13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T5d4,

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

Distinguish Y, XZ, -Y and -XZ