Auto chess is a type of strategic game with elements similar to chess. In the preparation phase, players place characters on the battlefield, and then the characters battle against the opponent's characters without direct control from the players.
Kwords is developing a new auto chess game in which one character attacks by eliminating all enemies within a $$$45$$$-degree angle in front of it. However, Kwords doesn't know how to find the best direction for the character to destroy as many enemies as possible. Therefore, he has thrown this problem to you.
To simplify the problem, the chessboard can be viewed as a two-dimensional plane. The character's location is the origin $$$(0, 0)$$$. $$$n$$$ different two-dimensional integer coordinates represent the coordinates of the $$$n$$$ enemies. All enemies within the $$$45$$$-degree angle between the two rays firing from the origin will be eliminated, including those on the rays themselves. Given the corresponding chessboard data, calculate the maximum number of enemies the character can eliminate.
The first line contains an integer $$$n$$$ $$$(1 \le n \le 10^5)$$$ — the number of enemies.
Then follow $$$n$$$ lines, each contains of two integers $$$x,y$$$ $$$(-10^4\leq x,y\leq 10^4)$$$ representing a coordinate of an enemy. It is guaranteed that $$$x \ne 0$$$ or $$$y \ne 0$$$, and all coordinates are distinct.
A single integer — the maximum number of enemies the character can eliminate.
2 1 2 2 1
2
2 1 100 100 1
1
3 1 1 2 2 3 3
3
