CF1364C.Ehab and Prefix MEXs

普及/提高-

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题目描述

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.

输入格式

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 $1\le i < n$ .

输出格式

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.

输入输出样例

输入#1
```
3
1 2 3
```
输出#1
```
0 1 2
```
输入#2
```
4
0 0 0 2
```
输出#2
```
1 3 4 0
```
输入#3
```
3
1 1 3
```
输出#3
```
0 2 1
```

说明/提示

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

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