Can someone explain the definition of four square roots as it pertains to groups in Z*p? So I'm given the following as a problem:

When $p$ and $q$ are distinct odd primes and $N = pq$, the points in $Z^∗_N$ have either
zero or four square roots. A quarter of the points have four square roots; the rest have no square
root. The four square roots of $x ∈ Z^∗_N$ will look like $±a, ±b$. (Of course, −a means N − a since
we’re working modulo N.) Suppose that I give you an efficient deterministic algorithm S that, on
input x that has square roots, finds some square root. (If x does not have a square root, it returns
⊥.)
Use S to make an efficient probabilistic algorithm F that factors N.

I am not asking for a solution to the problem, rather an understanding of what "four square roots" could possibly mean? How can a single element $x∈ Z^∗_N$ have "four square roots"?
"$x$ has four square roots" means there are four distinct elements $r$ in the group such that $r^2 = x$.

For example, in $\mathbf{Z}_{15}^\times$ the element $1$ has four square roots, which are $1$, $4$, $11$, and $14$ (note that $11 \equiv -4$ and $14 \equiv -1  \pmod{15}$).