Prime Cryptarithm

The following cryptarithm is a multiplication problem that can be solved by substituting digits from a specified set of $N$ digits into the positions marked with *. If the set of prime digits $2,3,5,7$ is selected, the cryptarithm is called a PRIME CRYPTARITHM.

   * * *
 x  * *
----------
  * * * *
  * * * *
----------
* * * * *

Write a program that will find all solutions to the cryptarithm above for any subset of digits from the set $1,2,3,4,5,6,7,8,9$.

Sample Run

ENTER A SET OF DIGITS: $23468$

   2 2 2
x    2 2
-----------
   4 4 4 <3 more not shown>
   4 4 4
------------
 4 8 8 4

The number of unique solutions = $4$

Test your program with the prime digits $2357$.What is the number of unique solutions?

Source:1993 USACO Qualifying Round 1