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.Objects;
import java.util.StringTokenizer;

import static java.lang.Double.parseDouble;
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.System.exit;


public class Solution {

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;
    static boolean isLocal = false;

    long[] seg;

    void update(int l, int r, int v) {
        if (l > r) return;
        seg[l] += v;
        seg[r] -= v;
    }

    void Case() throws IOException {
        int n = nextInt(), k = nextInt();
        int a[] = na(n);
        seg = new long[2 * k + 2];
        for (int i = 0; i < n / 2; i++) {
            int sum = a[i] + a[n - i - 1];
            int mn = min(a[i], a[n - i - 1]);
            int mx = max(a[i], a[n - i - 1]);
            mn += 1;
            mx += k;
            update(2, mn, 2);
            update(mn, sum, 1);
            update(sum + 1, mx + 1, 1);
            update(mx + 1, 2 * k + 1, 2);
        }
        int ans = n, cur = 0;
        for (int i = 2; i <= 2 * k; i++) {
            cur += seg[i];
            ans = min(ans, cur);
        }
        out.println(ans);
    }

    void solve() throws Exception {
        int t = nextInt();
        for (int i = 1; i <= t; i++) {
            Case();
        }
    }

    int min(int x, int y) {
        return Integer.min(x, y);
    }

    int max(int x, int y) {
        return Integer.max(x, y);
    }

    long min(long x, long y) {
        return Long.min(x, y);
    }

    long max(long x, long y) {
        return Long.max(x, y);
    }

    int[] sort(int[] arr) {
        sort(arr, 0, arr.length - 1);
        return arr;
    }

    void sort(int arr[], int l, int r) {
        if (l < r) {
            int m = (l + r) / 2;
            sort(arr, l, m);
            sort(arr, m + 1, r);
            merge(arr, l, m, r);
        }
    }

    void merge(int arr[], int l, int m, int r) {
        int n1 = m - l + 1;
        int n2 = r - m;
        int L[] = new int[n1];
        int R[] = new int[n2];
        for (int i = 0; i < n1; ++i)
            L[i] = arr[l + i];
        for (int j = 0; j < n2; ++j)
            R[j] = arr[m + 1 + j];
        int i = 0, j = 0;
        int k = l;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) {
                arr[k] = L[i];
                i++;
            } else {
                arr[k] = R[j];
                j++;
            }
            k++;
        }
        while (i < n1) {
            arr[k] = L[i];
            i++;
            k++;
        }
        while (j < n2) {
            arr[k] = R[j];
            j++;
            k++;
        }
    }

    class Seg implements Comparable<Seg> {
        int st, end;

        public Seg(int st, int end) {
            this.st = st;
            this.end = end;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Seg seg = (Seg) o;
            return st == seg.st &&
                    end == seg.end;
        }

        @Override
        public int hashCode() {
            return Objects.hash(st, end);
        }

        @Override
        public int compareTo(Seg seg) {
            return st == seg.st ? Integer.compare(end, seg.end) : Integer.compare(st, seg.st);
        }
    }

    private int[] na(int n) throws IOException {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = nextInt();
        return a;
    }

    private long[] nal(int n) throws IOException {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = nextLong();
        return a;
    }

    int nextInt() throws IOException {
        return parseInt(next());
    }

    long nextLong() throws IOException {
        return parseLong(next());
    }

    double nextDouble() throws IOException {
        return parseDouble(next());
    }

    String next() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    public static void main(String[] args) throws Exception {
        try {
            if (isLocal) {
                in = new BufferedReader(new FileReader("src/tests/sol.in"));
                out = new PrintWriter(new BufferedWriter(new FileWriter("src/tests/sol.out")));
            } else {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(new OutputStreamWriter(System.out));
            }
//            long lStartTime = System.currentTimeMillis();
            new Solution().solve();
//            long lEndTime = System.currentTimeMillis();
//            out.println("Elapsed time in seconds: " + (double) (lEndTime - lStartTime) / 1000.0);
            in.close();
            out.close();
        } catch (Throwable e) {
            e.printStackTrace();
            exit(1);
        }
    }
}