Jezzball

JezzBall is a game in which "atoms" bounce around a rectangular field. The player advances by walling off space with rays until enough of the field is enclosed. In this problem we use a continuous (non-discrete) version: coordinates and motion are real-valued, measured in pixels.

The playing field is 1024 x 768 pixels. Each atom is an infinitely thin point (not a round ball). Atoms move at constant speed and change direction only when they reach an edge of the field ($x = 0$, $x = 1024$, $y = 0$, or $y = 768$), bouncing with no loss of energy. Atoms never collide with each other.

The player divides the field by shooting a ray from a fixed point. A ray is either horizontal or vertical and extends from that point in both directions at once (up and down for a vertical ray, left and right for a horizontal ray) at a constant 200 pixels per second, until each end reaches an edge of the field. Rays are infinitely thin. If no atom touches the ray at any moment while it is still extending, the field is successfully divided; otherwise the player loses a life.

Two situations do NOT count as a hit: an atom touching the moving endpoint of an extending arm, and an atom touching the ray at the exact instant it finishes extending.

Given the atoms' initial positions and velocities and the fixed firing point, determine the minimum time the player must wait before starting to extend a ray (horizontal or vertical, whichever is safe) so that no atom hits it before the ray is complete.

The input contains several test cases. Each test case begins with a line containing an integer $n$ ($1 \le n \le 10$), the number of atoms. The next line contains two integers $x$ and $y$ ($0 < x < 1024$, $0 < y < 768$), the fixed point from which both ends of a ray start extending. Each of the next $n$ lines contains four integers $x$, $y$, $vx$, $vy$ ($0 < x < 1024$, $0 < y < 768$, $1 \le |vx| \le 200$, $1 \le |vy| \le 200$): the atom's initial position $(x, y)$ and its velocity ($vx$ along the x-axis, $vy$ along the y-axis). Within a test case all listed positions (the firing point and the atoms) are distinct. The input ends with a line containing $n = 0$, which is not processed. There are at most 25 test cases.

For each test case, print on its own line the minimum time, in seconds with exactly 5 digits after the decimal point, at which the player can begin extending either a horizontal or a vertical ray without any atom colliding with it while it is being drawn. Each input is constructed so that the first such moment lies inside an open time interval at least $10^{-5}$ seconds long. If no safe moment exists within the first 10000 seconds, print Never instead.