MYTS 2019 - Grade 7 - Round 2 Question 6

Positive real numbers $a_1\le a_2\le\cdots\le a_{2018}\le a_{2019}$ satisfy the following condition: for every $1\le i<j<k\le2019$, the product $a_i a_j a_k$ is one of the 2019 listed numbers. Prove that $a_2=a_3=\cdots=a_{2018}=1$.