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 stdin,stdout
from math import gcd,sqrt,floor,ceil,log2
from itertools import combinations
# Fast I/O
input = stdin.readline
#print = stdout.write

def list_inp(x):return list(map(x,input().split()))
def map_inp(x):return map(x,input().split())

def lcm(a,b): return (a*b)/gcd(a,b)

t = int(input())
for _ in range(t):
    n = int(input())
    if n %4 == 0 :
        print('YES')
        i = 2
        for j in range(n//2):
            print(i,end = ' ')
            i+=2
        arr = []
        for i in range(1,n+1,2):
            arr.append(i)
        arr[-1]+= (n//2)
        print(str(arr).replace(',','').strip('[').strip(']'))


    else:
        print('NO')