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())
import math

for _ in range(t):
    n, k = map(int, input().split())
    k-=1
    l = list(map(int, input().split()))
    d={}
    f={}
    m={}
    tot = set()
    for i in range(n//2):
        a, b= l[i]-1, l[-i-1]-1
        a, b = sorted([a,b])
        
        if a in d:
            d[a]+=1
        else:
            d[a]=1
            
        if b+k in f:
            f[b+k]+=1
        else:
            f[b+k] = 1
            
        if a+b in m:
            m[a+b]+=1
        else:
            m[a+b]=1
            
        tot.add(a)
        tot.add(b+k)
        tot.add(a+b)
    tot = sorted(list(tot))
    score = n
    mini = score
    #print(tot)
    #print(m)
    #print(d)
    #print(f)
    for x in tot:
        if x in d:
            score-=d[x]
        if x in m:
            score -= m[x]
            mini = min(mini, score)
            score += m[x]
        else:
            mini = min(mini, score)
        if x in f:
            score+=f[x]
    print(mini)