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.lang.reflect.Array;
import java.util.*;
import static java.lang.Math.*;
public class MAIN {

    static int visited[];
    static ArrayList<ArrayList<Integer>> adjlist;
    static class edge implements  Comparator<edge>{
        int dest;
        int cost;

        public edge(int dest, int cost) {
            this.dest = dest;
            this.cost = cost;
        }

        @Override
        public int compare(edge o1, edge o2) {
            return o1.cost-o2.cost;
        }
    }

    static int dist[];
    static class Graph{
        int V;
        ArrayList<ArrayList<Node>> adj;
        PriorityQueue<edge> pq;

        public Graph(int V){
            this.V = V;
            adj = new ArrayList<>(V);
            pq = new PriorityQueue<>(V,new edge(-1,-1));
            dist = new int[V];
            for(int i=0; i<V; i++){
                dist[i] = Integer.MAX_VALUE;
                adj.add(i,new ArrayList<>());
            }
        }

        void addedge(int u, int v, int w ){
            adj.get(u).add(new Node(v,w));
            adj.get(v).add(new Node(u,w));
        }

        void DFS(int src){
            Stack<Node> st = new Stack<>();
            boolean visited[] = new boolean[V];
            visited[src] = true;
            st.push(new Node(src,0));
            dist[src] = 0;
            while (!st.empty()){
                int u = st.peek().value;
                st.pop();
                for(int i=0; i<adj.get(u).size(); i++){
                    if(!visited[adj.get(u).get(i).value]){
                        adj.get(u).get(i).level = dist[u]+1;
                        dist[adj.get(u).get(i).value] = dist[u]+1;
                        visited[adj.get(u).get(i).value] = true;

                    }
                }
            }
        }
    }


/*
        void dijkstra(int src){
            for(int i=0; i<V; i++){
                dist[i] = Integer.MAX_VALUE;
            }
            dist[src] = 0;
            pq.add(new edge(src,0));
            while (!pq.isEmpty()){
                int u = pq.poll().dest;
                for(int i=0; i<adj.get(u).size(); i++){
                    int v = adj.get(u).get(i).dest;
                    int w = adj.get(u).get(i).cost;
                    if(dist[u]+w<=dist[v]){
                        dist[v] = dist[u] + w;
                        pq.add(new edge(v,dist[v]));
                    }
                }
            }

        }


    }

 */



    static  int I[];
    static  int L[];
    static void LIS(int n, int arr[]){
        I = new int[n+1];
        L = new int[n];
        I[0] = Integer.MIN_VALUE;
        for(int i=1;i<=n; i++){
            I[i] = Integer.MAX_VALUE;
        }
        int lisLength = 1;

        for(int i=n-1; i>=0; i--) {
            int low = 1;
            int high = lisLength;
            int mid = 0;
            while (low < high) {
                mid = (low + high) >> 1;
                if (I[mid] <= arr[i]) {
                    high = mid;
                } else {
                    low = mid + 1;
                }
            }
            I[high] = arr[i];
            L[i] = high;
            if(lisLength<=high){
                lisLength++;
            }
        }
    }

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

        return gcd(b%a, a);
    }

    static long nCr(long n, long r)
    {
        return fact(n) / (fact(r) * fact(n - r));
    }

    // Returns factorial of n
    static long fact(long n)
    {
        long res = 1;
        for (int i = 2; i <= n; i++)
            res = (res * i)%MOD;
        return res;
    }

    static class Node implements Comparator<Node> {
        int value;
        int child;
        int level;

        public Node(int value, int level) {
            this.value = value;
            this.level = level;
        }

        @Override
        public int compare(Node o1, Node o2) {
            return (o1.level-o1.child)-(o2.level-o2.child);
        }
    }

    static int MOD = 1000000007;
    static int power(int x, int y, int p)
    {

        // Initialize result
        int res = 1;

        // Update x if it is more than or
        // equal to p
        x = x % p;

        while (y > 0)
        {

            // If y is odd, multiply x
            // with result
            if (y % 2 == 1)
                res = (res * x) % p;

            // y must be even now
            y = y >> 1; // y = y/2
            x = (x * x) % p;
        }

        return res;
    }

    // Returns n^(-1) mod p
    static int modInverse(int n, int p)
    {
        return power(n, p-2, p);
    }

    static int nCrModPFermat(int n, int r,
                             int p)
    {

        if (r == 0)
            return 1;


        int[] fac = new int[n+1];
        fac[0] = 1;

        for (int i = 1 ;i <= n; i++)
            fac[i] = fac[i-1] * i % p;

        return (fac[n]* modInverse(fac[r], p)
                % p * modInverse(fac[n-r], p)
                % p) % p;
    }
    public static long log2(long N)
    {

        // calculate log2 N indirectly
        // using log() method
        long result = (long)(Math.log(N) / Math.log(2));

        return result;
    }

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

        int testcase = sc.nextInt();

        while(testcase-->0){
            int n = sc.nextInt();
            if((n/2)%2!=0){
                pw.println("NO");
            }else{
                pw.println("YES");
                long res[] = new long[n];
                long even = 2;
                for(int i=0; i<n/2; i++, even+=2){
                    res[i] = even;
                }
                int j =n-2;
                res[n/2] = 1;
                res[n-1] = even-2+1;
                for(int i=n/2+1; i<=(3*(n/4)) && j>=(3*n/4); i++,j--){
                    res[i] = res[i-1]+2;
                    res[j] = res[j+1]-2;
                }
                for(int i=0; i<n; i++ ){
                    if(i!=n-1) {
                        pw.print(res[i] + " ");
                    }else{
                        pw.print(res[i]);
                    }
                }
                pw.println("");
            }
        }

        pw.close();

    }

    static void debug(Object...obj) {
        System.err.println(Arrays.deepToString(obj));
    }

    static class FastReader {
        InputStream is;
        private byte[] inbuf = new byte[1024];
        private int lenbuf = 0, ptrbuf = 0;

        public FastReader(InputStream is) {
            this.is = is;
        }

        public int readByte(){
            if(lenbuf == -1)throw new InputMismatchException();
            if(ptrbuf >= lenbuf){
                ptrbuf = 0;
                try {
                    lenbuf = is.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if(lenbuf <= 0)
                    return -1;
            }
            return inbuf[ptrbuf++];
        }
        public boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }
        public int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b)) ;
            return b;
        }
        public String next(){
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while(!(isSpaceChar(b))) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public String nextLine(){
            int b = readByte();
            StringBuilder sb = new StringBuilder();
            while(b != '\n' || b != '\r'){
                sb.appendCodePoint(b);
            }
            return sb.toString();
        }
        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }
        public long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
        public char[] next(int n){
            char[] buf = new char[n];
            int b = skip(), p = 0;
            while (p < n && !(isSpaceChar(b))) {
                buf[p++] = (char) b;
                b = readByte();
            }
            return n == p ? buf : Arrays.copyOf(buf, p);
        }
        public char nextChar () {
            return (char) skip();
        }
    }
}