Near Sizedoku

In this puzzle, clues in the form of arrows are sometimes placed between adjacent cells in the same cage.  Arrows always point from the larger number to the smaller number.  The main rule is that arrows are placed if, and only if, the numbers in those cells are either one or two apart.  For example a cell with a 6 must have an arrow pointing to adjacent cells that contain a 3,4 or 5, but would not have an arrow pointing to a cell containing a 1 or 2.  Since arrows are placed when numbers are close to each other in size, we call this puzzle a Near Sizedoku.  A filled in sample cage might look something like this:

To be a bit more specific, this is actually what I'd call a "Near Three" Sizedoku, in the sense that arrows are placed exactly when the distance is three or less.  Some interesting things happen when we switch from three to certain other numbers, but we'll leave those puzzles for another time.  

I'm including both an easier and harder version of this puzzle.  The arrow clues are the same in both, the only difference being whether some cells are revealed at the start.  The harder version isn't much more difficult if you spot the right place to start filling in.  There is a hint below next to the solution and higher quality PDF versions.

Since this is one of the puzzle types featured in my book, I figured I'd put a link to both the Amazon and AMS pages for people visiting for the first time.  For this blog post, I shrunk the arrows and colored them based on the basic direction they were facing, just for fun.  

High quality printable PDF (Easier Version)

High quality printable PDF (Harder Version)

Solution

Highlight this text for hint: The positions of every 1 can be determined from the arrows alone before any other cells are filled in.