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:
/*
 *
 * @Author  Ajudiya_13(Bhargav Girdharbhai Ajudiya)
 * Dhirubhai Ambani Institute of Information And Communication Technology
 *
 */


import java.util.*;
import java.io.*;
import java.lang.*;

public class Code41
{

    public static void main(String[] args)
    {
        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        int test_case = in.nextInt();
        for(int t=0;t<test_case;t++)
        {
            int n = in.nextInt();
            int k = in.nextInt();
            int[] a = in.nextIntArray(n);
            int[] sum = new int[2*k+5];
            int[] pref = new int[2*k+5];
            int i = 0;
            int j = n-1;
            while(i<j){
                sum[a[i]+a[j]]++;
                int min = Math.min(a[i],a[j]);
                int max = Math.max(a[i],a[j]);
                pref[min+1]++;
                pref[max+k+1]--;
                i++;
                j--;
            }
            for(i=1;i<2*k+5;i++)
                pref[i]+=pref[i-1];
            int min = Integer.MAX_VALUE;
            for(i=2;i<=2*k;i++){
                int cur = pref[i]-sum[i];
                cur += (2*((n/2)-pref[i]));
                min = Math.min(min,cur);
            }
            pw.println(min);
        }
        pw.flush();
        pw.close();
    }

    static class InputReader
    {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }

        public int snext()
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars)
            {
                curChar = 0;
                try
                {
                    snumChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n)
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt();
            }
            return a;
        }

        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine()
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c)
        {
            return c == '\n' || c == '\r' || c == -1;
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }

    public static long mod = 1000000007;
    public static int d;
    public static int p;
    public static int q;

    public static int[] suffle(int[] a,Random gen)
    {
        int n = a.length;
        for(int i=0;i<n;i++)
        {
            int ind = gen.nextInt(n-i)+i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }

    public static void swap(int a, int b){
        int temp = a;
        a = b;
        b = temp;
    }

    public static HashSet<Integer> primeFactorization(int n)
    {
        HashSet<Integer> a =new HashSet<Integer>();
        for(int i=2;i*i<=n;i++)
        {
            while(n%i==0)
            {
                a.add(i);
                n/=i;
            }
        }
        if(n!=1)
            a.add(n);
        return a;
    }

    public static void sieve(boolean[] isPrime,int n)
    {
        for(int i=1;i<n;i++)
            isPrime[i] = true;

        isPrime[0] = false;
        isPrime[1] = false;

        for(int i=2;i*i<n;i++)
        {
            if(isPrime[i] == true)
            {
                for(int j=(2*i);j<n;j+=i)
                    isPrime[j] = false;
            }
        }
    }

    public static int GCD(int a,int b)
    {
        if(b==0)
            return a;
        else
            return GCD(b,a%b);
    }

    public static long GCD(long a,long b)
    {
        if(b==0)
            return a;
        else
            return GCD(b,a%b);
    }

    public static void extendedEuclid(int A,int B)
    {
        if(B==0)
        {
            d = A;
            p = 1 ;
            q = 0;
        }
        else
        {
            extendedEuclid(B, A%B);
            int temp = p;
            p = q;
            q = temp - (A/B)*q;
        }
    }

    public static long LCM(long a,long b)
    {
        return (a*b)/GCD(a,b);
    }

    public static int LCM(int a,int b)
    {
        return (a*b)/GCD(a,b);
    }

    public static int binaryExponentiation(int x,int n)
    {
        int result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=result * x;
            x=x*x;
            n=n/2;
        }
        return result;
    }

    public static long binaryExponentiation(long x,long n)
    {
        long result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=result * x;
            x=x*x;
            n=n/2;
        }
        return result;
    }

    public static int modularExponentiation(int x,int n,int M)
    {
        int result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=(result * x)%M;
            x=(x*x)%M;
            n=n/2;
        }
        return result;
    }

    public static long modularExponentiation(long x,long n,long M)
    {
        long result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=(result * x)%M;
            x=(x*x)%M;
            n=n/2;
        }
        return result;
    }

    public static int modInverse(int A,int M)
    {
        return modularExponentiation(A,M-2,M);
    }

    public static long modInverse(long A,long M)
    {
        return modularExponentiation(A,M-2,M);
    }

    public static boolean isPrime(int n)
    {

        if (n <= 1)  return false;
        if (n <= 3)  return true;

        if (n%2 == 0 || n%3 == 0)
            return false;

        for (int i=5; i*i<=n; i=i+6)
        {
            if (n%i == 0 || n%(i+2) == 0)
                return false;
        }

        return true;
    }

    static class pair implements Comparable<pair>
    {
        Integer x, y;
        pair(int x,int y)
        {
            this.x=x;
            this.y=y;
        }

        public int compareTo(pair o) {
            int result = x.compareTo(o.x);
            if(result==0)
                result = y.compareTo(o.y);

            return result;
        }

        public String toString()
        {
            return x+" "+y;
        }

        public boolean equals(Object o)
        {
            if (o instanceof pair)
            {
                pair p = (pair)o;
                return (Math.abs(p.x-x)==0 && Math.abs(p.y-y)==0);
            }
            return false;
        }

        public int hashCode()
        {
            return new Long(x).hashCode()*31 + new Long(y).hashCode();
        }
    }
}