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
for _ in range(int(input())):
    Map={}
    n,k=map(int, input().split())
    a=list(map(int, input().split()))
    max_sum=[0 for i in range(2*k+1)]
    min_sum=[0 for i in range(2*k+1)]
    for i in range(n//2):
        s=a[i]+a[n-1-i]
        min_sum[min(a[i],a[n-1-i])+1]+=1
        max_sum[max(a[i],a[n-1-i])+k]+=1
        if s not in Map:
            Map[s]=0
        Map[s]+=1
    for i in range(1,2*k+1):
        min_sum[i]+=min_sum[i-1]
        max_sum[i]+=max_sum[i-1]
    ans=sys.maxsize
    for i in range(2,2*k+1):
        two=max_sum[i-1]+min_sum[2*k]-min_sum[i]
        two*=2
        res=two+(n-two)//2
        if i in Map:
            res-=Map[i]
        ans=min(ans, res)
    print(ans)