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.math.*;
     
    public class Main {
        static PrintWriter out = new PrintWriter(System.out);
        static Reader in = new Reader();
        public static void main(String[] args) throws IOException {
            //Scanner sc = new Scanner();
            Main solver = new Main();
            solver.solve();
            out.flush();
            out.close();
     
        }
     
        static int INF = (int)1e9;
        static int maxn = (int)1e5+5;
        static int mod  = 998244353;
        static int n,m,q,k,t;
        
        void solve() throws IOException{
            t = in.nextInt();
            
            while (t --> 0) {
                n = in.nextInt();
                k = in.nextInt();
                
                int up[] = new int[k*2+1];
                int[] arr = new int[n];
                for (int i = 0; i < n; i++) arr[i] = in.nextInt();
                
                int x, y, min = 0, max = 0;
                for (int i = 0; i < n/2; i++) {
                    x = arr[i]; y = arr[n-i-1];
                    min = Math.min(x, y);
                    max = Math.max(x, y);
                    if (min < k) {
                        up[x+y+1]++;
                        if (max < k) {
                            up[x+y-min+k+1]++;
                        }
                    }
                }
                
                for (int i = 2; i <= 2*k; i++) {
                    up[i] += up[i-1];
                }
                
                int[] down = new int[2*k+1];
                for (int i = 0; i < n/2; i++) {
                    x = arr[i]; y = arr[n-i-1];
                    min = Math.min(x, y);
                    max = Math.max(x, y);
                    if (max > 1) {
                        down[x+y-max+1]++;
                        down[x+y]--;
                        if (min > 1) {
                            down[2]+=2;
                            down[x+y-max+1]-=2;
                        }
                    }
                }
                for (int i = 2; i <= 2*k; i++)
                    down[i] += down[i-1];
                
                int ans = Integer.MAX_VALUE;
                for (int i = 2; i <= 2*k; i++) {
                    //out.println(i+" "+down[i]+" "+up[i]);
                    ans = Math.min(ans, down[i]+up[i]);
                }
                out.println(ans);
                
            }
        }
        
        //<>
        
        static class Reader {
     
        private InputStream mIs;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
     
        public Reader() {
            this(System.in);
        }
     
        public Reader(InputStream is) {
            mIs = is;
        }
     
        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
     
        }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = mIs.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }
     
        public String nextLine() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }
     
        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
     
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
     
        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
     
        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
     
        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
     
        }
    }