Let C be the circle in the complex plane with centre $z_0=\frac{1}{2}(1+3 i)$ and radius $r=1$. Let $z_1=1+i$ and the complex number $z 2$ be outside the circle $C$ such that $|z 1-z 0||z 2-z 0|=1$. If $z 0, z 1$ and $z 2$ are collinear, then the smaller value of $|z 2|^2$ is equal to-
