Problem: * Point in the Figure

The figure consists of 6 blocks with size h * h, placed as in the figure below. The lower left angle of the building is on position {0, 0}. The upper right angle of the figure is on position {2*h, 4*h}. The coordinates given in the figure are for h = 2:

Write a program that enters an integer h and the coordinates of a given point {x, y} (integers) and prints whether the point is inside the figure (inside), outside of the figure (outside) or on any of the borders of the figure (border).

Sample Input and Output

Input Output Input Output
2
3
10		 outside 2
3
1		 inside
Input Output Input Output
2
2
2		 border 2
6
0		 border
Input Output Input Output
2
0
6		 outside 15
13
55		 outside
Input Output Input Output
15
29
37		 inside 15
37
18		 outside
Input Output Input Output
15
-4
7		 outside 15
30
0		 border

Hints and Guidelines

A possible logic for solving the task (not the only correct one):

  • We might split the figure into two rectangles with a common side:

  • A point is outer (outside) for the figure, when it is outside both of the rectangles.
  • A point is inner (inside) for the figure, if it is inside one of the rectangles (excluding their borders) or lies on their common side.
  • In other case the point lies on the border of the rectangle (border).

Implementation of the Proposed Idea

An exemplary implementation of the described idea (parts of the code are blurred with the purpose of stimulating logical thinking and solving skills):

Testing in the Judge System

Test your solution here: https://judge.softuni.org/Contests/Practice/Index/508#12.

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