Problem A7

Statement
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Description:
You are given an operation that implements a single-qubit unitary transformation: either the Y gate (possibly with an extra global phase of $$$-1$$$) or the sequence of Pauli Z and Pauli X gates (the Z gate applied first and the X gate applied second; possibly with an extra global phase of $$$-1$$$). The operation will have Adjoint and Controlled variants defined.

Your task is to perform necessary operations and measurements to figure out which unitary it was and to return

- 0 if it was the Y gate,
- 1 if it was the $$$-$$$XZ gate,
- 2 if it was the $$$-$$$Y gate,
- 3 if it was the XZ gate.

You are allowed to apply the given operation and its adjoint/controlled variants at most three times.

You have to implement an operation which takes a single-qubit operation as an input and returns an integer. Your code should have the following signature:

Input Format:
None

Output Format:
None

Note:
None