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.*;
import java.util.*;
import java.math.BigInteger; 
import java.lang.Object;


public class Main {
    
    
    
    
   static class sort implements Comparator<int[]>
   {
        public int compare(int[] a,int[] b)
        {
            
            //if(a[0] == b[0]) return a[1]-b[1];
           /*if(a[1] < b[1]) return -1;
           else if(a[1] > b[1]) return 1;
           return a[0]-b[0];*/
           int l1,l2;
           l1=(a[1]-a[0]);
           l2=(b[1]-b[0]);
           if(l1>l2)
           {
                return -1;
           }
           else if(l2>l1)
           {
                return 1;
           }
           else 
           {
               if(a[1]<=b[0])
               {
                    return -1;
               }
               return 1;
           }
        }
   }
   static class sort1 implements Comparator<double[]>
   {
        public int compare(double[] a,double[] b)
        {
            //if(a[0] == b[0]) return a[1]-b[1];
           if(a[1] < b[1]) return -1;
           else if(a[1] > b[1]) return 1;
           return 0;
        }
   }
   public static String[] F(BufferedReader bf) throws Exception
    {
        return (bf.readLine().split(" "));
    }
    
   public static void pr(PrintWriter out,Object o)
   {
      
    out.println(o.toString());out.flush();
    
   }
   public static void prW(PrintWriter out,Object o)
   {
      
    out.print(o.toString());out.flush();
    
   }
   public static int intIn(String st)
   {
      return Integer.parseInt(st);
   }
   
   
    
    public static void pr(Object o)
    {
        System.out.println(o.toString());
    }
    public static void prW(Object o)
    {
        System.out.print(o.toString());
    }
    
   
    public static int inInt(String s)
    {
        return Integer.parseInt(s);
    }
    public static long in(String s)
    {
        return Long.parseLong(s);
    }


    static int[] toIntArray(String[] m) 
    { 
        int[] p=new int[m.length];
        for(int o=0;o<m.length;o++)
        {
            p[o]= inInt(m[o]);
        }
        return p;
    }
    static double[] toDArray(String[] m) 
    { 
        double[] p=new double[m.length];
        for(int o=0;o<m.length;o++)
        {
            p[o]= Double.parseDouble(m[o]);
        }
        return p;
    }
    static long[] toLArray(String[] m) 
    { 
       long[] p=new long[m.length];
        for(int o=0;o<m.length;o++)
        {
            p[o]= in(m[o]);
        }
        return p;
    }
    
    static int[][] di={{0,1},{1,0},{0,-1},{-1,0}};
    static int[] dir = {4,3,2,-4,-3,-2};
    public static void F(int i,int c,int[] vis,List<Integer> res,int n)
    {
        vis[i]=1;
        res.add(i);
        for(int x : dir)
        {
            int v = i+x;
            if(v<=0 || v>n) continue;

            if(vis[v] == 0)
            {
                F(v,c,vis,res,n);
            }
        }
    }
     static long gcd(long a, long b)
        {
          if (b == 0)
            return a;
          return gcd(b, a % b); 
        }
        static long Gp(long l,long b,long lcm)
        {
            long c1,c2;
                c1 = (l/lcm);
                long sum=0l;
                sum += (c1-1l)*(b);
                long las = (l/lcm)*lcm;
                sum += Math.min(l-las+1l,b);
                return sum;
        }
    public static boolean ok(int mid,int[] arr,int[][] mat,int q)
    {
        int tot=0;
        for(int[] a : mat)
        {
            int p=a[0];
            int l = a[1];
            int ans=q+1;
            int g = Math.abs(p);
            if(p==0) continue;
            for(int o=0;o<arr.length;o++)
            {
                if((arr[o]*p) < 0)
                {
                    int sp = Math.abs(arr[o]);
                    int v = (g/sp);
                    if((g%sp) != 0) v++;
                    if(v<=mid)
                    {
                        ans=Math.min(ans,Math.abs(l-o));
                    }
                }
            }

            if(ans > q ) return false;
            tot += ans;
        }

        return tot<=q;
    }
    public static void main (String[] args) throws Exception {
        
        BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);;;
        
        //int[] map=new int[1000001];
      
       int yy=Integer.parseInt(bf.readLine());
        for(int w=0;w<yy;w++)
        {

            String[] xlp = bf.readLine().split(" ");;;;;;
            //String st = bf.readLine();
           int n,t;//boolean bol=false;
           int m;//long a,b,c;
           int k;
          n=inInt(xlp[0]);m=inInt(xlp[1]);//k=inInt(xlp[2]);//t=inInt(xlp[3]);
          k=m;
           int[] arr = toIntArray(F(bf));
           int[] pre = new int[2*k+2];
           for(int o=0;o<n/2;o++)
           {
              int v1,v2;
              v1 = arr[o];
              v2 = arr[n-1-o];
              int min = Math.min(v1,v2)+1;
              int max=Math.max(v1,v2)+k;
              pre[min]+=1;
              pre[max+1]-=1;
           }
           int res=n;
           int[] count = new int[2*k+1];
          for(int o=0;o<n/2;o++)
           {
              int v1,v2;
              v1 = arr[o];
              v2 = arr[n-1-o];
              count[v1+v2]++;
           }
           int c=0;
           for(int o=0;o<pre.length;o++)
           {
               pre[o] = pre[o]+c;;
               c=pre[o];
           }
           //for(int g : pre) prW(out,g+" ");
          //  pr(out,"");
           for(int o=2;o<=2*k;o++)
           {
                int hu = pre[o]-count[o] + (n/2-pre[o])*2;
                res = Math.min(res,hu); 
           }
           pr(out,res);



