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.*;
import java.io.*;
import java.math.*;
public class D636{

	public static void main(String args[]){
		FastReader sc = new FastReader();
		StringBuilder sb=new StringBuilder();
		int t,i,n,k,left,right,sum,min,one,zero,two,tot;
		t=sc.nextInt();
		while(t-->0){
            n=sc.nextInt();
            k=sc.nextInt();
            int a[]=new int[n];
            for(i=0;i<n;i++)
                a[i]=sc.nextInt();
            int f[]=new int[2*k+5];
            int pref[]=new int[2*k+5];
            for(i=0;i<n/2;i++){
                if(a[i]>a[n-i-1]){
                    int temp=a[i];
                    a[i]=a[n-i-1];
                    a[n-i-1]=temp;
                }
                sum=a[i]+a[n-i-1];
                left=a[i]+1;
                right=a[n-i-1]+k;
                pref[left]++;
                pref[right+1]--;
                f[sum]++;
            }
            for(i=1;i<=2*k+4;i++)
                pref[i]+=pref[i-1];
            min=Integer.MAX_VALUE;
            for(i=2;i<=2*k;i++){
                zero=f[i];
                one=pref[i]-f[i];
                two=(n/2-one-zero)*2;
                tot=one+two;
                min=Math.min(tot,min);
            }
            sb.append(min).append('\n');
		}
		sb.deleteCharAt(sb.length()-1);
		out.println(sb);
	}

	static PrintWriter out;
	static class FastReader{
		BufferedReader br;
		StringTokenizer st;
		public FastReader(){
			br=new BufferedReader(new InputStreamReader(System.in));
			out=new PrintWriter(System.out,true);
		}
		String next(){
			while(st==null || !st.hasMoreElements()){
				try{
					st= new StringTokenizer(br.readLine());
				}
				catch (IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		int nextInt(){
			return Integer.parseInt(next());
		}
		long nextLong(){
			return Long.parseLong(next());
		}
		double nextDouble(){
			return Double.parseDouble(next());
		}
		String nextLine(){
			String str = "";
			try{
				str=br.readLine();
			}
			catch(IOException e){
				e.printStackTrace();
			}
			return str;
		}
	}

	public static boolean isPrime(int n) {
		if(n<2) return false;
		for(int i=2;i<=(int)Math.sqrt(n);i++) {
			if(n%i==0) return false;
		}
		return true;
	}

	public static void print(int a[],int l,int r){
		int i;
		for(i=l;i<=r;i++)
			out.print(a[i]+" ");
		out.println();
	}

	public static long fastexpo(long x, long y, long p){
		long res=1;
		while(y > 0){
			if((y & 1)==1)
				res= ((res%p)*(x%p))%p;
			y= y >> 1;			
			x = ((x%p)*(x%p))%p;
		}
		return res;
	}

	public static boolean[] sieve (int n) {
		boolean primes[]=new boolean[n+1];
		Arrays.fill(primes,true);
		primes[0]=primes[1]=false;
		for(int i=2;i*i<=n;i++){
			if(primes[i]){
				for(int j=i*i;j<=n;j+=i)
					primes[j]=false;
			}
		}
		return primes;
	}

	public static long gcd(long a,long b){
        return (BigInteger.valueOf(a).gcd(BigInteger.valueOf(b))).longValue();
    }

    public static void merge(int a[],int l,int m,int r){
        int n1,n2,i,j,k;
        n1=m-l+1;
        n2=r-m;

        int L[]=new int[n1];
        int R[]=new int[n2];

        for(i=0;i<n1;i++)
            L[i]=a[l+i];
        for(j=0;j<n2;j++)
            R[j]=a[m+1+j];

        i=0;j=0;

        k=l;
        while(i<n1&&j<n2){
            if(L[i]<=R[j]){
                a[k]=L[i];
                i++;
            }
            else{
                a[k]=R[j];
                j++;
            }
            k++;
        }

        while(i<n1){
            a[k]=L[i];
            i++;
            k++;
        }
        while(j<n2){
            a[k]=R[j];
            j++;
            k++;
        }
    }
    public static void sort(int a[],int l,int r){
        int m;
        if(l<r){
            m=(l+r)/2;
            sort(a,l,m);
            sort(a,m+1,r);
            merge(a,l,m,r);
        }
    }
}