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 (>>=) x f = match x with None -> None | Some x -> f x

let rec rm_rightest temp i = function
  | [] -> None
  | b::bs -> 
     if i = b then Some (b, List.fold_left (fun acc b -> b::acc) bs temp) 
     else rm_rightest (b::temp) (i - 1) bs

let solve bs n =
  let rec inner ans n = function
    | [] -> Some ans
    | bs ->
(*       print_string "n: "; print_endline @@ string_of_int n;
       print_string "bs: "; List.iter (fun n -> print_int n; print_string "; ") bs;
       print_endline ""; *)
       rm_rightest [] n bs >>= fun (b, bs) ->
(*       print_string "b, bs: "; print_int b; print_string " | ";
       List.iter(fun n -> print_int n; print_string "; ") bs;
       print_endline "";*)
       inner (b::ans) (n - 1) bs
  in inner [] n bs

let print_result = function
  | None -> print_int (-1)
  | Some ans -> List.iter (fun n -> print_int n; print_endline "") ans

let _ =
  let n = Scanf.scanf "%d\n" (fun n -> n) in
  let bs = ref [] in
  for i = 0 to n - 1 do
    Scanf.scanf (if i <> n - 1 then "%d " else "%d\n") (fun b -> bs := b::!bs)
  done;
  solve !bs n
  |> print_result