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 PYTHON):

Solution:
from sys import stdin

rints = lambda: [int(x) for x in stdin.readline().split()]
out = []

for _ in range(int(input())):
    n, k = rints()
    a, mem = rints(), [0] * ((k * 2) + 2)

    for i in range(n // 2):
        s = a[i] + a[-1 - i]
        mi, ma = min(a[i], a[-1 - i]), max(a[i], a[-1 - i])

        mem[s + 1] += 1
        mem[mi + 1] += 1
        mem[s] -= 1
        mem[k + ma + 1] += 1
        if s != 2:
            mem[2] += 2
            mem[mi + 1] -= 2

    # print(mem)
    tem, ans = 0, float('inf')

    for j in mem[2:-1]:
        tem += j
        ans = min(ans, tem)

    out.append(str(ans))
print('\n'.join(out))