In the Hackneyed Technocrat Center (HTC for short), everyone there write desultory codes with decrepit coding style. Unfortunately, you are exactly the manager of a desperate project that even yourself would like to discard it once got a chance. Fortunately, your dexterous skill save you and now you’re discreetly doing the refactoring on the codes that your team made.

All the codes were written in binary, and, since you are in Triangle Country, a good coding style includes removing discombobulated even palindromes from the codes. It turns out that the main job is to simplify the code. To preserve the correctness on function of the codes, whenever an even length palindrome is detected, one may remove the right part without any harm. (If you don’t know which is the right part, it’s the right part that after removing no part of the right part left.)

Now the dreary problem comes up, what is the minimum length of the code that needs to stay if you choose the order of palindrome elimination correctly?

For example, “0110” can be refactored into “010” or “01”, where “01” is shortest one and cannot be shorten anymore.