Structure of Cardinality 3+ where Every Permutation is Automorphism is Idempotent

Theorem
Let $S$ be a set whose cardinality is at least $3$.

Let $\struct {S, \circ}$ be an algebraic structure on $S$ such that every permutation on $S$ is an automorphism on $\struct {S, \circ}$.

Then $\circ$ is an idempotent operation.