Question 66
Let $f: \mathbb{R} \to \mathbb{R}$ be a continuous function. Let us call a chord a segment of integer length parallel to the axis $Ox$ whose endpoints belong to the graph $y = f(x)$. It is known that the graph $y = f(x)$ has exactly $N$ chords, and moreover, among them there is a chord of length $2025$. Find the least possible value of $N$.