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()]
    arr=[int(x) for x in input().split()]

    # Now the sum can range from 2 to 2*k
    '''
    Since the sum can vary from 2 to 2*k we create a prefix array and each element in the array is a value of x that give the number of pairs that can give that x in one change
    '''

    count=[0 for i in range(2*k+1)]
    pref=[0 for i in range(2*k+2)]
    for i in range(len(arr)//2):
        summ=arr[i]+arr[-(i+1)]
        count[summ]+=1
        minval=1+min(arr[i],arr[-(i+1)])
        maxval=k+max(arr[i],arr[-(i+1)])
        pref[minval]+=1
        pref[maxval+1]-=1
    
    # print(count)


    for i in range(1,len(pref)):
        pref[i]+=pref[i-1]

    # print(pref)
    ans=n
    for i in range(2,2*k+1):
        #Assume the current x is i and calculate the total number of changes required
        changes=pref[i] - count[i]+(n//2 - pref[i])*2
        ans=min(ans,changes)

    print(ans)