  We construct a total Boolean function $f$ satisfying
$R(f)=\tilde{\Omega}(Q(f)^{5/2})$, refuting the long-standing conjecture that
$R(f)=O(Q(f)^2)$ for all total Boolean functions. Assuming a conjecture of
Aaronson and Ambainis about optimal quantum speedups for partial functions, we
improve this to $R(f)=\tilde{\Omega}(Q(f)^3)$. Our construction is motivated by
the G\"o\"os-Pitassi-Watson function but does not use it.
