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 t in range(T):

    n , k = map(int , input().split())

    values = list(map(int , input().split()))

    zero = [0]*(2*k+2)
    one = [0]*(2*k+2)
    prefix_one = [0]*(2*k+2)
    two = [0]*(2*k+2)
    
    for i in range(n//2):
    	temp = values[i] + values[n-i-1]
    	min_sum = min(values[i] ,values[n-i-1]) + 1
    	max_sum = max(values[i] ,values[n-i-1]) + k + 1
    	one[min_sum] += 1
    	one[max_sum] -= 1
    	zero[temp] += 1
    		
    for i in range(2,2*k+1):
    	prefix_one[i] = prefix_one[i-1] + one[i]
    	
    for i in range(2,2*k+1):
    	two[i] = n//2 - prefix_one[i]
    	
    #print(zero , prefix_one ,two) 
    ans = prefix_one[2] + 2*two[2] - zero[2]
    
    for i in range(3,2*k+1):
    	ans = min(ans , 1*prefix_one[i] + 2*two[i] - zero[i])
    	
    print(ans)