Let $S$ be a collection of $n$ objects, each with a unique integer key $a_i \in \{0,1,2,\ldots,n^2-1\}$. Consider hashing all the objects in $S$ into an array $A[0..m-1]$ of $m=\lceil n^{1.5}\rceil$ buckets. Each bucket stores a (singly) linked list of all objects hashed into the same bucket. The hashing algorithm works as follows. The algorithm first picks a hash function $h$ uniformly at random from a hash family $\mathcal H$. Then, for each object $i \in S$, the algorithm computes $h(a_i)$ and inserts the object into the bucket $A[h(a_i)]$. The number of collisions $\tau$ is defined to be the total number of (unordered) object pairs hashed into the same bucket. We focus on the choice of the hash family $\mathcal H$ and the worst-case expected number of collisions $\mathbf E[\tau]$. Note that the term worst-case refers to the choice of the input set $S$. Select all statement(s) that are correct for every sufficiently large $n$.