You have two pictures of an unusual kind of clock. The clock
has $n$ hands, each having
the same length and no kind of marking whatsoever. Also, the
numbers on the clock are so faded that you can’t even tell
anymore what direction is up in the picture. So the only thing
that you see on the pictures, are $n$ shades of the $n$ hands, and nothing else.
You’d like to know if both images might have been taken at
exactly the same time of the day, possibly with the camera
rotated at different angles.
Task
Given the description of the two images, determine whether
it is possible that these two pictures could be showing the
same clock displaying the same time.
Input
The first line contains a single integer $n$ ($2
\leq n \leq 200\, 000$), the number of hands on the
clock.
Each of the next two lines contains $n$ integers $a_ i$ ($0 \leq a_ i < 360\, 000$),
representing the angles of the hands of the clock on one of the
images, in thousandths of a degree. The first line represents
the position of the hands on the first image, whereas the
second line corresponds to the second image. The number
$a_ i$ denotes the angle
between the recorded position of some hand and the upward
direction in the image, measured clockwise. Angles of the same
clock are distinct and are not given in any specific order.
Output
Output one line containing one word: possible if
the clocks could be showing the same time, impossible
otherwise.
Sample Input 1 
Sample Output 1 
6
1 2 3 4 5 6
7 6 5 4 3 1

impossible

Sample Input 2 
Sample Output 2 
2
0 270000
180000 270000

possible

Sample Input 3 
Sample Output 3 
7
140 130 110 120 125 100 105
235 205 215 220 225 200 240

impossible
