maps preserving strong jordan multiple ∗-product on∗-algebras

Let a be an arbitrary ∗-algebra with unit i over the real or complex field f that contains a nontrivial idempotent p1 and n ≥ 1 a natural number and φ : a → a be a surjective map on a such that φ satisfies condition φ(p) •n−1 φ(p) • φ(a) = p •n−1 p • a, for every a ∈ a and projection p ∈ {p1, i − p1}, where a •n−1 a with repeat n − 1 times a is the jordan multiple ∗-product. then φ(a) = φ(i)a for all a ∈ a and φ(i)² = i.