Two planets experience a gravitation force between them $F.$ If the mass of flanet $1$ increases by $2,$ the mass of planet $2$ increases by $4,$ and the distance between them increases by $4,$ what is the new gravitation force between the planets?

$\frac{F}{2}$

$2F$

$16F$

$\frac{F}{4}$

$\frac{F}{16}$

$4F$