Ehab and Prefix MEXs

Description:

Input:

The first line contains an integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, $$$\ldots$$$, $$$a_n$$$ ($$$0 \le a_i \le i$$$) — the elements of the array $$$a$$$. It's guaranteed that $$$a_i \le a_{i+1}$$$ for $$$1\le i < n$$$.

Output:

If there's no such array, print a single line containing $$$-1$$$.

Otherwise, print a single line containing $$$n$$$ integers $$$b_1$$$, $$$b_2$$$, $$$\ldots$$$, $$$b_n$$$ ($$$0 \le b_i \le 10^6$$$)

If there are multiple answers, print any.

Sample Input:

3
1 2 3

Sample Output:

0 1 2 

Sample Input:

4
0 0 0 2

Sample Output:

1 3 4 0 

Sample Input:

3
1 1 3

Sample Output:

0 2 1 

Note:

In the second test case, other answers like $$$[1,1,1,0]$$$, for example, are valid.