2021 IMO Shortlist A3

Given a positive integer $n$, find the smallest value of $\left\lfloor\frac{a_{1}}{1}\right\rfloor+\left\lfloor\frac{a_{2}}{2}\right\rfloor+\cdots+\left\lfloor\frac{a_{n}}{n}\right\rfloor$ over all permutations $\left(a_{1}, a_{2}, \ldots, a_{n}\right)$ of $(1,2, \ldots, n)$.

给定一个正整数 $n$，在所有排列 \left(a_{1}, a_{2},(1,2,\ldots, n)的\ldots, a_{n}\right)。