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: Accepted)

import qualified Data.Foldable as F
import qualified Data.List     as L
import           Data.Monoid

main :: IO ()
main = do
    n <- readLn :: IO Int
    xs <- map read.words <$> getLine
    case solve n xs of
        Just ys -> putStr . unlines $ map show ys
        Nothing -> print (-1)

solve :: Int -> [Int] -> Maybe [Int]
solve n xs = go [] xs
  where
    eq :: Int -> Int -> Maybe Int
    eq x y
        | x == y = Just x
        | otherwise = Nothing

    go acc [] = Just acc
    go acc xs = do
        x <- getLast . F.foldMap Last $ zipWith eq [1..] xs
        go (x:acc) $ L.delete x xs