INMO 2020 Problem 4

Let $n \geq 3$ be an integer and let $1<a_{1} \leq a_{2} \leq a_{3} \leq \cdots \leq a_{n}$ be $n$ real numbers such that $a_{1}+a_{2}+a_{3}+\cdots+a_{n}=2 n$. Prove that

$$a_{1} a_{2} \cdots a_{n-1}+a_{1} a_{2} \cdots a_{n-2}+\cdots+a_{1} a_{2}+a_{1}+2 \leq a_{1} a_{2} \cdots a_{n}$$