Minimize the Distance

You are given two line segments $\mathsf{AB}$ and $\mathsf{CD}$ in $N$-dimensional space. Find the minimum distance between them, i.e. the minimum distance $\mathsf{|PQ|}$ over all points $\mathsf{P} \in \mathsf{AB}$ and $\mathsf{Q} \in \mathsf{CD}$. **Note**: Because of large I/O, please use fast I/O methods. ### Input - The first line of the input contains a single integer $T$ denoting the num