Problem E
                                       Flipping Container
                                       Time limit: 2 seconds
A large, cuboid-shaped shipping container has been delivered to
your shipping yard. Before you can open it up, you first need to
move the container to a different location in your yard.
Normally, you would simply lift up the container using a crane
and drop it in its target location. Unfortunately, your crane is
broken, and the only way for you to move the container is by
carefully flipping the container over one of its bottom four edges,
resulting in a 90-degree rotation around the axis running along
that edge. Your hope is that you will eventually be able to reach
the target location by repeating this action enough times.
Just how many times will you need to perform this flip operation
to get the container to the right spot? Note that the orientation of                        Generated by ChatGPT 4o

the container changes as you move it across the yard, but in the
end it needs to be in the same orientation as at the start. Two orientations are considered the same when
they have the same length along each of the three axes of the coordinate system. The three side lengths
of the container are distinct.

Input

The first line contains three distinct integers a, b and c (1 ≤ a, b, c ≤ 1 000), the dimensions of the
container in meters. In the initial orientation of the container, the sides of length a run in east-west
direction, the sides of length b run in north-south direction, and the sides of length c run in up-down
direction.
The second line contains two integers x and y (−1018 ≤ x, y ≤ 1018 ) giving the target location of the
container. The container needs to be moved by x meters in the east-west direction and by y meters in
the north-south direction (positive numbers indicate moving to the east/north, negative numbers indicate
west/south).

Output

Output the least number of times the container needs to be flipped to reach its target location. If it is not
possible to reach the target location, output impossible.

 Sample Input 1                                           Sample Output 1
 3 4 5                                                    2
 8 0

 Sample Input 2                                           Sample Output 2
 3 4 5                                                    4
 -8 9

48th ICPC World Championship Problem E: Flipping Container © ICPC Foundation                                     9

Sample Input 3                                Sample Output 3
3 4 5                                         40
123 45

Sample Input 4                                Sample Output 4
20 10 30                                      impossible
13 37

48th ICPC World Championship Problem E: Flipping Container © ICPC Foundation   10