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 N = 510;
vector<int> ans;
int a[N];
int n;
void move(int x, int t) {
  while (t--) {
    ans.push_back(x);
    int tmp = a[x + 2];
    a[x + 2] = a[x + 1];
    a[x + 1] = a[x];
    a[x] = tmp;
  }
  if (0)
    for (int i = 1; i <= n; ++i) printf("%d%c", a[i], " \n"[i == n]);
}
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    scanf("%d", &n);
    for (int i = 1; i <= n; ++i) scanf("%d", a + i);
    int tot = 0;
    ans.clear();
    bool flag = true;
    for (; tot < n;) {
      int num = 1e9;
      for (int i = tot + 1; i <= n; ++i) num = min(num, a[i]);
      if (0) printf("deal %d:\n", num);
      for (int i = tot + 1; i <= n; ++i) {
        if (a[i] != num) continue;
        if (0) printf("found a[%d]=%d\n", i, a[i]);
        tot++;
        if ((i - tot) % 2 == 0) {
          for (int j = i; j - 2 >= tot; j -= 2) move(j - 2, 1);
          continue;
        }
        if (tot >= 2 && a[tot - 1] == num) {
          for (int j = i; j - 2 >= tot; j -= 2) move(j - 2, 1);
          move(tot - 1, 1);
          continue;
        }
        if (tot + 1 < n) {
          for (int j = i; j - 2 >= tot; j -= 2) move(j - 2, 1);
          move(tot, 2);
          continue;
        }
        int same = n - 2;
        for (; same > 1 && a[same] != a[same - 1]; --same)
          ;
        if (same <= 1) {
          flag = false;
          break;
        }
        int rep = (tot - same) % 2 == 0 ? tot : n;
        for (int j = rep; j - 2 >= same; j -= 2) move(j - 2, 1);
        move(same - 1, 1);
        for (int j = same + 1; j + 2 <= n; j += 2) move(j, 2);
      }
    }
    if (!flag)
      puts("-1");
    else {
      int ans_size = ans.size();
      printf("%d\n", ans_size);
      for (int i = 0; i < ans_size; ++i)
        printf("%d%c", ans[i], " \n"[i == ans_size - 1]);
      if (ans_size == 0) puts("");
    }
  }
  return 0;
}