Problem. Ramanujan's Taxi Redux

Problem 5. (Ramanujan's Tari Reduz) Srinivasa Ramanujan was an Indian mathematician who became famous for his intuition for numbers. When the English mathematician G. H. Hardy came to visit him one day, Hardy remarked that the number of his taxi was 1729, a rather dull number. To which Ramanujan replied, "No, Hardy! It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways." Verify this claim by writing a program Ramanujan. java that takes a command-line argument N and prints out al integers less than or equal to N that can be expressed as the s of two cubes in two different ways. In other words, find distinct positive integers i, j, k, and l such that i3 +j3-k" + 13. In Homework 2, you used four nested for loops to solve the problem A much more sophisticated implementation of the same program is using a minimum-oriented priority queue Initialize a minimum-oriented pity que with pairs (1,2), (2,3), (3, 4) (i, i 1) such ai