Euclidean hypersurfaces with genuine deformations in codimension two

We classify hypersurfaces of rank two of Euclidean space ${\mathbb{R}}^{n+1}$ that admit genuine isometric deformations in ${\mathbb{R}}^{n+2}$. That an isometric immersion $\widehat{f}\text{\hspace{0.17em}⁣}:M^n\to {\mathbb{R}}^{n+2}$ is a genuine isometric deformation of a hypersurface $f\text{\hspace{0.17em}⁣}:M^n\to {\mathbb{R}}^{n+1}$ means that $\widehat{f}$ is nowhere a composition $\widehat{f}=\widehat{F}\circ f$, where $\hat F\colon,V\subset \R^{n+1}\to\R^{n+2}$isanisometricimmersionofanopensubset$V$containing$f(M)$.