A15950. Indivisible

You're given a positive integer $n$ .

Find a permutation $a_1, a_2, \dots, a_n$ such that for any $1 \leq l < r \leq n$ , the sum $a_l + a_{l+1} + \dots + a_r$ is not divisible by $r-l+1$ .

A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ( $2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ( $n=3$ but there is $4$ in the array).

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 100$ ). Description of the test cases follows.

The first line of each test case contain a single integer $n$ ( $1 \leq n \leq 100$ ) — the size of the desired permutation.

For each test case, if there is no such permutation print $-1$ .

Otherwise, print $n$ distinct integers $p_1, p_{2}, \dots, p_n$ ( $1 \leq p_i \leq n$ ) — a permutation satisfying the condition described in the statement.

If there are multiple solutions, print any.

In the first example, there are no valid pairs of $l < r$ , meaning that the condition is true for all such pairs.

In the second example, the only valid pair is $l=1$ and $r=2$ , for which $a_1 + a_2 = 1+2=3$ is not divisible by $r-l+1=2$ .

in the third example, for $l=1$ and $r=3$ the sum $a_1+a_2+a_3$ is always $6$ , which is divisible by $3$ .