Let $\vec A=2\vec i+\vec j-2\vec k$ and $\vec B=\vec i+\vec j$.
If $\vec C$ is a vector such that
$\vec A\cdot\vec C=|\vec C|$,
$|\vec C-\vec A|=2\sqrt2$
and the angle between $\vec A\times\vec B$ and $\vec C$ is $30^\circ$,
then $|(\vec A\times\vec B)\times\vec C|$ is equal to