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 double PI = acos(-1.0);
const double epsilon = PI / 180.0;
vector<long long> path;
long long move(vector<long long> &arr, long long &i, long long start) {
  if (i - start >= 2) {
    path.push_back(i - 2);
    swap(arr[i], arr[i - 1]);
    swap(arr[i - 2], arr[i - 1]);
    i -= 2;
    return arr[i] < arr[i + 1];
  } else {
    path.push_back(i - 1);
    swap(arr[i], arr[i + 1]);
    swap(arr[i - 1], arr[i]);
    i += 1;
    return 1;
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int q = 1;
  cin >> q;
  while (q--) {
    long long n;
    cin >> n;
    vector<long long> arr(n);
    long long i = 0;
    for (auto &num : arr) {
      cin >> num;
    }
    path = {};
    long long cnt = 0, start = 0, ans = 0;
    while (cnt <= n * n && start + 2 < arr.size()) {
      long long idx = min_element(arr.begin() + start, arr.end()) - arr.begin();
      while (idx != start) {
        ans += move(arr, idx, start);
        ++cnt;
      }
      ++start;
    }
    int end = (int)arr.size() - 2;
    for (; end > 0; --end) {
      if (arr[end] <= arr[end + 1]) {
        continue;
      }
      ++cnt;
      path.push_back(end - 1);
      swap(arr[end], arr[end + 1]);
      swap(arr[end], arr[end - 1]);
    }
    if (is_sorted(arr.begin(), arr.end())) {
      cout << path.size() << endl;
      for (auto x : path) cout << x + 1 << " ";
      cout << endl;
    } else {
      cout << -1 << endl;
    }
  }
  return 0;
}