You silently observe the tables from a distance and look at the shop entrance behind them with longing eyes. Maybe it’s the current arrangement of the round tables, but you feel like — with a good plan — today might be the day you finally manage to navigate around the round tables to the entrance of the shop, and get your oh-so-wanted candy.
The round tables are represented as a set of non-intersecting circles, each of diameter $80$ centimetres. The front of the shop is represented as the infinite $x$-axis facing the positive $y$ direction. The entrance to the shop is represented as a line segment on the $x$-axis, with midpoint $(0,0)$ and length $80$ centimetres. You are represented as a circle of diameter $50$ centimetres. Although you can touch the front of the shop and the edges of the tables, you cannot walk through walls and you will certainly not climb over or under the tables. You’re not willing to take any such chances!
Given the locations of the tables in centimetres relative to the midpoint of the shop entrance, can you navigate past the tables and reach the entrance? You are currently far enough from the entrance that your precise location is irrelevant.
The input consists of:
One line with one integer $n$ ($0 \le n \le 5\, 000$), the number of round tables.
$n$ lines, the $i$th of which contains two integers $x_ i$ and $y_ i$ ($|x_ i| \le 10^9$, $40 \le y_ i \le 10^9$), the location of the center of the $i$th round table in centimetres relative to the midpoint of the shop entrance.
No two tables intersect, and each table is at least $2$ metres away from the shop entrance.
Output “possible” if it is possible to reach the entrance. Otherwise output “impossible”.
|Sample Input 1||Sample Output 1|
5 -300 40 -300 300 0 300 300 300 300 40
|Sample Input 2||Sample Output 2|
10 273 245 171 255 -154 273 -237 205 -280 137 280 76 231 168 -32 280 66 275 -278 46