Smart Feeder#49
When the owner goes on vacation, they install a smart feeder for their cat at position . The feeder has fish stored for the cat. Each fish is represented by the coordinates of its head and tail. The cat can reach any point within distance from the feeder. The cat can eat a fish if it can reach at least one point on it. The cat needs to eat at least fish per day to stay satisfied. On the first day when the cat eats fewer than fish, it will feel hungry.
The first line contains the integers , , and .
Each of the next lines contains the coordinates of the head (x_{1i}, y_{1i}) and the tail (x_{2i}, y_{2i}) of each fish.
All numbers are integers and do not exceed in absolute value.
Print the number of the first day on which the cat will feel hungry.
Example 1