23662번 - Heretical Möbius 다국어

Rikka was walking around the school building curiously until a strange room with a door number of 404 caught her eyes.

It seemed like a computer room --- there were dozens of computers lying orderly, but papers, pens, and whiteboards everywhere built up a nervous atmosphere. Suddenly, Rikka found some mysterious codes displayed on a computer which seemed to have nothing different from others --- is this a message from inner world?

Excited Rikka started her exploration. The message was generated by a program named for_patterns_in_mobius which outputted a string $s$ of length $10^9$, containing the value of $\lvert \mu(x) \rvert$ for $x = 1, 2, \dots, 10^9$ in order.

Suddenly, Rikka heard footsteps outside. She quickly took a screenshot and left. The screenshot recorded a string $t$ of length $200$, perhaps a substring of $s$. Now Rikka wonders if it is really a substring of $s$, and if so, where it first appears in $s$.

Could you help her to decipher the codes?

There are $10$ lines in total. Each line contains $20$ characters, each of which is either "0" or "1". $t$ is the concatenation of them --- the result of concatenating them in order.

Output a single integer in the only line. If $t$ is a substring of $s$, output the first position it appears in $s$, that is, the minimum positive integer $p$ such that all the digits $\lvert \mu(p+i) \rvert$ for $i = 0, 1, \dots, 199$ form the string $t$. Otherwise output $-1$.

The definition of $\mu()$ is as follows: 

For any positive integer $x$, let $x = \prod_{i=1}^k {p_i}^{c_i}$ be the regular factorization of $x$, where $p_i$ is a unique prime, $c_i$ is a positive integer, and if $x=1$ then $k=0$. Consequently, $\mu(x)$ is defined as $$ \mu(x)= \begin{cases} 0 & \exists c_i>1, \\ (-1)^k & \text{otherwise} \\ \end{cases} $$