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
import collections
import itertools
input = sys.stdin.readline


def main():
    t = int(input())
    for _ in range(t):
        N, K = [int(x) for x in input().split()]
        A = [int(x) for x in input().split()]


        ans = N // 2
        c = collections.Counter()
        x = 0
        y = 0
        B = [0] * (2 * K + 2)
        for i in range(N // 2):
            B[min(A[i], A[-1 - i]) + 1] += 1
            B[max(A[i], A[-1 - i]) + K + 1] -= 1
            c[A[i] + A[-1 - i]] += 1

        ruiseki = list(itertools.accumulate(B))
        for i, v in enumerate(ruiseki):
            tmp = N
            tmp -= c[i]
            tmp -= v
            ans = min(ans, tmp)

        print(ans)



        

    

if __name__ == '__main__':
    main()