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>
int main() {
  long long int a, b, c = 0, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t,
                      u, v, w, x, y, z;
  scanf("%lld", &t);
  for (j = 1; j <= t; j++) {
    scanf("%lld", &n);
    if (n < 4) {
      printf("-1\n");
    } else {
      a = n;
      if (n % 2 != 0) {
        a = n - 1;
      }
      for (i = a; i > 0; i = i - 2) {
        if (i != 4) {
          printf("%lld ", i);
        } else {
          printf("2 4 ");
          break;
        }
      }
      a = n;
      if (n % 2 == 0) {
        a = n - 1;
      }
      for (i = 1; i <= a; i = i + 2) {
        printf("%lld", i);
        if (i != a) {
          printf(" ");
        } else {
          printf("\n");
        }
      }
    }
  }
}
