Develop the following subroutines for an MD NPT ensemble code using fortran programming language $($f$90)$ for a simple system of Lennard$-$Jones particles. $1.$ subroutine initialize$\_$particles$($x$,$ y$,$ z$,$ vx$,$ vy$,$ vz$,$ n$\_$particles$),2.,$ subroutine$\_$calc forces$($r$,$f$,$etot,vir,p$)3.$ subroutine velocity$\_$verlet$($x$,$ y$,$ z$,$ vx$,$ vy$,$ vz$,$ fx$,$ fy$,$ fz$,$ n$\_$particles$)4.$ subroutine berendsen$\_$thermostat$($vx$,$ vy$,$ vz$,$ temperature, thermostat$\_$scale$)$

$5.$ subroutine berendsen$\_$barostat$($pressure$,$ barostat$\_$scale$)$