Let $f(n)$ be the product of non-zero digits of positive integer $n$ in base $10$ and let $f(0) = 1$. For example, $f(420) = 4 \cdot 2 = 8$. Also, let $s(n) =\sum^n_{i=0}f(i)$. Find the maximum value of positive integer $k$ such that for every non-negative integer $n$, $10^{2023} | n + 1$ implies $k | s(n)$. Note: For positive integers $a$ and $b$, $a | b$ means that $a$ is a divisor of $b$.