           
          
    }
    out.close();
}}


/*


1
8
7 4
9 10
4 8
3 1
1 7
9 5
1 4
2 5

100663319,201326611,402653189,805306457,1610612741
Kickstart
 String rp;
            rp = "Case #"+(w+1)+": "+(n-ans)+" ";
static int[][] dir={{0,1},{1,0},{-1,0},{0,-1}};

static class SegmentTreeRMQ 
    { 
    int st[]; 
    int minVal(int x, int y) { 
        return (x > y) ? x : y; 
    } 
  
    
    int getMid(int s, int e) { 
        return s + (e - s) / 2; 
    } 
  
    
    int RMQUtil(int ss, int se, int qs, int qe, int index) 
    { 
        
        if (qs <= ss && qe >= se) 
            return st[index]; 
  
        // If segment of this node is outside the given range 
        if (se < qs || ss > qe) 
            return Integer.MIN_VALUE; 
  
        // If a part of this segment overlaps with the given range 
        int mid = getMid(ss, se); 
        return minVal(RMQUtil(ss, mid, qs, qe, 2 * index + 1), 
                RMQUtil(mid + 1, se, qs, qe, 2 * index + 2)); 
    } 
  
    // Return minimum of elements in range from index qs (query 
    // start) to qe (query end).  It mainly uses RMQUtil() 
    int RMQ(int n, int qs, int qe) 
    { 
        // Check for erroneous input values 
        
  
        return RMQUtil(0, n - 1, qs, qe, 0); 
    } 
  
    // A recursive function that constructs Segment Tree for 
    // array[ss..se]. si is index of current node in segment tree st 
    int constructSTUtil(int arr[], int ss, int se, int si) 
    { 
        // If there is one element in array, store it in current 
        //  node of segment tree and return 
        if (ss == se) { 
            st[si] = arr[ss]; 
            return arr[ss]; 
        } 
  
        // If there are more than one elements, then recur for left and 
        // right subtrees and store the minimum of two values in this node 
        int mid = getMid(ss, se); 
        st[si] = minVal(constructSTUtil(arr, ss, mid, si * 2 + 1), 
                constructSTUtil(arr, mid + 1, se, si * 2 + 2)); 
        return st[si]; 
    } 
  
    
    void con(int arr[]) 
    { 
        // Allocate memory for segment tree 
  
        //Height of segment tree 
        int n = (arr.length);
        int x = (int) (Math.ceil(Math.log(n) / Math.log(2))); 
  
        //Maximum size of segment tree 
        int max_size = 2 * (int) Math.pow(2, x) - 1; 
        st = new int[max_size]; // allocate memory 
  
        // Fill the allocated memory st 
        constructSTUtil(arr, 0, n - 1, 0); 
    }
    }
     static class DSU {
    
    int[] p;int[] sz;int op;int c;;
    int[] last;
    public void G(int n)
    {
        last=new int[n];
        p=new int[n];
        sz=new int[n];c=n;
        op=n;
        for(int h=0;h<n;h++)
        {
            sz[h]=1;p[h]=h;
            last[h]=h;
        }
    }
    public int find(int x)
    {
        int y=x;
        while(x!=p[x]) x=p[x];
        while(y!=p[y])
        {
            int tem=p[y];
            p[y]=x;y=tem;
        }
        return p[y];
    }
    public void union(int a,int b)
    {
        int x,y;
        x=find(a);y=find(b);
        if(x==y) return;
        if(sz[x]>sz[y])
        {
            p[y] = x;
            sz[x]+=sz[y];
            last[x]=Math.max(last[x],last[y]);
        }
        else
        {
            p[x]=y;sz[y]+=sz[x];
            last[y]=Math.max(last[y],last[x]);
        }
        c--;
        
    }}

    static long pow(long x, long y, long p)
      {
        long res = 1; // Initialize result
     
        x = x % p; // Update x if it is more than or
        // equal to p
     
        if (x == 0)
          return 0l; // In case x is divisible by p;
     
        while (y > 0)
        {
     
          // If y is odd, multiply x with result
          if ((y & 1) != 0)
            res = (res * x) % p;
     
          // y must be even now
          y = y >> 1; // y = y/2
          x = (x * x) % p;
        }
        return res;
      }
      static long gcd(long a, long b)
        {
          if (b == 0)
            return a;
          return gcd(b, a % b); 
        }
        static int gcd(int a, int b,int o)
        {
          if (b == 0)
            return a;
          return gcd(b, a % b,o); 
        }

Geometric median

public static double F(double[] x,double[] w)
    {
        double d1,d2;
        double S=0.00;
        for(double dp : w) S += dp;
        int k = 0;
        double sum = S - w[0]; // sum is the total weight of all `x[i] > x[k]`

        while(sum > S/2)
        {
            ++k;
            sum -= w[k];
        }
        d1=x[k];
        return d1;
        k = w.length-1;
       sum = S - w[k]; // sum is the total weight of all `x[i] > x[k]`

        while(sum > S/2)
        {
            --k;
            sum -= w[k];
        }
        d2=x[k];
        return new double[]{d1,d2};
    }
*/