We prove that for every nowhere dense class of graphs C, positive integer d, and ε > 0, the following holds: in every n-vertex graph G from C one can find two disjoint vertex subsets A, B ⊆ V (G) such that • |A| (1/2 − ε) • n and |B| = Ω(n 1−ε ); and • either dist(a, b) d for all a ∈ A and b ∈ B, or dist(a, b) > d for all a ∈ A and b ∈ B.We also show some stronger variants of this statement, including a generalization to the setting of First-Order interpretations of nowhere dense graph classes.