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 deque
from collections import OrderedDict
import math

maxValue = 2*100000+2
#dp1 = [[0] *100000 for i in range(4)]

for t in range(int(input())):
    n, k = map(int, input().split())
    arrIn = input().split()
    dp = [0]*(2*max(k+1, n+1))
    dp1 = [0]*(2*max(k+1, n+1))
    for i in range(len(arrIn)):
        arrIn[i]=int(arrIn[i])   
    for i in range(len(arrIn)//2):
        x = arrIn[i]
        y = arrIn[len(arrIn)-i-1]
        dp[2]+=2
        dp[min(x,y)+1]-=2
        dp[min(x,y)+1]+=1
        dp[x+y]-=1
        dp[x+y+1]+=1
        dp[max(x,y)+k+1]-=1
        dp[max(x,y)+k+1]+=2
    for i in range(1,k*2+1):
        dp1[i]=dp1[i-1]+dp[i]
    answer = maxValue
    for i in range(2,k*2+1):
        answer = min(answer, dp1[i])
    print(answer)