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

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

hide comments
2020-04-17 11:06:13
You should know that 101 will have 1 valid decoding while 10001 will have 0 valid decoding. Now try the problem :)
2020-04-14 14:37:48
Ok guys, I was stuck on this for 3 hours. Apart from all these comments (which mention the boundary cases), please see that the range for decoding if 1-26 and NOT 1-25. I was only considering numbers till 25 and hence messed up.
2020-04-14 08:08:08
AC using bottom-up dp, TLE using top-down dp (due to recursion depth)
2020-04-12 00:13:17
AC in one go :)
Take care of corner cases like 20201
2020-04-11 18:13:15
try 109 as tc
2020-03-30 22:14:26
1 WA which got corrected after reading comments
2020-03-30 07:20:31
Dude i am so mad right now :( i lost 2 wa for testcases that include '0' :(
2020-03-22 20:19:49
try taking the input as string as the numbers are large even for long long int
2020-03-07 08:21:58
Ugh, got AC after 3 TLE, 2 SIGABRT and 2 WA... I better do some more DP problems...
2020-03-05 17:30:56
Try 19 or 18 :)
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