The Earliest and Latest Rounds Where Players Compete

Given n players paired each round as i-th from front vs i-th from end (with a middle bye if odd) and winners reseeded by original indices, compute the earliest and latest round two designated players—who always beat others—can meet assuming you can choose outcomes of all other matches. The core challenge is exploring possible match-outcome choices under symmetric pairings and reseeding to minimize or maximize the meeting round (typically solved by state search/DP).