A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,

a^2 + b^2 = c^2

For example:

3^2 + 4^2 = 5^2
9 + 16 = 25

Therefore:

a + b + c
3 + 4 + 5
= 12

There exists exactly one Pythagorean triplet for which

a + b + c = 1000.

Find the product abc.