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 = 2e5 + 55;
int a[maxn];
int ans[maxn * 2];
int solve() {
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (int i = 0; i < n / 2; ++i) {
    int mn = min(a[i], a[n - i - 1]);
    int mx = max(a[i], a[n - i - 1]);
    ans[2] += 2;
    ans[mn + 1]--;
    ans[mn + mx]--;
    ans[mn + mx + 1]++;
    ans[mx + k + 1]++;
    ans[2 * k + 1] -= 2;
  }
  int answer = n;
  for (int i = 2; i <= k * 2; ++i) {
    ans[i] += ans[i - 1];
    answer = min(answer, ans[i]);
  }
  for (int i = 0; i <= k * 2 + 2; ++i) ans[i] = 0;
  cout << answer << '\n';
  return 0;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  int t;
  cin >> t;
  while (t--) solve();
  return 0;
}