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 JAVA):

Solution:
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class ProblemD {
    public static void main(String[] args) {
        Scanner scn=new Scanner(System.in);
        int T=scn.nextInt();
        for(int t=0;t<T;t++){

            int N=scn.nextInt();
            int K=scn.nextInt();
            int[] onesPrefixSum=new int[2*K+2];
            int[] A=new int[N];
            for(int i=0;i<N;i++){
                A[i]=scn.nextInt();
            }
            int[] zeros=new int[2*K+1];
            int min, max;
            for(int i=0;i<N/2;i++){
                zeros[A[i]+A[N-1-i]]++;
                min=Math.min(A[i], A[N-1-i]);
                max=Math.max(A[i], A[N-1-i]);
                onesPrefixSum[min+1]++;
                onesPrefixSum[max+K+1]--;
            }

            int prefixSum=0;
            for(int i=2;i<2*K+1;i++){
                prefixSum=prefixSum+onesPrefixSum[i];
                    onesPrefixSum[i]=prefixSum;
            }

            List<Integer> list=new ArrayList<>();
            int one, zero,two;
            for(int i=2;i<2*K+1;i++){
                zero=zeros[i];
                one=onesPrefixSum[i]-zero;
                two=N/2-zero-one;
                list.add(2*two+one);
            }
            System.out.println(Collections.min(list));
        }
    }
}