Let $0 ≤ a, b, c, d ≤ 1$. Prove that at least one of the products $a(1 − b), b(1 − c), c(1 − d), d(1 − a)$ is $\leq \frac{1}{4}$ .

Question

From this question, I can tell that it's obvious that one of the products would be less than $\frac{1}{4}$. However I have a hard time trying to prove it. This supposedly uses AM GM Inequality. Can someone kindly help. Thank you in advance