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>
const int MAXN = 2e5 + 5;
std::unordered_map<int, int> cnt;
int A[MAXN];
int D[MAXN * 2];
int K, N, T;
int solve() {
  scanf(" %d%d", &N, &K);
  for (int i = 0; i < N; ++i) {
    scanf("%d", &A[i]);
  }
  int K2 = K * 2;
  int N2 = N / 2;
  cnt.clear();
  cnt.reserve(N2);
  for (int i = 0; i <= K2; ++i) {
    D[i] = 0;
  }
  for (int i = 0; i < N2; ++i) {
    int sum = A[i] + A[N - i - 1];
    ++cnt[sum];
    int lo = std::min(A[i], A[N - i - 1]);
    int hi = std::max(A[i], A[N - i - 1]);
    ++D[lo + 1];
    --D[hi + K + 1];
  }
  for (int i = 1; i <= K2; ++i) {
    D[i] += D[i - 1];
  }
  int ret = N;
  for (int i = 2; i <= K2; ++i) {
    int cost = D[i] + 2 * (N2 - D[i]);
    if (cnt.count(i)) {
      cost -= cnt.at(i);
    }
    ret = std::min(cost, ret);
  }
  return ret;
}
int main() {
  scanf("%d", &T);
  for (int t = 0; t < T; ++t) {
    printf("%d\n", solve());
  }
  return 0;
}