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;
long long int power(long long int x, long long int y) {
  long long int res = 1;
  while (y) {
    if (y % 2) res = (res * x) % 998244353;
    y /= 2;
    x = (x * x) % 998244353;
  }
  return res;
}
void cycshift(long long int pos, long long int* a) {
  long long int temp = a[pos];
  a[pos] = a[pos + 2];
  a[pos + 2] = a[pos + 1];
  a[pos + 1] = temp;
}
int main() {
  long long int t, i, j, n;
  cin >> t;
  while (t--) {
    cin >> n;
    long long int a[n];
    vector<long long int> v;
    for (i = 0; i < n; i++) {
      cin >> a[i];
    }
    for (i = 0; i < n; i++) {
      long long int mn = 1000000000000, pos = -1;
      for (j = i; j < n; j++) {
        if (mn > a[j]) {
          mn = a[j];
          pos = j;
        }
      }
      if ((pos - i) == 1 && pos == n - 1) break;
      for (j = pos - 2; j >= i; j -= 2) {
        v.push_back(j);
        cycshift(j, a);
      }
      if ((pos - i) % 2) {
        for (j = 0; j < 2; j++) {
          v.push_back(i);
          cycshift(i, a);
        }
      }
    }
    long long int z = -1;
    if (a[n - 3] == a[n - 1]) {
      cycshift(n - 3, a);
      v.push_back(n - 3);
      i = n - 1;
    }
    for (j = 0; j < n - 1; j++)
      if (a[j] == a[j + 1]) z = j;
    if (i < n - 1 && z == -1)
      cout << -1 << endl;
    else {
      if (i == n - 2) {
        for (j = n - 3; j >= z; j -= 2) {
          cycshift(j, a);
          v.push_back(j);
        }
        cycshift(z, a);
        v.push_back(z);
        if ((n - 1 - z) % 2) z++;
        for (i = z + 1; i <= n - 4; i += 2) {
          for (j = 0; j < 2; j++) {
            v.push_back(i);
            cycshift(i, a);
          }
        }
      }
      cout << v.size() << endl;
      for (j = 0; j < v.size(); j++) cout << v[j] + 1 << " ";
      cout << endl;
    }
  }
  return 0;
}