**Input:** An operation that implements a single-qubit unitary transformation:
either the $Z$ gate or the $S$ gate. 

**Output:**  0 if the given operation is the $Z$ gate, 1 if the given operation is the $S$ gate.

The operation will have Adjoint and Controlled variants defined.
You are allowed to apply the given operation and its adjoint/controlled variants at most **twice**.
