There are n points in a $3$-dimensional space. If two points are exactly $1$ unit from each other, a line is joint between them. Let the number of total lines being joint be $\ell$. Suppose the maximum possible value of $\frac{\ell}{ n^2}$ is $\frac{p}{q}$ , where $p$ and $q$ are positive integers that are relatively prime to each other. Enter $100p + q$.