Consider the cube in the first octant with sides OP, OQ and OR of length 1 , along the $x$-axis, $y$-axis and $z$ axis, respectively, where $\mathrm{O}(0,0,0)$ is the origin. Let $S\left(\frac{1}{2}, \frac{1}{2}, \frac{1}{2}\right)$ be the centre of the cube and T be the vertex of the cube opposite to the origin O such that S lies on the diagonal OT . If $\vec{p}=\overrightarrow{S P}, \vec{q}=\overrightarrow{S Q}, \vec{r}=\overrightarrow{S R}$ and $\vec{t}=\overrightarrow{S T}$, then the value of $|(\vec{p} \times \vec{q}) \times(\vec{r} \times \vec{t})|$ is $\_\_\_\_$。