HMMT November 2015 H9

Consider a $9 \times 9$ grid of squares. Haruki fills each square in this grid with an integer between 1 and 9 , inclusive. The grid is called a super-sudoku if each of the following three conditions hold:

• Each column in the grid contains each of the numbers $1,2,3,4,5,6,7,8,9$ exactly once.
• Each row in the grid contains each of the numbers $1,2,3,4,5,6,7,8,9$ exactly once.
• Each $3 \times 3$ subsquare in the grid contains each of the numbers $1,2,3,4,5,6,7,8,9$ exactly once.

How many possible super-sudoku grids are there?