Fill the grid with eight non-overlapping 2x4 regions oriented horizontally (i.e. 2 rows and 4 columns), such that each region contains the digits from 1 to 8 once each and no digit repeats in any row or column. Cells outside regions don't contain digits. Draw a single one-cell-wide loop in the grid that travels orthogonally, doesn't branch, and isn't allowed to touch itself, not even diagonally, and doesn't pass through any of the empty cells. Any two adjacent cells along this loop must include one extreme digit [1,2,7,8] and one medium digit [3,4,5,6]. For each region N, the digit N must be on the loop within this region. (Regions are numbered in reading order, based on the position of their top left cell, i.e. a region with its top left cell further down in the grid than another region will have the higher region number. If two regions have their top left cell in the same row, the region on the right will have the higher region number.) Digits along marked diagonals sum to the number indicated outside the grid.