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()[2:])
# s = input()
# while t:s = s.replace('BG','GB');t-=1
# print (s)

t = int(input())
n = [0 for x in range(0, t)]
for i in range(t):
    n[i] = int(input())
for i in n:
    if i % 4 != 0:
        print("No")
    else:
        print('YES')
        print(*range(2,i+1,2),*range(1,i-1,2),(i*3)//2-1)

# print(n[x] for x in n)

# for j in range(1, 1001):
#     if (j*k)%10 == 0 :
#         print(j)
#         break
#     else:
#         if (j*k)%10 == r:
#             print(j)
#             break

# print(237%10)
# j = 0
# s = [0 for x in range(0, 27)]
# for i in a:
#     if i.isalpha():
#         s[ord(i) - 97] += 1
# for x in s:
#     if x != 0:
#         j += 1
# print(j)