Enumerate Round-Robin Match Schedules (Generate All Possible Pairings by Round)

There are n teams labeled 1..n that need to play a round-robin schedule: There are n-1 rounds when n is even, or n rounds when n is odd (introduce a bye each round). In each round, each team plays at most one match. Every pair of distinct teams plays exactly once (for odd n, one team has a bye each round, but every pair still meets exactly once). Task: Generate all possible schedules (each schedule is a list of rounds, each round is a list of pairings (a,b)). Output format A list of schedules; each schedule is: list of rounds; each round: list of matches; each match is a pair (a,b). Example For n = 4, one valid schedule is: [ [ (1,2), (3,4) ], [ (1,3), (2,4) ], [ (1,4), (2,3) ] ] Constraints 1 <= n <= 8 (assume small n since we must enumerate all solutions) The order of matches within a round and the order within each pair do not matter; avoid trivial duplicates. Must handle both even and odd n (for odd n, use a dummy team 0 as a bye). Example Input 4 Output (output is a JSON list of schedules; one valid schedule includes [[(1,2),(3,4)],[(1,3),(2,4)],[(1,4),(2,3)]] )