Refrigerant $134-$a is compressed in a two$-$stage compressor. It enters the first stage of the compressor as saturated vapor at $-10$C and leaves at $900$ kPa and $60$C$.$ It then enters the second stage compressor as saturated vapor at $900$ kPa and leaves it at $1\mathrm{.}4$ MPa and $80$C$.$ The mass flow rate of the refrigerant through both stages is $3$ kg$/$s$.$ If the total heat loss from the compressor per unit mass of refrigerant is $20$ kJ$/$kg of the refrigerant, what is the total power input to the compressor?