Circles (2) P39799

Statement

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To solve this exercise you will need the definitions and the procedures of problems P46254 and P84786.

Write a procedure that reads a point:

void read(Point& p);

which is in the input with the two reals x and y in this order.

Write also a procedure that reads a circle:

void read(Circle& c);

which is in the input with the three reals x, y, and radius in this order.

Use all this to write a program that reads a circle c and an initial point p, and moves p according to the input, and prints when p go in or go out of c. Suppose that p will never be exactly in the border of c.

Input

Input starts with a line with the circle c (three reals, the last one strictly positive) and a line with the point p (two reals). Then a natural number n comes followed by n lines, each one with a point that indicates the following move of p.

Output

Your program must print the initial situation of p regard to c, and the moments that the point goes in or goes out of the circle. Follow the format of the examples.

Public test cases

Input

Output

initially inside
in the step 1 has gone out
in the step 3 has gone in
in the step 5 has gone out

Input

5 10 2.5
2 2
3
-1 -1
-1 -1
-1 -1

Output

initially outside

Information

Author: Salvador Roura
Language: English
Translator: Carlos Molina
Original language: Catalan
Other languages: Catalan
Official solutions: C++
User solutions: C++