Meromorphic functions sharing two finite sets

Let S1 = {∞} and S2 = {w: Ps(w) = 0}, Ps(w) being a uniqueness polynomial under some restricted conditions. Then, for any given nonconstant meromorphic function f, there exist at most finitely many nonconstant meromorphic functions g such that f−1(Si) = g−1(Si), (i = 1,2), where f−1(Si) and g−1(Si) denote the pull-backs of Si considered as a divisor, namely, the inverse images ofSi counted with multiplicities, by f and g respectively.