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 8.8.3) (judge verdict: Accepted)

import qualified Data.ByteString.Char8 as BS
import Data.Maybe
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

readInt = fst . fromJust . BS.readInt

readIntList = map readInt . BS.words

getInt = readInt <$> BS.getLine

getIntList = readIntList <$> BS.getLine

search v n n' = do
  p <- VUM.read v (n - 1)
  if p == 0
    then do
      if n == 1
        then return 0
        else search v (n - 1) n'
    else
      if p == n'
        then do
          VUM.write v (n - 1) 0
          return p
        else
          if n == 1
            then return 0
            else search v (n - 1) (n' - 1)

simulate v xs n n' = do
  x <- search v n n'
  if x == 0
    then print (-1)
    else do
      let xs' = x : xs
      if n' == 1
        then do
          mapM_ print xs'
        else simulate v xs' n (n' - 1)

main = do
  n <- getInt
  bs <- getIntList
  v <- VU.thaw (VU.fromList bs)
  simulate v [] n n