Low distortion embeddings into Asplund Banach spaces

We give a simple example of a countable metric space $M$ that does not embed bi-Lipschitz with distortion strictly less than 2 into any Asplund space. Actually, if $M$ embeds with distortion strictly less than 2 to a Banach space $X$, then $X$ contains an isomorphic copy of ${\mathrm{\ell }}_1$. We also show that the space $M$ does not embed with distortion strictly less than $2$ into ${\mathrm{\ell }}_1$ itself but it does embed isometrically into a space that is isomorphic to ${\mathrm{\ell }}_1$.