The grid is covered in fog that hides cells underneath it. Placing correct digits will reveal surrounding cells. Construct nine non-overlapping 3x3 regions in the grid containing digits 1-9 once each. The rest of the grid must be left empty. Digits must not repeat along any row or column. Digits on a grey thermometer must strictly increase from the bulb-end. The sum of digits along a diagonal indicated by a clue outside the grid must satisfy either the given inequality or the corresponding relationship with other such clues.