A13520. Ehab and Prefix MEXs

Given an array $a$ of length $n$ , find another array, $b$ , of length $n$ such that:

- for each $i$ $(1 \le i \le n)$ $MEX(\{b_1$ , $b_2$ , $\ldots$ , $b_i\})=a_i$ .

The $MEX$ of a set of integers is the smallest non-negative integer that doesn't belong to this set.

If such array doesn't exist, determine this.

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 $1\le i < n$ .

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.

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