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:
t = int(input())

for _ in range(t):
  n,k = map(int,input().split())
  arr = list(map(int, input().split()))
  
  m = n // 2
  arr = [0] + arr
  a = [0] * (2*k+1)
  b = [0] * (2*k+1)
  c = [0] * (2*k+1)
  
  for i in range(1,m+1):
    x = arr[i]
    y = arr[n-i+1]
    a[min(x,y)+1] += 1
    b[x+y] += 1
    c[max(x,y)+k] += 1
  
  cum_a = [0]
  cum_b = [0]
  cum_c = [0]

  for i in range(1,2*k+1):
    cum_a.append(cum_a[-1] + a[i])
    cum_b.append(cum_b[-1] + b[i])
    cum_c.append(cum_c[-1] + c[i])
  
  # print(cum_a)
  # print(cum_b)
  # print(cum_c)
  sol = []
  for i in range(1,2*k+1):
    s1 = cum_a[-1] - cum_a[i]
    s2 = cum_a[i]
    s3 = cum_b[i] - cum_b[i-1]
    s4 = cum_c[i-1]
    sol.append(2*s1 + s2 - s3 + s4)
    # print([s1, s2, s3, s4])
  print(min(sol))