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
blueranger: 2016-06-21 17:43:55

only 5 line recursion function ... easy one!
BEWARE! ... got 1 WA because of presentation error :(

sarvesh_19: 2016-03-31 16:34:47

took time ...nice one :)

SHOBHIT SHEKHAR: 2016-03-30 23:25:08

would have been a better question if it had strict constraints

Bhuvnesh Jain: 2016-01-26 14:23:43

Bad test cases. Brute force passes as well. Should either improve test cases or increase the length of string.

anshal dwivedi: 2015-12-26 10:09:10

another DP!

naruto09: 2015-12-19 18:13:37

same time with and without dp..;)

priyank: 2015-12-12 10:46:14

time limit is too weak

Prateek Agarwal: 2015-12-04 08:38:54

Wthout memoization!

Anubhav Gupta: 2015-10-02 05:25:28

Awesome question!!!

Harsh Vardhan Ladha: 2015-09-09 09:28:14

My 100th :D
did with top-down DP!

Last edit: 2015-09-09 09:31:29

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