real analysis - Let $f:mathbb{I} to mathbb{R}$ continuous function such that $f(0)=f(1)$.

$\mathbb{I} = [0,1]$

Let $f:\mathbb{I} \to \mathbb{R}$ continuous function such that $f(0)=f(1)$. Prove that for all $n \in \mathbb{N}$ there $x \in \mathbb{I}$ such that $x + \frac{1}{n} \in \mathbb{I}$ and $f( x + \frac{1}{n})=f(x)$

Could you help me by giving me an idea of ​​how to do it?