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: 2020-03-30 22:14:26

1 WA which got corrected after reading comments

jopdhiwaala: 2020-03-30 07:20:31

Dude i am so mad right now :( i lost 2 wa for testcases that include '0' :(

frustrated_c: 2020-03-22 20:19:49

try taking the input as string as the numbers are large even for long long int

ianc1339: 2020-03-07 08:21:58

Ugh, got AC after 3 TLE, 2 SIGABRT and 2 WA... I better do some more DP problems...

bulanfil: 2020-03-05 17:30:56

Try 19 or 18 :)

hirbod313: 2020-02-27 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: 2020-02-21 11:17:46

I got it right but it took me well over an hour. Need to practice more

sudhanshu751: 2020-01-25 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.
It will be easier to get to solution if you think in reverse order. Begin from end of the string and build the solution towards the start.

singhaditya97: 2020-01-09 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.
may God help me.

elzahaby: 2020-01-06 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:2005-07-09
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