You are given a qubit which is guaranteed to be in one of the following states:

$$$|A\rangle = \frac{1}{\sqrt{2}} \big( |0\rangle + |1\rangle \big)$$$,
$$$|B\rangle = \frac{1}{\sqrt{2}} \big( |0\rangle + \omega |1\rangle \big)$$$, or
$$$|C\rangle = \frac{1}{\sqrt{2}} \big( |0\rangle + \omega^2 |1\rangle \big)$$$, where $$$\omega = e^{2i\pi/3}$$$.

These states are not orthogonal, and thus can not be distinguished perfectly. Your task is to figure out in which state the qubit is not. More formally:

If the qubit was in state $$$|A\rangle$$$, you have to return 1 or 2.
If the qubit was in state $$$|B\rangle$$$, you have to return 0 or 2.
If the qubit was in state $$$|C\rangle$$$, you have to return 0 or 1.
In other words, return 0 if you're sure the qubit was not in state $$$|A\rangle$$$, return 1 if you're sure the qubit was not in state $$$|B\rangle$$$, and return 2 if you're sure the qubit was not in state $$$|C\rangle$$$.

Your solution will be called 1000 times, each time the state of the qubit will be chosen as $$$|A\rangle$$$, $$$|B\rangle$$$ or $$$|C\rangle$$$ with equal probability. The state of the qubit after the operations does not matter.

You have to implement an operation which takes a qubit as an input and returns an integer. Your code should have the following signature:

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

    operation Solve (q : Qubit) : Int {
        // your code here
    }
}

Not A, not B or not C?