You are given a 9x9 grid of numbers such that:
a. each row,
b. column,
and
c. each of the nine 3x3 grids
has each number 1 through 9 exactly once.
Lets call it Sudoku puzzle's solution or SPS.
A grid with condition c. removed is called a Latin Square, LS.

1. (d2) how many 9x9 LS's are there?
2. (d4) And how many 9x9 SPS's ?