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
import math
import bisect
n=int(input())
arr=list(map(int,input().split()))
n,m=map(int,input().split())
t=sys.stdin.buffer.readline()
sys.stdin=open("input.txt")
sys.stdout=open("output.txt", 'w')
sys.stdout.write("Yes" + '\n')
s="abcdefghijklmnopqrstuvwxyz"
mod=1000000007
mod=998244353
vow=['a','e','i','o','u']
t=[[0 for i in range(n)]for j in range(n)]
pow(4,7)
def gcd(x,y):
    while y:
        x,y=y%x,x
    return y'''
for _ in range(int(input())):
    flag=0
    n=int(input())
    if n%4==0:
        print("YES")
        var=2
        for i in range(n//2):
            print(var ,end=" ")
            var+=2
        va=1
        for i in range(n//2):
            if i>=n//4:
                print(va+2,end=" ")
            else:
                print(va,end=" ")
            va+=2
    else:
        print("NO")
        flag=1

    if flag==0:
        print()