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.