## Goal

Given a list of `N` random integers `Ik`, you must return the maximum-length incrementing sequence contained in this list (for each `Ik` in the sequence, `Ik`=`I(k-1)`+1). The incrementing sequence must be ordered, but need not be adjacent in the given sequence.

In case of multiple maximum-length sequences, return the one with the lowest starting integer.
Input

**Line 1:** a single integer `N`.

**Line 2:** a list of `N` integers `Ik` separated by space.

Output

**Line 1:** a list of integers separated by space.

Constraints

-10^7 <= `Ik` <= 10^7

0 < `N` < 1500