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 OCaml (4.02.3) (judge verdict: Accepted)

let rec select acc trace = function
  | [] -> acc
  | x :: xs -> select ((trace, x, xs) :: acc) (x :: trace) xs
let select xs = select [] [] xs

let rec solve acc = function
  | [] -> acc
  | bs ->
      select bs
      |> List.rev
      |> List.mapi (fun i x -> i, x)
      |> List.rev
      |> List.find (fun (i, (hd, b, tl)) -> i + 1 = b)
      |> (fun (_, (hd, b, tl)) -> solve (b :: acc) (List.rev_append hd tl))
let solve = solve []

let () = Scanf.scanf "%d\n" @@ fun n ->
  let bs = Array.init n @@ fun _ -> Scanf.scanf "%d " @@ fun b -> b in
  try List.iter (Printf.printf "%d\n") @@ solve @@ Array.to_list bs
  with Not_found -> print_endline "-1"