Classical proof that well-ordering principle is equivalent to complete induction

Question

I want to prove that:

Well ordering principle ⟺ Complete Induction.

I am interested in both directions of the implication. That is, that if every non-empty set contains a least element then if a property P holds for all naturals less than n-1 it must hold for n. And viceversa.

I want the proof to be classical (I suspect this is quite difficult to prove constructively)