## Geometry - Problem: Align polygon

In this problem you are going to practice rotations with a problem that appears sometimes a sub-routine of more complex problems.

##### Align Polygon

Given as input a polygon defined by $$n$$ vertcies $$p_1, p_2, \ldots, p_n$$ your task is to transform it with a translation and a rotation so that:

1. The point $$p_1$$ becomes the origin $$(0, 0)$$
2. The segment $$\overline{p_1 p_2}$$ becomes thealigned with the x-axis in a way that $$p_2$$ becomes the point $$(d, 0)$$ where $$d$$ is the distance between $$p_1$$ and $$p_2$$.

The first sample input is illustrated in the following image. Input

• One line with a single integer $$n$$ giving the number of vertices in the polygon.
• $$n$$ lines each with two integers $$x$$ and $$y$$ giving the the coordinates of those vertices. The vertices are given in counterclockwise order.

Constraints

• $$3 \leq n \leq 1000$$
• $$-10^5 \leq x, y \leq 10^5$$

Output

• $$n$$ lines each with two integers $$x$$ and $$y$$ giving the the coordinates the resulting polygon.

The will be accepted as long as it is accurate up to $10^{-6}$ relative or absolute precision.

Sample Test Cases

Sample input 1

Sample output 1

Sample input 2

Sample output 2

Max file size: 1.0 MiB
Allowed extensions: .java, .cpp, .py