A kettle is filled with $1.0\ \text{kg}$ of ice cubes straight from a tray at exactly $0\ ^\circ\text{C}$. It must melt them, bring the water to the boil, and boil it all away. How much energy is that in all? (Latent heats $3.34 \times 10^{5}\ \text{J/kg}$ and $2.26 \times 10^{6}\ \text{J/kg}$; $c = 4186\ \text{J kg}^{-1}\text{K}^{-1}$.)