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 $\frac{n}{2}$ elements of $a$ are even (divisible by $2$);  the second $\frac{n}{2}$ 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 ($\sum\limits_{i=1}^{\frac{n}{2}} a_i = \sum\limits_{i=\frac{n}{2} + 1}^{n} a_i$). 

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 $t$ ($1 \le t \le 10^4$) — the number of test cases. Then $t$ test cases follow.

The only line of the test case contains one integer $n$ ($2 \le n \le 2 \cdot 10^5$) — 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 $2 \cdot 10^5$ ($\sum n \le 2 \cdot 10^5$).


-----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 $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$) 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

Difficulty: introductory

Starter code:

Solutions:
for _ in range(int(input())):
    n=int(input())
    if(n%4!=0):
        print('NO')
    elif(n%4==0):
        print('YES')
        a=[]
        for i in range(1,n//2+1):
            a.append(i*2)
        s=sum(a)
        s1=0
        for i in range(1,n//2):
            x=i*2-1
            a.append(x)
            s1+=x
        a.append(s-s1)
        print(*a)

t = int(input())
for rew in range(t):
	n = int(input())
	if n%4 == 2:
		print("NO")
	else:
		print("YES")
		n//=2
		pocz = [2*(i+1) for i in range(n)]
		kon = [2*i+1 for i in range(n-1)]
		dod = sum(pocz)-sum(kon)
		odp = pocz + kon + [dod]
		print(*odp)

for i in range(int(input())):
	n=int(input())
	k=int(n/2)
	if(k%2==1):
		print("NO")
	else:
		print("YES")
		s1=0
		for i in range(k):
			print(2*(i+1), end=" ")
			s1+=2*(i+1)
		s2=0
		for i in range(k-1):
			print(2*i+1, end=" ")
			s2+=2*i+1
		print(s1-s2)

from math import *
test = int(input())
for test_case in range(test):
	n = int(input())
	ans = []
	s = 0
	for i in range(1,n//2+1):
		ans.append(i*2)
		s += i*2
	for i in range(1,n//2):
		ans.append(i*2-1)
		s -= i*2-1
	if(s%2 == 0):
		print("NO")
		continue
	else:
		ans.append(s)
		print("YES")
		for i in ans:
			print(i,end = " ")
		print()

t = int(input())
for _ in range(t):
    n = int(input())
    if (n // 2) % 2:
        print("NO")
        continue
    a = []
    s = 0
    for i in range(n // 2):
        s += 2*(i + 1)
        a.append(2*(i + 1))
    for j in range(n // 2 - 1):
        s -= 2*j + 1
        a.append(2*j + 1)
    a.append(s)
    print("YES")
    print(*a)


# a = list(map(int,input().split()))
# n,m = map(int,input().split())



import sys
lines = sys.stdin.readlines()
T = int(lines[0].strip())
for t in range(1, T+1):
    n = int(lines[t].strip())
    if n % 4 == 2: print("NO"); continue
    print("YES")
    res = []
    tmp = 0
    for i in range(1, n//2+1):
        res.append(2*i)
        tmp += 2*i
    for i in range(1, n//2):
        res.append(2*i-1)
        tmp -= 2*i-1
    res.append(tmp)
    print(" ".join(map(str, res)))


from math import *

for zz in range(int(input())):
    n = int(input())
    if n % 4 != 0:
        print('NO')
    else:
        print('YES')
        a = []
        cs = 0
        ce = 2
        for i in range(n//2):
            a.append(ce)
            cs += ce
            ce += 2
        ce = 1
        for i in range(n//2, n - 1):
            a.append(ce)
            cs -= ce
            ce += 2
        a.append(cs)
        print(*a)


t = int(input())
for tt in range(t):
	n = int(input())
	if n % 4 == 0:
		print('YES')
		a = list(range(2, n + 1, 2)) + list(range(1, n - 1, 2)) + [sum(range(2, n + 1, 2)) - sum(range(1, n - 1, 2))]
		print(' '.join(map(str, a)))
	else:
		print('NO')


t = int(input())
for _ in range(t):
    n = int(input())
    if (n//2)%2 == 1:
        print("NO")
    else:
        print("YES")
        even = [i*2 for i in range(1, n//2 + 1)]
        odd = [(i*2 - 1) for i in range(1, n//2)]
        odd.append((sum(even) - sum(odd)))
        print(*even, *odd)