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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class ConstantPalindromeSum {
    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(f.readLine());
        PrintWriter out = new PrintWriter(System.out);
        for (int t1 = 0; t1 < t; t1++) {
            StringTokenizer tokenizer = new StringTokenizer(f.readLine());
            int n = Integer.parseInt(tokenizer.nextToken());
            int k = Integer.parseInt(tokenizer.nextToken());
            SegmentTree tree = new SegmentTree(2 * k + 1);
            int[] ar = new int[n];
            tokenizer = new StringTokenizer(f.readLine());
            for (int i = 0; i < n; i++) {
                ar[i] = Integer.parseInt(tokenizer.nextToken());
            }
            int[] sums = new int[2 * k + 1];
            for (int i = 0; i < n / 2; i++) {
                int min = Math.min(ar[i], ar[n - i - 1]);
                int max = Math.max(ar[i], ar[n - i - 1]);
                sums[max + min]++;
                tree.addNum(min + 1, max + k, 1);
            }

            int minMoves = Integer.MAX_VALUE;
            for (int i = 1; i <= 2*k; i++) {
                int used = sums[i];
                int moves = (int) tree.getSumOnInterval(i, i) - used;
                used = (int) tree.getSumOnInterval(i, i);
                moves += (n / 2 - used) * 2;

                minMoves = Math.min(minMoves, moves);
            }

            out.println(minMoves);
        }

        out.close();
    }

    private static class SegmentTree {
        long[] tree;
        int[] lazy;
        int n;

        public SegmentTree(int n) {
            this.tree = new long[4 * n + 5];
            this.lazy = new int[4 * n + 5];
            this.n = n;
        }

        private void push(int node, int a, int b) {
            int mid = (a + b) / 2;
            this.tree[node * 2] += (mid - a + 1) * this.lazy[node];
            this.tree[node * 2 + 1] += (b - mid) * this.lazy[node];
            this.lazy[node * 2] += this.lazy[node];
            this.lazy[node * 2 + 1] += this.lazy[node];
            this.lazy[node] = 0;
        }

        public long getSumOnInterval(int from, int to) {
            return this.getSumOnInterval(from, to, 1, 0, this.n - 1);
        }

        private long getSumOnInterval(int from, int to, int node, int a, int b) {
            if (from <= a && b <= to) {
                return this.tree[node];
            }

            if (this.lazy[node] != 0) {
                this.push(node, a, b);
            }

            long sum = 0;
            int mid = (a + b) / 2;
            if (from <= mid) {
                sum += getSumOnInterval(from, to, node * 2, a, mid);
            }
            if (to > mid) {
                sum += getSumOnInterval(from, to, node * 2 + 1, mid + 1, b);
            }

            return sum;
        }
        public void addNum(int from, int to, int add) {
            this.addNum(from, to, 1, 0, this.n - 1, add);
        }

        private void addNum(int from, int to, int node, int a, int b, int add) {
            if (from <= a && b <= to) {
                this.lazy[node] += add;
                this.tree[node] += (long) add * (b - a + 1);
                return;
            }

            if (this.lazy[node] != 0) {
                this.push(node, a, b);
            }

            int mid = (a + b) / 2;
            if (from <= mid) {
                addNum(from, to, node * 2, a, mid, add);
            }
            if (to > mid) {
                addNum(from, to, node * 2  + 1, mid + 1, b, add);
            }

            this.tree[node] = this.tree[node * 2] + this.tree[node * 2 + 1];
        }
    }

    private static class FenwickTree {
        int[] tree;

        public FenwickTree(int n) {
            this.tree = new int[n];
        }

        public int getSum(int r) {
            int res = 0;
            while (r >= 0) {
                res += tree[r];
                r = g(r) - 1;
            }

            return res;
        }

        public void add(int r, int delta) {
            while (r < tree.length) {
                tree[r] += delta;
                r = h(r);
            }
        }

        private static int g(int i) {
            return i & (i + 1);
        }

        private static int h(int i) {
            return i | (i + 1);
        }
    }
}