Problem: You are given an array a consisting of n integers (it is guaranteed that n is even, i.e. divisible by 2). All a_i does not exceed some integer k.

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index i from 1 to n and replace a_i with some integer in range [1; k]) to satisfy the following conditions:

  * after all replacements, all a_i are positive integers not greater than k; 
  * for all i from 1 to n/2 the following equation is true: a_i + a_{n - i + 1} = x, where x should be the same for all n/2 pairs of elements. 



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 first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 2 ⋅ 10^5) — the length of a and the maximum possible value of some a_i correspondingly. It is guratanteed that n is even (i.e. divisible by 2). The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the i-th element of a.

It is guaranteed that the sum of n (as well as the sum of k) over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ k ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — the minimum number of elements you have to replace in a to satisfy the conditions from the problem statement.

Example

Input


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


Output


0
1
4
2

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); } } }