Write a program brown.py that simulates two$-$dimensional Brown motion by the following crude

model. Particles move in discrete time steps, at each step advancing by a fixed distance in a

random direction, described by an angle drawn from a uniform distribution over $[0,2\backslash$pi $).$

Have your program simulate this motion for an ensemble of $5000$ particles over $1000$ time steps.

Have the program output a set of three histograms drawn in a common figure $($window$),$ describing

the distribution of the distance from the initial position of the particles forming the ensemble after

$50,250$ and $1000$ steps. The histograms should use $100$ bins and include titles and axis labels. Take

the time step as a unit of time, and the distance traveled in a single step as the unit of length.

Provide, either within the titles or in descriptive text incorporated into the pictures, the values of

mean distance traveled and its standard deviation over the ensemble of particles.