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:
#!/usr/bin/env python
# coding: utf-8

# In[14]:


t = int(input())
cnt = 0
while (cnt < t):
    cnt += 1
    n, k = [int(i) for i in input().split()]
    a = [int(i) for i in input().split()] 
    c = []
    for i in range(n // 2):
        c.append(((min(a[i] + 1, a[n - i - 1] + 1)), -1))
        c.append(((max(a[i] + k, a[n - i - 1] + k) + 1), 1))
    for i in range(n // 2):
        c.append((a[i] + a[n - i - 1], -1))
        c.append((a[i] + a[n - i - 1] + 1, 1))
    d = {}
    for i in range(len(c)):
        d[c[i][0]] = d.get(c[i][0], 0) + c[i][1]
    #print(d)
    counter = n
    val_res = n
    for key, val in sorted(list(d.items())):
        counter += val
        if val_res > counter:
            val_res = counter
    print(val_res)       


# In[ ]: