-- 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.

main = print $ head [ a*b*c | a <- [1..1000]
                    , b <- [a+1..1000-a]
                    , let c = 1000 - (a + b)
                    , a^2 + b^2 == c^2
                    ]