Problem:
Score : 400 points

Problem Statement

Snuke has an empty sequence a.

He will perform N operations on this sequence.

In the i-th operation, he chooses an integer j satisfying 1 \leq j \leq i, and insert j at position j in a (the beginning is position 1).

You are given a sequence b of length N. Determine if it is possible that a is equal to b after N operations. If it is, show one possible sequence of operations that achieves it.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq b_i \leq N

Input

Input is given from Standard Input in the following format:

N
b_1 \dots b_N

Output

If there is no sequence of N operations after which a would be equal to b, print -1.
If there is, print N lines. In the i-th line, the integer chosen in the i-th operation should be printed. If there are multiple solutions, any of them is accepted.

Sample Input 1

3
1 2 1

Sample Output 1

1
1
2

In this sequence of operations, the sequence a changes as follows:

After the first operation: (1)

After the second operation: (1,1)

After the third operation: (1,2,1)

Sample Input 2

2
2 2

Sample Output 2

-1

2 cannot be inserted at the beginning of the sequence, so this is impossible.

Sample Input 3

9
1 1 1 2 2 1 2 3 2

Sample Output 3

1
2
2
3
1
2
2
1
1

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

{-# LANGUAGE BangPatterns #-}

import           Control.Monad
import           Control.Monad.Trans.State
import qualified Data.ByteString.Unsafe    as B
import qualified Data.ByteString.Char8     as C8
import           Data.Bits
import           Data.Char
import           Data.List
import           Data.Maybe

type Input  = ([Int], [Int])
type Acc    = ([Int], [Int])
type Output = [([Int], [Int])]

main :: IO ()
main = do
  [n] <- readInts
  bs <- readInts
  mapM_ print $ reverse $ solve2 n bs $ solve ([1..], bs) ([],[])
  -- print $ solve ([1..], bs) ([],[])

solve :: Input -> Acc -> Output
solve (_, []) acc = [acc]
solve (i:is, x:xs) (js,acc) = concatMap (solve bs) [(j:js, insert' j acc) | j <- [1..i]]
  where bs = (is, xs)

insert' :: Int -> [Int] -> [Int]
insert' j xs = as ++ [j] ++ bs
  where
    (as, bs) = splitAt (j-1) xs

solve2 :: Int -> [Int] -> Output -> [Int]
solve2 _ _ [] = [-1]
solve2 n bs ((js,as):rest)
  | bs == as  = js
  | otherwise = solve2 n bs rest

-- utils
type Pair = (Int, Int)

readInts :: IO [Int]
readInts = map (fst . fromJust . C8.readInt) . C8.words <$> C8.getLine

readPair :: IO Pair
readPair = head . unfoldr readT <$> C8.getLine
  where
    readT = runStateT $
      (,) <$> StateT (C8.readInt . C8.dropWhile isSpace)
          <*> StateT (C8.readInt . B.unsafeTail)