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:
t=int(input())
for _ in range(t):
    n,k=[int(x) for x in input().split()]
    a=[int(x) for x in input().split()]
    b=[0 for x in range(2*k+1)]
    for i in range(n//2):
        b[0]+=2
        b[2*k]+=-2
        x=min(a[i],a[n-1-i])
        y=max(a[i],a[n-1-i])
        b[x]+=-1
        b[y+k]+=1
        b[x+y-1]+=-1
        b[x+y]+=1
        # print(b)
        # sumo=0
        # for x in b:
        #     sumo+=x
        #     print(sumo,end=" ")
        # print()
    mini=int(2e9)
    minidx=-1
    sumi=0
    for i in range(0,2*k):
        sumi+=b[i]
        if sumi<mini:
            mini=sumi
            minidx=i
    print(mini)
    # sumii=int(1e9+7)
    # for i in range(1,2*k+1):
    #     if len(b[i-1])!=0:
    #         sumjj=0
    #         for j in range(1,2*k+1):
    #             for x in b[j-1]:
    #                 #(x,j-x) x+A(1 to k)=i or j-x+b(1 to k)=i then 1 else 2
    #                 if (i!=j):
    #                     if ((i-x<=k and i-x>=1) or (i+x-j<=k and i+x-j>=1)): sumjj+=1
    #                     else: sumjj+=2
    #                 #%[i-k,i-1] +[j-i+1,j+k-i]
    #         sumii=min(sumii,sumjj)
    # print(sumii)
    
    # x,y-> i if x+y==i then 0 else if i-k<=x<=i-1 or i-k=<y<=i-1
    # x,y:-> [x+y,x+y]:->0 union([x+1,x+k],[y+1,y+k]) :->1 otherwise :-> 2
    # [0,2k]