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,bisect,random
input=sys.stdin.readline
T=int(input())
for _ in range(T):
    n,k=map(int,input().split())
    A=list(map(int,input().split()))
    K=[[0,0] for i in range((2*k)+2)]
    P=[]
    for i in range((n//2)):
        K[A[i]+A[n-i-1]][1]=K[A[i]+A[n-i-1]][1]-1
        K[min(A[i],A[n-i-1])+1][0]=K[min(A[i],A[n-i-1])+1][0]-1
        K[max(A[i],A[n-i-1])+k+1][0]=K[max(A[i],A[n-i-1])+k+1][0]+1
        K[0][0]=K[0][0]+2
    for i in range(1,len(K)):
        K[i][0]=K[i][0]+K[i-1][0]
    for i in range(1,len(K)-1):
        P.append([K[i][0]+K[i][1],i])
        
    v=min(P)
    print(v[0])