Problem:
Doubly Linked List

Your task is to implement a double linked list.

Write a program which performs the following operations:

insert x: insert an element with key x into the front of the list.

delete x: delete the first element which has the key of x from the list. If there is not such element, you need not do anything.

deleteFirst: delete the first element from the list.

deleteLast: delete the last element from the list.

Input

The input is given in the following format:

n

command1

command2

...

commandn

In the first line, the number of operations n is given. In the following n lines, the above mentioned operations are given in the following format:

insert x

delete x

deleteFirst

deleteLast

Output

Print all the element (key) in the list after the given operations. Two consequtive keys should be separated by a single space.

Constraints

The number of operations ≤ 2,000,000

The number of delete operations ≤ 20

0 ≤ value of a key ≤ 109

The number of elements in the list does not exceed 106

For a delete, deleteFirst or deleteLast operation, there is at least one element in the list.

Sample Input 1

7
insert 5
insert 2
insert 3
insert 1
delete 3
insert 6
delete 5

Sample Output 1

6 1 2

Sample Input 2

9
insert 5
insert 2
insert 3
insert 1
delete 3
insert 6
delete 5
deleteFirst
deleteLast

Sample Output 2

1

Solution in Haskell (judge verdict: Memory Limit Exceeded)

{-# OPTIONS_GHC -O2 #-}
{-# OPTIONS_GHC -funbox-strict-fields #-}
{-# OPTIONS_GHC -fno-warn-unused-imports #-}
{-# OPTIONS_GHC -fno-warn-missing-signatures #-}
{-# OPTIONS_GHC -fno-warn-unused-binds #-}
{-# OPTIONS_GHC -fno-warn-incomplete-patterns #-}
{-# OPTIONS_GHC -fno-warn-name-shadowing #-}
{-# LANGUAGE OverloadedStrings #-}
-- {-# LANGUAGE MultiWayIf #-}
{-# LANGUAGE BangPatterns #-}
-- {-# LANGUAGE ViewPatterns #-}
-- {-# LANGUAGE TupleSections #-}

import           System.IO hiding (char8)
import           Control.Applicative
import           Control.Monad
import           Data.List
import           Data.Tuple
import           Data.Int
import           Data.Char
import           Data.Function (on)
import           Data.Ord (comparing)
import           Data.Monoid (mappend)
import           Data.Array
-- import           Data.Array.Unboxed
-- import           Data.Array.IArray
-- import           Data.Array.ST
-- import           Data.Array.MArray
-- import           Data.Array.Unsafe
import           Data.Ix
import           Data.Maybe
-- import           Data.Monoid hiding ((<>))
import qualified Data.ByteString.Char8 as BS
import qualified Data.ByteString.Lazy.Char8 as BL
import           Data.ByteString.Builder
-- import           Data.Graph
-- import           Data.Vector.Unboxed ((//), (++), (!), (!?))
-- import qualified Data.Vector.Unboxed as U
-- import           Data.IntSet (IntSet)
-- import qualified Data.IntSet as IntSet
-- import           Data.IntMap.Strict (IntMap)
-- import qualified Data.IntMap.Strict as IntMap
-- import           Data.Sequence ((|>), (<|), (><),ViewR(..), ViewL(..), Seq)
-- import qualified Data.Sequence              as Seq
-- import           Data.Foldable (toList, minimumBy)
import           Debug.Trace

data Deque = Q ![Int] !Int ![Int] !Int deriving (Show)

emptyQ :: Deque
emptyQ = Q [] 0 [] 0

viewQ :: Deque -> [Int]
viewQ (Q xs _ ys _) = xs ++ reverse ys

insertQ :: Int -> Deque -> Deque
insertQ a (Q x lx y ly) = chk $! Q (a:x) (lx + 1) y ly

deleteQ :: Int -> Deque -> Deque
deleteQ a (Q x lx y ly)
  | a `elem` x = chk $! Q (delete a x) (lx - 1) y ly
  | a `elem` y = chk $! Q x lx (reverse $ delete a (reverse y)) (ly - 1)
  | otherwise = chk $! Q x lx y ly

deleteFirstQ :: Deque -> Deque
deleteFirstQ (Q (_:xs) lx y ly) = chk $! Q xs (lx - 1) y ly
deleteFirstQ (Q [] _ [_] _) = chk emptyQ

deleteLastQ :: Deque -> Deque
deleteLastQ (Q x lx (_:ys) ly) = chk $! Q x lx ys (ly - 1)

