Implement a quantum oracle on $N$ qubits which checks whether the number of bits equal to 1 in the input vector $\vec{x}$ is divisible by 3 (i.e., implements the function $f(\vec{x}) = 1$ if the number of $x_i = 1$ in $\vec{x}$ is divisible by 3, and 0 otherwise).

You have to implement an operation which takes the following inputs:

• an array of $N$ ($1 \le N \le 9$) qubits $x$ in an arbitrary state (input register),
• a qubit $y$ in an arbitrary state (output qubit),

and performs a transformation $|x\rangle|y\rangle \rightarrow |x\rangle|y \oplus f(x)\rangle$. The operation doesn't have an output; its "output" is the state in which it leaves the qubits. Note that the input register $x$ has to remain unchanged after applying the operation.

Your code should have the following signature:

namespace Solution {
    open Microsoft.Quantum.Primitive;
    open Microsoft.Quantum.Canon;

    operation Solve (x : Qubit[], y : Qubit) : Unit {
        body (...) {
            // your code here
        }
        adjoint auto;
    }
}

Note: the operation has to have an adjoint specified for it; adjoint auto means that the adjoint will be generated automatically. For details on adjoint, see Operation Declarations.

You are not allowed to use measurements in your operation.