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>
template <typename T>
void read(T &x);
template <typename T>
void read(T &x, T &y);
template <typename T>
void read(T &x, T &y, T &z);
template <typename T>
void write(T x);
template <typename T>
void writeC(T x);
template <typename T>
void writeN(T x);
signed main() {
  int t;
  read(t);
  while (t-- > 0) {
    int n;
    read(n);
    if (n == 2 || n == 3) {
      puts("-1");
      continue;
    } else if (n % 2 == 0) {
      for (int i = 1; i < n / 2 - 1; ++i) printf("%d ", i * 2 - 1);
      printf("%d %d ", n - 1, n - 3);
      for (int i = n / 2; i >= 1; i--) printf("%d ", i * 2);
    } else {
      for (int i = 1; i <= n / 2 + 1; ++i) printf("%d ", i * 2 - 1);
      printf("%d %d ", n - 3, n - 1);
      for (int i = n / 2 - 2; i >= 1; i--) printf("%d ", i * 2);
    }
    puts("");
  }
  return 0;
}
template <typename T>
void read(T &x) {
  x = 0;
  char c = getchar();
  T flag = 1;
  while (c < '0' || c > '9') {
    if (c == '-') flag = -flag;
    c = getchar();
  }
  while ('0' <= c && c <= '9') {
    x = x * 10 + c - '0';
    c = getchar();
  }
  x *= flag;
}
template <typename T>
void read(T &x, T &y) {
  read(x);
  read(y);
}
template <typename T>
void read(T &x, T &y, T &z) {
  read(x);
  read(y);
  read(z);
}
template <typename T>
void writeC(T x) {
  if (x < 0) x = ~x + 1, putchar('-');
  if (x > 9) writeC(x / 10);
  putchar(x % 10 + '0');
}
template <typename T>
void write(T x) {
  writeC(x);
  putchar(' ');
}
template <typename T>
void writeN(T x) {
  writeC(x);
  puts("");
}
