range(1, n - 2, 2):
            list4.append(number2)
        for number4 in list4:
            sum4 += number4
        list4.append(sum3 - sum4)
        list1.extend(list4)
    for items in list1:
        if type(items) is str:
            print(items)
        else:
            list5.append(items)
    if len(list5) > 0:
        print(' '.join(str(items) for items in list5))
    list1.clear()
    list2.clear()
    list3.clear()
    list4.clear()
    list5.clear()
    sum3 = 0
    sum4 = 0