Problem: You are given a positive integer n, it is guaranteed that n is even (i.e. divisible by 2).

You want to construct the array a of length n such that: 

  * The first n/2 elements of a are even (divisible by 2); 
  * the second n/2 elements of a are odd (not divisible by 2); 
  * all elements of a are distinct and positive; 
  * the sum of the first half equals to the sum of the second half (∑_{i=1}^{n/2} a_i = ∑_{i=n/2 + 1}^{n} a_i). 



If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

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 only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. It is guaranteed that that n is even (i.e. divisible by 2).

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

Output

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input


5
2
4
6
8
10


Output


NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO

Solution (in JAVA):

Solution:
import java.io.Writer;
import java.io.BufferedWriter;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.*;
import java.io.*;
import java.math.*;

public class A{

  static class ProblemSolver{
    public void solveTheProblem(InputReader in,OutputWriter out, NumberTheory nt){
      int test=in.nextInt();
      while(test-- >0){
        int n=in.nextInt();
        if(n%4!=0){
          System.out.println("NO");
        }
        else{
          int ar[]= new int[n];
          int k=0, sum1=0, sum2=0;
          for(int i=2;i<=n;i+=2){
            sum1+=i;
            ar[k++]=i;
          }
          // System.out.println(Arrays.toString(ar));
          for(int i=0;i<ar.length/2 -1;i++){
            ar[k++]=2*i+1;
            sum2+=2*i+1;
          }
          ar[k]=sum1-sum2;
          // System.out.println(Arrays.toString(ar));

          System.out.println("YES");
          for(int i=0;i<=k;i++)
            System.out.print(ar[i]+" ");
          System.out.println();
        }
      }
    }
  }

  public static void main(String[] args){
    InputStream inputStream=System.in;
    OutputStream outputStream=System.out;
    InputReader in=new InputReader(inputStream);
    OutputWriter out=new OutputWriter(outputStream);
    NumberTheory nt= new NumberTheory();
    ProblemSolver problemSolver=new ProblemSolver();
    problemSolver.solveTheProblem(in,out, nt);
    out.flush();
    out.close();
  }



  static class InputReader {
    private boolean finished = false;

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

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

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

    public int peek() {
      if (numChars == -1) {
        return -1;
      }
      if (curChar >= numChars) {
        curChar = 0;
        try {
          numChars = stream.read(buf);
        } catch (IOException e) {
          return -1;
        }
        if (numChars <= 0) {
          return -1;
        }
      }
      return buf[curChar];
    }

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

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

    public String nextLine() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      StringBuilder res = new StringBuilder();
      do {
        if (Character.isValidCodePoint(c)) {
          res.appendCodePoint(c);
        }
        c = read();
      } while (!isSpaceChar(c));
      return res.toString();
    }

    public boolean isSpaceChar(int c) {
      if (filter != null) {
        return filter.isSpaceChar(c);
      }
      return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private String readLine0() {
      StringBuilder buf = new StringBuilder();
      int c = read();
      while (c != '\n' && c != -1) {
        if (c != '\r') {
          buf.appendCodePoint(c);
        }
        c = read();
      }
      return buf.toString();
    }

    public String readLine() {
      String s = readLine0();
      while (s.trim().length() == 0) {
        s = readLine0();
      }
      return s;
    }

    public String readLine(boolean ignoreEmptyLines) {
      if (ignoreEmptyLines) {
        return readLine();
      } else {
        return readLine0();
      }
    }

    public BigInteger readBigInteger() {
      try {
        return new BigInteger(nextLine());
      } catch (NumberFormatException e) {
        throw new InputMismatchException();
      }
    }

    public char nextCharacter() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      return (char) c;
    }

    public double nextDouble() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      double res = 0;
      while (!isSpaceChar(c) && c != '.') {
        if (c == 'e' || c == 'E') {
          return res * Math.pow(10, nextInt());
        }
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c - '0';
        c = read();
      }
      if (c == '.') {
        c = read();
        double m = 1;
        while (!isSpaceChar(c)) {
          if (c == 'e' || c == 'E') {
            return res * Math.pow(10, nextInt());
          }
          if (c < '0' || c > '9') {
            throw new InputMismatchException();
          }
          m /= 10;
          res += (c - '0') * m;
          c = read();
        }
      }
      return res * sgn;
    }

