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Statement

 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
Example
Input
5
0 -1 1 2 4
Output
0 1 2
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