You are given an integer array of length $N$. You have to find $MEX$ of $i^{th}$ element for all $1 \leq i \leq N$.

$MEX$ of the $i^{th}$ element is the minimum element greater than or equal to $0$ which is not present in array till the $i^{th}$ index.

Input Format:

First line contains an integer $N$ denoting the size of array.

Next line contains $N$ integers denoting the elements of the array.

Output Format:

Print $N$ integers. $i^{th}$ element should be the $MEX$ of the array prefix till $i$

Constraints:

$1 \leq N \leq 2*10^5 \\ 0 \leq arr[i] \leq 2*10^5$