    public boolean isExhausted() {
      int value;
      while (isSpaceChar(value = peek()) && value != -1) {
        read();
      }
      return value == -1;
    }

    public String next() {
      return nextLine();
    }

    public SpaceCharFilter getFilter() {
      return filter;
    }

    public void setFilter(SpaceCharFilter filter) {
      this.filter = filter;
    }

    public interface SpaceCharFilter {
      public boolean isSpaceChar(int ch);
    }
    public int[] nextIntArray(int n){
      int[] array=new int[n];
      for(int i=0;i<n;++i)array[i]=nextInt();
      return array;
    }
    public int[] nextSortedIntArray(int n){
      int array[]=nextIntArray(n);
      Arrays.sort(array);
      return array;
    }
    public ArrayList<Integer> nextIntArrayList(int n){
      ArrayList<Integer> ar= new ArrayList<>();
      for(int i=0;i<n;i++)
        ar.add(nextInt());
      return ar;
    }
		public ArrayList<Long> nextLongArrayList(int n){
      ArrayList<Long> ar= new ArrayList<>();
      for(int i=0;i<n;i++)
        ar.add(nextLong());
      return ar;
    }

    public int[] nextSumIntArray(int n){
      int[] array=new int[n];
      array[0]=nextInt();
      for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
      return array;
    }
    public long[] nextLongArray(int n){
      long[] array=new long[n];
      for(int i=0;i<n;++i)array[i]=nextLong();
      return array;
    }
    public long[] nextSumLongArray(int n){
      long[] array=new long[n];
      array[0]=nextInt();
      for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
      return array;
    }
    public long[] nextSortedLongArray(int n){
      long array[]=nextLongArray(n);
      Arrays.sort(array);
      return array;
    }
    public int[][] nextIntMatrix(int n,int m){
      int[][] matrix=new int[n][m];
      for(int i=0;i<n;++i)
      for(int j=0;j<m;++j)
      matrix[i][j]=nextInt();
      return matrix;
    }

    public int[][] nextIntMatrix(int n){
      return nextIntMatrix(n,n);
    }

    public long[][] nextLongMatrix(int n,int m){
      long[][] matrix=new long[n][m];
      for(int i=0;i<n;++i)
      for(int j=0;j<m;++j)
      matrix[i][j]=nextLong();
      return matrix;
    }

    public long[][] nextLongMatrix(int n){
      return nextLongMatrix(n,n);
    }

    public char[][] nextCharMatrix(int n,int m){
      char[][] matrix=new char[n][m];
      for(int i=0;i<n;++i)
      matrix[i]=next().toCharArray();
      return matrix;
    }

    public char[][] nextCharMatrix(int n){
      return nextCharMatrix(n,n);
    }
  }

  static class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
      writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    // public void print(char[] array) {
    //     writer.print(array);
    // }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void print(int[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(double[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(long[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(char[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(String[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(int[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(double[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(long[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(char[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(String[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void println(int[] array) {
      print(array);
      writer.println();
    }

    public void println(double[] array) {
      print(array);
      writer.println();
    }

    public void println(long[] array) {
      print(array);
      writer.println();
    }

    // public void println(char[] array) {
    //     print(array);
    //     writer.println();
    // }

    public void println(String[] array) {
      print(array);
      writer.println();
    }

    public void println() {
      writer.println();
    }

    public void println(Object... objects) {
      print(objects);
      writer.println();
    }

    public void print(char i) {
      writer.print(i);
    }

    public void println(char i) {
      writer.println(i);
    }

    public void println(char[] array) {
      writer.println(array);
    }

    public void printf(String format, Object... objects) {
      writer.printf(format, objects);
    }

    public void close() {
      writer.close();
    }

    public void flush() {
      writer.flush();
    }

    public void print(long i) {
      writer.print(i);
    }

    public void println(long i) {
      writer.println(i);
    }

    public void print(int i) {
      writer.print(i);
    }

    public void println(int i) {
      writer.println(i);
    }

    public void separateLines(int[] array) {
      for (int i : array) {
        println(i);
      }
    }
  }
  static class NumberTheory{

