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;
void solve() {
  int n, k, mn, mx;
  cin >> n >> k;
  vector<int> a(n);
  int sum = 0;
  vector<int> chg(2 * k + 1, 0);
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n / 2; i++) {
    mn = min(a[i], a[n - i - 1]);
    mx = max(a[i], a[n - i - 1]);
    chg[mn + 1]--;
    chg[mn + mx]--;
    if (mn + mx < 2 * k) {
      chg[mn + mx + 1]++;
    }
    chg[mx + k + 1]++;
  }
  chg[0] = n;
  for (int i = 1; i < 2 * k + 1; i++) {
    chg[i] = chg[i - 1] + chg[i];
  }
  int mnn = INT32_MAX;
  for (int i = 1; i < 2 * k + 1; i++) {
    mnn = mnn > chg[i] ? chg[i] : mnn;
  }
  cout << mnn << endl;
}
int main() {
  int tc;
  cin >> tc;
  while (tc--) solve();
}