What is the test for determining whether a sanction is a punishment?

explained in the context of applying the state and federal protections against cruel and/or unusual punishment, a sanction designed and intended only to serve legitimate nonpenal objectives is not punishment ... simply because it may burden inconvenience, restrict, or deter in fact . [Citation.] On the other hand, that a given sanction may serve[ ] remedial purposes, does not establish that it is not punishment. [Citations.] In short, because sanctions frequently serve more than one purpose [citation] and have multiple effects, determining whether a given sanction constitutes punishment is often difficult." ( People v. Ruiz (2018) 4 Cal.5th 1100, 11071108, 232 Cal.Rptr.3d 714, 417 P.3d 191.)

The courts employ a two-stage analysis.