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:
for _ in range(int(input())):
    n = int(input())
    if (n % 2 == 1 or (n//2) % 2 == 1):
        print('NO')
        continue
    print('YES')

    arr = []
    i = 1
    while i <= n / 2:
        arr.append(i * 2)
        i += 1
    # print(arr)
    sumarr = sum(arr) // (n // 2)
    # print(sumarr)
    arrleft = []
    cur = 1
    if (sumarr % 2 == 0):
        cur = (sumarr - 1) - n // 2
    else:
        cur = (sumarr) - n // 2
    # print(cur)

    for i in range(0, n // 4):
        arrleft.append(cur)
        cur += 2

    cur += 2
    for i in range(0, n // 4):
        arrleft.append(cur)
        cur += 2
    print(*(arr + arrleft), sep=' ')

# for i in range(0, 10, 2):

# print(i)

# for i in range(n - 3):
#     index = close(l, x[len(x) -1])
#     x.append(l.pop(index))
# x.append(l.pop())
# print(*x, sep=' ')