A permutation of length n is an array p=[p_1,p_2,...,p_n], which contains every integer from 1 to n (inclusive) and, moreover, each number appears exactly once. For example, p=[3,1,4,2,5] is a permutation of length 5.

For a given number n (n ≥ 2), find a permutation p in which absolute difference (that is, the absolute value of difference) of any two neighboring (adjacent) elements is between 2 and 4, inclusive. Formally, find such permutation p that 2 ≤ |p_i - p_{i+1}| ≤ 4 for each i (1 ≤ i < n).

Print any such permutation for the given integer n or determine that it does not exist.

Input

The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.

Each test case is described by a single line containing an integer n (2 ≤ n ≤ 1000).

Output

Print t lines. Print a permutation that meets the given requirements. If there are several such permutations, then print any of them. If no such permutation exists, print -1.

Example

Input


6
10
2
4
6
7
13


Output


9 6 10 8 4 7 3 1 5 2 
-1
3 1 4 2 
5 3 6 2 4 1 
5 1 3 6 2 4 7 
13 9 7 11 8 4 1 3 5 2 6 10 12 
#include <bits/stdc++.h>
using namespace std;
void _print(long long t) { cout << t; }
void _print(int t) { cout << t; }
void _print(string t) { cout << t; }
void _print(char t) { cout << t; }
void _print(long double t) { cout << t; }
void _print(double t) { cout << t; }
void _print(unsigned long long t) { cout << t; }
template <class T, class V>
void _print(pair<T, V> p);
template <class T>
void _print(vector<T> v);
template <class T>
void _print(set<T> v);
template <class T, class V>
void _print(map<T, V> v);
template <class T>
void _print(multiset<T> v);
template <class T, class V>
void _print(pair<T, V> p) {
  cout << "{";
  _print(p.ff);
  cout << ",";
  _print(p.ss);
  cout << "}";
}
template <class T>
void _print(vector<T> v) {
  cout << "[ ";
  for (T i : v) {
    _print(i);
    cout << " ";
  }
  cout << "]";
}
template <class T>
void _print(set<T> v) {
  cout << "[ ";
  for (T i : v) {
    _print(i);
    cout << " ";
  }
  cout << "]";
}
template <class T>
void _print(multiset<T> v) {
  cout << "[ ";
  for (T i : v) {
    _print(i);
    cout << " ";
  }
  cout << "]";
}
template <class T, class V>
void _print(map<T, V> v) {
  cout << "[ ";
  for (auto i : v) {
    _print(i);
    cout << " ";
  }
  cout << "]";
}
void first() {
  long long n;
  cin >> n;
  if (n == 2 || n == 3) {
    cout << -1 << endl;
    return;
  }
  if (n == 4) {
    cout << "3 1 4 2\n";
    return;
  }
  vector<long long> ans(n, -1);
  long long j = n - 1;
  long long sub = n % 2;
  for (int i = n - sub; i >= 2; i -= 2) {
    ans[j--] = i;
  }
  if (j >= 0) {
    ans[j--] = 5;
  }
  if (j >= 0) {
    ans[j--] = 1;
  }
  if (j >= 0) {
    ans[j--] = 3;
  }
  for (int i = 7; i <= n; i += 2) {
    if (j >= 0) {
      ans[j--] = i;
    }
  }
  for (long long i = 0; i < n; i++) {
    if (ans[i] == -1) {
      cout << -1 << endl;
      return;
    }
  }
  for (auto x : ans) {
    cout << x << " ";
  }
  cout << endl;
}
int main() {
  int queries = 1;
  cin >> queries;
  while (queries--) {
    first();
  }
}
