Eccoci.

For every positive integer $n$ the Fibonacci sequence modulo $n$ is periodic. The period depends on the value of $n$. This period is called the Pisano period for $n$, often shortened to $\pi(n)$.

There are three values of $n$ for which $\pi(n)$ equals $18$: $19$, $38$ and $76$. The sum of those smaller than $50$ is $57$.

Find the sum of the values of $n$ smaller than $1\,000\,000\,000$ for which $\pi(n)$ equals $120$.