A standard 9x9 Sudoku grid is entirely empty except for two numbers in the bottom row. The bottom row looks like: 1, blank, 2, blank, blank, blank, blank, blank, blank.

The standard Sudoku rules apply: Each row and column must contain all the digits 1 to 9 and the smaller 3x3 blocks must also contain all the digits 1 to 9.

Two additional rules apply: Each of the positive diagonals must contain no repeating digits, and the adjacent digits along each positive diagonal must have a difference of 4 or more.

Note: the positive (sloped) diagonals are diagonals that run from southwest to northeast. To obey the difference rule, for example, the major positive diagonal can begin: 1, 5, 9, 3, ... but not 1, 6, 9, 3, ... because the difference between 9 and 6 is less than 4.

Find the unique solution for the full grid.