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

    sums = {}
    rangeArr = [0] * (2 * k + 2)
    tempRangeArr = [0] * (2 * k + 2)
    for i in range(n//2):
        s = arr[i] + arr[n - i - 1]
        sums[s] = sums[s] + 1 if s in sums else 1
        tempRangeArr[min(arr[i], arr[n - i - 1]) + 1] += 1
        tempRangeArr[max(arr[i], arr[n - i - 1]) + k + 1] += -1
    
    
    rangeArr[0] = tempRangeArr[0]
    for i in range(1, len(tempRangeArr)):
        rangeArr[i] = rangeArr[i - 1] + tempRangeArr[i]
    
    #print(rangeArr)
    bestMin = 9999999
    
    for x in range(2, 2 * k + 1):
        x1Counts = rangeArr[x]
        x0Counts = sums[x] if x in sums else 0
        x2Counts = n//2 - x1Counts
        minCount = x1Counts + x2Counts * 2 - x0Counts
        if minCount < bestMin:
            bestMin = minCount
    
    print(bestMin)


'''
8 7
5 5 5 5 5 6 5 5


[(1 2) (3 4) (1 3) (2 4) (3 7)]

[2 1 1 -1 -2 0 0 -1]
[2 3 4 3 1 1 0 0]'''