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: Accepted)

import Data.List
main :: IO ()
main = do
    n:p <- input <$> getContents
    let (a,b) = answer $ map snd $ sortOn fst $ zip p [1..]
    putStrLn $ showans a
    putStrLn $ showans b

input :: String -> [Int]
input = fmap read . words

answer :: [Int] -> ([Int],[Int])
answer p = let a = tail $ reverse $ foldl (\acc n -> ( (n + head acc):acc )) [0] p
               b = map (\n -> last a - n) $ take (length p) (0:a)
           in (a,b)

showans :: [Int] -> String
showans [] = ""
showans (x:xs) = (show x) ++ " " ++ (showans xs)