Functions are awesome!!!

Algebra Level 4

Find the number of functions f:RR f : \mathbb{R} \rightarrow \mathbb{R} such that f(x+y)=f(x)f(y)f(xy)f(x+y)=f(x)\cdot f(y)\cdot f(xy) for all x,yx,y in R \mathbb{R} .

Note: R \mathbb{R} denotes the set of real numbers.

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