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#1870. Zju2361 Area

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Description

给出N条直线,问他们将一个无限大平面分成了多少份,每一份的面积是多少。
(N<=80,不考虑面积小于1e-8的多边形)

Input

The first line of the input file contains N  
the number of lines (1 <= N <= 80). 
Each of next N lines contains four integer numbers x1, y1, x2 and y2 
- the coordinates of two different points of the line. 
All coordinates do not exceed 102 by their absolute value. No two lines coincide.

Output

First output K - the number of finite parts among those the lines divide the plane to. 
Next K lines of the output file must contain area parts sorted in non-decreasing order. 
You answer must be accurate up to 10-4. Due to floating point precision losses possible, 
do not consider parts with area not exceeding 10-8.

Sample Input

1
5
0 0 1 0
1 0 1 1
1 1 0 1
0 1 0 0
0 0 1 1

Sample Output

2
0.5000
0.5000

Hint

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