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 : thekushalghosh
    Team   : CodeDiggers
"""
import sys,math,cmath,time
start_time = time.time()
################# ---- USER DEFINED INPUT FUNCTIONS ---- #################
def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(s[:len(s) - 1])
def invr():
    return(map(int,input().split()))
##########################################################################
################# ---- THE ACTUAL CODE STARTS BELOW ---- #################

def solve():
    n = inp()
    if n % 4 == 0:
        q = [-4]
        for i in range(n // 2):
            if i % 2 != 0:
                q.append(q[-1] + 2)
            else:
                q.append(q[-1] + 6)
        q.pop(0)
        for i in range(n // 2):
            if i % 2 != 0:
                q.append(q[-n // 2] + 1)
            else:
                q.append(q[-n // 2] - 1)
        print("YES")
        print(*q)
    else:
        print("NO")
    
################## ---- THE ACTUAL CODE ENDS ABOVE ---- ##################
##########################################################################
ONLINE_JUDGE = __debug__
if not ONLINE_JUDGE:
    sys.stdin = open('input.txt','r')
    sys.stdout = open('output.txt','w')
else:
    input = sys.stdin.readline
t = 1
t = inp()
for tt in range(t):
    solve()
if not ONLINE_JUDGE:
    print("Time Elapsed:",time.time() - start_time,"seconds")
sys.stdout.close()