Score : 300 points
I am a Summoner who can invoke monsters. I can embody the pictures of monsters drawn on sketchbooks.
I recently have received a request from Primate Research Institute of Kyoto University to invoke "Hundred Eyes Monster".
What an great honor it is to contribute to the prosperity of the primate research of Kyoto University! I decided to paint an extremely high-quarity monster to the best of my ability.
I have already painted the forehead and mouth and this time I am going to paint as many eyes as possible between the forehead and mouth. Well...I cannot wait to see the complete painting.
Two circles A, B are given on a two-dimensional plane. The coordinate of the center and radius of circle A is (x_A, y_A) and r_A respectively. The coordinate of the center and radius of circle B is (x_B, y_B) and r_B respectively. These two circles have no intersection inside. Here, we consider a set of circles S that satisfies the following conditions.
Write a program that finds the maximum number of elements in S.
The input consists of multiple test cases and is given from Standard Input in the following format:
T testcase_1 : testcase_TEach test case is given with the following format.
x_A y_A r_A x_B y_B r_B
The output consists of T lines. On line i (1 \leq i \leq T), putput the maximum number of elements in S in i-th test case.
4 0 -3 2 0 3 2 0 0 9 8 8 2 0 0 9 10 10 5 0 0 707 1000 1000 707
3 10 21 180You can arrange circles ,for example, like the following images in Sample 1, 2.