      /**
       * Modular Arithmetic:
       *  1. (a+b)%c=(a%c+b%c)%c
       *  2. (a*b)%c=(a%c*b%c)%c
       *  3. (a-b)%c=(a%c-b%c+c)%c
       *  4. (a/b)%c=(a%c*(b^-1)%c)%c -- (b^-1 is multiplicative modulo inverse)
       */
      //Modular Addition
      public int modularAddition(int a,int b,int MOD){
          return (a%MOD+b%MOD)%MOD;
      }
      public long modularAddition(long a,long b,long MOD){
          return (a%MOD+b%MOD)%MOD;
      }
      //Modular Multiplication
      public int modularMultiplication(int a,int b,int MOD){
          return ((a%MOD)*(b%MOD))%MOD;
      }
      public long modularMultiplication(long a,long b,long MOD){
          return ((a%MOD)*(b%MOD))%MOD;
      }
      //Modular Subtraction
      public int modularSubtraction(int a,int b,int MOD){
          return (a%MOD-b%MOD+MOD)%MOD;
      }
      public long modularSubtraction(long a,long b,long MOD){
          return (a%MOD-b%MOD+MOD)%MOD;
      }

      /**
       * Binary Exponentiation
       */
      public int binaryExponentiation(int x,int n){
          if(n==0)return 1;
          else if(n%2==0)return binaryExponentiation(x*x,n/2);
          else return x*binaryExponentiation(x*x,(n-1)/2);
      }
      public long binaryExponentiation(long x,long n){
          long result=1;
          while(n>0){
              if(n%2==1)result*=x;
              x=x*x;
              n/=2;
          }
          return result;
      }

      /**
       * Modular Exponentiation
       */
      public int modularExponentiation(int x,int n,int MOD){
          if(n==0)return 1%MOD;
          else if(n%2==0)return modularExponentiation(modularMultiplication(x,x,MOD),n/2,MOD);
          else return modularMultiplication(x,modularExponentiation(modularMultiplication(x,x,MOD),(n-1)/2,MOD),MOD);
      }
      public long modularExponentiation(long x,long n,long MOD){
          long result=1;
          while(n>0){
              if(n%2==1)result=modularMultiplication(result,x,MOD);
              x=modularMultiplication(x,x,MOD);
              n/=2;
          }
          return result;
      }

      /**
       * Factorial of a number
       */
      public long factorials(long n){
          if(n==0)return 1;
          return n*factorials(n-1);
      }

      /**
       * Prime factors of a number
       */
      public ArrayList<Integer> distinctPrimeFactors(int n){
          ArrayList<Integer> factorials=new ArrayList<>();
          int limit=(int)Math.sqrt(n);
          if(n%2==0){
              factorials.add(2);
              while(n%2==0)n/=2;
          }
          for(int i=3;i<=limit;i+=2){
              if(n%i==0){
                  factorials.add(i);
                  while(n%i==0)n/=i;
              }
          }
          if(n>2)factorials.add(n);
          return factorials;
      }

      public ArrayList<Long> distinctPrimeFactors(long n){
          ArrayList<Long> factorials=new ArrayList<>();
          long limit=(long)Math.sqrt(n);
          if(n%2==0){
              factorials.add((long)2);
              while(n%2==0)n/=2;
          }
          for(long i=3;i<=limit;i+=2){
              if(n%i==0){
                  factorials.add(i);
                  while(n%i==0)n/=i;
              }
          }
          if(n>2)factorials.add(n);
          return factorials;
      }

      public ArrayList<Integer> primeFactors(int n){
          ArrayList<Integer> factorials=new ArrayList<>();
          int limit=(int)Math.sqrt(n);
          if(n%2==0){
              factorials.add(2);
              while(n%2==0)n/=2;
          }
          for(int i=3;i<=limit;i+=2){
              if(n%i==0){
                  factorials.add(i);
                  while(n%i==0)n/=i;
              }
          }
          if(n>2)factorials.add(n);
          return factorials;
      }

      public ArrayList<Long> primeFactors(long n){
          ArrayList<Long> factorials=new ArrayList<>();
          long limit=(long)Math.sqrt(n);
          if(n%2==0){
              factorials.add((long)2);
              while(n%2==0)n/=2;
          }
          for(long i=3;i<=limit;i+=2){
              if(n%i==0){
                  factorials.add(i);
                  while(n%i==0)n/=i;
              }
          }
          if(n>2)factorials.add(n);
          return factorials;
      }

