Monday Mutant 14: Fencing Match (crosslink)

Monday Mutants is a series in which I will attempt to experiment with "mutant" puzzles. These could be existing puzzle types with an unusual change in the rules, hybrids combining elements from multiple puzzle types, or puzzle types neither invented nor popularized by Nikoli.
In this Fencing Match puzzle, the loop may pass through a dot twice, but only if the loop goes straight through that dot both times, once horizontally and once vertically. The rules are otherwise unchanged.