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:
DEBUG = False
t = int(input())
for case in range(t):
    n, k = map(int, input().split())
    p = n // 2

    sums = (2*k-1)*[0]
    bottom_half, top_half = k*[0], k*[0]

    array = [int(x) for x in input().split()]
    for i in range(p):
        a = min(array[i], array[n-i - 1])
        b = max(array[i], array[n-i - 1])

        bottom_half[a-1] += 1
        top_half[b-1] += 1
        sums[a+b-2] += 1

    #--- generate partial sums bottom half
    countb = 0
    cum_bottom = k*[0]
    for i in range(k):
        countb += bottom_half[k-i-1]
        cum_bottom[k-i-1] += countb

    countt = 0
    cum_top = k*[0]
    for i in range(k):
        countt += top_half[i]
        cum_top[i] += countt

    if DEBUG:
        print (cum_bottom)
        print (cum_top)

    cum_bottom.pop(0)
    cum_top.pop()
    combined_halves = cum_bottom + [0] + cum_top

    answer = p
    for m in range(2*k-1):
        answer = min(p - sums[m] + combined_halves[m], answer)
    print (answer)
        
        
        
        
        
        

    if DEBUG:
        print (combined_halves)
        print (sums)