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 os
import sys
from io import BytesIO, IOBase

def main(): 
    
    t = int(input())
    for _ in range (t): 

        n,k = map(int, input().split()) 
        L = list(map(int, input().split())) 
        size = 2*k + 1 
        count = [0]*size 
        ans = [0]*size 

        i,j = 0,n-1 
        while i<j: 
            count[L[i]+L[j]] += 1
            i += 1 
            j -= 1 

        i,j = 0,n-1 
        while i<j: 
            a,b = L[i],L[j] 
            ans[min(a,b)+1] += 1 
            try: 
                ans[max(a,b)+k+1] -= 1 
            except IndexError: 
                pass 
            i += 1 
            j -= 1 

        for i in range (2, size): 
            ans[i] += ans[i-1] 

        # print (ans[2:])
        for i in range (2, size): 
            ans[i] -= count[i] 
        for i in range (2, size): 
            ans[i] += 2*(n//2 - (count[i] + ans[i])) 

        # print (count) 
        print (min(ans[2:]))
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = lambda s: self.buffer.write(s.encode()) if self.writable else None

    def read(self):
        if self.buffer.tell():
            return self.buffer.read().decode("ascii")
        return os.read(self._fd, os.fstat(self._fd).st_size).decode("ascii")

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline().decode("ascii")

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


def print(*args, sep=" ", end="\n", file=sys.stdout, flush=False):
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(end)
    if flush:
        file.flush()

sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

# endregion
sys.setrecursionlimit(10000)
if __name__ == "__main__":
    main()