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:
import sys
input = sys.stdin.readline

def main():
    test = int(input())
    for _ in range(test):
        n, k = map(int, input().split())
        arr = [int(x) for x in input().split()]
        zeromove = [0 for i in range(2*k+2)]
        onemove = [0 for i in range(2*k+2)]

        for idx in range(0,n//2):
            zeromove[arr[idx] + arr[n-idx-1]] += 1
            left = min(arr[idx], arr[n-idx-1]) + 1
            right = max(arr[idx], arr[n-idx-1]) + k
            onemove[left] += 1
            onemove[right+1] -= 1

        ans = n
        for pairsum in range(2,2*k+1):
            onemove[pairsum] += onemove[pairsum-1]
            zero = zeromove[pairsum]
            one = onemove[pairsum] - zero
            two = n//2 - one -zero
            ans = min(ans, one + 2*two)
            assert(one >= 0)
            assert(two >= 0)
            #print(f"pairsum {pairsum} zero {zero} one {one} two{two}")
        
        print(ans)
        

if __name__ == "__main__":
    main()