A space ship warp engine has enough energy to perform two warp$-$jumps going between star systems

$($i$.$e$.,$ the warp battery has $2$ units of charge$).$ The ship can operate in two modes: survey the current

system or charge battery. On a given day the ship will complete the survey of the current system

with probability $0\mathrm{.}24.$ Then, if battery has capacity, it will move to a new system, consuming $1$ unit

of charge. If the battery is empty, the ship will switch to the charging mode. In the charging mode,

the ship will recover $1$ unit of charge on a given day with probability $0\mathrm{.}95.$ The ship will stay in the

charging mode until the battery is full. Model the behavior of the ship as a Markov chain.