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 Main
{

    public static void process()throws IOException
    {
        int n=ni(),k=ni(),arr[]=new int[n+1];
        for(int i=1;i<=n;i++) arr[i]=ni();

        int f[]=new int[2*k+10],sum_freq[]=new int[2*k+10];

        for(int i=1;i<=n/2;i++){
            int sum=arr[i]+arr[n-i+1];
            sum_freq[sum]++;

            int l=Math.min(arr[i], arr[n-i+1])+1;
            int r=Math.max(arr[i], arr[n-i+1])+k+1;

            f[l]++;
            f[r]--;
        }

        for(int i=1;i<=2*k;i++)
            f[i]+=f[i-1];

        int res=Integer.MAX_VALUE;

        for(int i=1;i<=2*k;i++){
            //to form no. i

            int req=f[i]+(n/2-f[i])*2-sum_freq[i];
            res=Math.min(res, req);
        }

        pn(res);
    }   


    static AnotherReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc=new AnotherReader();
        boolean oj = true;

        oj = System.getProperty("ONLINE_JUDGE") != null;
        if(!oj) sc=new AnotherReader(100);

        long s = System.currentTimeMillis();
        int t=1;
        t=ni();
        while(t-->0)
            process();
        out.flush();
        if(!oj)
            System.out.println(System.currentTimeMillis()-s+"ms");
        System.out.close();  
    }
    
    
    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);System.out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    static boolean multipleTC=false;
    static long mod=(long)1e9+7l;

    static void r_sort(int arr[],int n){
        Random r = new Random(); 
        for (int i = n-1; i > 0; i--){ 
            int j = r.nextInt(i+1); 
                  
            int temp = arr[i]; 
            arr[i] = arr[j]; 
            arr[j] = temp; 
        } 
        Arrays.sort(arr); 
    }

    static long mpow(long x, long n) {
        if(n == 0)
            return 1;
        if(n % 2 == 0) {
            long root = mpow(x, n / 2);
            return root * root % mod;
        }else {
            return x * mpow(x, n - 1) % mod;
        }
    }
    
    static long mcomb(long a, long b) {
        if(b > a - b)
            return mcomb(a, a - b);
        long m = 1;
        long d = 1;
        long i;
        for(i = 0; i < b; i++) {
            m *= (a - i);
            m %= mod;
            d *= (i + 1);
            d %= mod;
        }
        long ans = m * mpow(d, mod - 2) % mod;
        return ans;
    }
/////////////////////////////////////////////////////////////////////////////////////////////////////////

    static class AnotherReader{BufferedReader br; StringTokenizer st;
    AnotherReader()throws FileNotFoundException{
    br=new BufferedReader(new InputStreamReader(System.in));}
    AnotherReader(int a)throws FileNotFoundException{
    br = new BufferedReader(new FileReader("input.txt"));}
    String next()throws IOException{
    while (st == null || !st.hasMoreElements()) {try{
    st = new StringTokenizer(br.readLine());}
    catch (IOException  e){ e.printStackTrace(); }}
    return st.nextToken(); } int nextInt() throws IOException{
    return Integer.parseInt(next());}
    long nextLong() throws IOException
    {return Long.parseLong(next());}
    double nextDouble()throws IOException { return Double.parseDouble(next()); }
    String nextLine() throws IOException{ String str = ""; try{
    str = br.readLine();} catch (IOException e){
    e.printStackTrace();} return str;}}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}