Viva Confetti

Time Limit:3000MS     Memory Limit:0KB     64bit IO Format:%lld
& %llu

Submit Status Practice UVALive
2572

Appoint description: 
System Crawler  (2015-04-19)

Description

Do you know confetti? They are small discs of colored paper, and people throw them around during parties or festivals. Since people throw lots of confetti, they may end up stacked one on another, so
there may be hidden ones underneath.

A handful of various sized confetti have been dropped on a table. Given their positions and sizes, can you tell us how many of them you can see?

The following figure represents the disc configuration for the first sample input, where the bottom disc is still visible.

Input

The input is composed of a number of configurations of the following form.

n
x1	y1	r1
x2	y2	r2
xn	yn	rn

The first line in a configuration is the number of discs in the configuration (a positive integer not more than 100), followed by one Ine descriptions of each disc: coordinates of its center and radius, expressed as real numbers in decimal notation, with up
to 12 digits after the decimal point. The imprecision margin is 5 x 10^-13 . That
is, it is guaranteed that variations of less than 5 x 10^-13 on input values do
not change which discs are visible. Coordinates of all points contained in discs are between -10 and 10.

Confetti are listed in their stacking order, x₁y₁r₁ being the bottom
one and x_ny_nr_n the top one. You are observing from the top.

The end of the input is marked by a zero on a single line.

Output

For each configuration you should output the number of visible confetti on a single line.

Sample Input

3
0 0 0.5
-0.9 0 1.00000000001
0.9 0 1.00000000001
5
0 1 0.5
1 1 1.00000000001
0 2 1.00000000001
-1 1 1.00000000001
0 -0.00001 1.00000000001
5
0 1 0.5
1 1 1.00000000001
0 2 1.00000000001
-1 1 1.00000000001
0 0 1.00000000001
2
0 0 1.0000001
0 0 1
2
0 0 1
0.00000001 0 1
0

Sample Output

3
5
4
2

题意：已知n个圆盘，依次放到桌面的上。现按照放置的顺序，一次给出各个圆盘的圆心位置和半径，问最后有多少圆盘可见？

【分析】：还没想好~~~~~~~容我思考一晚。