Klein Bottle Sudoku

Rules:

-Ordinary sudoku rules DO NOT apply. Please read carefully.

-This puzzle takes place on a klein bottle. The top and bottom of the grid are glued together–they obey periodic boundary conditions. The left and right side are twisted and then glued together. The little klein bottles denote the separation of two horizontal 9 square “klein rows.” Each column and box behave normally. Every column, box, and klein row must contain the digits 1-9 exactly once. You may notice that the 1’s in the puzzle are in the same “ordinary row” but they are separated by a klein bottle and are therefore in different klein rows.

try it here