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 org.omg.CORBA.INTERNAL;

import java.io.*;
import java.nio.charset.Charset;
import java.util.*;

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

        int tc = in.nextInt();

        while ((tc--) > 0) {
            int n = in.nextInt();
            int k = in.nextInt();
            int[] a = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                a[i] = in.nextInt();
            }
            int[] dp = new int[2 * k + 10];
            for (int i = 1; i <= n / 2; i++) {
                int sum = a[i] + a[n - i + 1];
                if (sum <= 2 * k) dp[sum]--;
                if (sum <= 2 * k) dp[sum + 1]++;
                int mn = Integer.min(a[i], a[n - i + 1]) + 1;
                int mx = Integer.max(a[i], a[n - i + 1]) + k;
                if (mn <= 2 * k) dp[mn]--;
                if (mx + 1 <= 2 * k) dp[mx + 1]++;
                dp[0] += 2;
            }
            int ans = 2 * n;
            for (int i = 1; i <= 2 * k; i++) {
                dp[i] += dp[i - 1];
                ans = Integer.min(ans, dp[i]);
            }
            pw.println(ans);
        }

        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);
        }
    }


    private static int[] bfs(ArrayList<Integer>[] g, int a, int n) {
        int dist[] = new int[n + 1];
        for (int i = 0; i < n + 1; i++) {
            dist[i] = n + 10;
        }
        Queue<Integer> q = new LinkedList<>();
        boolean vis[] = new boolean[n + 1];
        dist[a] = 0;
        q.add(a);
        while (!q.isEmpty()) {
            int p = q.poll();
            if (vis[p] == true) {
                continue;
            }
            vis[p] = true;
            for (Integer i : g[p]) {
                if (!vis[i]) {
                    dist[i] = Integer.min(dist[i], dist[p] + 1);
                    q.add(i);
                }
            }
        }
        return dist;
    }


}