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:
def findMaxGuests(arrl, exit, n): 
  
    # Sort arrival and exit arrays 
    arrl.sort(); 
    exit.sort(); 
  
    # guests_in indicates number of  
    # guests at a time 
    guests_in = 1; 
    max_guests = 1; 
    time = arrl[0]; 
    i = 1; 
    j = 0; 
  
    # Similar to merge in merge sort to  
    # process all events in sorted order 
    while (i < n and j < n): 
          
        # If next event in sorted order is  
        # arrival, increment count of guests 
        if (arrl[i] <= exit[j]): 
      
            guests_in = guests_in + 1; 
  
        # Update max_guests if needed 
            if(guests_in > max_guests): 
          
                max_guests = guests_in; 
                time = arrl[i]; 
                  
            # increment index of arrival array 
            i = i + 1;  
      
        else: 
            guests_in = guests_in - 1; 
            j = j + 1; 
    
    return max_guests

for _ in range(int(input())):
    n,k = map(int,input().split())
    ar = list(map(int,input().split()))
    start = []
    end = []
    for i in range(n//2):
        start.append(min(ar[i],ar[i*-1 -1]) + 1)
        end.append(max(ar[i],ar[i*-1 -1]) + k)
        start.append(ar[i]+ar[i*-1 -1])
        end.append(ar[i]+ar[i*-1 -1])
    print(n-findMaxGuests(start,end,len(start)))