chk :: Deque -> Deque
chk (Q [] 0 [] 0) = Q [] 0 [] 0
chk (Q [x] 1 [] 0) = Q [] 0 [x] 1
chk (Q x lx y ly)
  | lx > c * ly + 1 = Q x' i y' j
  | ly > c * lx + 1 = Q x'' i y'' j
  | otherwise = Q x lx y ly
  where
    c = 3 -- constant value > 1
    i = (lx + ly) `div` 2
    j = lx + ly - i
    x' = take i x
    y' = y ++ reverse (drop i x)
    x'' = x ++ reverse (drop i y)
    y'' = take i y

main = do
  n <- readInt1 <$> BS.getLine
  qs <- map BS.words <$> replicateM n BS.getLine
  putIntN $ solve qs

solve = viewQ . foldl' f emptyQ where
  f' q query = traceShowId $ f q query
  f !q (x:xs)
    | x == "insert" = insertQ (readInt1 $ head xs) q
    | x == "delete" = deleteQ (readInt1 $ head xs) q
    | x == "deleteFirst" = deleteFirstQ q
    | x == "deleteLast" = deleteLastQ q


readInt321 :: BS.ByteString -> Int32
readInt321 = fromIntegral . fst . fromJust . BS.readInteger

-- putInt32N :: [Int32] -> IO ()
-- putInt32N [] = return ()
-- putInt32N xs = BL.putStrLn . toLazyByteString . foldl1 mappend . intersperse (char8 ' ') $ map int32Dec xs
putIntN :: [Int] -> IO ()
putIntN = putStrLn . unwords . map show


--  --  --  --  --  --  --  --  --  --  --  --  --  --  --  --  --  --  --  --

format :: Show a => Maybe a -> IO ()
format Nothing = putStrLn "NO"
format (Just a) = putStrLn "YES" >> print a

-- [1,2,3] -> 1 2 3
-- putIntN :: [Int] -> IO ()
-- putIntN [] = return ()
-- putIntN xs = BL.putStrLn . toLazyByteString . foldl1 mappend . intersperse (char8 ' ') $ map intDec xs

readInt1 :: BS.ByteString -> Int
readInt1 = fst . fromJust . BS.readInt

readInt2 :: BS.ByteString -> (Int,Int)
readInt2 = toTuple . readIntN

readInt3 :: BS.ByteString -> (Int,Int,Int)
readInt3 = toTriple . readIntN

readIntN :: BS.ByteString -> [Int]
readIntN =  map readInt1 . BS.words

readInt641 :: BS.ByteString -> Int64
readInt641 = fromIntegral . fst . fromJust . BS.readInteger

readInt642 :: BS.ByteString -> (Int64,Int64)
readInt642 = toTuple . readInt64N

readInt643 :: BS.ByteString -> (Int64,Int64,Int64)
readInt643 = toTriple . readInt64N

readInt64N :: BS.ByteString -> [Int64]
readInt64N =  map readInt641 . BS.words

readInteger1 :: BS.ByteString -> Integer
readInteger1 = fst . fromJust . BS.readInteger

readInteger2 :: BS.ByteString -> (Integer,Integer)
readInteger2 = toTuple . readIntegerN

readInteger3 :: BS.ByteString -> (Integer,Integer,Integer)
readInteger3 = toTriple . readIntegerN

readIntegerN :: BS.ByteString -> [Integer]
readIntegerN =  map readInteger1 . BS.words

toTuple :: [a] -> (a, a)
toTuple [x, y] = (x, y)

toTriple :: [a] -> (a, a, a)
toTriple [x, y, z] =(x, y, z)

fromTuple :: (a, a) -> [a]
fromTuple (x, y) = [x, y]

fromTriple :: (a, a, a) -> [a]
fromTriple (x, y, z) = [x, y, z]

-- if not applying, use "const"

applyTuple :: (a -> a') -> (b -> b') -> (a, b) -> (a', b')
applyTuple f g (x, y) = (f x, g y)

applyTriple :: (a -> a') -> (b -> b') -> (c -> c') -> (a, b, c) -> (a', b', c')
applyTriple f g h (x, y, z) = (f x, g y, h z)

-- @since 4.8.0.0
sortOn' :: Ord b => (a -> b) -> [a] -> [a]
sortOn' f =
  map snd . sortBy (comparing fst) . map (\x -> let y = f x in y `seq` (y, x))