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D - Opposite

Score : $400$ points

Problem Statement

On a two-dimensional coordinate plane where the $\mathrm{x}$ axis points to the right and the $\mathrm{y}$ axis points up, we have a regular $N$-gon with $N$ vertices $p_0, p_1, p_2, \dots, p_{N - 1}$.
Here, $N$ is guaranteed to be even, and the vertices $p_0, p_1, p_2, \dots, p_{N - 1}$ are in counter-clockwise order.
Let $(x_i, y_i)$ denotes the coordinates of $p_i$.
Given $x_0$, $y_0$, $x_{\frac{N}{2}}$, and $y_{\frac{N}{2}}$, find $x_1$ and $y_1$.

Constraints

• $4 \le N \le 100$
• $N$ is even.
• $0 \le x_0, y_0 \le 100$
• $0 \le x_{\frac{N}{2}}, y_{\frac{N}{2}} \le 100$
• $(x_0, y_0) \neq (x_{\frac{N}{2}}, y_{\frac{N}{2}})$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$x_0$ $y_0$

$x_{\frac{N}{2}}$ $y_{\frac{N}{2}}$

Output

Print $x_1$ and $y_1$ in this order, with a space in between.
Your output is considered correct when, for each value printed, the absolute or relative error from our answer is at most $10^{-5}$.

4
1 1
2 2

2.00000000000 1.00000000000

We are given $p_0 = (1, 1)$ and $p_2 = (2, 2)$.
The fact that $p_0$, $p_1$, $p_2$, and $p_3$ form a square and they are in counter-clockwise order uniquely determines the coordinates of the other vertices, as follows:

• $p_1 = (2, 1)$
• $p_3 = (1, 2)$

6
5 3
7 4

5.93301270189 2.38397459622