In a room are several people, some of which always lie and all others always tell the truth. Their ages are pairwise distinct. Each person says one of the following phrases: "In this room, there is an equal number of truth-sayers older than me and of liars younger than me" or "In this room, there is an equal number of truth-sayers younger than me and of liars older than me" What is the maximum possible number of truth-sayers in the room? Find an example in which this maximum is achieved and prove a higher number is impossible.