Parallelepiped

You are given three positive integers representing the areas of three pairwise adjacent rectangular faces of a rectangular parallelepiped (box).

Let the edge lengths be $a$, $b$, and $c$. Then the three face areas are:

• $ab$
• $ac$
• $bc$

Your task is to recover one valid triple $(a, b, c)$ of positive integers that matches the given face areas.

If multiple answers are possible, any valid one is acceptable.

Notes

• The three given values are guaranteed to come from some integer box.
• The order of the three edges in the output does not matter.

Input Format

The input consists of three integers $x$, $y$, and $z$ — the areas of the three faces.

Output Format

Print three positive integers $a$, $b$, and $c$ such that:

• $ab = x$
• $ac = y$
• $bc = z$

Any valid ordering is accepted.

Constraints

• $1 \le x, y, z \le 10^9$
• A valid integer solution exists.

Hints

• Try multiplying the three equations together.
• Once you know $abc$, each edge length can be recovered by dividing by the right face area and taking a square root where appropriate.