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 sys import maxsize
#input = stdin.readline().strip


def solve(n):
    a = [0]*(n+1)
    for i in range(1, n//2+1):
        a[i] = 2*i
    for i in range(n//2+1, 3*n//4+1):
        a[i] = a[i-n//2]-1
    for i in range(3*n//4+1, n+1):
        a[i] = a[i-n//2]+1
    for i in range(1, n+1):
        print(a[i], end=' ')
    pass


test = 1
test = int(input())
for t in range(0, test):
    # brr = [list(map(int,input().split())) for i in range(rows)]              # 2D array row-wise input
    n = int(input())
    # s = list(input())                                                        # String Input, converted to mutable list.
    # n, x = list(map(int, input().split()))
    # arr = [int(x) for x in input().split()]
    if(n % 4 != 0):
        # print(n)
        print("NO")
    else:
        print('YES')
        ans = solve(n)
        print()


'''
rows, cols = (5, 5)
arr = [[0]*cols for j in range(rows)]                                         # 2D array initialization
b=input().split()                                                             # list created by spliting about spaces
brr = [[int(b[cols*i+j]) for j in range(cols)] for i in range(rows)]          # 2D array Linear Input
rows,cols=len(brr),len(brr[0])                                                # no of rows/cols for 2D array
arr.sort(key = lambda x : x[1])                                               # sort list of tuples by 2nd element, Default priority - 1st Element then 2nd Element
s=set()                                                                       # empty set
a=maxsize                                                                     # initializing infinity
b=-maxsize                                                                    # initializing -infinity
mapped=list(map(function,input))                                              # to apply function to list element-wise
try:                                                                          # Error handling
    #code 1
except:                                                                       # ex. to stop at EOF
    #code 2 , if error occurs
'''