{-# OPTIONS_GHC -Wall #-}
 
 
toDigits :: Integer -> [Integer]
toDigits  a
 | a<=0 =[]
 |otherwise  = reverse(toDigitsRev(a))


toDigitsRev :: Integer -> [Integer]
toDigitsRev  a
 | a<=0 =[]
 | otherwise  = mod a 10 : toDigitsRev (div a 10)


intListLength :: [Integer] -> Integer
intListLength []     = 0
intListLength (x:xs) = 1 + intListLength xs

doubleEveryOther :: [Integer] -> [Integer]
doubleEveryOther [] = []
doubleEveryOther [a] = [a]
doubleEveryOther (a:b:fin)
 | (intListLength (a:b:fin) `mod` 2 <= 0 )= a*2:b:doubleEveryOther fin
 | otherwise = a: b*2 :doubleEveryOther fin

sumDigits :: [Integer] -> Integer
sumDigits [] = 0
sumDigits (a:as) = sum(toDigits a) + sumDigits as

validate :: Integer -> Bool
validate a = (mod (sumDigits(doubleEveryOther(toDigits a))) 10 <= 0)