F - Minimum Divides Maximum

You are given an integer $n$. You want to find a permutation$^\dagger$ $p$ of the integers $\{1, 2, \ldots, n\}$ such that the number of indices $i$ ($1 \le i \le n$) where $\max(p_1, p_2, \ldots, p_i)$ is divisible by $\min(p_1, p_2, \ldots, p_i)$ is as small as possible. Print the minimum value possible if you choose $p$ optimally. $^\dagger$ A permutation of the integers $\{1, 2, \ldots, n\}