Consider three vectors $\vec a,\vec b,\vec c$. Let $|\vec a|=2$, $|\vec b|=3$ and $\vec a=\vec b\times\vec c$. If $\alpha\in[0,\tfrac{\pi}{3}]$ is the angle between $\vec b$ and $\vec c$, then the minimum value of $27,|\vec c-\vec a|^{2}$ is: