{-# LANGUAGE BangPatterns #-}
 
import Data.Bits (xor)
import Data.List (sort)
 
mex :: [Int] -> Int
mex = mexSorted 0 . sort
 
mexSorted :: Int -> [Int] -> Int
mexSorted !i xs@(x : xs') | x < i = mexSorted i xs'
mexSorted i xs@(x : xs') | x == i = mexSorted (i + 1) xs'
mexSorted i _ = i
 
-- |@nimValues !! n@ is the nim-value (aka Sprague-Grundy number) of the game described in
-- http://c...content-available-to-author-only...e.com/questions/16228 on the path with n vertices.
 
nimValues :: [Int]
nimValues = 0 : 1 : map f [0 ..]
  where
    f s = mex $ zipWith xor (take (s `div` 2 + 1) nimValues) (reverse (take (s + 1) nimValues))
 
-- |Report the values of n (≤ 100) such that the first player loses in the game
-- on the path with n vertices (including 0, meaning the empty graph).
 
main :: IO ()
main = print $ map fst $ filter (\(_, nim) -> nim == 0) $ zip [0 :: Int .. 100] nimValues

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