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;
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n, k;
    cin >> n >> k;
    int a[n];
    for (int i = 0; i < n; i++) {
      cin >> a[i];
    }
    map<int, int> pos;
    vector<int> min_v, max_v;
    for (int i = 0; i < n / 2; i++) {
      pos[a[i] + a[n - i - 1]]++;
      min_v.push_back(-min(a[i], a[n - i - 1]));
      max_v.push_back(max(a[i], a[n - i - 1]));
    }
    sort(min_v.begin(), min_v.end());
    sort(max_v.begin(), max_v.end());
    int best = 1e8;
    for (int i = 2; i <= 2 * k; i++) {
      int cnt = n / 2 - pos[i];
      cnt += lower_bound(max_v.begin(), max_v.end(), i - k) - max_v.begin();
      cnt += lower_bound(min_v.begin(), min_v.end(), -i + 1) - min_v.begin();
      best = min(best, cnt);
    }
    cout << best << endl;
  }
}