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 long long mod = 1e9 + 7;
const long long inf = INT64_MAX;
void solve() {
  long long n, k;
  cin >> n >> k;
  vector<long long> v(n);
  vector<long long> aux(2 * k + 2, 0);
  for (long long i = 0; i < n; i++) {
    cin >> v[i];
  }
  for (long long i = 0; i < n / 2; i++) {
    long long a = v[i];
    long long b = v[n - 1 - i];
    long long r = (a + b) + max(k - a, k - b);
    long long l = (a + b) - max(a - 1, b - 1);
    aux[l] -= 1;
    aux[r + 1] += 1;
    aux[a + b] -= 1;
    aux[a + b + 1] += 1;
  }
  long long cur = n, best = cur;
  for (long long i = 1; i <= 2 * k; i++) {
    cur += aux[i];
    best = min(best, cur);
  }
  cout << best << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int test = 1;
  cin >> test;
  while (test-- > 0) {
    solve();
  }
  return 0;
}