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 sys
from random import choice,randint
inp=sys.stdin.readline
out=sys.stdout.write
flsh=sys.stdout.flush
 
sys.setrecursionlimit(10**9)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
 
def MI(): return map(int, inp().strip().split())
def LI(): return list(map(int, inp().strip().split()))
def LLI(): return [list(map(int, l.split())) for l in sys.stdin.readlines().strip()]
def LI_(): return [int(x)-1 for x in inp().strip().split()]
def LF(): return [float(x) for x in inp().strip().split()]
def LS(): return inp().strip().split()
def I(): return int(inp().strip())
def F(): return float(inp().strip())
def S(): return inp().strip()
def pf(s): return out(s+'\n')
def JA(a, sep): return sep.join(map(str, a))
def JAA(a, s, t): return s.join(t.join(map(str, b)) for b in a)

def main():
    t = I()
    l = []
    for _ in range(t):
        n = I()
        a = []
        if n==2:
            print("NO")
        else:
            for i in range(n//2):
                a.append((i+1)*2)
            sm = sum(a)
            for i in range(n//2):
                z = (i*2)+1
                a.append(z)
                sm -=z
            if sm==0:
                print("YES")
                print(*a)
            else:
                x = a.pop()
                if (sm+x)%2==0:
                    print("NO")
                else:
                    a.append(sm+x)
                    print("YES")
                    print(*a)
    # for i in range(t):
    #     pf(str(l[i]))

if __name__ == "__main__":
    main()