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 math
import sys
from collections import defaultdict
from collections import Counter
from collections import deque
import bisect
from itertools import accumulate
input = iter(sys.stdin.buffer.read().decode().splitlines()).__next__
ilele = lambda: map(int,input().split())
alele = lambda: list(map(int, input().split()))
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]

for _ in range(int(input())):
    n,k = ilele()
    A = alele()
    B= [];mark = {};mins = [0]*(2*k +2);maxs = mins.copy()
    for i in range(n//2):
        x = A[i]
        y = A[n-i-1]
        mark[x+y] = mark.get(x+y,0) + 1
        if x>y:
            x,y = y,x
        mins[x + 1] += 1
        maxs[y + k + 1] += 1
    v = 0;Ans = n//2
    for i in range(len(mins)):
        v += mins[i] - maxs[i]
        if i in mark:
            one = v - mark[i]
            two = (n//2) - v
            sw = one + 2 * two
            Ans = min(Ans,sw)
    print(Ans)