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:
# https://codeforces.com/problemset/problem/1343/D

import sys

# sys.stdin = open(r"./file/input.txt", 'r')
# sys.stdout = open(r"./file/output.txt", 'w')

t = int(input())

for _ in range(t):
    arr = input().split(" ")
    n = int(arr[0])
    k = int(arr[1])

    arr = input().split()
    arr = list(map(int, arr))

    ks = [0] * (2 * k + 2)
    # print(ks)
    for i in range(int(n/2)):
        left = arr[i]
        right = arr[n - i - 1]

        if left > right:
            left, right = right, left

        """
        2 : [2, left], [right + k + 1, 2*k]
        1 ：[left + 1, left + right - 1], [left + right + 1, right + k]
        0 : [left + right, left + right]
        """

        ks[2] += 2
        ks[left + 1] -= 1
        ks[left + right] -= 1
        ks[left + right + 1] += 1
        ks[right + k + 1] += 1

    sum = 0
    minvalue = 99999999
    for i in range(2, k * 2 + 1):
        sum += ks[i]
        minvalue = min(minvalue, sum)
    
    print(minvalue)