GAIC Math 2024 Problem 2

Let $A_l = (4l+1)(4l+2) \cdots \left(4(5^5+1)l\right)$. Given a positive integer $l$ such that $5^{25l} \mid A_l$ and $5^{25l+1} \nmid A_l$, the minimum value of $l$ satisfying these conditions is \underline{\hspace{2cm}}.