Description

He encountered two puzzles:

• In a plane, the line segment $DE$ intersects the line $FG$ at point $O$. Given $\angle DOF=x^{\circ}$, find a point $P$ on the line $FG$ such that $\triangle DOP$ is an isosceles triangle, and compute the measure of $\angle D$. (If the answer is not an integer, keep $1$ decimal place.)

• Given a right triangle with two sides $m,n$, find the length of the third side (keep $5$ decimal places).

Write a program to compute the answers to the problems.

Input Format

One line with three positive integers: $x,m,n$.

Output Format

Output two lines. The first line is the answer to the first question, and the second line is the answer to the second question.

If there are multiple solutions, separate them with spaces and output them in increasing order.

60 1 1

30 60
1.41421

Hint

Sample Explanation

Problem $1$:

• When point $P$ is to the left of point $O$, the formed $\triangle DOP$ is an equilateral triangle, so $\angle D=60^{\circ}$.

• When point $P$ is to the right of point $O$, in the formed $\triangle DOP$, $\angle DOP=180^{\circ}-60^{\circ}=120^{\circ}$ is the vertex angle, so $\angle D=(180^{\circ}-120^{\circ})/2=30^{\circ}$.

Problem $2$:

The third side is the hypotenuse, with length $\sqrt{1^2+1^2}=\sqrt{2}=1.41421\dots$.

Constraints and Notes

$x<90,m\leq n\leq 10^9$.

Problem Setter's Hint

There are countless methods, but reading carefully comes first. Multiple solutions are not considered, and a wrong answer brings two lines of tears.

Translated by ChatGPT 5