Here is a screenshot of a semi-answer which froze my computer when I hit 'post':

![alt text][1x] [<sup>(Source: Wayback Machine)</sup>][1]

  [1]: https://web.archive.org/web/20141117081358im_/http://www2.bc.edu/~hansendd/satotate.png
  [1x]: https://i.sstatic.net/E1KA8.png