Visible Spheres

Geometry Level 5

There are 2015 identical spheres with radius 1 such that no two spheres are touching. A point on the surface of the sphere is considered visible if it can be "seen" by another sphere, i.e. the point can be connected to a particular point on the surface of another sphere by a straight line unobstructed. Let \(S\) be the total surface area of the points on the surface of the 2015 spheres that are NOT visible. Find the value of \(\lfloor S \rfloor\).

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