35. (5 points)
Forty thieves want to hide some identical gold coins in a $4 \times 4$ maze, with the following requirements:
(1) Each maze cell can contain at most 1 gold coin;
(2) Each row and each column must contain at least one gold coin;
(3) The number of gold coins in each row must be different, and the number of gold coins in each column must also be different.
The number of different ways to place the coins is $\qquad$.
$576$