Andrey loves slot machines very much, and this time he found a new one--- the <<Titanic>> slot machine. It has $n$ lifeboats located on a plane, with the $i$-th lifeboat positioned at the coordinates $(x_i, y_i)$. There is also a rescue boat that, after starting the slot machine, begins to move at a constant speed from point $A$ to point $B$.

The rescue boat has a hook that can shoot perpendicularly to the boat's movement in both directions. The hook shoots at an incredibly fast speed, and if a lifeboat is in the path of the hook, it catches it and starts pulling it towards the boat. The hook retracts slowly---if the distance between your boat and the lifeboat at the moment of shooting and catching was $d$, the rescue boat will travel a distance of $d$ while the hook is retracting. While the hook is retracting, you cannot shoot to save other lifeboats.

Initially, your score of saved lifeboats is $0$. The moment the hook is fully retracted, your score increases by 1, and you can shoot again. When the boat reaches point $B$, the game ends. If the hook manages to retract exactly at that moment, the saved lifeboat is counted; if the hook does not manage to retract fully, the lifeboat is not considered saved, and the score does not increase.

Andrey wondered if there was a catch in the machines and wanted to calculate the maximum score he could achieve. Unfortunately, Andrey decided to find this out through trial and error, so help him---calculate the maximum score that can be achieved in the machine before Andrey spends all your tokens!