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
g = lambda x: map( x, input().split() )

def main():
    n = int( input() )
    
    while n:
        n -= 1
        a = int( input() )
        v = [None] * a
        k = a // 2
        x = 2
        i = 0
        c1, c2 = 0, 0
        while i < a / 2:
            v[i] = x
            c1 += v[i]
            v[k] = x - 1
            c2 += v[k]
            i += 1
            if not( i < a / 2 ): break
            k += 1
            x += 2
            v[i] = x
            c1 += v[i]
            v[k] = x + 1
            c2 += v[k]
            i += 1
            k += 1
            x += 4
        if not( c1 == c2 ):
            print("NO")
        else:
            print( "YES" )
            for i in v:
                print( i, end= " " )
            print()
main()