Upper bound of $ \sum_{n\leq x}f(n) $ where $ f(n)=\sum_{r=1}^{n-1}\mu(r)\mu(n-r) $

Question

$Cx^2$ is a trivial bound by just counting the total number of terms in these sums. From here I have attempted to use $$ \sum_{n\leq x} \mid \mu(n) \mid =\frac{6}{\pi^2}x(1+o(1)) \text{, } x \to \infty$$ but had no luck. This is reminiscent of Selbergs sieve. Any related identities or results would be much appreciated !