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SQUAREV  Revenge of the squares 
I think it's time to not only solve problems but also create some.
So here is my first attempt:
Given a number calculate the product N of their digits bigger than zero. The output is the number R of different presentations of N in the form A*A+B*B with A and B being positive integers including zero. 1*1+2*2 and 2*2+1*1 are not different presentations. So for input 5 the output is 1.
See also this similar task.
Input
One hundred tests with one positive integer < 10^20.
Output
Print the illustrated above number R for each test.
Example
Input: 5
7
78185824586267361855 Output: 1
0
3
Added by:  HWK 
Date:  20110227 
Time limit:  2.394s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: SCM qobi 
hide comments
20110529 06:59:26 HWK
@Jander: Well done. I've already awaited this. But in BALLSREM 51 bytes are still waiting for you. ;) Last edit: 20110529 07:02:32 

20110527 18:52:47 HWK
@clytorock: You did it! 

20110310 11:46:02 HWK
@hallvabo: It was a pleasure for me to challenge you. I used Perl for my solution. @ .::Debanjan::. : Sometimes a spoiler could also be interesting. 

20110309 20:49:07 :(){ :: & };:
@HWK: If by my interesting remarks you meant the link to the paper I posted before then I believed it to be a spoiler hence I removed it. 

20110309 16:43:45 Hallvard Norheim Bø
@HWK: Thanks for a great challenge! I did struggle a bit at first myself. Which language do you use for the 47 bytes solution? 

20110309 14:27:09 HWK
@ .::Debanjan::. : It's a pity that you've removed your first comment. Now hallvabos answer is a little bit out of context. And your remarks were quite interesting. So why have you erased it? 

20110227 22:14:14 Hallvard Norheim Bø
Hint: remember it is the product of digits in the input number you should process, not the input number itself. Thus you already have a (partial) factorization. 

20110227 21:59:53 :(){ :: & };:
@hallvabo: Thanks for your suggestion I did utilize your hint to solve it in the main site. Last edit: 20110307 18:33:32 