Problem 2. (Ramanujan's Tari) 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 Ramanujan1. java that accepts n (int) as command-line argument and writes to standard output all integers less than or equal to n that can be expressed as the sum of two cubes in two different ways. In other words, find distinct positive integers a, b, c, and d such that a3 + 63 = c3 + d' un. "/workspace/exercise4 $ java Ramanujan1 10000 1729 = 1 3 + 12 3 = 9-3 + 10-3 4104 = 23 16-3 3 = 9-3 + 15-3 Directions: . Use four nested for loops, with these bounds on the loop variables: 0 { 1 usage L5 private int i; // first number in the pair 1 usage private int j; // second number in the pair 3 usages private int sumOfCubes; // i^3 + j^3 // Constructs a pair (i, j). public Pair (int i, int j) { this. i = i; this . j = j; sumOfCubes = i * i * i + j * j * j; 5 6 // Returns a comparison of pairs this and other based on their sum-of-cubes values. 27 Of @ public int compareTo (Pair other) { return sumOfCubes - other . sumOfCubes; }