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: Time Limit Exceeded)

let rec for_obvious s = function
  | [] -> false
  | b::bs -> if b > s then true else for_obvious (s + 1) bs

let rec dfs ans left bs s n =
  if bs = [] && left = [] then Some ans
  else if s > n then None
  else
    begin
      match bs with
      | [] -> Some ans
      | b::bs -> 
         if b > s then None
         else if b = s then 
           begin
             match dfs (b::ans)
                     [] (List.fold_left (fun acc l -> l::acc) bs left)
                     1 (n - 1) with
             | None -> dfs ans (b::left) bs (s + 1) n
             | Some ans -> Some ans
           end
         else dfs ans (b::left) bs (s + 1) n
    end

let _ =
  let n = Scanf.scanf "%d\n" (fun n -> n) in
  let bs = Array.make n 0 in
  for i = 0 to n - 1 do
    Scanf.scanf (if i <> n - 1 then "%d " else "%d\n") (fun b -> bs.(i) <- b)
  done;
  let ls = Array.to_list bs in
  if for_obvious 1 ls then print_int (-1)
  else
    dfs [] [] (Array.to_list bs) 1 n 
    |> (function | None -> print_int (-1) 
                 | Some ans -> List.iter (fun n -> print_endline @@ string_of_int n) ans)