Vectors in Space · Superchallenge problem

Vectors $\mathbf u$ and $\mathbf v$ in space satisfy $\mathbf u \times \mathbf v = (2, -1, 2)$ and $\mathbf u \cdot \mathbf v = 4$. Find the smallest possible value of $\lVert\mathbf u\rVert^2 + \lVert\mathbf v\rVert^2$.