Total Overlap

You are given two sets of segments on a line, $A$ and $B$. Set $A$ contains $N$ segments (numbered $1$ through $N$); for each valid $i$, the $i$-th of these segments is $S_{A,i} = [L_{A,i}, R_{A,i}]$. Set $B$ contains $M$ segments (numbered $1$ through $M$); for each valid $i$, the $i$-th of these segments is $S_{B,i} = [L_{B,i}, R_{B,i}]$. Find $\sum_{i=1}^N \sum_{j=1}^M |S_{A,i} \cap S_{B,j}