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:
namespace Solution { open Microsoft.Quantum.Intrinsic;
operation Solve (unitary : (Qubit => Unit is Adj+Ctl)) : Int { // your code here } }