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:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sun May  3 17:02:53 2020

@author: neb0123
"""

def max_overlap(start, end):
    n = len(start)
 
    start.sort()
    end.sort()
 
    inter = 1
    max_inter = 1
    i = 1
    j = 0
    while i < n and j < n:
        if start[i] <= end[j]:
            inter += 1
            if inter > max_inter:
                max_inter = inter
            i += 1
        else:
            inter -= 1
            j += 1
 
    return max_inter
  

def solution(A, n, k):
    arrl = []
    ext = []
    
    for i in range(n // 2):
        x, y = A[i], A[-i-1]
        arrl.append(1 + min(x,y))
        ext.append(k + max(x,y))
        arrl.append(x+y)
        ext.append(x+y)
        
    x = max_overlap(arrl, ext)
    
    return n - x
        

if __name__ == "__main__":
    # inputs = input()
    # string = str(inputs)
    # map(int, input().split(" "))
    
    t = int(input())
    
    for _ in range(t):
        n, k = map(int, input().split(' '))
        A = list(map(int, input().split(' ')))

        print(solution(A,n,k))