A proposition on an irreducible polynomial over a non-archimedean field

Question

Suppose $K$ is a non-archimedean complete field(i.e. a field with a non-archimedean valuation). Let $f(x)=\sum_{i=0}^{n} a_{i} x^{i} \in K[x]$ and suppose $f(x)$ is irreducible. How to prove $\max \left\{\left|a_{i}\right|\right\}=\max \left\{\left|a_{0}\right|,\left|a_{k}\right|\right\}$ ?