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 NO(): return print("NO")
def YES(): return print("YES")
def INT(): return int(input())
def LIST(): return list(map(int, input().split()))
def STR(): return input()
def MAP(): return map(int, input().split())

for _ in range(INT()):
    n = INT()
    even = [2]
    odd = [1]
    cnteven = 4
    cntodd = 3
    ans = []
    if int(n/2)&1: NO()
    else:
        YES()
        for i in range(int(n/2)-1):
            even.append(cnteven)
            if len(odd) < int(n/2-1): odd.append(cntodd)
            cnteven += 2
            cntodd += 2
        odd.append(sum(even)-sum(odd))
        ans = even + odd
        for i in range(len(ans)):
            print(ans[i], end=" ")
        print("")