Count or construct all valid point sets formed from a simple geometric rule over integer coordinates.
You are given a positive integer . Consider a set of points with integer coordinates on a 2D plane. A set is called beautiful if it satisfies the geometric rule described in the task and contains exactly points.
Your job is to determine whether such a set exists, and if so, construct one valid example of a beautiful set of points.
The intended solution is based on observing the pattern of valid point placement and building the answer directly rather than searching over all possibilities.
Example 1
Input
3
Output
0 0 1 0 0 1
Explanation
This is a small illustrative construction of three integer points. The exact validity depends on the hidden geometric condition from the original problem statement.
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