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:
# cook your dish here
from sys import stdin, stdout
import math
from itertools import permutations, combinations
from collections import defaultdict
from bisect import bisect_left 
from bisect import bisect_right
 
def L():
    return list(map(int, stdin.readline().split()))
 
def In():
    return map(int, stdin.readline().split())
 
def I():
    return int(stdin.readline())
 
P = 1000000007
def main():
    for t in range(I()):
        n = I()
        if n%4 != 0:
            print('NO')
        else:
            flag = 1
            arr = []
            sm = 0
            for i in range(1, n//2+1):
                arr.append(2*i)
                sm += 2*i
            for i in range(n//2-1):
                arr.append(2*(i+1)-1)
                sm -= (2*(i+1)-1)
                if sm <= 0:
                    flag = 0
                    break
            arr.append(sm)
            if flag:
                print('YES')
                for i in arr:
                    print(i, end = " ")
                print()
            else:
                print('NO')
    
if __name__ == '__main__':
    main()