-- If p is the perimeter of a right angle triangle with integral length sides,
-- {a,b,c}, there are exactly three solutions for p = 120.
--
--   {20,48,52}, {24,45,51}, {30,40,50}
--
-- For which value of p ≤ 1000, is the number of solutions maximised?

import Euler

solutions :: Int -> [(Int, Int, Int)]
solutions p = do
   a <- [1 .. p `div` 2]
   b <- [a .. p - 2 * a]
   let c = p - (a + b)
   guard $ a^2 + b^2 == c^2
   return (a, b, c)

main = print $ maximumBy (compare `on` snd) $ map (id &&& length . solutions) [3..1000]