A $2\mathrm{.}2-$ mole sample of a monatomic ideal gas with an initial volume of $5\mathrm{.}75$ L and initial pressure of $5\mathrm{.}5$ MPa undergoes a complete cycle as follows.

Step $1$: the gas expands isothermally until its volume doubles.

Step $2$: the gas undergoes isochoric cooling as its pressure is reduced to Po$/5.$

Step $3$: The gas is compressed in an isothermal process until it is back to volume the initial and its pressure is $2$Po$/5.$

Step $4$: The gas temperature increases as it goes through an isochoric process which returns it to pressure Po and volume Vo$.$

Determine the work done by the gas in joules as it completes all four steps in the cycle.

W$=\_\_\_\_\_$J