Background

Special for beginners, ^_^

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）

Format

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.

Samples

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

2
0.5000
0.5000

Limitation

1s, 1024KiB for each test case.