Fill each cell in the grid above – even the ones with grey numbers – with a digit between 1 and 9 so that each row, column, and outlined 3-by-3 region contains each digit once.

Each grey number shown below is equal to the product of 2 of the orthogonally adjacent cells in the completed grid.

The answer to this puzzle is the sum of the squares of the numbers that are written over the gray numbers in the completed grid.