JMO 1993 Problem 5

Prove that there existed a positive number $C,$ irrelevant to $n$ and $a_1,\ a_2,\ \cdots a_n,$ satisfying the following condition.

Condition: For arbiterary positive numbers $n$ and arbiterary real numbers $a_1,\ \cdots a_n,$ the following inequality holds.

$$\max_{0\leq x\leq 2}\prod_{j=1}^n |x-a_j|\leq C^n \max_{0\leq x\leq 1}\prod_{j=1}^n |x-a_j|.$$