Problem: You are given an array a consisting of n integers (it is guaranteed that n is even, i.e. divisible by 2). All a_i does not exceed some integer k.

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index i from 1 to n and replace a_i with some integer in range [1; k]) to satisfy the following conditions:

  * after all replacements, all a_i are positive integers not greater than k; 
  * for all i from 1 to n/2 the following equation is true: a_i + a_{n - i + 1} = x, where x should be the same for all n/2 pairs of elements. 



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 first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 2 ⋅ 10^5) — the length of a and the maximum possible value of some a_i correspondingly. It is guratanteed that n is even (i.e. divisible by 2). The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the i-th element of a.

It is guaranteed that the sum of n (as well as the sum of k) over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ k ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — the minimum number of elements you have to replace in a to satisfy the conditions from the problem statement.

Example

Input


4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4


Output


0
1
4
2

Solution (in PYTHON3):

Solution:
from itertools import accumulate

### TEMPLATE <<<
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return (map(int,input().split()))
### TEMPLATE >>>

def sgn(x):
    if x>0:
        return '+'
    else:
        return '-'

def solve(n, k, a):
    h = [0] * (2*k + 5)
 #   print(h)
    for i in range(n//2):
        j = n - i - 1
        h[0] += 2;
        h[min(a[i], a[j]) + 1] -= 1
        h[a[i] + a[j]] -= 1
        h[a[i] + a[j] + 1] += 1
        h[max(a[i], a[j]) + k + 1] += 1

    pref = list(accumulate(h))
    return min(pref)

def main():
    T = int(input())
    for tt in range(T):
        n, k = invr()
        a = list(invr())
        print(solve(n, k, a))
main()