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())
for i in range(t):
    n = int(input())
    j = 0
    i = 1
    c = c1 = 0
    sum = 0;
    sum1 = 0
    a = []
    b = []
    d = []
    j = 2
    if n % 2 == 0:
        while j % 2 == 0:
            c = c + 1
            sum = sum + j
            a.append(j)
            j = j + 2
            if c == n // 2:
                break

        while i % 2 != 0:
            c1 = c1 + 1
            if c1 > n // 2:
                break
            if c1 < n // 2:
                sum1 = sum1 + i
                b.append(i)
                i = i + 2
            while c1 == n // 2:
                sum1 = sum1 + i
                if sum1>sum:
                    break
                if sum1 == sum:
                    b.append(i)

                    break
                else:
                    sum1 = sum1 - i
                    i = i + 2
    if sum == sum1:
        d = a + b
        print("YES")
        print(*d,sep=" ")

    else:
        print("NO")