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.