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>
#pragma GCC optimize(2)
using namespace std;
const int man = 2e5 + 10;
template <typename T>
inline T read() {
  T sum = 0, fl = 1;
  int ch = getchar();
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') fl = -1;
  for (; isdigit(ch); ch = getchar()) sum = sum * 10 + ch - '0';
  return sum * fl;
}
template <typename T>
inline void write(T x) {
  static int sta[35];
  int top = 0;
  do {
    sta[top++] = x % 10, x /= 10;
  } while (x);
  while (top) putchar(sta[--top] + 48);
}
template <typename T>
T gcd(T a, T b) {
  return b == 0 ? a : gcd(b, a % b);
}
template <typename T>
T exgcd(T a, T b, T &g, T &x, T &y) {
  if (!b) {
    g = a, x = 1, y = 0;
  } else {
    exgcd(b, a % b, g, y, x);
    y -= x * (a / b);
  }
}
const long long mod = 1e9 + 7;
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    if (n == 2 || n == 3) {
      cout << -1 << endl;
      continue;
    }
    vector<int> sp;
    for (int i = n; i >= 1; i--) {
      if (i & 1) sp.push_back(i);
    }
    sp.push_back(4);
    for (int i = 2; i <= n; i += 2) {
      if (i != 4) sp.push_back(i);
    }
    for (int i = 0; i < sp.size(); i++) {
      cout << sp[i] << " ";
    }
    cout << endl;
  }
  return 0;
}
