Online JudgeProblem SetAuthorsOnline ContestsUser
Web Board
Home Page
F.A.Qs
Statistical Charts
Problems
Submit Problem
Online Status
Prob.ID:
Register
Update your info
Authors ranklist
Current Contest
Past Contests
Scheduled Contests
Award Contest
User ID:
Password:
  Register
Language:
Banal Tickets
Time Limit: 5000MSMemory Limit: 32000K
Total Submissions: 1414Accepted: 156

Description

Peter is fond of number theory. That's why he is looking for interesting bus tickets. Ticket with the number of length 2N is called interesting if the product of the first N digits of its number is equal to the product of the last N digits. Other tickets are called banal.
Peter has found a used ticket in his pocket. Unfortunately the ticket was punched, so Peter cannot recognize some digits. He wonders whether this ticket was an interesting one. Moreover he wants to know how many different interesting and banal tickets could be punched to get this one.
Help Peter to find answers to his questions.

Input

The first line of the input file contains an integer N(1 <= N<=18). The next line contains a string representing the ticket number. If some digit is punched out it is denoted by "?" otherwise it is denoted by itself.

Output

On the first line of the output file print the number of interesting tickets. On the second line print the number of banal tickets.

Sample Input

2 
2??3

Sample Output

4 
96 

Source

Northeastern Europe 2003, Northern Subregion

[Submit]   [Go Back]   [Status]   [Discuss]

Home Page   Go Back  To top


All Rights Reserved 2003-2013 Ying Fuchen,Xu Pengcheng,Xie Di
Any problem, Please Contact Administrator