Water boils at $100^{\circ} \mathrm{C}$ at atmospheric pressure, i.e., at sea level. The boiling point is defined as the temperature at which the vapor pressure of water is equal to the atmospheric pressure. This has consequences for cooking in places like Denver and Santa Fe where it takes quite a bit longer to make a hard-boiled egg than it would in New York. If the vapor pressure of water obeys the Antoine equation (below), and the albumen in an egg needs to reach $90^{\circ} \mathrm{C}$ for the protein to coagulate, at what height would it be impossible to hard boil an egg?

\[\text { Antoine Equation } \ln P_{v a p}(\mathrm{kPa})=16.262-\frac{3799.89}{T\left({ }^{\circ} \mathrm{C}\right)+226.35}\]