Suppose you are given two coordinates in n-dimensional space, p = (p1, p2, pn), and q = (q1, q2, qn). the golden distance d between p, and q is defined as d(p, q) = pn i=1(pi −qi) 4 . let pσ be formed by permuting the elements of p, and let qπ be formed by permuting the elements of q. for example, if p = (1, 2, 3) and q = (1, 3, 5), then one possible way to form the permutations could be pσ = (2, 1, 3) and qπ = (5, 3, 1). the golden distance, d(pσ , qπ ), of these two points would be (2 − 5)4 + (1 − 3)4 + (3 − 1)4 = 113. (a) design a greedy algorithm that chooses the permutations for pσ and qπ that maximizes their golden distance, d(pσ , qπ ). analyze the time complexity of your algorithm. (b) prove the correctness of your algorithm. (hint: you may use the following fact without proof (d − a) 4 + (c − b) 4 ≥ (b − a) 4 + (d − c) 4 for any numbers a, b, c, d such that a ≤ c