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.util.*;
import java.io.*;
import static java.lang.Math.*;
public class Reader_ {
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String nextLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int ni() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nl() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nd() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    public static void main(String[] args) {
        new Thread(null, null, "Rahsut", 1 << 25) {
            public void run() {
                try {
                    Freak();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }

    static long modPow(long x, long p, long m) {
        if (p == 0)
            return 1;
        if (p % 2 == 0)
            return modPow((x * x) % m, p >> 1, m) % m;
        return x * (modPow(x, p - 1, m) % m) % m;
    }

    static long mul(long a, long b, long m) {
        a %= m;
        b %= m;
        return (a * b) % m;
    }

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

    static long lcm(long a, long b) {
        a /= gcd(a, b);
        return a * b;
    }

    public static class Pair implements Comparable<Pair> {
        long x, y;

        Pair(long x, long y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(Pair o) {
            if (x != o.x)
                return (int) x - (int) o.x;
            return (int) y - (int) o.y;
        }

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

    //global variable
    static Reader sc = new Reader();
    static StringBuilder sb = new StringBuilder();
    static PrintWriter pw = new PrintWriter(System.out, true);
    static int dir1[][] = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
    static int dir2[][] = {{1, -1}, {-1, 1}, {1, 1}, {-1, -1}};
    static int dp[][], mod = (int) 1e9 + 7;
    static int arr[], len1, len2, n, q, t, brr[], m, k, size;
    static Pair tree1[], tree2[];
    static void Freak() throws IOException {
        // code goes here
        int t = sc.ni();
        while(t-->0) {
             n = sc.ni();k = sc.ni();
            int arr[]= new int[n];
            HashMap<Integer,Integer> map = new HashMap<>();
            for(int i =0;i<n;i++) {
                arr[i]=sc.ni();
            }

            for(int i =0;i<n/2;i++) {
                int sum = arr[i]+arr[n-1 -i];
                if(map.containsKey(sum))
                    map.put(sum,map.get(sum)+1);
                else
                    map.put(sum,1);
            }
            long brr[]= new long[2*k +2];
            for(int i =0;i<n/2;i++) {
                int min = min(arr[i],arr[n-1-i]);
                int max = max(arr[i],arr[n-1-i])+k;
                brr[min+1]++;
                brr[max+1]--;
            }

            long cnt = Integer.MAX_VALUE;
            for(int i =1;i<2*k+2;i++) {
                brr[i] += brr[i - 1];
                long new_cnt = brr[i] + (n/2 - brr[i])*2;
                if(map.containsKey(i))
                    new_cnt -= map.get(i);
                cnt = min(cnt,new_cnt);
            }
            sb.append(cnt+"\n");
        }
        pw.println(sb);
        pw.flush();
        pw.close();
    }
}