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).

Input

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.

Output

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.

见题面 Input 部分

见题面 Output 部分

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 $3$.