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 long long N = 200009, OO = 1e12;
int n, a[N], pos[N], t[N];
void upd(int id) {
  for (; id <= n; id += id & -id) ++t[id];
}
int get(int id) {
  int ans = 0;
  for (; id > 0; id -= id & -id) ans += t[id];
  return ans;
}
void RE(int v, int u, vector<int> &ans) {
  while (u != v) {
    if (u - v >= 2) {
      ans.push_back(u - 2);
      swap(a[u], a[u - 2]);
      swap(a[u], a[u - 1]);
      pos[a[u]] = u;
      pos[a[u - 2]] = u - 2;
      pos[a[u - 1]] = u - 1;
      u -= 2;
    } else {
      ans.push_back(u - 1);
      ans.push_back(u - 1);
      swap(a[u], a[u - 1]);
      swap(a[u], a[u + 1]);
      pos[a[u]] = u;
      pos[a[u + 1]] = u + 1;
      pos[a[u - 1]] = u - 1;
      --u;
    }
  }
}
void print_ans() {
  vector<int> ans;
  for (int i = 1; i <= n; ++i) {
    if (pos[i] != i) RE(i, pos[i], ans);
  }
  cout << ans.size() << endl;
  for (auto x : ans) cout << x << ' ';
  cout << endl;
}
void IO() {
  int test;
  cin >> test;
  while (test--) {
    cin >> n;
    vector<pair<int, int> > v;
    pair<int, int> sww = make_pair(0, 0);
    int x;
    for (int i = 0; i <= n; ++i) pos[i] = 0;
    for (int i = 1; i <= n; ++i) {
      cin >> x;
      v.push_back(make_pair(x, i));
      if (!pos[x])
        pos[x] = i;
      else if (!sww.first) {
        sww = make_pair(pos[x], i);
      }
    }
    sort(v.begin(), v.end());
    int run = 0, inver = 0;
    for (int i = 0; i <= n; ++i) pos[i] = 0, t[i] = 0;
    for (auto x : v) {
      a[x.second] = ++run;
      pos[a[x.second]] = x.second;
    }
    for (int i = 1; i <= n; ++i) {
      inver += i - 1 - get(a[i] - 1);
      upd(a[i]);
    }
    if (inver % 2 == 1 && sww.first == 0)
      cout << -1 << endl;
    else {
      if (inver % 2 == 1) swap(a[sww.first], a[sww.second]);
      pos[a[sww.first]] = sww.first;
      pos[a[sww.second]] = sww.second;
      print_ans();
    }
  }
}
int main() {
  IO();
  return 0;
}