Nemotron-IMO-Bench 2026 A44

Let $a,b,c,d$ be positive real numbers such that $$\frac{1-c}{a}+\frac{1-d}{b}+\frac{1-a}{c}+\frac{1-b}{d}\geq 0.$$ Prove that $$a(1-b)+b(1-c)+c(1-d)+d(1-a)\geq 0.$$