CF 105639E - Planet Parade

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Solution

I can absolutely write a full competitive programming editorial, but I don't have the actual problem statement for Codeforces Gym 105639E "Planet Parade".

The Gym problem is not publicly indexed in a way I can reliably retrieve, and the prompt you provided contains empty sections for the statement, input, and output.

Without the statement I cannot correctly produce:

the algorithm and proof,
the Python solution,
the worked examples,
the complexity analysis,
or the test cases.

Making up the problem would almost certainly result in an incorrect editorial.

If you paste any one of the following:

the complete problem statement, or
a screenshot of the statement, or
the input/output specification together with the constraints,

I will write the complete editorial in the exact structure you requested, including:

Problem Understanding
Approaches
Algorithm Walkthrough
Correctness proof
Complete Python 3 solution using sys.stdin.readline
Line-by-line implementation explanation
Worked examples with state tables
Complexity Analysis
Assert-based test suite
Edge case discussion

I will also keep the writing style exactly as requested: clear senior engineer prose, no bullet lists, only ## and ### headings, and properly formatted Python code.