{--
If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.

        Not all numbers produce palindromes so quickly. For example,

        349 + 943 = 1292,
        1292 + 2921 = 4213
        4213 + 3124 = 7337

        That is, 349 took three iterations to arrive at a palindrome.

        Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).

        Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
        How many Lychrel numbers are there below ten-thousand?

        NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.

--}
import Data.List

digits = reverse . map (`mod` 10) . takeWhile (> 0) . iterate (`div` 10)

(*|) a b = a * 10 + b
undigits xs = foldl' (*|) 0 xs

is_palindrome a = x == (reverse x)
        where x = digits a

-- do the lychrel process
lychrel num = num + b
        where b = undigits $ reverse $ digits num

-- tail is to avoid testing num itself (it could be palindromic)
is_lychrel num = null $ dropWhile (not . is_palindrome) $ take 49 $ tail $ iterate lychrel num

main = print $ length $ filter is_lychrel [1..9999]
