Above is a cube \(ABCDEFGH\). \(ABCD\) is the ceiling, \(EFGH\) is the floor, and the rest are the walls. Additionally, \(AB = 2\). A lizard is on point \(F\) and is wanting to go to point \(A\). If the lizard can only travel via walls, what is the measure of the shortest distance the lizard can take in order to reach its destination?

The answer can be expressed in the form of \(A + B\sqrt{C}\) such that \(A\), \(B\) and \(C\) are prime numbers or \(0\). Find \(A + \frac{C}{B} \).

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