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Problem

Alice is still not satisfied with Bob's math skills so she gave him a new challenge.

Given a positive integer $N$, find any $3$ distinct positive integers $A, B, C$ such that:

• The product of any two of these $3$ integers is a divisor of $N$.
• The product of all three integers is a multiple of $N$.

If multiple solutions exist, you may print any of them.
Print $-1$ if no solution exists.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• The first and only line of each test case contains a single integer, $N$.

Output Format

For each test case, output on a new line three space-separated integers satisfying the given condition.
Print $-1$ if the answer does not exist.

Constraints

Sample 1:

3
30
24
3

2 3 5
2 6 4
-1

Explanation:

Test case $1$: We have $A = 2, B = 3, C = 5$. They satisfy all the conditions:

• $AB = 6, AC = 10, BC = 15$ are all divisors of $N = 30$
• $ABC = 30$ is a multiple of $N = 30$

Test case $2$: We have $A = 2, B = 6, C = 4$. They satisfy all the conditions:

• $AB = 12, AC = 8, BC = 24$ are all divisors of $N = 24$
• $ABC = 48$ is a multiple of $N = 24$

Test case $3$: It can be shown that no three positive integers $A, B, C$ satisfy the conditions.