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 Data.List                                                                                                                                      
main :: IO ()                                                                                                                                         
main = do                                                                                                                                             
  getLine                                                                                                                                             
  bs <- map read . words <$> getLine                                                                                                                  
  putStrLn $ case solve [(bs,[])] of                                                                                                                  
    Nothing -> "-1"                                                                                                                                   
    Just x -> init $ unlines $ map show x                                                                                                             
                                                                                                                                                      
                                                                                                                                                      
solve :: [([Int],[Int])] -> Maybe [Int]                                                                                                               
solve [] = Nothing                                                                                                                                    
solve (([],ps):_) = Just ps                                                                                                                           
solve ((xs,ps):xss) =                                                                                                                                 
  let check = filter (\(x,y) -> x==y) $ zip xs [1..]                                                                                                  
  in if null check                                                                                                                                    
     then solve xss                                                                                                                                   
     else solve $ (map fst $ delete (last check) (zip xs [1..]), (:ps) . fst $ last check) : xss