Suppose that the hypothesis H₀ concerns the independence of two random variables X and Y . That is, we wish to test H₀ : F(x, y) = F₁(x)F₂(y), where F, F₁, and F₂ are the respective joint and marginal distribution functions of the continuous type, against all alternatives. Let (X₁, Y₁), (X₂, Y₂), . . . , (X_n, Y_n) be a random sample from the joint distribution. Under H₀, the order statistics of X₁,X₂, . . .,X_n and the order statistics of Y₁, Y₂, . . . , Y_n are, respectively, complete sufficient statistics for F₁ and F₂. Use r_S, r_qc, and r_N to create an adaptive distribution-free test of H₀.