analysis - A problem from Zorich

I am trying to read Mathematical Analysis I by Zorich on my own. Here is an exercise that I could not solve:

For all $l \in \mathbb{R}$ that is not of the form $\frac{1}{n}$ for some $n \in \mathbb{N}$, there exists a continuous function $f: [0, 1] \Rightarrow \mathbb{R}$ such that $f(0) = f(1)$ and the graph of $f$ contains no horizontal chord with length $l$.

I was wondering how to prove this? Thanks in advance.