Say Hello
Description
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.
Input
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
Output contains one integer number that represents how many times friends will say "Hello!" to each other.
Samples
4
2 5
0 0 0 10
5 5 5 6
5 0 10 5
14 7 10 5
2
Note
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 $B3=B4$.