  We show that a special alternating knot with sufficiently large number (more
than $63$) of twist regions has no chirally cosmetic surgeries, a pair of Dehn
surgeries producing orientation-reversingly homeomorphic $3$-manifolds. In the
course of proof, we provide the optimal upper bounds of the primitive finite
type invariants of degree 2 and 3 that solve Willerton's conjecture.
