A heat pump with a COP of $4\mathrm{.}8$ maintains a house at an ambient temperature of $21\backslash$deg C$.$ When the outdoor air temperature is $5\backslash$deg C the house loses heat to the outside at an average rate of $90,000$ kJ$/$hr$.$ Energy is generated within the house due to the effect of people, lights, appliances, etc of $4,800$ kJ$/$hr$.$ Determine the work input required to the compressor, give your answer to $1$ decimal place in kilowatts.