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:
"""
Author: guiferviz
Time: 2020-04-21 16:35:02
"""

def solve():
    # Read input.
    n, k = list(map(int, input().split()))
    a = list(map(int, input().split()))

    h = n // 2
    c = [0] * (2*k+2)
    for i in range(h):
        # Two changes
        c[0] += 2
        # No change in this pair.
        p = a[i] + a[n-i-1]
        c[p] += -1
        c[p+1] += 1
        # Only one change.
        min_sum_1 = min(a[i], a[n-i-1]) + 1
        max_sum_1 = max(a[i], a[n-i-1]) + k
        c[min_sum_1] += -1
        c[max_sum_1+1] += 1
    # Compute prefix sum.
    s = 0
    for i in range(len(c)):
        s += c[i]
        c[i] = s

    print(min(c))


def main():
    t = int(input())
    for _ in range(t):
        solve()


if __name__ == "__main__":
    main()