Three-stack deque ($\Phi =3||F|-|B||$)

A deque can use two permanent stacks holding the front and back portions, plus an empty temporary stack. When removal encounters an empty side, park the top half of the other side in the temporary stack, reverse its remaining half into the empty side, and restore the parked half. This preserves order and balances the permanent stacks. The potential method with $\Phi =3||F|-|B||$ pays for the linear time transfer from the previous size imbalance, giving constant amortized cost for all four endpoint operations with only a fixed number of size counters.