Tetrahedron

Geometry Level pending

Let \(ABCD\) be a tetrahedron such that \(AB \perp AC \perp AD \perp AB\) with integer side lengths \(AB,AC,AD,BC\) and \(CD\). Let \(E\) be the midpoint of \(CD\). If the volume of the tetrahedron \(ABCE\) is 2016, how many distinct possible values of \(BD\) are there?

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