F. Fraction Again!
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a positive integer $$$k$$$. Find any three positive integers $$$x$$$, $$$y$$$, and $$$z$$$ such that

$$$$$$ \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = k, $$$$$$

or report that no such triple exists.

Input

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases.

The first and only line of each test case contains a single integer $$$k$$$ ($$$1 \le k \le 100$$$) — the target value of the sum.

Output

For each test case, if a valid triple exists, output three space-separated positive integers $$$x$$$, $$$y$$$, and $$$z$$$ on a single line. If there are multiple valid triples, you may output any of them.

If no valid triple exists, output $$$-1$$$ instead.

Example
Input
2
1
17
Output
2 3 6
-1
Note

In the first test case, $$$k = 1$$$, and $$$(x, y, z) = (2, 3, 6)$$$ works because $$$\frac{1}{2} + \frac{1}{3} + \frac{1}{6} = 1$$$. Other triples are valid too, for example $$$(6, 2, 3)$$$ and $$$(3, 3, 3)$$$.

In the second test case, $$$k = 17$$$, and it can be shown that no triple of positive integers satisfies the equation, so the answer is $$$-1$$$.