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

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.