An Easy Ordinal Assignment for Typed Terms

Let $\Lambda^{\to}$ be the set of simply typed lambda terms. Construct an ``easy'' map $\#:\Lambda^{\to}\to\mathrm{Ord}$ to the ordinals such that, for every one-step beta reduction,

$$M\longrightarrow_\beta N \quad\Longrightarrow\quad \#M>\#N.$$

The construction must directly establish strong normalization rather than presuppose it; the source intentionally leaves ``easy'' as the qualitative criterion of this koan.