Let f(x) be a quadratic polynomial such that f(-4)=-22, f(-1)=2, and f(2)=-1. Let g(x)=f(x)^16. Find the sum of the coefficients of the terms in g(x) with even exponents. (For example, the sum of the coefficients of the terms in -7x^3+4x^2+10x-5 with even exponents is 4+(-5)=-1.)