      /**
       * Combination: nCr
       */
      //Naive version
      //(n,r)=(n-1,r-1)+(n-1,r) for r!=0 or r!=n
      //(n,0)=(n,n)=1
      public int binomialCoefficientRecursive(int n,int k){
          if(k==0 || k==n)return 1;//base case
          return binomialCoefficientRecursive(n-1,k-1)+binomialCoefficientRecursive(n-1,k);//recursion
      }

      //Dynamic Programming version(Uses bottom up approach to fill the table)
      //Time complexity: O(n*k)
      //Space complexity: O(n*k)
      public long binomialCoefficientIterative(int n,int k){
          long[][] C=new long[n+1][k+1];
          for(int i=0;i<=n;++i){
              for(int j=0;j<=Math.min(n,k);++j){
                  if(j==0 || j==i)C[i][j]=1;
                  else C[i][j]=C[i-1][j-1]+C[i-1][j];
              }
          }
          return C[n][k];
      }

      //Pascal's Triangle version(Space efficient program)
      //Time complexity: O(n*k)
      //Space complexity: O(k)
      public long nCr(int n,int r){
          int[] C=new int[r+1];
          C[0]=1;//nC0=1
          for(int i=1;i<=n;++i)
              for(int j=Math.min(i,r);j>0;--j)
                  C[j]=C[j]+C[j-1];
          return C[r];
      }

      /**
       * Catlan number:
       *  - Time complexity: O(n*n)
       *  - Auxiliary space: O(n)
       *
       *  NOTE: Time complexity could be reduced to O(n) but it is
       *        possible if and only if n is small or else there is
       *        a chance of getting an overflow. To decrease the time
       *        complexity to O(n) just remember nCr=nCn-r
       */
      public long catlanNumber(int n){
          long[] catlan=new long[n+1];
          catlan[0]=catlan[1]=1;
          for(int i=2;i<=n;++i)
              for(int j=0;j<i;++j)
                  catlan[i]+=catlan[j]*catlan[i-1-j];

          return catlan[n];
      }

      /**
       * Greatest Common Divisor(GCD)
       *  - It is also known as Highest Common Factor(HCF)
       *  - Time complexity: log(min(a,b))
       *  - Auxiliary Space: O(1)
       */
      public int gcd(int a,int b){
          if(b==0)return a;
          return gcd(b,a %b);
      }

      public long gcd(long a,long b){
          if(b==0)return a;
          return gcd(b,a%b);
      }

      /**
       * Extended Euclid's Algorithm:
       *  - ax+by=gcd(a,b)
       *  - Time complexity:
       *  -
       */


      /**
       * Least Common Multiple(LCM):
       *  - Time complexity: log(min(a,b))
       *  - Auxiliary Space: O(1)
       */
      public long lcm(long a,long b){
          return (a*b)/gcd(a,b);
      }

  }
}
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//                                            I88,              ______   __
//                           ______           "I88__        .mI88I88I88I88I88,
//                      .,mI88I88I88, ,mI88,   I88"""     ,mI8". . . . "I8,..8,
//                    ,I888' . . . "I88.\ "8,  I88      ,I8". . . .  / :;I8 \ 8,
//                  .mI8' . . .  / .:"I8.\ 88  "88,    ,8". . .  / .;mI8I8I8,\ 8
//                 ,I8'. . .  / . .:;,I8I8I888  I88   ,8". .  / .:mI8"'   "I8,:8
//                ,I8'. . . / . .:;,mI8"  `"I88 I88   I8. .  / .m8"         "I8I
//               ,I8 . .  / . .:;,mI8"      "I88888   88,.  / ,m8            "8'
//               I8'. .  / . .;,mI8"          "II888 ,I8I8,.,I8"
//               I8 . . / . .,mI8"              I8888888' """
//               `I8,.  / ;,mI8"                 II888
//                "I8I, /,mI8"                 __I888
//                  "I8888"                   """I88
//                    ""                         I88
//                                               I88__
//                                               I88"""
//                                               I88
//                                               I88
//                                             __I88
//                                            """I88
//                                               I88
//                                               I88
//                                               I88__
//                                               I88"""
//                                               I88
//                                        BITSY  ___  CHUCK