Breaking the Loop #1

I first encountered "Breaking the Loop" in WPC15 Bulgaria. The puzzle type is invented (I believe) by Vladimir Portugalov, who is quite pleasant to meet while I was in the WPC. Initially I thought this puzzle is impossibly hard to solve, but after I've solved the WPC instance of the puzzle with the help of my officemate, I got quite interested in it and made one myself.

Instruction: Find a loop that visits all grid nodes, and locate 16 breakpoints (some of which are marked by "x" in the diagram). There are two breakpoints in each row and each column of nodes. The 16 breakpoints break the loop into 16 segments, and the midpoints of all 16 segments are shown as dots. For an example, see this page.

I have two versions of the same puzzle in here. The hard version is shown here, and I think this might be just a bit too hard. An easier version is hidden behind this link. It's the hard version with a few more breakpoints added, making it (what I believe) a more reasonable puzzle.