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 sys import stdin,stdout

for case in range(int(stdin.readline())):
    n,k = [int(x) for x in stdin.readline().split()]

    a = [int(x) for x in stdin.readline().split()]

    a1 = a[:n//2]
    a2 = a[n//2:][::-1]

    for x in range(n//2):
        if a1[x] > a2[x]:
            a1[x], a2[x] = a2[x], a1[x]

    lows = {}
    lowCount = [0 for x in range(max(a1)+1)]
    highCount = [0 for x in range(max(a2)+1)]

    for x in a1:
        lowCount[x] += 1
    for x in a2:
        highCount[x] += 1

    lowSums = [highCount[0]]
    highSums = [lowCount[-1]]

    for x in highCount[1:]:
        lowSums.append(lowSums[-1]+x)

    for x in lowCount[:-1][::-1]:
        highSums.append(highSums[-1]+x)
    highSums = highSums[::-1]
        
    sums = {}

    for x in range(n//2):
        if a1[x]+a2[x] in sums:
            sums[a1[x]+a2[x]] += 1
        else:
            sums[a1[x]+a2[x]] = 1

    best = n//2

    for x in sums:
        total = n//2-sums[x]
        if x > k:
            total += lowSums[x-k-1]
        if x < len(highSums):
            total += highSums[x]
        best = min(best, total)
        
    print(best)