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 n, arr[505], flag;
vector<int> v, w;
void myfun(int m, int num) {
  int pos;
  for (pos = m - 1; arr[pos] != num; pos++)
    ;
  if ((pos - (m - 1)) % 2 == 0) {
    for (int i = pos; i > m - 1; i--) arr[i] = arr[i - 1];
    arr[m - 1] = num;
    for (int i = pos; i > m - 1; i -= 2) v.push_back(i - 1);
  } else {
    for (int i = pos; i > m; i--) arr[i] = arr[i - 1];
    arr[m] = num;
    for (int i = pos; i > m; i -= 2) v.push_back(i - 1);
    v.push_back(m);
    v.push_back(m);
    arr[m] = arr[m + 1];
    arr[m + 1] = arr[m - 1];
    arr[m - 1] = num;
  }
  return;
}
int main(void) {
  int t, T;
  scanf("%d", &T);
  for (t = 0; t < T; t++) {
    v.clear();
    w.clear();
    scanf("%d", &n);
    for (int i = 0; i < n; i++) {
      scanf("%d", arr + i);
      w.push_back(arr[i]);
    }
    sort(w.begin(), w.end());
    for (flag = 1; flag < n; flag++)
      if (w[flag] == w[flag - 1]) break;
    if (flag < n) {
      for (int i = 1; i < flag; i++) myfun(i, w[i - 1]);
      for (int i = flag + 1; i < n; i++) myfun(i - 1, w[i - 1]);
      int p;
      if (arr[n - 1] == w[flag])
        p = n - 1;
      else
        p = n - 2;
      for (int i = p; i > flag; i -= 2) v.push_back(i - 1);
      printf("%d\n", v.size());
      for (int i : v) printf("%d ", i);
      printf("\n");
    } else {
      for (int i = 1; i < n - 1; i++) {
        myfun(i, w[i - 1]);
      }
      if (arr[n - 1] == w[n - 1]) {
        printf("%d\n", v.size());
        for (int i : v) printf("%d ", i);
        printf("\n");
      } else {
        printf("-1\n");
      }
    }
  }
  return 0;
}