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.

3
1 2 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: $(1,2,1)$

2
2 2

-1

$2$ cannot be inserted at the beginning of the sequence, so this is impossible.

9
1 1 1 2 2 1 2 3 2

1
2
2
3
1
2
2
1
1