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 = 2e6 + 10;
const int inf = 0x3f3f3f3f;
const int M = 1e9 + 7;
long long a[maxn];
vector<int> ans;
int n;
void move(int i) {
  ans.push_back(i);
  int t = a[i + 1];
  a[i + 1] = a[i];
  a[i] = a[i - 1];
  a[i - 1] = t;
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    cin >> n;
    ans.clear();
    for (int i = (0); i < (n); i++) cin >> a[i];
    for (int i = (0); i < (n - 2); i++) {
      int k = i;
      for (int j = (i + 1); j < (n); j++) {
        if (a[k] > a[j]) k = j;
      }
      if (k == i) continue;
      while (k - i > 1) {
        move(k - 1);
        k -= 2;
      }
      if (k - i == 1) move(k);
      k++;
      if (k - i == 2) move(k - 1);
      k -= 2;
    }
    if (a[n - 2] > a[n - 1]) {
      int p = -1, pp;
      for (int i = (0); i < (n - 1); i++) {
        if (a[i] == a[i + 1]) {
          p = i + 1;
        }
      }
      pp = p - 1;
      if (p == -1) {
        if (a[n - 3] == a[n - 1]) {
          p = n - 1;
          pp = n - 3;
        } else {
          cout << -1 << endl;
          continue;
        }
      }
      while (n - 1 - p > 2) {
        move(p + 1);
        p++;
        move(p);
        p++;
      }
      if (n - 1 - p == 2)
        move(p + 1), p++;
      else if (n - 1 - p == 1)
        move(p), p++;
      while (p - pp > 1) {
        move(p - 1);
        p -= 2;
      }
      if (p - pp == 1) move(p);
      p++;
      if (p - pp == 2) move(p - 1);
      p -= 2;
    }
    cout << (int)(ans).size() << endl;
    for (int x : ans) cout << x << ' ';
    cout << endl;
  }
}