The compound shown is 1,2,3,4-tetramethylcyclobutane (no configuration specified). Treat the ring as planar and count configurational stereoisomers only. How many of its stereoisomers are optically inactive? Give the answer as an integer.

Place the four methyl groups up (u) or down (d) around the ring. Up to rotation, reflection in the ring plane and the ring symmetry, the distinct patterns are uuuu (all cis), uuud, uudd (two adjacent up, two adjacent down) and udud (alternating). These are four diastereomers. Each pattern has at least one mirror plane perpendicular to the ring (through two opposite ring atoms or through the midpoints of two opposite bonds) that maps the pattern onto itself, so all four are achiral. Hence 4 stereoisomers exist and all 4 are optically inactive (explicit enumeration confirms 4 stereoisomers, 0 chiral).