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:
x=int(input())
for b in range(x):
    y=list(map(int,input().split()))
    z=list(map(int,input().split()))
    d={}
    s1=[]
    s=sum(z)/(y[0]/2)
    arr=[0 for i in range(int(y[1]*2)+2)]
    for a in range(y[0]//2):
        s2=z[a]+z[y[0]-a-1]
        d[s2]=d.get(s2,0)+1
        arr[max(z[a],z[y[0]-a-1])+y[1]+1]-=1
        arr[min(z[a],z[y[0]-a-1])+1]+=1
    for a in range(1,len(arr)):
        arr[a]+=arr[a-1]
    #print(arr)
    #print(d)
    ans=100000000000
    for each in d:
        ans=min(ans,arr[each]+(y[0]//2-arr[each])*2-d[each])
    print(min(ans,max(arr)+(y[0]//2-max(arr))*2))
    '''
    for a in range(y[0]//2):
        s2=z[a]+z[y[0]-a-1]
        if abs(s-s2)<d:
            d=abs(s-s2)
            s1=[s2]
        elif abs(s-s2)==d:
            s1.append(s2)
    s1.append(s)
    r=100000000000
    for each in s1:
        r1=0
        #print(each)
        for a in range(y[0]//2):
            s2=z[a]+z[y[0]-a-1]
            if s2<each:
                if max(z[a],z[y[0]-a-1])+y[1]>=each:
                    r1+=1
                else:
                    r1+=2
            elif s2>each:
                if min(z[a],z[y[0]-a-1])+1<=each:
                    r1+=1
                else:
                    r1+=2
            print(s2)
            print(r1)
            print('-')
        r=min(r,r1)
        print('======')
    print(r)'''