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The calculator performs the participant placement with two following conditions: 1) Each participant must start from each starting position. 2) Each participant must encounter every other participant.
Note: The result may not be optimal because "greedy algorithm" is used. In general, optimal results in such problems is computationally difficult because we are dealing with combinatorics and the tasks of a similar type, such as "schoolgirls problem" or "social golfers problem" are NP-complete. By the way, for some special cases, the solutions are known and published.