Mt Everest of the Skies

Alice and Bob live the in the city of ‘Hawa Mahal’ which is located in between the clouds in the sky. It is a small hill station among the clouds and containing $N$ hills, some are low and some are tall. Alice and Bob decide to play a game. Living in the area, they know the height of each hill in their station. Alice and Bob together want to make a hypothetical ‘Mt. Everest of the skies’. T