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:
from sys import *
input = stdin.readline

for _ in range(int(input())):
    
    n,k = map(int,input().split())
    a = list(map(int,input().split()))
    b = [0]*(2*k+1)
    c = [0]*(2*k+1)
    mn = 1e18
    for i in range(n//2):
        x,y = a[i],a[n-i-1]
        x,y = min(x,y),max(x,y)
        sn = x + y
        if(sn+1<=2*k):
            b[sn+1] += 1
        if(sn-1>=0):
            c[sn-1] += 1
        if(sn-(y)>=0):
            c[sn-y] += 1
        if(sn+(k-x)+1<=2*k):
            b[sn+(k-x)+1] += 1
    #print(b,c)
    for i in range(1,2*k+1):
        b[i] += b[i-1]
    for i in range(2*k-1,-1,-1):
        c[i] += c[i+1]
        
    for i in range(2*k+1):
        mn = min(mn,b[i]+c[i])
    
    print(mn)