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 sys
input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)


t=int(input())
for _ in range(t):
    n,k=[int(x) for x in input().split()]
    arr=[int(x) for x in input().split()]
    
    sumCnts=[0 for __ in range(2*k+1)] #number of pairs summing to this (need 0 change)
    minimumSumsChange1=[0 for __ in range(2*k+1)]
    maximumSumsChange1=[0 for __ in range(2*k+1)]
    r=n-1
    for l in range(n):
        if l>r:
            break
        a,b=arr[l],arr[r]
        sumCnts[a+b]+=1
        minimumSumsChange1[min(a,b)+1]+=1
        maximumSumsChange1[max(a,b)+k]+=1
        r-=1
        
    change1=[0 for __ in range(2*k+1)] #number of pairs that can sum to i with at most 1 change (inclusive of those needing 0 change)
    cnt=0
    for i in range(2*k+1):
        cnt+=minimumSumsChange1[i]
        change1[i]=cnt
        cnt-=maximumSumsChange1[i]
    change2=[0 for __ in range(2*k+1)]
    for i in range(2*k+1):
        change2[i]=n//2-change1[i]
    ans=float('inf')
    for x in range(2,2*k+1):
        ans=min(ans,change1[x]-sumCnts[x]+2*change2[x])
    print(ans)