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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 505;
int arr[MAXN];
int arr_copy[MAXN];
void rotate(int ind) {
  int num1 = arr[ind], num2 = arr[ind + 1], num3 = arr[ind + 2];
  arr[ind] = num3;
  arr[ind + 1] = num1;
  arr[ind + 2] = num2;
}
void swap_back(int ind, int distance, vector<int>& actions) {
  if (distance == 0) return;
  if (distance == 1) {
    actions.push_back(ind - 1);
    actions.push_back(ind - 1);
    rotate(ind - 1);
    rotate(ind - 1);
    return;
  }
  actions.push_back(ind - 2);
  rotate(ind - 2);
  swap_back(ind - 2, distance - 2, actions);
}
void swap_back2(int ind, int distance, vector<int>& actions) {
  if (distance <= 1) return;
  actions.push_back(ind - 2);
  rotate(ind - 2);
  swap_back2(ind - 2, distance - 2, actions);
}
int main() {
  ios_base::sync_with_stdio(0);
  int t;
  cin >> t;
  for (int test = 1; test <= t; test++) {
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++) {
      cin >> arr[i];
      arr_copy[i] = arr[i];
    }
    vector<int> actions;
    for (int i = 1; i <= n - 2; i++) {
      int min_ind = -1, min_val = 1e9;
      for (int j = i; j <= n; j++) {
        if (arr[j] < min_val) min_val = arr[j], min_ind = j;
      }
      swap_back(min_ind, min_ind - i, actions);
    }
    if (arr[n - 1] <= arr[n]) {
      cout << actions.size() << '\n';
      for (int i : actions) cout << i << ' ';
      cout << '\n';
      continue;
    }
    for (int i = 1; i <= n; i++) arr[i] = arr_copy[i] * 501;
    int done = 0;
    for (int i = 1; i <= n; i++) {
      int num = arr[i] + 1;
      for (int j = i + 1; j <= n; j++) {
        if (arr[i] == arr[j]) {
          arr[j] = num;
          num++;
        }
      }
    }
    actions.clear();
    for (int i = 1; i <= n - 2; i++) {
      int min_ind = -1, min_val = 1e9;
      for (int j = i; j <= n; j++) {
        if (arr[j] < min_val) min_val = arr[j], min_ind = j;
      }
      swap_back(min_ind, min_ind - i, actions);
    }
    if (arr[n - 1] / 501 <= arr[n] / 501) {
      cout << actions.size() << '\n';
      for (int i : actions) cout << i << ' ';
      cout << '\n';
      continue;
    }
    for (int i = 1; i <= n; i++) arr[i] = arr_copy[i] * 501;
    done = 0;
    for (int i = 1; i <= n; i++) {
      int num = arr[i] + 1;
      for (int j = i + 1; j <= n; j++) {
        if (arr[i] == arr[j]) {
          arr[j] = num;
          num++;
        }
      }
    }
    for (int i = 1; i <= n; i++) {
      for (int j = i + 1; j <= n; j++) {
        if (arr[j] == arr[i] + 1) {
          swap(arr[i], arr[j]);
          done = 1;
          break;
        }
      }
      if (done) break;
    }
    actions.clear();
    for (int i = 1; i <= n - 2; i++) {
      int min_ind = -1, min_val = 1e9;
      for (int j = i; j <= n; j++) {
        if (arr[j] < min_val) min_val = arr[j], min_ind = j;
      }
      swap_back(min_ind, min_ind - i, actions);
    }
    if (arr[n - 1] / 501 <= arr[n] / 501) {
      cout << actions.size() << '\n';
      for (int i : actions) cout << i << ' ';
      cout << '\n';
      continue;
    } else
      cout << -1 << '\n';
  }
  return 0;
}