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:
import sys
input=sys.stdin.readline
m=1000000007
def power(x,y): 
    res = 1
    while (y > 0):  
        if ((y & 1) == 1) : 
            res = (res * x )%m
        y = y >> 1
        x =( x * x )%m
      
    return res%m
##dp=[0]*30
##dp[0]=1
##for i in range(1,30):
##    dp[i]=dp[i-1]+power(2,i)

'''
5
2
4
6
8
10

'''
def main():
    for _ in range(int(input())):
        n=int(input())
        if(n%4!=0):
            print("NO")
        else:
            l=[i for i in range(2,2*(n//2)+1,2)]
            for i in range(n//2):
                if(i<n//4):
                    l.append(l[i]-1)
                else:
                    l.append(l[i]+1)
            print("YES")
            print(*l)
            

##        l=list(map(int,input().split()))
##        a,b=map(int,input().split())






















if __name__== "__main__":
  main()