INMO 2001 Problem 6

Let $\mathbf{R}$ denote the set of all real numbers. Find all functions $f: \mathbf{R} \rightarrow \mathbf{R}$ satisfying the condition

$$f(x+y)=f(x) f(y) f(x y)$$

for all $x, y$ in $\mathbf{R}$.