A5. Distinguish Z from -Z
time limit per test
1 second
memory limit per test
256 megabytes
standard input
standard output

You are given an operation that implements a single-qubit unitary transformation: either the Z gate or the -Z gate (i.e., the $$$-|0\rangle\langle0| + |1\rangle\langle1|$$$ gate: $$$(-Z)(\alpha|0\rangle + \beta|1\rangle) = -\alpha|0\rangle + \beta|1\rangle$$$). 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 Z gate or 1 if it was the -Z gate.

You are allowed to apply the given operation and its adjoint/controlled variants exactly once.

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