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;
void swap(vector<int> &v, int j) {
  int temp = v[j];
  v[j] = v[j + 2];
  v[j + 2] = v[j + 1];
  v[j + 1] = temp;
  return;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int T;
  cin >> T;
  for (int t = 0; t < T; ++t) {
    int n;
    cin >> n;
    vector<int> v;
    for (int i = 0; i < n; i++) {
      int a;
      cin >> a;
      v.push_back(a);
    }
    vector<int> indi;
    for (int i = 0; i < n - 1; i++) {
      for (int j = 0; j < n - i - 2; j++) {
        if (v[j] > v[j + 1] && v[j] > v[j + 2]) {
          indi.push_back(j);
          indi.push_back(j);
          swap(v, j);
          swap(v, j);
        } else {
          if (v[j + 1] > v[j + 2]) {
            swap(v, j);
            indi.push_back(j);
          }
        }
      }
    }
    if (v[0] > v[1]) {
      int c = 0;
      if (v[2] == v[0]) {
        indi.push_back(0);
        indi.push_back(0);
        swap(v, 0);
        swap(v, 0);
        c = 1;
      }
      for (int i = 0; i < n; i++) {
        if (v[i] == v[i + 1] && c == 0) {
          c = 1;
          if (i % 2 == 0) {
            int e = 0;
            int o = 1;
            while (e != i) {
              indi.push_back(o);
              swap(v, o);
              indi.push_back(e);
              swap(v, e);
              e += 2;
              o += 2;
            }
          } else {
            int e = 0;
            int o = 1;
            while (o != i) {
              indi.push_back(o);
              swap(v, o);
              indi.push_back(e);
              swap(v, e);
              e += 2;
              o += 2;
            }
            indi.push_back(e);
            swap(v, e);
            indi.push_back(e);
            swap(v, e);
          }
        }
      }
      if (c == 0) {
        cout << -1 << "\n";
        continue;
      }
    }
    cout << indi.size() << "\n";
    for (int i = 0; i < indi.size(); i++) {
      cout << indi[i] + 1 << " ";
    }
    cout << "\n";
  }
}