IPS - Interleaved Periodic String

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An interleaved periodic string S can be written down using the following procedure :

  1. Write down any two strings s1 and s2 of lengths p1 and p2 respectively. The strings must consist of only 0s and 1s, and can possibly be empty.
  2. Concatenate some copies of the string s1 to obtain string S1.
  3. Concatenate some copies of the string s2 to obtain string S2.
  4. Interleave the strings S1 and S2 to obtain S.

To interleave two strings, merge their characters arbitrarily, maintaining the relative order in which they occur in both strings. For example, the strings "101" and "011" can be interleaved to get "011011" or "101011", however they cannot be interleaved to form "110110". Given S, find the minimum possible value of (p1 + p2).

Input :
The input consists of multiple test cases. The first line contains the number of test cases T. Each of the next T lines contain a string S consisting of only 0's and 1's.

Input Constraints
1 ≤ T ≤ 20
1 ≤ length of S ≤ 16

Output :

Output T lines, one corresponding to each test case, containing the minimum value      of (p1 + p2) for the corresponding test case.

Sample Input :

Example Output :


hide comments
Ravi Kiran: 2010-03-01 11:12:14

I dont think this was that bad a question to be moved in to tutorial.
There are many more qns in the classical set that have had to be moved before we moved this.

Pritam Bhattacharya: 2010-01-19 18:12:19

well, problems even easier than this one do exist in the classical problemset .. still, I may consider !

Luka Hrabar: 2010-01-19 18:12:19

Last edit: 2010-09-17 06:33:50

Added by:Pritam Bhattacharya
Time limit:0.100s
Source limit:1000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Resource:ACM ICPC 2009 Regionals (Asia-Amritapuri site)