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
aryan29:
20200330 22:14:26
1 WA which got corrected after reading comments 

jopdhiwaala:
20200330 07:20:31
Dude i am so mad right now :( i lost 2 wa for testcases that include '0' :( 

frustrated_c:
20200322 20:19:49
try taking the input as string as the numbers are large even for long long int


ianc1339:
20200307 08:21:58
Ugh, got AC after 3 TLE, 2 SIGABRT and 2 WA... I better do some more DP problems... 

bulanfil:
20200305 17:30:56
Try 19 or 18 :) 

hirbod313:
20200227 10:55:26
imagine you want know how many decodings are valid for s[i], solve s[i] with valid decodings of s[i  1] and s[i  2](if it's possible) 

testadizzy:
20200221 11:17:46
I got it right but it took me well over an hour. Need to practice more 

sudhanshu751:
20200125 12:54:13
For everyone facing difficulty in building up the solution, try thinking about the number of possible decodings from the end of the string towards the starting.


singhaditya97:
20200109 07:20:20
i am new to programming and believe that it will take me at least a life time to reach the solution to this problem.


elzahaby:
20200106 18:20:51
i acctually backtracked it and i was thinking about all the cases that not overlapping so i didn't memoize it and got timelimit second day i memoize it after seeing the video in the other comment and got the AC xDDD 
Added by:  Adrian Kuegel 
Date:  20050709 
Time limit:  0.5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  ACM East Central North America Regional Programming Contest 2004 