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;
struct FASTINPUT {
  void f(string& s) {
    char buf[400005];
    long long a = scanf("%s", buf);
    a++;
    s = buf;
  }
  void f(long long& x) {
    long long a = scanf("%lld", &x);
    a++;
  }
  void f(int& x) {
    long long a = scanf("%d", &x);
    a++;
  }
  void f(double& x) {
    long long a = scanf("%lf", &x);
    a++;
  }
  template <typename A, typename B>
  void f(pair<A, B>& p) {
    f(p.first);
    f(p.second);
  }
  template <typename A>
  void f(vector<A>& x) {
    for (auto& y : x) f(y);
  }
  void read() {}
  template <typename Head, typename... Tail>
  void read(Head& H, Tail&... T) {
    f(H);
    read(T...);
  }
};
struct FASTOUTPUT {
  void f(string s) { printf("%s", s.c_str()); }
  void f(long long x) { printf("%lld", x); }
  void f(int x) { printf("%d", x); }
  void f(double x) { printf("%.20f", x); }
  void f(char x) { printf("%c", x); }
  void f(const char* a) { printf("%s", a); }
  void print() {}
  template <typename Head, typename... Tail>
  void print(Head H, Tail... T) {
    f(H);
    print(T...);
  }
};
struct DEBUG {
  string open = "[", close = "]", sep = ", ";
  string f(string s) { return s; }
  string f(char c) { return string(1, c); }
  string f(int x) { return to_string(x); }
  string f(long long x) { return to_string(x); }
  string f(double x) { return to_string(x); }
  string f(const char* a) { return a; }
  template <typename A, typename B>
  string f(pair<A, B> p) {
    return open + f(p.first) + sep + f(p.second) + close;
  }
  template <typename A>
  string f(A v) {
    string s = open;
    for (auto a : v) {
      if (s != open) {
        s += sep;
      }
      s += f(a);
    }
    s += close;
    return s;
  }
  void show() { cout << endl; }
  template <typename Head, typename... Tail>
  void show(Head H, Tail... T) {
    cout << " " << f(H);
    show(T...);
  }
};
vector<long long> di = {0, 0, 1, -1, 1, -1, 1, -1};
vector<long long> dj = {1, -1, 0, 0, -1, -1, 1, 1};
long long ob(long long i, long long n) { return i < 0 || i >= n; }
long long tp(long long x) { return (1LL << x); }
long long roundup(long long a, long long b) {
  return a % b ? a / b + 1 : a / b;
}
template <typename A, typename B>
long long exist(A a, B b) {
  return a.find(b) != a.end();
}
vector<string> ssplit(string s) {
  vector<string> ans;
  stringstream ss;
  ss << s;
  while (ss >> s) ans.push_back(s);
  return ans;
}
void makemod(long long& x, long long m) {
  x %= m;
  x += m;
  x %= m;
}
long long powmod(long long a, long long b, long long m) {
  if (b == 0) return 1;
  long long h = powmod(a, b / 2, m);
  long long ans = h * h % m;
  return b % 2 ? ans * a % m : ans;
}
void upmin(long long& x, long long v) { x = min(x, v); }
void upmax(long long& x, long long v) { x = max(x, v); }
const long long inf = (long long)1e18 + 5;
const long long mod = 1e9 + 7;
const long long mod2 = 998244353;
const double eps = 1e-10;
const double pi = acos(0) * 2;
const string nl = "\n";
void solve() {
  long long n;
  do {
    FASTINPUT inp;
    inp.read(n);
  } while (false);
  if (n < 4) {
    do {
      FASTOUTPUT out;
      out.print(-1, nl);
    } while (false);
    return;
  }
  for (long long i = 1001; i >= 1; i -= 2) {
    if (i <= n) do {
        FASTOUTPUT out;
        out.print(i, ' ');
      } while (false);
  }
  do {
    FASTOUTPUT out;
    out.print(4, ' ');
  } while (false);
  do {
    FASTOUTPUT out;
    out.print(2, ' ');
  } while (false);
  for (long long i = 6; i <= 1000; i += 2) {
    if (i <= n) do {
        FASTOUTPUT out;
        out.print(i, ' ');
      } while (false);
  }
  do {
    FASTOUTPUT out;
    out.print(nl);
  } while (false);
}
signed main() {
  long long t = 1;
  do {
    FASTINPUT inp;
    inp.read(t);
  } while (false);
  for (long long i = 0; i < t; i++) solve();
  return 0;
}
