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;
inline void FAST_IO() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
template <class F, class S>
ostream& operator<<(ostream& os, pair<F, S>& p) {
  os << "(" << p.first << "," << p.second << ")";
  return os;
}
template <class T, class S>
ostream& operator<<(ostream& os, map<T, S>& v) {
  os << "{";
  for (auto& i : v) cout << "{" << i.first << "," << i.second << "}";
  os << "}";
  return os;
}
template <class T>
ostream& operator<<(ostream& os, set<T>& v) {
  os << "{";
  for (auto& i : v) cout << i << ",";
  os << "}";
  return os;
}
template <class T>
ostream& operator<<(ostream& os, vector<T>& v) {
  os << "[";
  if (v.size()) os << v[0];
  for (int i = 1; i < v.size(); ++i) os << "," << v[i];
  os << "]";
  return os;
}
int main() {
  int t;
  cin >> t;
  while (t-- > 0) {
    int n, k;
    scanf("%d %d", &n, &k);
    vector<vector<int>> acc(2, vector<int>(2 * k + 2));
    vector<int> a(n);
    for (int i = 0; i < n; ++i) {
      scanf("%d", &a[i]);
    }
    for (int i = 0; i < n / 2; ++i) {
      int lo = a[i];
      int hi = a[n - i - 1];
      acc[0][lo + hi] += 1;
      acc[1][min(lo, hi) + 1] += 1;
      acc[1][max(lo, hi) + k + 1] -= 1;
    }
    int delta = 0;
    for (int j = 0; j < 2 * k + 2; ++j) {
      delta += acc[1][j];
      acc[1][j] = delta;
    }
    int resp = ~(1 << 31);
    for (int i = 2; i <= 2 * k; ++i) {
      int ta = acc[0][i];
      int tb = acc[1][i];
      int tc = n / 2;
      tc -= tb;
      tb -= ta;
      resp = min(resp, tb + tc * 2);
    }
    printf("%d\n", resp);
  }
  return 0;
}