Beyond Erdos conjecture

Brocard's Problem:

n! + 1 = m^2

Erdos conjectured that (5,4),(11,5),(71,7) are the only 3 pairs.

Now, I ask : how many solutions to

n! = x^2 + y^2

are there?

0!, 1!, 2! and 6! can be written as sum of two perfect squares. Any others?