You are an usher in a theater with n balconies for a children’s matinee performance with n children in attendance. you are given a list of m statements of the form "i hates j." if i hates j, then you do not want to seat i above or in the same balcony as j, otherwise i will throw popcorn at j instead of watching the play. give an algorithm that assigns balconies to children (or determines that no feasible assignment exists) in time o(m + n). we can assume that balconies are numbered ascending with height.（when you are asked to ‘give’ an algorithm, be sure to prove that it is correct and exhibits the desired running time!