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 = 9 + 16 = 25 = 5^2.

There exists exactly one Pythagorean triplet for which a + b + c = 1000.

Find the product a*b*c.

(This problem and its text come from Project Euler).