If  $f\left(x\right)$ is a polynomial with positive leading coefficient satisfying  $f\left(0\right)=0$  $f\left(f\left(x\right)\right)=x\underset{0}{\overset{x}{\int }}f\left(t\right)dt\forall x\in R,$ then locus of point of intersection of two perpendicular tangents can be drawn to the curve  $y=f\left(x\right)$ can be given by  $a{x}^2+2hxy+b{y}^2+2gx+2fy+\sqrt{3}=0$, then the value of  $a^2-\sqrt{5}{h}^3+\sqrt{2}{b}^4+\sqrt{3}{g}^5+f=$