as know Max good video game player friend her friend jealous create actual game prove she s good game the game play direct acyclic graph DAG n vertex m edge there s character write edge lowercase english letter Max Lucas playing game Max go Lucas Max each player marble initially locate vertex each player hisher turn hisher marble edge player marble vertex v vertex u there s outgoing edge v u if player move hisher marble vertex v vertex u character round character write edge v u there s additional rule ASCII code character round great equal ASCII code character round i1 i1 the round number player ie Max go odd number Lucas go number the player can not lose game the marble vertex timesince game Lucas Max focus find Dart do not time play so ask play optimally win gameyou determine winner game initial position marble