#abc197d. [abc197_d]Opposite

[abc197_d]Opposite

Problem Statement

On a two-dimensional coordinate plane where the mathrmx\\mathrm{x} axis points to the right and the mathrmy\\mathrm{y} axis points up, we have a regular NN-gon with NN vertices p0,p1,p2,dots,pN1p_0, p_1, p_2, \\dots, p_{N - 1}.
Here, NN is guaranteed to be even, and the vertices p0,p1,p2,dots,pN1p_0, p_1, p_2, \\dots, p_{N - 1} are in counter-clockwise order.
Let (xi,yi)(x_i, y_i) denotes the coordinates of pip_i.
Given x0x_0, y0y_0, xfracN2x_{\\frac{N}{2}}, and yfracN2y_{\\frac{N}{2}}, find x1x_1 and y1y_1.

Constraints

  • 4leNle1004 \\le N \\le 100
  • NN is even.
  • 0lex0,y0le1000 \\le x_0, y_0 \\le 100
  • 0lexfracN2,yfracN2le1000 \\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:

NN x0x_0 y0y_0 xfracN2x_{\\frac{N}{2}} yfracN2y_{\\frac{N}{2}}

Output

Print x1x_1 and y1y_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 10510^{-5}.


Sample Input 1

4
1 1
2 2

Sample Output 1

2.00000000000 1.00000000000

We are given p0=(1,1)p_0 = (1, 1) and p2=(2,2)p_2 = (2, 2).
The fact that p0p_0, p1p_1, p2p_2, and p3p_3 form a square and they are in counter-clockwise order uniquely determines the coordinates of the other vertices, as follows:

  • p1=(2,1)p_1 = (2, 1)
  • p3=(1,2)p_3 = (1, 2)

Sample Input 2

6
5 3
7 4

Sample Output 2

5.93301270189 2.38397459622