Let $L_1=0$ be a focal chord of the parabola $P:y^2=4ax$ . $L_1=0$ Meets the parabola at “L” and “M”. The tangents at “L” and “M” intersect at “N”.
$S_1$: Focus is the foot of the perpendicular from “N” to  $L_1=0$
$S_2:\angle NML=90°$
$S_3:\frac{1}{SM}+\frac{1}{SL}=\frac{2}{a}$ ( $S$ is focus of the parabola)
$S_4$: “N” lie on the directrix
The number of correct statements among $S_1,S_2,S_3,S_4$ is