Problem:
Score : 400 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

You are given a permutation p of the set {1, 2, ..., N}. Please construct two sequences of positive integers a_1, a_2, ..., a_N and b_1, b_2, ..., b_N satisfying the following conditions:

1 \leq a_i, b_i \leq 10^9 for all i

a_1 < a_2 < ... < a_N

b_1 > b_2 > ... > b_N

a_{p_1}+b_{p_1} < a_{p_2}+b_{p_2} < ... < a_{p_N}+b_{p_N}

Constraints

2 \leq N \leq 20,000

p is a permutation of the set {1, 2, ..., N}

Input

The input is given from Standard Input in the following format:

N
p_1 p_2 ... p_N

Output

The output consists of two lines. The first line contains a_1, a_2, ..., a_N seperated by a space. The second line contains b_1, b_2, ..., b_N seperated by a space.

It can be shown that there always exists a solution for any input satisfying the constraints.

Sample Input 1

2
1 2

Sample Output 1

1 4
5 4

a_1 + b_1 = 6 and a_2 + b_2 = 8. So this output satisfies all conditions.

Sample Input 2

3
3 2 1

Sample Output 2

1 2 3
5 3 1

Sample Input 3

3
2 3 1

Sample Output 3

5 10 100
100 10 1

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

{-# LANGUAGE BangPatterns #-}
import Control.Arrow
import Control.Monad
import Control.Monad.Fix
import Data.Int
import Data.Foldable
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.ByteString.Char8 as B
import Data.ByteString.Internal (accursedUnutterablePerformIO)
import Debug.Trace

solve :: Int -> VU.Vector Int -> (VU.Vector Int, VU.Vector Int)
solve !n !pn = accursedUnutterablePerformIO $ do
  an <- VU.thaw $ VU.fromList [1 .. n]
  bn <- VU.thaw $ VU.reverse $ VU.fromList [1 .. n]

  _  <- VU.foldM'
    (\(!pj) (!pi) -> case () of
      () | pj == -1 -> return pi
      () | pj < pi  -> do
        d <- liftM3 (\x y z -> x - y + z)
                    (VUM.read bn pj)
                    (VUM.read bn pi)
                    (VUM.read an pj)
        VUM.write an pi (d + 1)

        return pi
      () | pj > pi -> do
        d <- liftM3 (\x y z -> x - y + z)
                    (VUM.read an pj)
                    (VUM.read an pi)
                    (VUM.read bn pj)
        VUM.write bn pi (d + 1)

        return pi
    )
    (-1)
    (VU.map (\n -> n - 1) pn)

  (,) <$> VU.freeze an <*> VU.freeze bn

main = do
  let readInt :: Integral a => B.ByteString -> Maybe (a, B.ByteString)
      readInt = fmap (first fromIntegral . second B.tail) . B.readInt

  n  <- (\vec -> (vec VU.! 0)) . VU.unfoldrN 1 readInt <$> B.getLine
  pn <- VU.unfoldrN n readInt <$> B.getLine
  let (an, bn) = solve n pn
  VU.forM_ an $ \i -> do
    putStr $ show i
    putStr " "
  putStrLn ""

  VU.forM_ bn $ \i -> do
    putStr $ show i
    putStr " "
  putStrLn ""