import Data.List (permutations, nub)
 
-- Parte 1, Solução 1, corrigida
somaPerm :: (Integral a, Read a, Show a) => a -> a
somaPerm = sum . map read . nub . permutations . show
 
-- Parte 1, Solução 2, corrigida
somaPerm2 n = fact ((ndig n) - diff n) * (sum . digs $ n) * (ones $ length $ show n)
  where
    diff n = (ndig n) - (length $ nub . show $ n) + 1
    ndig n = length $ show n
 
    fact n = product [1..n]
 
    digs 0 = []
    digs n = (n `mod` 10) : digs (n `div` 10)
 
    ones n = (1+) . sum . map (10^) $ [1..n-1]
 
-- Parte 2
capicua n = (show n) == (reverse $ show n)
soma1000cap = nub $ filter capicua $ map somaPerm [10..1000]
capicuas = let cap x = capicua $ somaPerm x in nub $ filter cap [10..1000]
 
main :: IO()
main = do
  n <- (readLn :: IO Int)
  putStrLn $ "Metodo 1: " ++ (show $ somaPerm n)
  putStrLn $ "Metodo 2: " ++ (show $ somaPerm2 n)
  putStrLn $ "10 a 1000, quais dao capicuas: " ++ show capicuas
  putStrLn $ "Capicuas distintas, de 10 a 1000: " ++ show soma1000cap

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