Special Pythagorean triplet

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 $abc$.