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:
#                               #
    # author : samars_diary #
    # 02-09-2020 │ 07:20:39 #
#                               #

import sys, os.path

# if(os.path.exists('input.txt')):
#     sys.stdin = open('input.txt',"r")
#     sys.stdout = open('output.txt',"w")

sys.setrecursionlimit(10 ** 5)

def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))

def evensum(n):
    n=int(n/2)
    return n*(n+1)

def oddsum(n):
    n=int(n/2)-1
    return n*n

def solve():
    n=II()
    if (n/2)%2==0:
        print("YES")
        for _ in range(1, int(n/2)+1):
            print(2*_, end=" ")
        for _ in range(1, int(n/2)):
            print(2*_-1, end=" ")
        print(evensum(n)-oddsum(n), end=" ")
        print()
        return False
    else:
        flag=False
    if flag == False:
        print("NO")

for _ in range(II()):
    solve()