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
import random
import sys
from bisect import bisect_left, bisect_right
from collections import Counter, UserDict, defaultdict, deque, namedtuple
from functools import cmp_to_key, lru_cache, reduce
from heapq import heapify, heappop, heappush
from itertools import (chain, combinations, combinations_with_replacement,
                       permutations, product)
# import numpy as np

sys.setrecursionlimit(10**5 + 1)
input = sys.stdin.buffer.readline

MOD = 10**9 + 7

def f(k):
    return 2**k - 1


if __name__ == "__main__":
    T = int(input())

    for _ in range(T):
        n = int(input())
        if n % 4:
            print('NO')
        else:
            print('YES')
            half = n//2
            nums = list(range(2, n+1, 2)) + list(range(1, n-1, 2)) + [n-1+half]
            print(*nums)