C. Geometry Killer
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Pacha got bored of teaching computational geometry to the insabrossos, so he decided to put a Euclidean geometry problem in the SanSi Cup 2025.

In the figure, $$$AB$$$ is perpendicular to $$$BC$$$ and $$$AB = c$$$ units of length. $$$AC$$$ and $$$DB$$$ intersect at point $$$I$$$, and $$$IG$$$ is perpendicular to $$$BC$$$. Given that $$$DC = b$$$ units and $$$BC = a$$$ units, compute the length of $$$IG$$$.

Express the result with two numbers $$$p, q$$$ that represent the length of $$$IG$$$ as the irreducible fraction $$$p / q$$$ (it is guaranteed that the result is unique and expressible as an irreducible fraction). For example, $$$3/4$$$ is an irreducible fraction and $$$6/8$$$ is not.

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 10^5$$$), the number of test cases.

Each of the next $$$t$$$ lines contains $$$3$$$ integers $$$a, b, c$$$ ($$$1 \le a, b, c \le 10^9$$$).

Output

For each test case, print two integers $$$p, q$$$ representing the length of $$$IG$$$ as the irreducible fraction $$$p / q$$$.

Example
Input
1
2 2 2
Output
1 1