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 oddIntegers(n, k, l):
    if (n % 2 != k % 2):
        return -1;
    sum = 0;
    i = 1;
    j = 1;
    while (j < k):
        sum += i;
        # print(i,end= " ");
        l.append(i)
        i += 2;
        j += 1;
    fin = int(n - sum);
    l.append(fin)


t = int(input())
for _ in range(t):
    n = int(input())
    n1 = n / 2
    su = n1 * (n1 + 1)
    k = []
    for i in range(2, n + 1, 2):
        k.append(i)
    l = []
    if oddIntegers(su, n1, l) != -1:
        k += l
        print('YES')
        for i in k:
            print(i, end=' ')
    else:
        print('NO')