A beaker contains a thick layer of oil (shown in green) of density ?₂ floating on water (shown in blue), which has density ?₃. A cubical block of wood of density ?₁ with side length L is gently lowered into the beaker, so as not to disturb the layers of liquid, until it floats peacefully between the layers, as shown. (Figure 1)

What is the distance d between the top of the wood cube (after it has come to rest) and the interface between the oil and water? Express your answer in terms of quantities given in the problem introduction.