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)

{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE RankNTypes #-}
import qualified Data.ByteString.Lazy.Char8 as B
import Data.Maybe
-- import Data.List
import qualified Data.Vector.Unboxed as VU
-- import qualified Data.Vector.Unboxed.Mutable as VUM
-- import Control.Monad
-- import Control.Monad.ST
-- import Debug.Trace
-- trace _ = id

solve :: Int -> [Int] -> [Int]
solve n bs = case stage [] n vec of
               Nothing -> [-1]
               Just acc -> acc
  where
  vec = VU.fromListN (n+1) (0:bs)
  

  stage acc 0 v = Just acc
  stage acc k v | null ls = Nothing
                | otherwise = stage (k0:acc) (k-1) vNext
    where
    ls = [i | i <- [1..k], v VU.! i == i]
    k0 = maximum ls
    vNext = (VU.slice 0 k0 v) VU.++ (VU.slice (k0+1) (k-k0) v)

readBInt :: B.ByteString -> Int
readBInt = fst . fromJust . B.readInt

tmain :: B.ByteString -> [Int]
tmain cont =
  let remLines0 = map B.words (B.lines cont)
      [bs_n]:remLines1 = remLines0
      n = readBInt bs_n
      line2:remLines2 = remLines1
      bs = map readBInt line2
  in solve n bs

outAnswer :: [Int] -> IO ()
outAnswer xs = putStr $ unlines $ map show xs

main :: IO ()
main = outAnswer . tmain =<< B.getContents