Special Pythagorean triplet

A Pythagorean triplet is a set of three natural numbers, a < b < c, for
which,
a2 + b2 = c2

For example, 32 + 42 = 9 + 16 = 25 = 52.

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.