Linköping has a quite complex water transport system.
Around Linköping there are several wells from which water is
drawn. The water is then transported to other locations using
pipes. Each pipe is a straight canal from one of the wells to
some location in the city.
All the pipes are at the same depth under ground. Therefore,
whenever two pipes cross, they form an intersection. Luckily
the pipe system was constructed in such a way that exactly two
pipes meet at each such intersection. The wells do not count as
intersections. Any number of pipes (including zero or more than
two) may originate at each well.
The intersections pose a problem, since dirt (a mixture of
lime and other “remains”) tends to get stuck there. This dirt
causes the pipes to degrade and collapse, leading to the
formation of large sink holes. Such sink holes have a
mesmerising effect on the students in Linköping, causing them
to neglect their studies and remain uneducated, which in the
long run will lead to a collapse of not just the pipe system
but of the very fabric of society. Therefore it is imperative
that the pipes are regularly cleaned. The Nordic Water
Extraction and Redistribution Company (NWERC) – which is in
charge of Linköping’s waterpipes – has an ample fleet of robots
to perform this task. A robot can be inserted into a pipe at
the well where the pipe begins. The robot then goes through the
pipe all the way to its end and cleans all intersections along
the way. After reaching the end, the robot turns around and
returns back to the well where it started. In order to prevent
robot collisions, government regulations stipulate that
whenever two pipes intersect, at most one of them may contain a
robot.
Since the whole water system has to be shut down while it is
being cleaned (another government regulation), the NWERC would
like to do the cleaning quickly, by using a single batch of
cleaning robots, all started at the same time.
Your task is to verify whether this can be done – i.e.,
whether we can simultaneously insert robots into a subset of
the pipes in such a way that the robots will clean all
intersections and there will be no risk of two robots
colliding.
Input
The input consists of:

one line with two integers $w$ ($1 \le w \le 1\, 000$), the number
of wells, and $p$
($1 \le p \le 1\,
000$), the number of pipes;

$w$ lines, the
$i$th of which
contains two integers $x_
i$ and $y_ i$
($10\, 000 \le x, y \le 10\,
000$), the position of well number $i$ (the wells are numbered from
$1$ to $w$);

$p$ lines each with
three integers $s$
($1 \le s \leq w$),
the well at which the pipe starts, and $x$ and $y$ ($10\, 000 \le x, y \le 10\,
000$), the position at which the pipe ends.
Each pipe will contain exactly one well, the one at which it
starts. Any point shared by more than two pipes will be a well.
Any two pipes share at most one common point. The common point
of two pipes may be the endpoint of one or both of them. All
pipes have positive length.
Output
If it is possible to clean all intersections as described
above, output “possible”. Otherwise,
output “impossible”.
Sample Input 1 
Sample Output 1 
3 3
0 0
0 2
2 0
1 2 3
2 2 2
3 0 3

impossible

Sample Input 2 
Sample Output 2 
2 3
0 0
0 10
1 5 15
1 2 15
2 10 10

possible
