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 (4.10.0) (judge verdict: Accepted)

Scanf.scanf "%d" (fun n ->
    let b = Array.init n (fun _ -> Scanf.scanf " %d" (fun b -> b)) in
    let search b =
        let k = Array.length b in
        let rec loop i =
            if i < 0 then None else
                if b.(i) = i + 1 then Some i else loop (i - 1)
        in
        loop (k - 1)
    in
    let remove b x =
        let k = Array.length b in
        let b2 = Array.make (k - 1) 0 in
        let rec loop i j =
            if i = k then b2 else 
                if i = x then loop (i + 1) j else (
                    b2.(j) <- b.(i);
                    loop (i + 1) (j + 1)
                )
        in
        loop 0 0
    in
    let rec loop b i history =
        if i = 0 then history else
            match search b with
            | Some x -> loop (remove b x) (i - 1) ((x + 1) :: history)
            | None -> []
    in
    let k = loop b n [] in
    if k = [] then print_endline "-1" else
        List.iter (Printf.printf "%d\n") k
)