Given a sequence S=(x₀,x₁, . . . ,x_n−1) of numbers, describe an O(n²)-time algorithm for finding a longest subsequence T = (x_i0,x_i1, . . . ,x_ik−1) of numbers, such that i_j < i_j+1 and x_ij > xi_j+1. That is, T is a longest decreasing subsequence of S.