  Nonlinear signal even from a single molecule becomes visible at hot spots of
plasmonic nanoparticles. In these structures, Fano resonances can control the
nonlinear response in two ways. \textit{(i)} A linear Fano resonance can
enhance the hot spot field, resulting enhanced nonlinear signal. \textit{(ii)}
A nonlinear Fano resonance can enhance the nonlinear signal without enhancing
the hot spot. In this study, we compare the enhancement of second harmonic
signal at the steady-state obtained via these two methods. Since we are
interested in the steady-state signal, we adapt a linear enhancement which
works at the steady-state. This is different than the dark-hot resonances that
appears in the transparency window due to enhanced plasmon lifetime.
