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:
import math,sys
def li(): return list(map(int,sys.stdin.readline().split()))
def ls(): return list(map(int,list(input())))
def ii():  return int(input())
def isPrime(n):
    i= 2
    if n == 1:
        return False
    while i <= int(math.sqrt(n)):
        if n%i == 0:
            return False
        i = i + 1
    return True
def gcd(a,b):
    if b == 0:
        return a
    return gcd(b,a%b)
t = ii()
for _ in range(t):
    n = ii()
    if (n//2) % 2 == 0 :
        even = []
        odd = []
        for x in range(1,(n//2) + 1):
            even.append(2*x)
            odd.append(2*x-1)
        odd[-1] = sum(even)-sum(odd[0:(n//2)-1])
        even.extend(odd)
        print('YES')
        print(*even)
    else:
        print('NO')