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:
def max_overlap(start, end):
    n = len(start)

    start.sort()
    end.sort()
    # print('Start', start)
    # print('End', end)

    inter = 1
    max_inter = 1
    # time = start[0]
    i = 1
    j = 0
    while i < n and j < n:
        if start[i] <= end[j]:
            inter += 1
            if inter > max_inter:
                max_inter = inter
                # time = start[i]
            i += 1
        else:
            inter -= 1
            j += 1

    # print('Time', time)
    return max_inter


t = int(input())
for _ in range(t):
    n, k = map(int, input().split())
    a = list(map(int, input().split()))

    total = 0
    start = []
    end = []
    for i in range(n//2):
        small, big = a[i], a[n-i-1]
        if small > big:
            small, big = big, small

        mini = small + 1
        maxi = big + k

        start.append(mini)
        end.append(maxi+0.1)

        start.append(big+small)
        end.append(big+small+0.1)

    overlap = max_overlap(start, end)
    # print('Overlap', overlap)
    print(n - overlap)
    # print('')