{-
The sum of the squares of the first ten natural numbers is,
  1^2 + 2^2 + ... + 10^2 = 385

The square of the sum of the first ten natural numbers is,
  (1 + 2 + ... + 10)^2 = 55^2 = 3025

Hence the difference between the sum of the squares
  of the first ten natural numbers and the square
  of the sum is 3025 - 385 = 2640

Find the difference between the sum of the squares
  of the first one hundred natural numbers
  and the square of the sum.
-}
upperRange :: Integer
upperRange = 1_000_000

square :: Num a => a -> a
square n = n^2

squares :: [Integer]
squares = map square [1..upperRange]

sum' :: [Integer] -> Integer
sum' = go 0
  where
    go acc []     = acc
    go acc (x:xs) = go (acc+x) xs

sumOfSquares :: Integer
sumOfSquares = sum squares

squareOfTheSum :: Integer
squareOfTheSum = sum [1..upperRange] ^2

solution :: Integer
solution = squareOfTheSum - sumOfSquares

main :: IO ()
main = print solution