ANARC05H - Chop Ahoy! Revisited!


Given a non-empty string composed of digits only, we may group these digits into sub-groups (but maintaining their original order) if, for every sub-group but the last one, the sum of the digits in a sub-group is less than or equal to the sum of the digits in the sub-group immediately on its right. Needless to say, each digit will be in exactly one sub-group.

For example, the string 635 can only be grouped in one sub-group [635] or in two sub-groups as follows: [6-35] (since 6 < 8.) Another example is the string 1117 which can be grouped in one sub-group [1117] or as in the following: [1-117], [1-1-17], [1-11-7], [1-1-1-7], [11-17] and [111-7] but not any more, hence the total number of possibilities is 7.

Write a program that computes the total number of possibilities of such groupings for a given string of digits.

Input

Your program will be tested on a number of test cases. Each test case is specified on a separate line. Each line contains a single string no longer than 25, and is made of decimal digits only.

The end of the test cases is identified by a line made of the word "bye" (without the quotes.) Such line is not part of the test cases.

Output

For each test case, write the result using the following format:

k. n

where k is the test case number (starting at 1,) and n is the result of this test case.

Example

Input:
635
1117
9876
bye

Output:
1. 2
2. 7
3. 2

hide comments
Apoorv Dwivedi: 2015-08-28 01:00:20

why is recursion better than dp for this question?

Rishabh Joshi: 2015-06-14 20:39:28

Nice Problem.
Took size 30 and assumed max of sum is 256. got AC.

Rishit Sanmukhani: 2015-06-11 11:31:48

1. Simple recursion works.
2. Be careful of input/output format

coderforcoding: 2015-06-01 07:53:18

.

Last edit: 2015-06-01 07:53:56
Shubham Jadhav: 2015-05-10 21:01:33

simple recursion without memoization works..

GAURAV CHANDEL: 2015-04-28 15:01:46

dp needs practice...

Mauro Persano: 2014-12-24 02:26:55

Very nice problem, but had to filter out non-digit characters from input before my Scheme solution was accepted. Careful with garbage at the end of input lines. :-(

Infinity: 2014-10-29 08:36:37

DP would be a bad choice here if you want the best :P

p.s. i used dp

Last edit: 2014-10-29 09:57:39
Varun Vohra: 2014-10-26 11:46:30

simple recursion gives ac in 0.00s
but with memoisation, time increases to 0.01s :P

Rajat (1307086): 2014-10-08 01:26:56

Solved using top down DP style......with tabulation.
Still waiting to solve DP without any help.

Last edit: 2014-10-08 01:28:02

Added by:~!(*(@*!@^&
Date:2009-07-05
Time limit:1s-2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ANARC 2005