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 itertools
numcases = int(input())

def minmoves(asum, a, k):
    count = {x: 0 for x in range(2*k + 1)}
    ans = 1000000
    moves = 0
    for sum in asum:
        count[sum] = count[sum] + 1
    #+1s
    rangex = [0 for i in range(2*k + 2)]
    lower, upper, = 0, 0
    for i in range(int(n/2)):
        lower = min(a[i], a[n - 1 - i]) + 1
        upper = max(a[i], a[n - 1 - i]) + k
        rangex[lower] += 1
        rangex[upper + 1] -=1
    prefix = list(itertools.accumulate(rangex))
    for i in range(2, 2*k +1):
        moves = prefix[i] - count[i] + 2*(n/2 - prefix[i])
        if moves < ans:
            ans = moves
    return ans
        
for z in range(numcases):
    n, k, = map(int, input().split())
    a = list(map(int, input().split()))
    asum = []
    sols = []
    for i in range(int(n/2)):
        asum.append(a[i] + a[n - 1 - i])
    ans = minmoves(asum, a, k)
    print(int(ans))