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)

main = do
  n <- readLn
  bs <- map read.words<$>getLine
  putStr.unlines.map show $ solve n bs

solve n bs
  | head ans == -1 = [-1]
  | otherwise = ans
  where
  ans = reverse.go n.reverse$bs
  go _ [] = []
  go n bs
    | del == -1 = [-1]
    | otherwise = del : go (n-1) remaining
    where
    del = find n bs
    remaining = take (n-del) bs ++ drop (n-del+1) bs
    find _ [] = -1
    find i (b:bs)
      | i == b = i
      | otherwise = find (i-1) bs