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())
# i =1
# 2 4 1 5
# 6 8 3 11
# 10 12 7 15
# 14 16 9 21
# 18 20 13
# odd = [ for i in range()]
for _ in range(T):
    n = int(input())
    if (n/2)%2 != 0:
        print ("NO")
        continue
    print("Yes")

    ans_odd = {}
    ans_even = {}
    even = 1
    for i in range(1,int(n/2)+1,2):
        first, second = 2*i, 2*(i+1)
        ans_odd[first] = 1
        ans_odd[second] = 1
        s = first + second

        while(True):
            # print (first, second, s, even, s-even)
            if even not in ans_even and s-even not in ans_even:
                ans_even[even] =1
                ans_even[s-even]=1
                break
            even +=2
    print (' '.join([str(x) for x in sorted(list(ans_odd.keys())) + sorted(list(ans_even.keys()))]))