ACODE - Alphacode


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

Output:

6
89
1

hide comments
sucide: 2017-03-27 18:30:40

WA in 1st go :3
Simple 1d dp

deep_1: 2017-03-26 22:15:38

yippee AC!

starbot: 2017-03-17 12:47:53

AC....hint...first make normal recursive solution and then the idea of top down will hit you :)..also the testcases in comments are enough to remove WA...

achilles155: 2017-03-12 20:34:06

The problem is so confusing.. got so many WAs.. guys, do check out the test cases in the comments before submitting as it is not clear in the question.

mike_mack: 2017-03-04 22:42:00

Problem wording: The problem really should specify that '01' through '09' are not valid pairs. For those getting WA, make sure you are not treating *any* substring that starts with '0' as valid. Otherwise- cool problem. :)

anshul_srivas: 2017-02-22 18:57:16

Take care of test cases where 0's appear in between.

nilabja16180: 2017-02-09 18:09:59

Thanks for Test Cases, AC in one go!

manas0008: 2017-02-04 09:38:27

thanks @l0gic_b0mb for your testcases!

tni_mdixit: 2017-01-01 21:53:03

bottom up rocks !! :)

scorpion_ajay: 2017-01-01 15:36:16

nice dp to practice :)


Added by:Adrian Kuegel
Date:2005-07-09
Time limit:0.341s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:ACM East Central North America Regional Programming Contest 2004