Snakes

Buffalo Bill must cross a $1000 \times 1000$ square field from its west edge to its east edge. Several snakes rest on the field; each snake can strike a fixed distance in any direction from its position. Bill is bitten if at any moment he comes strictly closer to a snake than that snake's strike distance. Determine whether Bill can cross the field without being bitten.

The southwest corner of the field is at $(0, 0)$ and the northwest corner at $(0, 1000)$. Thus the west edge is the line $x = 0$ and the east edge is the line $x = 1000$, and the $y$ coordinate increases from south ($0$) to north ($1000$). Bill enters at some point on the west edge ($x = 0$, $0 \le y \le 1000$) and must leave at some point on the east edge ($x = 1000$, $0 \le y \le 1000$).

The first line contains the number of snakes $n$ ($0 \le n \le 1000$). Each of the next $n$ lines contains three real numbers $x$, $y$, $r$: the snake's location $(x, y)$ and its strike distance $r$. Every snake lies inside the field ($0 \le x \le 1000$, $0 \le y \le 1000$). A snake bites anything that passes strictly closer than $r$ to its location; a point at distance exactly $r$ is safe.

Print Bill can make the trip. if Bill can cross from the west edge to the east edge without ever coming within striking distance of any snake. Otherwise print Bill will be bitten.