I. Say Hello
time limit per test
2 seconds
memory limit per test
256 megabytes
standard input
standard output

Two friends are travelling through Bubble galaxy. They say "Hello!" via signals to each other if their distance is smaller or equal than $$$d_1$$$ and

  • it's the first time they speak to each other or
  • at some point in time after their last talk their distance was greater than $$$d_2$$$.

We need to calculate how many times friends said "Hello!" to each other. For $$$N$$$ moments, you'll have an array of points for each friend representing their positions at that moment. A person can stay in the same position between two moments in time, but if a person made a move we assume this movement as movement with constant speed in constant direction.


The first line contains one integer number $$$N$$$ ($$$2 \leq N \leq 100\,000$$$) representing number of moments in which we captured positions for two friends.

The second line contains two integer numbers $$$d_1$$$ and $$$d_2 \ (0 < d_1 < d_2 < 1000)$$$.

The next $$$N$$$ lines contains four integer numbers $$$A_x,A_y,B_x,B_y$$$ ($$$0 \leq A_x, A_y, B_x, B_y \leq 1000$$$) representing coordinates of friends A and B in each captured moment.


Output contains one integer number that represents how many times friends will say "Hello!" to each other.

2 5
0 0 0 10
5 5 5 6
5 0 10 5
14 7 10 5

Explanation: Friends should send signals 2 times to each other, first time around point $$$A2$$$ and $$$B2$$$ and second time during A's travel from point $$$A3$$$ to $$$A4$$$ while B stays in point $$$B3=B4$$$.