Let $h, r, g$ be real numbers satisfying

$\frac{(h-2r)(r-2g)(g-2h)}{hrg}=10$

$\frac{(h+r)(r+g)(g+h)}{hrg}=24$

Given that $\frac{h}{r}+\frac{r}{g}+\frac{g}{h}$ can be expressed as $\frac{d}{m}$, where $d, m$ are relatively prime positive integers.

$d+m+2!=?$