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:

from collections import defaultdict
import sys

stream = sys.stdin
# stream = open('input.txt', 'r')
t = int(stream.readline())

for line in stream:
    n, k = line.split()
    n, k = map(int, (n, k))
    
    sums_rating = defaultdict(int)
    open_close = defaultdict(int)
    
    numbers = stream.readline().split()
    for i in range(n//2):
        n1 = int(numbers[i])
        n2 = int(numbers[-(i+1)])
        
        sums_rating[n1+n2] += 1
        
        mini = min(n1, n2)
        maxi = max(n1, n2)
        open_close[mini + 1] += 1
        open_close[maxi + k + 1] -= 1
        
    # print(sums_rating, open_close)
            
    curr_modifier = 0
    best_result = -float('inf')
    
    for i in range(2, 2*k+1):
        curr_modifier += open_close[i]
        
        if sums_rating[i] + curr_modifier > best_result:
            best_result = sums_rating[i] + curr_modifier
            
    print(n - best_result)
    
    # break