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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.StringTokenizer;
import java.util.*;

public class ConstantPalindromeSum {
	public static void main(String[] args) throws IOException {
		MyScanner s = new MyScanner();
		Print p = new Print();
		int t = s.nextInt();
		while( t --> 0) {
			int n = s.nextInt();
			int k = s.nextInt();
			int[] a = new int[n];
			for(int i=0; i<n; i++) {
				a[i] = s.nextInt();
			}
			int[] cnt = new int[2 * k + 1];
			for (int i = 0; i < n / 2; ++i) {
				++cnt[a[i] + a[n - i - 1]];
			}
			int[] pref = new int[2 * k + 2];
			for (int i = 0; i < n / 2; ++i) {
				int l1 = 1 + a[i], r1 = k + a[i];
				int l2 = 1 + a[n - i - 1], r2 = k + a[n - i - 1];
				++pref[Math.min(l1, l2)];
				--pref[Math.max(r1, r2) +1];
			}
			for (int i = 1; i <= 2 * k + 1; ++i) {
				pref[i] += pref[i - 1];
			}
			int ans = Integer.MAX_VALUE;
			for (int sum = 2; sum <= 2 * k; ++sum) {
				ans = Math.min(ans, (pref[sum] - cnt[sum]) + (n / 2 - pref[sum]) * 2);
			}
			p.println(ans);
			
		}
		p.close();
	}
	
	public static class Pair implements Comparable<Pair> {
		int first;
		int second;
		
		public Pair( int a, int b ) {
			this.first = a;
			this.second = b;
		}

		@Override
		public int compareTo(Pair o) {
			// TODO Auto-generated method stub
			return o.first - first;
		}
		
		
	}
	
	
    static class Print {
        private BufferedWriter bw;
 
        public Print() {
            this.bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }
        public void print(Object object) throws IOException {
            bw.append("" + object);
        }
        public void println(Object object) throws IOException {
            print(object);
            bw.append("\n");
        }
        public void close() throws IOException {
            bw.close();
        }
    }
	
	
	
	
	
	
    public static class MyScanner {
	      BufferedReader br;
	      StringTokenizer st;
	 
	      public MyScanner() {
	         br = new BufferedReader(new InputStreamReader(System.in));
	      }
	 
	      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;
	      }
	}


}