Peter is bored during his operating systems class, so he
draws doodles on a sheet of paper. He feels like drawing
abstract art using his ruler: he draws line segments by
choosing two points in the plane and connecting them. Lots of
them.
Can you write a program that counts the number of distinct
points at which the line segments he drew intersect or
touch?
Input
The first line in the input contains an integer $n$ ($1
\le n \le 1\, 000$) which is the number of lines. The
following $n$ lines
contain four integers $x_0 \ \
y_0 \ \ x_1 \ \ y_1$ ($1\, 000\, 000 \le x_0, \ y_0, \ x_1, \ y_1
\le 1\, 000\, 000$). Lines have nonzero length, i.e.,
the two points will be distinct: $x_0 \ne x_1$ or $y_0 \ne y_1$ or both.
Output
Output the number of distinct points for which there is at
least one pair of line segments that intersects or touches at
this point. If there are infinitely many such points, output
1.
Sample Input 1 
Sample Output 1 
3
1 3 9 5
2 2 6 8
4 8 9 3

3

Sample Input 2 
Sample Output 2 
3
5 2 7 10
7 4 4 10
2 4 10 8

1

Sample Input 3 
Sample Output 3 
3
2 1 6 5
2 5 5 4
5 1 7 7

1

Sample Input 4 
Sample Output 4 
2
1 2 1 1
1 2 1 1

1

Sample Input 5 
Sample Output 5 
2
0 0 2 2
1 1 5 5

1
