We are given a partially filled nxn board. We are also given subgrids of the input board and the expected product of numbers in each subgrid of the solved board. 
- Empty cells need to be filled with numbers from 1-n
- Numbers already on the board in the input can't be removed/replaced from the board
- Each number can appear at most once in any row or column
- The numbers should be placed such that for each subgrid specified in the input, the numbers in the solved board must multiply to the intended product of that subgrid as specified in the input