Problem Statement

Given is a number sequence of length $N$: $p_1, ..., p_N$.

For each $i=1, 2, ..., N$, find the minimum non-negative integer that is not equal to any of the numbers $p_1, ..., p_i$.

Constraints

• $1 \\leq N \\leq 200,000$
• $0 \\leq p_i \\leq 200,000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $p_1$ $...$ $p_N$

Output

Print $N$ lines in total.

The $i$-th line ($1 \\leq i \\leq N$) should contain the minimum non-negative integer that is not equal to any of the numbers $p_1, ..., p_i$.

Sample Input 1

4
1 1 0 2

Sample Output 1

0
0
2
3

• The minimum non-negative integer that is not equal to $p_1=1$ is $0$.
• The minimum non-negative integer that is not equal to any of $p_1=1, p_2=1$ is $0$.
• The minimum non-negative integer that is not equal to any of $p_1=1, p_2=1, p_3=0$ is $2$.
• The minimum non-negative integer that is not equal to any of $p_1=1, p_2=1, p_3=0, p_4=2$ is $3$.

Sample Input 2

10
5 4 3 2 1 0 7 7 6 6

Sample Output 2

0
0
0
0
0
6
6
6
8
8