Batman is an atypical "superhero". Unlike Spider-man, Batman has no special powers (unless you count being filthy rich a superpower). That said, he is, for better or worse, greatly respected for being a crime-fighter by his many fans. Despite his dour demeanor, Batman at times displays moments of humor and periodically manifests his modest intellect.

In this programming challenge, Batman is locked in a battle of wits with the Riddler. Once again, the green supervillain has a mind-bending, brain-teasing challenge for the masked avenger:

Find all the pairs of `5`-digit numbers that use the digits `0` through `9` once each, such that the first number divided by the second is equal to some integer `N`, where `N` is between `2` and `100` (inclusive).

That is, given the digits `0, 1, 2, 3, 4, 5, 6, 7, 8, 9` and a number `N`, find all permutations of these digits such that:

``abcde / fghij = N``

where each letter represents a different digit. The first digit of one of the numerals is allowed to be `0`.

Because Batman lacks any significant superpower (besides money), he begs that you help him defeat the Riddler by using your programming superpowers.

## Input

Each line of input consists of a valid integer `N`. An input of `0` terminates the program (no output should be displayed for it).

### Example Input

``````61
62
0``````

## Output

The program should display ALL pairs of numerals that match the description above. The numerators should be sorted by increasing numerator and denominator and displayed in the following format:

``````XXXXX / XXXXX = N
XXXXX / XXXXX = N
...``````

If there are no pairs of numerals satisfying the atypical division condition, then the program should display: "There are no solutions for N".

Separate the output for two different values of `N` by a blank line.

### Example Output

``````There are no solutions for 61.

79546 / 01283 = 62
94736 / 01528 = 62``````

#### Programming Challenges

This is based on the Division problem on the UVa Online Judge.

## Submission

To submit your work, follow the same procedure you used for Reading 00:

``````\$ cd path/to/cse-30872-fa19-assignments     # Go to assignments repository
\$ git checkout master                       # Make sure we are on master
\$ git pull --rebase                         # Pull any changes from GitLab

\$ git checkout -b challenge07               # Create and checkout challenge07 branch

\$ \$EDITOR challenge07/program.cpp           # Edit your code

\$ git add challenge07/program.cpp           # Stage your changes
\$ git commit -m "challenge07: done"         # Commit your changes

\$ git push -u origin challenge07            # Send changes to GitLab``````

To check your code, you can use the `.scripts/submit.py` script or curl:

``````\$ .scripts/submit.py
Submitting challenge07 assignment ...

Submitting challenge07 code ...
Result Success
Score 6.00
Time 0.16

\$ curl -F source=@challenge07/program.cpp  https://dredd.h4x0r.space/code/cse-30872-fa19/challenge07
{"score": 6, "result": "Success"}``````

Once you have commited your work and pushed it to GitLab, remember to create a merge request. Refer to the Reading 04 TA List to determine your corresponding TA for the merge request.