Normal sudoku rules apply. Draw a single path through the centres of cells. The path may not branch, cross itself, or visit any cell more than once. Segments of the path alternate between diagonal segments, joining two cells that touch at a corner, and vertical segments, joining two vertically adjacent cells. Any four consecutive cells along the path contain digits with four different remainders when divided by 4. Every square lies on the path; every circle lies off the path. If a square contains digit N, then digit N occurs exactly N times on the path. If a circle contains digit N, then digit N occurs exactly N times in cells not on the path.