Problem:
Score : 400 points

Problem Statement

In this problem, we only consider strings consisting of lowercase English letters.

Strings s and t are said to be isomorphic when the following conditions are satisfied:

|s| = |t| holds.

For every pair i, j, one of the following holds:

s_i = s_j and t_i = t_j.

s_i \neq s_j and t_i \neq t_j.

For example, abcac and zyxzx are isomorphic, while abcac and ppppp are not.

A string s is said to be in normal form when the following condition is satisfied:

For every string t that is isomorphic to s, s \leq t holds. Here \leq denotes lexicographic comparison.

For example, abcac is in normal form, but zyxzx is not since it is isomorphic to abcac, which is lexicographically smaller than zyxzx.

You are given an integer N.
Print all strings of length N that are in normal form, in lexicographically ascending order.

Constraints

1 \leq N \leq 10

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Assume that there are K strings of length N that are in normal form: w_1, \ldots, w_K in lexicographical order.
Output should be in the following format:

w_1
:
w_K

Sample Input 1

1

Sample Output 1

a

Sample Input 2

2

Sample Output 2

aa
ab

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import           Control.Monad
import           Control.Monad.ST
import qualified Data.Array                    as A
import qualified Data.Array.Unboxed            as AU
import qualified Data.Array.ST                 as ST
import qualified Data.ByteString.Char8         as BS
import           Data.Char
import           Data.Foldable                  ( toList )
import           Data.Int
import qualified Data.IntMap                   as IM
import           Data.List
import qualified Data.Map                      as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                      as S
import qualified Data.Sequence                 as SQ
import           Data.Time
import qualified Data.Vector                   as V
import qualified Data.Vector.Mutable           as VM
import qualified Data.Vector.Unboxed           as VU
import qualified Data.Vector.Unboxed.Mutable   as VUM

readInt = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine
readInts n = replicateM n readInt
readString = map BS.unpack . BS.words <$> BS.getLine
readStrings n = replicateM n readString
toPair [x, y] = (x, y)

main = do
  [n] <- readInt
  mapM_ putStrLn $ solve n

solve n = nums
 where
  nums = concatMap
    (map (map (\x -> m x ['a', 'b' .. 'z'])))
    (zipWith (\a as -> take (length as `div` a) as) [1 ..] $ map (f n) [1 .. n])

f n m =
  filter (\nums -> length (group $ sort nums) == m) $ replicateM n [1 .. m]

m 1 (s : ss) = s
m n (s : ss) = m (n - 1) ss