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 a[200005];
long long ans[400005];
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n, k;
    int mi, ma;
    long long min1 = 0x3f3f3f3f;
    cin >> n >> k;
    int nn = n / 2;
    for (int i = 1; i <= n; i++) {
      cin >> a[i];
    }
    for (int i = 1; i <= nn; i++) {
      mi = min(a[i], a[n - i + 1]);
      ma = max(a[i], a[n - i + 1]);
      if (mi >= 2) {
        ans[2] += 2;
        ans[mi + 1] -= 2;
      }
      if (a[i] + a[n - i + 1] - 1 >= mi + 1) {
        ans[mi + 1] += 1;
        ans[a[i] + a[n - i + 1]] -= 1;
      }
      if (ma + k >= a[i] + a[n - i + 1] + 1) {
        ans[a[i] + a[n - i + 1] + 1] += 1;
        ans[ma + k + 1] -= 1;
      }
      if (2 * k >= ma + k + 1) {
        ans[ma + k + 1] += 2;
        ans[2 * k + 1] -= 2;
      }
    }
    for (int i = 2; i <= 2 * k; i++) {
      ans[i] = ans[i - 1] + ans[i];
      min1 = min(min1, ans[i]);
      ans[i - 2] = 0;
    }
    ans[2 * k - 1] = 0, ans[2 * k] = 0, ans[2 * k + 1] = 0;
    cout << min1 << endl;
  }
}