Differentiation

Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a thrice differentiable function such that \(f(0)=0, f(1)=1, f(2)=-1, f(3)=2\) and \(f(4)=-2\). Then, the minimum number of zeros of \(\left(3 f^{\prime} f^{\prime \prime}+f f^{\prime \prime \prime}\right)(x)\) is __________.