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:

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