The Shaastra Online Programming Contest provides the perfect platform for programmers to showcase their abilities by cracking some of the most challenging problems and attempting to solve it faster than some of the best in the business. The focus of this contest is not just on solving problems from a wide variety of areas, but also on the elegance of the solution. The notion of efficiency of your solution is critical, and this contest will be algorithm-intensive, with the running time complexity of your solution (as Computer Science people know it) and attention to detail (read 'boundary conditions') taking centre-stage.
The Shaastra OPC has grown in stature, having been held for just two years, but brimming with over 700 registered teams and loads of international participation last year.
Gear up, for one of the top programming contests held in India! May the source be with you!
OPC 2008 Registrations have begun! Teams can register here
These problems have been taken from the Sphere Online Judge site.
Alice and Bob need to send secret messages to each other and are discussing ways to encode their messages:
Alice: "Let's just use a very simple code: We'll assign 'A' the code word 1, 'B' will be 2, and so on down to 'Z' being assigned 26."
Bob: "That's a stupid code, Alice. Suppose I send you the word 'BEAN' encoded as 25114. You could decode that in many different ways!"
Alice: "Sure you could, but what words would you get? Other than 'BEAN', you'd get 'BEAAD', 'YAAD', 'YAN', 'YKD' and 'BEKD'. I think you would be able to figure out the correct decoding. And why would you send me the word 'BEAN' anyway?"
Bob: "OK, maybe that's a bad example, but I bet you that if you got a string of length 5000 there would be tons of different decodings and with that many you would find at least two different ones that would make sense."
Alice: "How many different decodings?"
Bob: "Jillions!"
For some reason, Alice is still unconvinced by Bob's argument, so she requires a program that will determine how many decodings there can be for a given string using her code.
Input
Input will consist of multiple input sets. Each set will consist of a single line of at most 5000 digits representing a valid encryption (for example, no line will begin with a 0). There will be no spaces between the digits. An input line of '0' will terminate the input and should not be processed.
Output
For each input set, output the number of possible decodings for the input string. All answers will be within the range of a 64 bit signed integer.
Example Input
25114
1111111111
3333333333
0
Example Output
6
89
1
Certain positive integers have their decimal representation consisting only of ones and zeros, and having at least one digit one, e.g. 101. If a positive integer does not have such a property, one can try to multiply it by some positive integer to find out whether the product has this property.
Input
Number K of test cases.In each of the next K lines there is one integer n (1 <= n <= 20000)
Output
For each test case, your program should compute the smallest multiple of the number n consisting only of digits 1 and 0 (beginning with 1).
Example Input
3
17
11011
17
Example Output
11101
11011
11101
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