FINDSR - Find String Roots

In mathematics, the N-th root of a number M, is a number K such that KN = M , i.e. KKK ... K = M where K is multiplied N times.

We can translate this into strings. In string notation, the juxtaposition is concatenation instead of multiplication. So, the N-th root of a string S is another string T such that TN = S, where T N = TTT ... T is the string T concatenated N times. For instance, if S = “abcabcabcabc”, for N = 2 the string T = “abcabc” is the N-th root of S, while for N = 4 its N-th root is T = “abc”. Note that for N = 1 any string S is the N-th root of S itself.

Given a string S you have to find the maximum N such that the N-th root of S exists. In the above example the answer would be 4, because there is no N-th root of S = “abcabcabcabc” for N > 4.

Input

The input contains several test cases, each one described in a single line. The line contains a non-empty string S of at most 105 characters, entirely formed of digits and lowercase letters. The last line of the input contains a single asterisk (“*”) and should not be processed as a test case.

Output

For each test case output a single line with the greatest integer N such that there exists a string T that concatenated N times is equal to S.

Example

Input:
abcabcabcabc
abcdefgh012
aaaaaaaaaa
*

Output:
4
1
10

Added by:Pablo Ariel Heiber
Date:2010-08-22
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS OBJC PERL6 VB.NET
Resource:FCEyN UBA ICPC Selection 2009

hide comments
2013-04-07 13:45:42 Vitalis Salis
I didn't use any string algorithm, yet got accepted. I could say it is an ad hoc problem.
2012-10-04 13:04:58 Raghavendran Ramachandran
www.spoj.pl/problems/PERIOD
2012-08-28 18:36:30 Shubham.IIITM
----Removed After AC----
Wow Accepted!!! A good question seriously :)

Last edit: 2012-08-28 19:08:00
2012-06-23 14:07:50 :)
plz give hint ...
2012-05-17 03:30:41 Grandmaster
wow.. cant believe the way it got accepted :P .. a new lesson learned.

Last edit: 2012-05-17 03:36:44
2010-10-29 05:26:33 Michael T
I guess some string algorithm would be needed then.)

Last edit: 2010-10-29 05:27:26
2010-10-26 21:15:14 numerix
You can even get it AC with a pure Python solution (without psyco) ...
2010-10-24 05:25:31 Michael T
Indeed. Even in python (psyco req though).

Last edit: 2010-10-24 05:28:24
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