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)

(* O(n^2) *)
let n = Scanf.scanf " %d" @@ (+) 0
let bs = Array.init n @@ fun _ -> Scanf.scanf " %d" @@ (+) 0
let search_backi a f =
  let i = ref @@ Array.length a - 1 in
  let found = ref false in
  while not !found && !i >= 0 do if f !i a.(!i) then found := true; decr i done;
  !i + if !found then 1 else 0
let remove a i =
  let a' = Array.make (Array.length a - 1) a.(0) in
  Array.iteri (fun j x -> if j < i then a'.(j) <- x else if j > i then a'.(j - 1) <- x) a;
  a'
let rec f acc a n =
  if n = 0 then acc
  else
    let i = search_backi a (fun i x -> i + 1 = x) in
    if i = -1 then (print_endline "-1"; exit 0)
    else f (a.(i) :: acc) (remove a i) @@ n - 1
let ans = f [] bs n
let _ = ans |> List.iter @@ Printf.printf "%d\n"