Distinguish Y, XZ, -Y and -XZ

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
    }
}