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= [int(x) for x in input().strip().split()]
    a = [int(x) for x in input().strip().split()]
    dic = {}
    seg= [0 for i in range(2*k+5)]
    l = 0
    h = n-1
    while l<h:
        s= a[h]+a[l]
        if s not in dic:
            dic[s]=0
        dic[s]+=1

        mn = min(a[l],a[h])+1
        mx = max(a[l],a[h])+k
        # if mn not in seg:
        #     seg[mn]=0
        seg[mn]+=1
        # if mx+1 not in seg:
        #     seg[mx+1]=0
        seg[mx+1]-=1
        l+=1
        h-=1

    

    tot = n//2

    s = 0
    for i in range(2*k+5):
        s+=seg[i]
        seg[i]=s

    res = n
    for i in range(2*k+5):
        curr = seg[i]
        if i in dic:
            onere=curr-dic[i]
            ca = dic[i]
        else:
            onere = curr
            ca = 0

        
        if ca>=tot:
            res=0
            break
        else:
            currres=onere
            if onere+ca>=tot:
                res = min(res,currres)
            else:
                rem = tot-ca-onere
                currres+=2*rem
                res = min(res, currres)
    
    print(res)