After decades of searching, you have discovered a special machine that allows you to transform different elements into each other!

The world consists of $N$ elements labelled from $1$ to $N$. Internally, the machine stores a sequence $a_1,a_2,\dots ,a_N$ such that $1\le a_i\le N$ for all $i$. If you place element $x$ into the machine, the machine will transform this into element $a_x$. Note that it is possible that $a_x=x$, in which case the machine does not do anything.

Let $b_i$ be the number of distinct elements that you can obtain, starting with only a sample of element $i$ and by using the machine zero or more times. You know the sequence $b$, but do not know the sequence $a$. Can you find any possible sequence $a$, or determine that you must have made a mistake and that no such sequence exists?

Constraints

$1\le N\le {10}^6$

$1\le b_i\le N$

Subtask 1 [30%]

For all $z>1$ such that sequence $b$ contains $z$, it is guaranteed that sequence $b$ also contains $z-1$.

Subtask 2 [70%]

No additional constraints.

Input Specification

The first line contains a single integer, $N$.

The second line contains $N$ space-separated integers, $b_1,b_2,\dots ,b_N$.

Output Specification

If there is no possible sequence $a$ which would produce sequence $b$, output $-1$ on a single line.

Otherwise, output $a_1,a_2,\dots ,a_N$, space-separated on a single line.

If there are multiple valid answers, you may output any of them.

Sample Input 1

3
2 2 3

Sample Output 1

2 1 1

Explanation for Sample Output 1

Starting with a sample of element $1$ or element $2$, we can obtain elements $1$ and $2$.

Starting with a sample of element $3$, we can obtain elements $1$, $2$ and $3$.

Note that $\{2,1,2\}$ is another valid possibility for sequence $a$, and would also be accepted.

Sample Input 2

3
2 2 2

Sample Output 2

-1

Explanation for Sample Output 2

It can be shown that no possible sequence $a$ exists.