Problem: You are given an array a consisting of n integers.

In one move, you can choose some index i (1 ≤ i ≤ n - 2) and shift the segment [a_i, a_{i + 1}, a_{i + 2}] cyclically to the right (i.e. replace the segment [a_i, a_{i + 1}, a_{i + 2}] with [a_{i + 2}, a_i, a_{i + 1}]). 

Your task is to sort the initial array by no more than n^2 such operations or say that it is impossible to do that.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (3 ≤ n ≤ 500) — the length of a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 500), where a_i is the i-th element a.

It is guaranteed that the sum of n does not exceed 500.

Output

For each test case, print the answer: -1 on the only line if it is impossible to sort the given array using operations described in the problem statement, or the number of operations ans on the first line and ans integers idx_1, idx_2, ..., idx_{ans} (1 ≤ idx_i ≤ n - 2), where idx_i is the index of left border of the segment for the i-th operation. You should print indices in order of performing operations.

Example

Input


5
5
1 2 3 4 5
5
5 4 3 2 1
8
8 4 5 2 3 6 7 3
7
5 2 1 6 4 7 3
6
1 2 3 3 6 4


Output


0

6
3 1 3 2 2 3 
13
2 1 1 6 4 2 4 3 3 4 4 6 6 
-1
4
3 3 4 4 

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.text.*;
import java.math.*;
import java.lang.Math.*;

public class cyclic_shifts_sorting {
	
	public static void main(String[] args) throws Exception {new cyclic_shifts_sorting().run();}
	public FastIO file = new FastIO();
	public int ntc, ctc;
	public final long MOD = 1000000007L; //998244353L; 
	public final int M0D = 1000000007; //998244353
	public final int N = 200005, dx[] = { 0, 1, 0, -1 }, dy[] = { 1, 0, -1, 0 };
	
	public void run() throws Exception {
		ntc = nextInt();
		for (ctc = 1; ctc <= ntc; ++ctc) solve();
		file.out.flush(); file.out.close();
	}
	
	
	
	void solve() {
		int n = nextInt(), a[] = new int[n];
		for (int i = 0; i < n; ++i)
			a[i] = nextInt();
		ArrayList<Integer> mvs = new ArrayList<>();
		for (int i = 2; i < n; ++i) {
			for (int j = 0; j < n - i; ++j) {
				if (a[j] > a[j + 1] && a[j] > a[j + 2]) {
					mvs.add(j);
					int tmp = a[j];
					a[j] = a[j+2];
					a[j+2] = a[j+1];
					a[j+1] = tmp;
				}
			}
			if (a[n - i] > a[n - i + 1]) {
				mvs.add(n - i - 1);
				int tmp = a[n - i - 1];
				a[n - i - 1] = a[n - i - 1 +2];
				a[n - i - 1 + 2] = a[n - i - 1 +1];
				a[n - i - 1 + 1] = tmp;
			}
		}
		for (int i = 0; i < n - 2; ++i) {
			for (int j = 0; j < 3; ++j) {
				if (a[i] <= a[i+1] && a[i] <= a[i+2])
					break;
				mvs.add(i);
				int tmp = a[i];
				a[i] = a[i+2];
				a[i+2] = a[i+1];
				a[i+1] = tmp;
			}
		}
		boolean sorted = mvs.size() <= n * n;
		for (int i = 1; i < n; ++i)
			sorted &= a[i] >= a[i-1];
		if (!sorted) {
			println(-1); return;
		}
		println(mvs.size());
		for (int i = 0; i < mvs.size(); ++i) {
			if (i > 0) print(" ");
			print(mvs.get(i) + 1);
		}
		println("");
	}
	
	void sort(long[] a) { shuffle(a); Arrays.sort(a); }
	void sort(int[] a) { shuffle(a); Arrays.sort(a); }
	void shuffle(long[] a) {
		for (int i = a.length - 1; i >= 0; i--) { int j = (int) (Math.random() * (i + 1)); a[i] ^= a[j] ^ (a[j] = a[i]); } }
	void shuffle(int[] a) {
		for (int i = a.length - 1; i >= 0; i--) { int j = (int) (Math.random() * (i + 1)); a[i] ^= a[j] ^ (a[j] = a[i]); } }
	long gcd(long a, long b) { return b == 0 ? a : gcd(b, a % b); }
	long lcm(long x, long y) { return x / gcd(x, y) * y; }
	long mod(long n, long mod) { return (n % mod + mod) % mod; }
	long max(long a, long b) { return Math.max(a, b); }
	int max(int a, int b) { return Math.max(a, b); }
	long min(long a, long b) { return Math.min(a, b); }
	int min(int a, int b) { return Math.min(a, b); }
	long pow(long n, long p, long mod) { long ret = 1L;
	while (p > 0) { if (p % 2 != 0L) ret = mod(ret * n, mod); n = mod(n * n, mod); p >>= 1L; } return ret; }
	long pow(long n, long p) { long ret = 1L;
	while (p > 0) { if (p % 2 != 0L) ret *= n; n *= n; p >>= 1L; } return ret; }
	boolean isPrime(int n) { 
		if (n <= 1) return false; if (n <= 3) return true; if (n % 2 == 0 || n % 3 == 0) return false;
		for (int i = 5; i * i <= n; i = i + 6) if (n % i == 0 || n % (i + 2) == 0) return false; return true; }
	String next() {return file.next();}
	int nextInt() {return file.nextInt();}
	long nextLong() {return file.nextLong();}
	double nextDouble() {return file.nextDouble();}
	String nextLine() {return file.nextLine();}
	void print(Object o) {file.out.print(o);}
	void println(Object o) {file.out.println(o);}
	void printf(String s, Object... o) {file.out.printf(s, o);}
	class FastIO {
		BufferedReader br;
		StringTokenizer st;
		PrintWriter out;
		public FastIO() {br = new BufferedReader(new InputStreamReader(System.in));out = new PrintWriter(System.out);}
		String next() {while (st == null || !st.hasMoreElements()) {try {st = new StringTokenizer(br.readLine());} catch (IOException e) {e.printStackTrace();}}return st.nextToken();}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong() {return Long.parseLong(next());}
		double nextDouble() {return Double.parseDouble(next());}
		String nextLine() {String str = "";try {str = br.readLine();} catch (IOException e) {e.printStackTrace();} return str;}
		void print(Object o) {out.print(o);}
		void println(Object o) {out.println(o);}
		void printf(String s, Object... o) {out.printf(s, o);} }
	class Pair<A, B> implements Comparable {
		A fi; B se;
		public Pair(A fi, B se) { this.fi = fi; this.se = se; }
		public boolean equals(Object o) { if (this == o) return true;
		if (o == null || getClass() != o.getClass()) return false;
		Pair<?, ?> p = (Pair<?, ?>) o; if (!fi.equals(p.fi)) return false; return se.equals(p.se); }
		public int hashCode() { return 31 * fi.hashCode() + se.hashCode(); }
		public String toString() { return fi.toString() + " " + se.toString(); }
		<A, B> Pair<A, B> of(A a, B b) { return new Pair<A, B>(a, b); }
		public int compareTo(Object o) { Pair<?, ?> p = (Pair<?, ?>) o;
		if (fi.equals(p.fi)) return ((Comparable) se).compareTo(p.se); return ((Comparable) fi).compareTo(p.fi); } } }